Oyarzun, B.A.; Van Westen, T.; Vlugt, T.J.H.
2013-01-01
he liquid crystal phase behavior of linear and partially flexible hard-sphere chain fluids and the solubility of hard spheres in hard-sphere chain fluids are studied by constant pressure Monte Carlo simulations. An extensive study on the phase behavior of linear fluids with a length of 7, 8, 9, 10,
Molecular dynamics of a dense fluid of polydisperse hard spheres
Sear, Richard P.
2000-01-01
Slow dynamics in a fluid are studied in one of the most basic systems possible: polydisperse hard spheres. Monodisperse hard spheres cannot be studied as the slow down in dynamics as the density is increased is preempted by crystallisation. As the dynamics slow they become more heterogeneous, the spread in the distances traveled by different particles in the same time increases. However, the dynamics appears to be less heterogeneous than in hard-sphere-like colloids at the same volume fractio...
Nonadditive hard-sphere fluid mixtures: A simple analytical theory
Fantoni, Riccardo; Santos, Andrés
2011-01-01
We construct a non-perturbative fully analytical approximation for the thermodynamics and the structure of nonadditive hard-sphere fluid mixtures. The method essentially lies in a heuristic extension of the Percus-Yevick solution for additive hard spheres. Extensive comparison with Monte Carlo simulation data shows a generally good agreement, especially in the case of like-like radial distribution functions.
Nonadditive hard-sphere fluid mixtures: a simple analytical theory.
Fantoni, Riccardo; Santos, Andrés
2011-10-01
We construct a nonperturbative fully analytical approximation for the thermodynamics and the structure of nonadditive hard-sphere fluid mixtures. The method essentially lies in a heuristic extension of the Percus-Yevick solution for additive hard spheres. Extensive comparison with Monte Carlo simulation data shows a generally good agreement, especially in the case of like-like radial distribution functions.
Stochastic hard-sphere dynamics for hydrodynamics of nonideal fluids.
Donev, Aleksandar; Alder, Berni J; Garcia, Alejandro L
2008-08-15
A novel stochastic fluid model is proposed with a nonideal structure factor consistent with compressibility, and adjustable transport coefficients. This stochastic hard-sphere dynamics (SHSD) algorithm is a modification of the direct simulation Monte Carlo algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nanoparticle suspended in a compressible solvent.
Low-Density Fluid Phase of Dipolar Hard Spheres
Sear, Richard P.
1996-03-01
Unexpectedly, recent computer simulation studies [Weis and Levesque, Phys. Rev. Lett. 71, 2729 (1993); Leeuwen and Smit, ibid. 71, 3991 (1993)] failed to find a liquid phase for dipolar hard spheres. We argue that the liquid was not observed because the dipolar spheres form long chains which interact only weakly. To support this argument we derive a simple theory for noninteracting chains of dipolar spheres and show that it provides a reasonable description of the low-density fluid phase.
Transport properties of the rough hard sphere fluid.
Kravchenko, Olga; Thachuk, Mark
2012-01-28
Results are presented of a systematic study of the transport properties of the rough hard sphere fluid. The rough hard sphere fluid is a simple model consisting of spherical particles that exchange linear and angular momenta, and energy upon collision. This allows a study of the sole effect of particle rotation upon fluid properties. Molecular dynamics simulations have been used to conduct extensive benchmark calculations of self-diffusion, shear and bulk viscosity, and thermal conductivity coefficients. As well, the validity of several kinetic theory equations have been examined at various levels of approximation as a function of density and translational-rotational coupling. In particular, expressions from Enskog theory using different numbers of basis sets in the representation of the distribution function were tested. Generally Enskog theory performs well at low density but deviates at larger densities, as expected. The dependence of these expressions upon translational-rotational coupling was also examined. Interestingly, even at low densities, the agreement with simulation results was sometimes not even qualitatively correct. Compared with smooth hard sphere behaviour, the transport coefficients can change significantly due to translational-rotational coupling and this effect becomes stronger the greater the coupling. Overall, the rough hard sphere fluid provides an excellent model for understanding the effects of translational-rotational coupling upon transport coefficients.
Hard sphere dynamics for normal and granular fluids.
Dufty, James W; Baskaran, Aparna
2005-06-01
A fluid of N smooth, hard spheres is considered as a model for normal (elastic collision) and granular (inelastic collision) fluids. The potential energy is discontinuous for hard spheres so that the pairwise forces are singular and the usual forms of Newtonian and Hamiltonian mechanics do not apply. Nevertheless, particle trajectories in the N particle phase space are well defined and the generators for these trajectories can be identified. The first part of this presentation is a review of the generators for the dynamics of observables and probability densities. The new results presented in the second part refer to applications of these generators to the Liouville dynamics for granular fluids. A set of eigenvalues and eigenfunctions of the generator for this Liouville dynamics system is identified in a special stationary representation. This provides a class of exact solutions to the Liouville equation that are closely related to hydrodynamics for granular fluids.
Second virial coefficient for the dipolar hard sphere fluid.
Henderson, Douglas
2011-07-28
The dipolar hard sphere fluid is a useful model for a polar fluid. Some years ago, the second virial coefficient, B(2), of this fluid was obtained as a series expansion in the inverse temperature or (dipole strength) by Keesom. Little work on this problem seems to have been done since that time. Using a result of Chan and Henderson for the spherical average of the Boltzmann factor of this fluid, more complete results are obtained for B(2). The more complete results are more negative than the Keesom series, as one would expect, but his expansion is remarkably accurate. This method can be used to obtain the second virial coefficient of the dipolar Lennard-Jones (Stockmayer) or dipolar Yukawa fluids.
Density Fluctuations of Hard-Sphere Fluids in Narrow Confinement
Nygârd, Kim; Sarman, Sten; Hyltegren, Kristin; Chodankar, Shirish; Perret, Edith; Buitenhuis, Johan; van der Veen, J. Friso; Kjellander, Roland
2016-01-01
Spatial confinement induces microscopic ordering of fluids, which in turn alters many of their dynamic and thermodynamic properties. However, the isothermal compressibility has hitherto been largely overlooked in the literature, despite its obvious connection to the underlying microscopic structure and density fluctuations in confined geometries. Here, we address this issue by probing density profiles and structure factors of hard-sphere fluids in various narrow slits, using x-ray scattering from colloid-filled nanofluidic containers and integral-equation-based statistical mechanics at the level of pair distributions for inhomogeneous fluids. Most importantly, we demonstrate that density fluctuations and isothermal compressibilities in confined fluids can be obtained experimentally from the long-wavelength limit of the structure factor, providing a formally exact and experimentally accessible connection between microscopic structure and macroscopic, thermodynamic properties. Our approach will thus, for example, allow direct experimental verification of theoretically predicted enhanced density fluctuations in liquids near solvophobic interfaces.
Chemical potential of a test hard sphere of variable size in a hard-sphere fluid
Heyes, David M.; Santos, Andrés
2016-12-01
The Labík and Smith Monte Carlo simulation technique to implement the Widom particle insertion method is applied using Molecular Dynamics (MD) instead to calculate numerically the insertion probability, P0(η ,σ0) , of tracer hard-sphere (HS) particles of different diameters, σ0, in a host HS fluid of diameter σ and packing fraction, η , up to 0.5. It is shown analytically that the only polynomial representation of -ln P0 (η ,σ0) consistent with the limits σ0→0 and σ0→∞ has necessarily a cubic form, c0(η ) +c1(η ) σ0 /σ +c2(η ) (σ0/σ ) 2 +c3(η ) (σ0/σ ) 3 . Our MD data for -ln P0 (η ,σ0) are fitted to such a cubic polynomial and the functions c0(η ) and c1(η ) are found to be statistically indistinguishable from their exact solution forms. Similarly, c2(η ) and c3(η ) agree very well with the Boublík-Mansoori-Carnahan-Starling-Leland and Boublík-Carnahan-Starling-Kolafa formulas. The cubic polynomial is extrapolated (high density) or interpolated (low density) to obtain the chemical potential of the host fluid, or σ0→σ , as β μex =c0+c1+c2+c3 . Excellent agreement between the Carnahan-Starling and Carnahan-Starling-Kolafa theories with our MD data is evident.
Chemical potential of a test hard sphere of variable size in a hard-sphere fluid
Heyes, David M
2016-01-01
The Lab\\'ik and Smith Monte Carlo simulation technique to implement the Widom particle insertion method is extended using Molecular Dynamics (MD) instead to calculate numerically the insertion probability, $P_0(\\eta,\\sigma_0)$, of tracer hard-sphere (HS) particles of different diameters, $\\sigma_0$, in a host HS fluid of diameter $\\sigma$ and packing fraction, $\\eta$, up to $0.5$. It is shown analytically that the only polynomial representation of $-\\ln P_0(\\eta,\\sigma_0)$ consistent with the limits $\\sigma_0\\to 0$ and $\\sigma_0\\to\\infty$ has necessarily a cubic form, $c_0(\\eta)+c_1(\\eta)\\sigma_0/\\sigma+c_2(\\eta)(\\sigma_0/\\sigma)^2+c_3(\\eta)(\\sigma_0/\\sigma)^3$. Our MD data for $-\\ln P_0(\\eta,\\sigma_0)$ are fitted to such a cubic polynomial and the functions $c_0(\\eta)$ and $c_1(\\eta)$ are found to be statistically indistinguishable from their exact solution forms. Similarly, $c_2(\\eta)$ and $c_3(\\eta)$ agree very well with the Boubl\\'ik--Mansoori--Carnahan--Starling--Leland and Boubl\\'ik--Carnahan--Starling-...
Criticality in charge-asymmetric hard-sphere ionic fluids.
Aqua, Jean-Noël; Banerjee, Shubho; Fisher, Michael E
2005-10-01
Phase separation and criticality are analyzed in z:1 charge-asymmetric ionic fluids of equisized hard spheres by generalizing the Debye-Hückel approach combined with ionic association, cluster solvation by charged ions, and hard-core interactions, following lines developed by Fisher and Levin for the 1:1 case (i.e., the restricted primitive model). Explicit analytical calculations for 2:1 and 3:1 systems account for ionic association into dimers, trimers, and tetramers and subsequent multipolar cluster solvation. The reduced critical temperatures, Tc* (normalized by z), decrease with charge asymmetry, while the critical densities increase rapidly with . The results compare favorably with simulations and represent a distinct improvement over all current theories such as the mean spherical approximation, symmetric Poisson-Boltzmann theory, etc. For z not equal to 1, the interphase Galvani (or absolute electrostatic) potential difference, Deltaphi(T), between coexisting liquid and vapor phases is calculated and found to vanish as absolute value (T-Tc) beta when T-->Tc-with, since our approximations are classical, beta = (1/2). Above Tc, the compressibility maxima and so-called k-inflection loci (which aid the fast and accurate determination of the critical parameters) are found to exhibit a strong z dependence.
Multicomponent fluid of nonadditive hard spheres near a wall.
Fantoni, Riccardo; Santos, Andrés
2013-04-01
A recently proposed rational-function approximation [Phys. Rev. E 84, 041201 (2011)] for the structural properties of nonadditive hard spheres is applied to evaluate analytically (in Laplace space) the local density profiles of multicomponent nonadditive hard-sphere mixtures near a planar nonadditive hard wall. The theory is assessed by comparison with NVT Monte Carlo simulations of binary mixtures with a size ratio 1:3 in three possible scenarios: a mixture with either positive or negative nonadditivity near an additive wall, an additive mixture with a nonadditive wall, and a nonadditive mixture with a nonadditive wall. It is observed that, while the theory tends to underestimate the local densities at contact (especially in the case of the big spheres) it captures very well the initial decay of the densities with increasing separation from the wall and the subsequent oscillations.
Multicomponent fluid of hard spheres near a wall.
Malijevský, Alexandr; Yuste, Santos B; Santos, Andrés; López de Haro, Mariano
2007-06-01
The rational function approximation method, density functional theory, and NVT Monte Carlo simulation are used to obtain the density profiles of multicomponent hard-sphere mixtures near a planar hard wall. Binary mixtures with a size ratio 1:3 in which both components occupy a similar volume are specifically examined. The results indicate that the present version of density functional theory yields an excellent overall performance. A reasonably accurate behavior of the rational function approximation method is also observed, except in the vicinity of the first minimum, where it may even predict unphysical negative values.
Using compressibility factor as a predictor of confined hard-sphere fluid dynamics
Mittal, Jeetain
2009-01-01
We study the correlations between the diffusivity (or viscosity) and the compressibility factor of bulk hard-sphere fluid as predicted by the ultralocal limit of the barrier hopping theory. Our specific aim is to determine if these correlations observed in the bulk equilibrium hard-sphere fluid can be used to predict the self-diffusivity of fluid confined between a slit-pore or a rectangular channel. In this work, we consider a single-component and a binary mixture of hard spheres. To represe...
Equation of state for hard sphere fluids offering accurate virial coefficients
Tian, Jianxiang; Gui, Yuanxing; Mulero, A
2016-01-01
The asymptotic expansion method is extended by using currently available accurate values for the first ten virial coefficients for hard sphere fluids. It is then used to yield an equation of state for hard sphere fluids, which accurately represents the currently accepted values for the first sixteen virial coefficients and compressibility factor data in both the stable and the metastable regions of the phase diagram.
Institute of Scientific and Technical Information of China (English)
Zhou Shi-Qi
2007-01-01
A universal theoretical approach is proposed which enables all hard sphere density functional approximations(DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.
Inhomogeneous quasistationary state of dense fluids of inelastic hard spheres.
Fouxon, Itzhak
2014-05-01
We study closed dense collections of freely cooling hard spheres that collide inelastically with constant coefficient of normal restitution. We find inhomogeneous states (ISs) where the density profile is spatially nonuniform but constant in time. The states are exact solutions of nonlinear partial differential equations that describe the coupled distributions of density and temperature valid when inelastic losses of energy per collision are small. The derivation is performed without modeling the equations' coefficients that are unknown in the dense limit (such as the equation of state) using only their scaling form specific for hard spheres. Thus the IS is the exact state of this dense many-body system. It captures a fundamental property of inelastic collections of particles: the possibility of preserving nonuniform temperature via the interplay of inelastic cooling and heat conduction that generalizes previous results. We perform numerical simulations to demonstrate that arbitrary initial state evolves to the IS in the limit of long times where the container has the geometry of the channel. The evolution is like a gas-liquid transition. The liquid condenses in a vanishing part of the total volume but takes most of the mass of the system. However, the gaseous phase, which mass grows only logarithmically with the system size, is relevant because its fast particles carry most of the energy of the system. Remarkably, the system self-organizes to dissipate no energy: The inelastic decay of energy is a power law [1+t/t(c)](-2), where t(c) diverges in the thermodynamic limit. This is reinforced by observing that for supercritical systems the IS coincide in most of the space with the steady states of granular systems heated at one of the walls. We discuss the relation of our results to the recently proposed finite-time singularity in other container's geometries.
Kravchenko, Olga; Thachuk, Mark
2011-03-21
A study is presented of tracer diffusion in a rough hard sphere fluid. Unlike smooth hard spheres, collisions between rough hard spheres can exchange rotational and translational energy and momentum. It is expected that as tracer particles become larger, their diffusion constants will tend toward the Stokes-Einstein hydrodynamic result. It has already been shown that in this limit, smooth hard spheres adopt "slip" boundary conditions. The current results show that rough hard spheres adopt boundary conditions proportional to the degree of translational-rotational energy exchange. Spheres for which this exchange is the largest adopt "stick" boundary conditions while those with more intermediate exchange adopt values between the "slip" and "stick" limits. This dependence is found to be almost linear. As well, changes in the diffusion constants as a function of this exchange are examined and it is found that the dependence is stronger than that suggested by the low-density, Boltzmann result. Compared with smooth hard spheres, real molecules undergo inelastic collisions and have attractive wells. Rough hard spheres model the effect of inelasticity and show that even without the presence of attractive forces, the boundary conditions for large particles can deviate from "slip" and approach "stick."
Stochastic Hard-Sphere Dynamics for Hydrodynamics of Non-Ideal Fluids
Donev, Aleksandar; Alder, Berni J.; Garcia, Alejandro L.
2008-01-01
A novel stochastic fluid model is proposed with non-ideal structure factor consistent with compressibility, and adjustable transport coefficients. This Stochastic Hard Sphere Dynamics (SHSD) algorithm is a modification of the Direct Simulation Monte Carlo (DSMC) algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and pair correlation function identical to that of a deterministic Hamiltonian sys...
Institute of Scientific and Technical Information of China (English)
李卫华; 诸蔚朝; 马红孺
2003-01-01
One component hard-sphere fluid confined in two planar hard walls is studied by means of density functional theory with Rosenfeld functional and molecular dynamics simulation. The validity of the Rosenfeld functional is examined. Chemical potential, grand potential and free energy as functions of the wall separation are obtained.
Diffusion and structure of a quasi-one-dimensional hard-sphere fluid
Lin, Binhua; Lee, Ji Hwan; Cui, Bianxiao
2001-03-01
We report the results of an experimental study of a quasi-one-dimensional hard-sphere fluid. The system consists of uncharged Si colloidal spheres confined in long, uncorrelated 1D-channels whose narrow width forbids mutual passage of spheres along the channel. By tracking the trajectories of the spheres using digital video microscopy, we studied the diffusion and structure of the system as a function of the density of the fluid. Our results show that the behavior of the spheres in self-diffusion is changed gradually from Fickian to non-Fickian near the onset of the collision between the spheres, indicating the correlation between the collision of the hard-spheres and the change in diffusion mechanism. At high density, the self-part of the van Hove function of the system is no longer a Gaussian distribution but a Poisson distribution which can be interpreted using a hydrodynamic analysis for effective wall-drag effect. The pair distribution function of the system can be explained by an analytical expression for a 1D hard-sphere fluid [1]. [1] Y. Rosenfeld, M. Schmidt, H. Lowen and P. Tarazona, Phys. Rev. E 55, 4245 (1997).
New Closed Virial Equation of State for Hard-Sphere Fluids
Tian, Jianxiang; Mulero, Angel
2016-01-01
A new closed virial equation of state of hard-sphere fluids is proposed which reproduces the calculated or estimated values of the first sixteen virial coefficients at the same time as giving very good accuracy when compared with computer simulation data for the compressibility factor over the entire fluid range, and having a pole at the correct closest packing density.
Equilibrium structure of the multi-component screened charged hard-sphere fluid.
Sánchez-Díaz, Luis E; Mendez-Maldonado, Gloria A; González-Melchor, Minerva; Ruiz-Estrada, Honorina; Medina-Noyola, Magdaleno
2011-07-07
The generalized mean spherical approximation of the structural properties of the binary charge-symmetric fluid of screened charged hard-spheres of the same diameter, i.e., the screened restricted primitive model, is extended to include binary charge-asymmetric and multi-component fluids. Molecular dynamics simulation data are generated to assess the accuracy of the corresponding theoretical predictions.
Density Functional Theory Approach for Charged Hard Sphere Fluids Confined in Spherical Micro-Cavity
Institute of Scientific and Technical Information of China (English)
KANG Yan-Shuang; WANG Hai-Jun
2009-01-01
Within the framework of the density functional theory for classical fluids,the equilibrium density profiles of charged hard sphere fluid confined in micro-cavity are studied by means of the modified fundamental measure theory.The dimension of micro-cavity,the charge of hard sphere and the applied electric field are found to have significant effects on the density profiles.In particular,it is shown that Coulomb interaction,excluded volume interaction and applied electric Geld play the central role in controlling the aggregated structure of the system.
Using compressibility factor as a predictor of confined hard-sphere fluid dynamics.
Mittal, Jeetain
2009-10-22
We study the correlations between the diffusivity (or viscosity) and the compressibility factor of bulk hard-sphere fluid as predicted by the ultralocal limit of the barrier hopping theory. Our specific aim is to determine if these correlations observed in the bulk equilibrium hard-sphere fluid can be used to predict the self-diffusivity of fluid confined between a slit-pore or a rectangular channel. In this work, we consider a single-component and a binary mixture of hard spheres. To represent confining walls, we use purely reflecting hard walls and interacting square-well walls. Our results clearly show that the correspondence between the diffusivity and the compressibility factor can be used along with the knowledge of the confined fluid's compressibility factor to predict its diffusivity with quantitative accuracy. Our analysis also suggests that a simple measure, the average fluid density, can be an accurate predictor of confined fluid diffusivity for very tight confinements ( approximately 2-3 particle diameters wide) at low to intermediate density conditions. Together, these results provide further support for the idea that one can use robust connections between thermodynamic and dynamic quantities to predict dynamics of confined fluids from their thermodynamics.
Chemical potential of a hard sphere fluid adsorbed in model disordered polydisperse matrices.
de Leon, Aned; Pizio, O; Sokołowski, S
2006-06-01
We consider a model for adsorption of a simple fluid in disordered polydisperse adsorbents. The fluid consists of hard sphere particles. On the other hand, the adsorbents of this study are modeled as a collection of hard spheres with their diameter obeying a certain distribution function. Our focus is in the evaluation of the chemical potential of the fluid immersed in such a polydisperse material. It permits us to obtain porosity and pore size distribution for the adsorbent, as well as a set of adsorption isotherms. The latter have been calculated theoretically and by grand canonical Monte Carlo simulations. We observe that the width of assumed polydispersity distribution affects all the properties of the system. Nevertheless, the effect of matrix packing is dominant in determining adsorption for this class of models. We are convinced that the matrix structures generated via more sophisticated algorithms would exhibit stronger effects of polydispersity on the entire set of properties of adsorbed simple fluids.
Sun, Jiu-Xun; Cai, Ling-Cang; Wu, Qiang; Jin, Ke
2013-09-01
Based on the expansion and extension of the virial equation of state (EOS) of hard-sphere fluids solved by the Percus-Yevick integration equation, a universal cubic (UC) EOS is developed. The UC EOS is applied to model hard-sphere and Lennard-Jones (LJ) fluids, simple Ar and N2 liquids at low temperatures, and supercritical Ar and N2 fluids at high temperatures, as well as ten solids, respectively. The three parameters are determined for the hard-sphere fluid by fitting molecular dynamics (MD) simulation data of the third to eighth virial coefficients in the literature; for other fluids by fitting isothermal compression data; and for solids by using the Einstein model. The results show that the UC EOS gives better results than the Carnahan-Starling EOS for compressibility of hard-sphere fluids. The Helmholtz free energy and internal energy for LJ fluids are predicted and compared with MD simulation data. The calculated pressures for simple Ar and N2 liquids are compared with experimental data. The agreement is fairly good. Eight three-parameter EOSs are applied to describe isothermals of ten typical solids. It is shown that the UC EOS gives the best precision with correct behavior at high-pressure limitation. The UC EOS considering thermal effects is used to analytically evaluate the isobaric thermal expansivity and isothermal compressibility coefficients. The results are in good agreement with experimental data.
Institute of Scientific and Technical Information of China (English)
周世琦
2003-01-01
Based on the functional integral procedure, a recently proposed bridge density function [J. Chem. Phys. 112 (2000) 8079] is developed to calculate global thermodynamic properties of non-uniform fluids. The resulting surface tension of a hard wall-hard sphere interface as a function of the bulk hard sphere fluid density is in good agreement with the available simulation data. The proposed numerical procedure from the approximation of non-uniform first=order direct correlation function to a non=uniform system with excess Helmholtz free energy is of fundamental importance for phase behaviour under the confined condition due to the fact that many available simple approximations in classical density functional theory are for non=uniform first=order direct correlation function.
Scaled Particle Theory for Multicomponent Hard Sphere Fluids Confined in Random Porous Media.
Chen, W; Zhao, S L; Holovko, M; Chen, X S; Dong, W
2016-06-23
The formulation of scaled particle theory (SPT) is presented for a quite general model of fluids confined in a random porous media, i.e., a multicomponent hard sphere (HS) fluid in a multicomponent hard sphere or a multicomponent overlapping hard sphere (OHS) matrix. The analytical expressions for pressure, Helmholtz free energy, and chemical potential are derived. The thermodynamic consistency of the proposed theory is established. Moreover, we show that there is an isomorphism between the SPT for a multicomponent system and that for a one-component system. Results from grand canonical ensemble Monte Carlo simulations are also presented for a binary HS mixture in a one-component HS or a one-component OHS matrix. The accuracy of various variants derived from the basic SPT formulation is appraised against the simulation results. Scaled particle theory, initially formulated for a bulk HS fluid, has not only provided an analytical tool for calculating thermodynamic properties of HS fluid but also helped to gain very useful insight for elaborating other theoretical approaches such as the fundamental measure theory (FMT). We expect that the general SPT for multicomponent systems developed in this work can contribute to the study of confined fluids in a similar way.
A comprehensive approach to an equation of state for hard spheres and Lennard-Jones fluids
Institute of Scientific and Technical Information of China (English)
S.B.Khasare
2011-01-01
We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way.We will guess equations of state by using suitable axiomatic functional forms(n ＝1,2,3,4,5)for surface tension Smnr,r≥d/2 with intermolecular separation r as a variable,where m is an arbitrary real number(pole).Among the equations of state obtained in this way are Percus-Yevick,scaled particle theory and Carnahan-Starling equations of state.In addition,we have found a simple equation of state for the hard sphere fluid in the region that represents the simulation data accurately.It is found that for both hard sphere fluids as well as Lennard-Jones fluids,with m ＝3/4 the derived equation of state(EOS)gives results which are in good agreement with computer simulation results.Furthermore,this equation of state gives the Percus-Yevick(pressure)EOS for the m ＝ 0,the Carnahan-Starling EOS for m ＝ 4/5,while for the value of m ＝ 1 it corresponds to a scaled particle theory EOS.
POLYMER MEAN SPHERICAL APPROXIMATION FOR THE FLUID OF FLEXIBLE HARD-SPHERE YUKAWA STAR MOLECULES
Directory of Open Access Journals (Sweden)
Yu.V.Kalyuzhnyi
2002-01-01
Full Text Available An extension of the product-reactant Ornstein-Zernike approach (PROZA for the fluid of flexible star molecules is proposed and the corresponding version of the mean spherical approximation (MSA, the so-called polymer MSA (PMSA, is formulated. Using Baxter-Wertheim factorization technique, an analytical solution of the PMSA for the fluid of star molecules with Yukawa hard-sphere interaction between the molecular segments is derived and closed form analytical expressions for the Helmholtz free energy, chemical potential and equation of state are presented. The structure properties of several different versions of the star fluid model are studied.
Directory of Open Access Journals (Sweden)
P.Orea
2003-01-01
Full Text Available We have performed Monte Carlo simulations in the canonical ensemble of a hard-sphere fluid adsorbed in microporous media. The pressure of the adsorbed fluid is calculated by using an original procedure that includes the calculations of the pressure tensor components during the simulation. In order to confirm the equivalence of bulk and adsorbed fluid pressures, we have exploited the mechanical condition of equilibrium and performed additional canonical Monte Carlo simulations in a super system "bulk fluid + adsorbed fluid". When the configuration of a model porous media permits each of its particles to be in contact with adsorbed fluid particles, we found that these pressures are equal. Unlike the grand canonical Monte Carlo method, the proposed calculation approach can be used efficiently to obtain adsorption isotherms over a wide range of fluid densities and porosities of adsorbent.
Pizio; Trokhymchuk; Henderson; Labik
1997-07-01
A model of hard spheres adsorbed in disordered porous media is studied using the associative replica Ornstein-Zernike (ROZ) equations. Extending previous studies of adsorption in a hard sphere matrices, we investigate a polymerized matrix. We consider an associating fluid of hard spheres with two intracore attractive sites per particle; consequently chains consisting of overlapping hard spheres can be formed due to the chemical association. This is the generalization of the model with sites on the surface of Wertheim that has been studied in the bulk by Chang and Sandler. The matrix structure is obtained in the polymer Percus-Yevick approximation. We solve the ROZ equations in the associative hypernetted chain approximation. The pair distribution functions, the fluid compressibility, the equation of state and chemical potential of the adsorbed fluid are obtained and discussed. It is shown that the adsorption of a hard sphere fluid in a matrix at given density, but consisting of longer chains of overlapping hard spheres, is higher than the adsorption of this fluid in a hard sphere matrix.
DEFF Research Database (Denmark)
Sloth, Peter
1990-01-01
Density profiles and partition coefficients are obtained for hard-sphere fluids inside hard, spherical pores of different sizes by grand canonical ensemble Monte Carlo calculations. The Monte Carlo results are compared to the results obtained by application of different kinds of integral equation...... approximations. Also, some exact, analytical results for the partition coefficients are given, which are valid in the case of (very) small pores or at low density, respectively. The Journal of Chemical Physics is copyrighted by The American Institute of Physics....
Santos, Andrés; de Haro, Mariano López; Yuste, Santos B.
2009-01-01
Different theoretical approaches for the thermodynamic properties and the equation of state for multicomponent mixtures of nonadditive hard spheres in $d$ dimensions are presented in a unified way. These include the theory by Hamad, our previous formulation, the original MIX1 theory, a recently proposed modified MIX1 theory, as well as a nonlinear extension of the MIX1 theory proposed in this paper. Explicit expressions for the compressibility factor, Helmholtz free energy, and second, third,...
On fluid-solid direct coexistence simulations: the pseudo-hard sphere model.
Espinosa, Jorge R; Sanz, Eduardo; Valeriani, Chantal; Vega, Carlos
2013-10-14
We investigate methodological issues concerning the direct coexistence method, an increasingly popular approach to evaluate the solid-fluid coexistence by means of computer simulations. The first issue is the impact of the simulation ensemble on the results. We compare the NpT ensemble (easy to use but approximate) with the NpzT ensemble (rigorous but more difficult to handle). Our work shows that both ensembles yield similar results for large systems (>5000 particles). Another issue, which is usually disregarded, is the stochastic character of a direct coexistence simulation. Here, we assess the impact of stochasticity in the determination of the coexistence point. We demonstrate that the error generated by stochasticity is much larger than that caused by the use of the NpT ensemble, and can be minimized by simply increasing the system size. To perform this study we use the pseudo hard-sphere model recently proposed by Jover et al. [J. Chem. Phys. 137, 144505 (2012)], and obtain a coexistence pressure of p∗ = 11.65(1), quite similar to that of hard spheres (only about 0.6% higher). Therefore, we conclude that this model can be reliably used to investigate the physics of hard spheres in phenomena like crystal nucleation.
A Thermodynamically-Consistent Non-Ideal Stochastic Hard-Sphere Fluid
Energy Technology Data Exchange (ETDEWEB)
Donev, A; Alder, B J; Garcia, A L
2009-08-03
A grid-free variant of the Direct Simulation Monte Carlo (DSMC) method is proposed, named the Isotropic DSMC (I-DSMC) method, that is suitable for simulating collision-dominated dense fluid flows. The I-DSMC algorithm eliminates all grid artifacts from the traditional DSMC algorithm and is Galilean invariant and microscopically isotropic. The stochastic collision rules in I-DSMC are modified to introduce a non-ideal structure factor that gives consistent compressibility, as first proposed in [Phys. Rev. Lett. 101:075902 (2008)]. The resulting Stochastic Hard Sphere Dynamics (SHSD) fluid is empirically shown to be thermodynamically identical to a deterministic Hamiltonian system of penetrable spheres interacting with a linear core pair potential, well-described by the hypernetted chain (HNC) approximation. We develop a kinetic theory for the SHSD fluid to obtain estimates for the transport coefficients that are in excellent agreement with particle simulations over a wide range of densities and collision rates. The fluctuating hydrodynamic behavior of the SHSD fluid is verified by comparing its dynamic structure factor against theory based on the Landau-Lifshitz Navier-Stokes equations. We also study the Brownian motion of a nano-particle suspended in an SHSD fluid and find a long-time power-law tail in its velocity autocorrelation function consistent with hydrodynamic theory and molecular dynamics calculations.
Góźdź, W T
2017-08-30
We have calculated the values of the critical packing fractions for the mixtures of symmetric nonadditive hard spheres at high densities for small values of the nonadditivity parameter. Calculations have been performed for solid-solid and fluid-fluid demixing transitions. A cluster algorithm for Monte Carlo simulations in a semigrand ensemble was used, and the waste recycling method was applied to improve the accuracy of the calculations. The finite size scaling analysis was employed to compute the critical packing fractions for infinite systems with high accuracy.
Energy Technology Data Exchange (ETDEWEB)
Hopkins, Paul; Schmidt, Matthias, E-mail: Paul.Hopkins@bristol.ac.u [H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL (United Kingdom)
2010-08-18
Using a fundamental measure density functional theory we investigate both bulk and inhomogeneous systems of the binary non-additive hard sphere model. For sufficiently large (positive) non-additivity the mixture phase separates into two fluid phases with different compositions. We calculate bulk fluid-fluid coexistence curves for a range of size ratios and non-additivity parameters and find that they compare well to simulation results from the literature. Using the Ornstein-Zernike equation, we investigate the asymptotic, r{yields}{infinity}, decay of the partial pair correlation functions, g{sub ij}(r). At low densities a structural crossover occurs in the asymptotic decay between two different damped oscillatory modes with different wavelengths corresponding to the two intra-species hard-core diameters. On approaching the fluid-fluid critical point there is a Fisher-Widom crossover from exponentially damped oscillatory to monotonic asymptotic decay. Using the density functional we calculate the density profiles for the planar free fluid-fluid interface between coexisting fluid phases. We show that the type of asymptotic decay of g{sub ij}(r) not only determines the asymptotic decay of the interface profiles, but is also relevant for intermediate and even short-ranged behaviour. We also determine the surface tension of the free fluid interface, finding that it increases with non-additivity, and that on approaching the critical point mean-field scaling holds.
Hopkins, Paul; Schmidt, Matthias
2010-08-18
Using a fundamental measure density functional theory we investigate both bulk and inhomogeneous systems of the binary non-additive hard sphere model. For sufficiently large (positive) non-additivity the mixture phase separates into two fluid phases with different compositions. We calculate bulk fluid-fluid coexistence curves for a range of size ratios and non-additivity parameters and find that they compare well to simulation results from the literature. Using the Ornstein-Zernike equation, we investigate the asymptotic, [Formula: see text], decay of the partial pair correlation functions, g(ij)(r). At low densities a structural crossover occurs in the asymptotic decay between two different damped oscillatory modes with different wavelengths corresponding to the two intra-species hard-core diameters. On approaching the fluid-fluid critical point there is a Fisher-Widom crossover from exponentially damped oscillatory to monotonic asymptotic decay. Using the density functional we calculate the density profiles for the planar free fluid-fluid interface between coexisting fluid phases. We show that the type of asymptotic decay of g(ij)(r) not only determines the asymptotic decay of the interface profiles, but is also relevant for intermediate and even short-ranged behaviour. We also determine the surface tension of the free fluid interface, finding that it increases with non-additivity, and that on approaching the critical point mean-field scaling holds.
Hoang, Hai; Galliero, Guillaume
2013-12-04
This work aims at providing a tractable approach to model the local shear viscosity of strongly inhomogeneous dense fluids composed of spherical molecules, in which the density variations occur on molecular distance. The proposed scheme, which relies on the local density average model, has been applied to the quasi-hard-sphere, the Week-Chandler-Andersen and the Lennard-Jones fluids. A weight function has been developed to deal with the hard-sphere fluid given the specificities of momentum exchange. To extend the approach to the smoothly repulsive potential, we have taken into account that the non-local contributions to the viscosity due to the interactions of particles separated by a given distance are temperature dependent. Then, using a simple perturbation scheme, the approach is extended to the Lennard-Jones fluids. It is shown that the viscosity profiles of inhomogeneous dense fluids deduced from this approach are consistent with those directly computed by non-equilibrium molecular dynamics simulations.
Santos, Andrés; López de Haro, Mariano; Yuste, Santos B
2010-05-28
Different theoretical approaches for the thermodynamic properties and the equation of state for multicomponent mixtures of nonadditive hard spheres in d dimensions are presented in a unified way. These include the theory by Hamad, our previous formulation, the original MIX1 theory, a recently proposed modified MIX1 theory, as well as a nonlinear extension of the MIX1 theory proposed in this paper. Explicit expressions for the compressibility factor, Helmholtz free energy, and second, third, and fourth virial coefficients are provided. A comparison is carried out with recent Monte Carlo data for the virial coefficients of asymmetric mixtures and with available simulation data for the compressibility factor, the critical consolute point, and the liquid-liquid coexistence curves. The merits and limitations of each theory are pointed out.
Directory of Open Access Journals (Sweden)
M.Valiskó
2005-01-01
Full Text Available A systematic Monte Carlo (MC simulation and perturbation theoretical (PT study is reported for the dielectric constant of the polarizable dipolar hard sphere (PDHS fluid. We take the polarizability of the molecules into account in two different ways. In a continuum approach we place the permanent dipole of the molecule into a sphere of dielectric constant ε∞ in the spirit of Onsager. The high frequency dielectric constant ε∞ is calculated from the Clausius-Mosotti relation, while the dielectric constant of the polarizable fluid is obtained from the Kirkwood-Fröhlich equation. In the molecular approach, the polarizability is built into the model on the molecular level, which makes the interactions non-pairwise additive. Here we use Wertheim's renormalized PT method to calculate the induced dipole moment, while the dielectric constant is calculated from our recently introduced formula. We also apply a series expansion for the dielectric constant both in the continuum and the molecular approach. These series expansions ensure a better agreement with simulation results. The agreement between our MC data and the PT results in the molecular approach is excellent for low to moderate dipole moments and polarizabilities. At stronger dipolar interactions ergodicity problems and anizotropic behaviour appear where simulation results become uncertain and the theoretical approach becomes invalid.
Monte Carlo Simulations of Density Profiles for Hard-Sphere Chain Fluids Confined Between Surfaces
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using extended continuum configurational-bias (ECCB) method. It is shown that the enrichment of beads near surfaces is happened at high densities due to the bulk packing effect, on the contrary, the depletion is revealed at low densities owing to the configurational entropic contribution. Comparisons with those calculated by density functional theory presented by Cai et al. indicate that the agreement between simulations and predictions is good. Compressibility factors of bulk HSCFs calculated using volume fractions at surfaces were also used to test the reliability of various equations of state of HSCFs by different authors.
Equation of state of sticky-hard-sphere fluids in the chemical-potential route
Rohrmann, René D.; Santos, Andrés
2014-04-01
The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route (μ route). As a consistency test, the results for one-dimensional sticky particles are shown to be exact. Results corresponding to the three-dimensional case (Baxter's model) are derived within the Percus-Yevick approximation by using different prescriptions for the dependence of the interaction potential of the extra particle on the coupling parameter. The critical point and the coexistence curve of the gas-liquid phase transition are obtained in the μ route and compared with predictions from other thermodynamics routes and from computer simulations. The results show that the μ route yields a general better description than the virial, energy, compressibility, and zero-separation routes.
Isotropic-nematic phase equilibria of hard-sphere chain fluids-Pure components and binary mixtures.
Oyarzún, Bernardo; van Westen, Thijs; Vlugt, Thijs J H
2015-02-14
The isotropic-nematic phase equilibria of linear hard-sphere chains and binary mixtures of them are obtained from Monte Carlo simulations. In addition, the infinite dilution solubility of hard spheres in the coexisting isotropic and nematic phases is determined. Phase equilibria calculations are performed in an expanded formulation of the Gibbs ensemble. This method allows us to carry out an extensive simulation study on the phase equilibria of pure linear chains with a length of 7 to 20 beads (7-mer to 20-mer), and binary mixtures of an 8-mer with a 14-, a 16-, and a 19-mer. The effect of molecular flexibility on the isotropic-nematic phase equilibria is assessed on the 8-mer+19-mer mixture by allowing one and two fully flexible beads at the end of the longest molecule. Results for binary mixtures are compared with the theoretical predictions of van Westen et al. [J. Chem. Phys. 140, 034504 (2014)]. Excellent agreement between theory and simulations is observed. The infinite dilution solubility of hard spheres in the hard-sphere fluids is obtained by the Widom test-particle insertion method. As in our previous work, on pure linear hard-sphere chains [B. Oyarzún, T. van Westen, and T. J. H. Vlugt, J. Chem. Phys. 138, 204905 (2013)], a linear relationship between relative infinite dilution solubility (relative to that of hard spheres in a hard-sphere fluid) and packing fraction is found. It is observed that binary mixtures greatly increase the solubility difference between coexisting isotropic and nematic phases compared to pure components.
Quasi-chemical Theory for the Statistical Thermodynamics of the Hard Sphere Fluid
Pratt, L R; Gómez, M A; Gentile, M E; Pratt, Lawrence R.; Violette, Randall A. La; Gomez, Maria A.; Gentile, Mary E.
2001-01-01
We develop a quasi-chemical theory for the study of packing thermodynamics in dense liquids. The situation of hard-core interactions is addressed by considering the binding of solvent molecules to a precisely defined `cavity' in order to assess the probability that the `cavity' is entirely evacuated. The primitive quasi-chemical approximation corresponds to a extension of the Poisson distribution used as a default model in an information theory approach. This primitive quasi-chemical theory is in good qualitative agreement with the observations for the hard sphere fluid of occupancy distributions that are central to quasi-chemical theories but begins to be quantitatively erroneous for the equation of state in the dense liquid regime of $\\rho d^3>$0.6. How the quasi-chemical approach can be iterated to treat correlation effects is addressed. Consideration of neglected correlation effects leads to a simple model for the form of those contributions neglected by the primitive quasi-chemical approximation. These c...
Microscopic theories of the structure and glassy dynamics of ultra-dense hard sphere fluids
Jadrich, Ryan; Schweizer, Kenneth
2013-03-01
We construct a new thermodynamically self-consistent integral equation theory (IET) for the equilibrium metastable fluid structure of monodisperse hard spheres that incorporates key features of the jamming transition. A two Yukawa generalized mean spherical IET closure for the direct correlation function tail is employed to model the distinctive short and long range contributions for highly compressed fluids. The exact behavior of the contact value of the radial distribution function (RDF) and isothermal compressibility are enforced, as well as an approximate theory for the RDF contact derivative. Comparison of the theoretical results for the real and Fourier space structure with nonequilibrium jammed simulations reveals many similarities, but also differences as expected. The new structural theory is used as input into the nonlinear Langevin equation (NLE) theory of activated single particle dynamics to study the alpha relaxation time, and good agreement with recent experiments and simulations is found. We demonstrate it is crucial to accurately describe the very high wave vector Fourier space to reliably extract the dynamical predictions of NLE theory, and structural precursors of jamming play an important role in determining entropic barriers.
Potential energy landscape and inherent dynamics of a hard-sphere fluid.
Ma, Qingqing; Stratt, Richard M
2014-10-01
Hard-sphere models exhibit many of the same kinds of supercooled-liquid behavior as more realistic models of liquids, but the highly nonanalytic character of their potentials makes it a challenge to think of that behavior in potential energy landscape terms. We show here that it is possible to calculate an important topological property of hard-sphere landscapes, the geodesic pathways through those landscapes, and to do so without artificially coarse-graining or softening the potential. We show, moreover, that the rapid growth of the lengths of those pathways with increasing packing fraction quantitatively predicts the precipitous decline in diffusion constants in a glass-forming hard-sphere mixture model. The geodesic paths themselves can be considered as defining the intrinsic dynamics of hard spheres, so it is also revealing to find that they (and therefore the features of the underlying potential energy landscape) correctly predict the occurrence of dynamic heterogeneity and nonzero values of the non-Gaussian parameter. The success of these landscape predictions for the dynamics of such a singular model emphasizes that there is more to potential energy landscapes than is revealed by looking at the minima and saddle points.
A highly accurate and analytic equation of state for a hard sphere fluid in random porous media.
Holovko, M; Dong, W
2009-05-07
An analytical equation of state (EOS) for a hard sphere fluid confined in random porous media is derived by extending the scaled particle theory to such complex systems with quenched disorders. A simple empirical correction allows us to obtain a highly accurate EOS with errors within the simulation ones. These are the first analytical results for non trivial off-lattice quench-annealed systems.
Competition of percolation and phase separation in a fluid of adhesive hard spheres
Miller, M.A.; Frenkel, D.
2003-01-01
Using a combination of Monte Carlo techniques, we locate the liquid-vapor critical point of adhesive hard spheres. We find that the critical point lies deep inside the gel region of the phase diagram. The (reduced) critical temperature and density are τc = 0.1133±0.0005 and ρc = 0.508±0.01. We compa
Large-amplitude jumps and non-Gaussian dynamics in highly concentrated hard sphere fluids.
Saltzman, Erica J; Schweizer, Kenneth S
2008-05-01
Our microscopic stochastic nonlinear Langevin equation theory of activated dynamics has been employed to study the real-space van Hove function of dense hard sphere fluids and suspensions. At very short times, the van Hove function is a narrow Gaussian. At sufficiently high volume fractions, such that the entropic barrier to relaxation is greater than the thermal energy, its functional form evolves with time to include a rapidly decaying component at small displacements and a long-range exponential tail. The "jump" or decay length scale associated with the tail increases with time (or particle root-mean-square displacement) at fixed volume fraction, and with volume fraction at the mean alpha relaxation time. The jump length at the alpha relaxation time is predicted to be proportional to a measure of the decoupling of self-diffusion and structural relaxation. At long times corresponding to mean displacements of order a particle diameter, the volume fraction dependence of the decay length disappears. A good superposition of the exponential tail feature based on the jump length as a scaling variable is predicted at high volume fractions. Overall, the theoretical results are in good accord with recent simulations and experiments. The basic aspects of the theory are also compared with a classic jump model and a dynamically facilitated continuous time random-walk model. Decoupling of the time scales of different parts of the relaxation process predicted by the theory is qualitatively similar to facilitated dynamics models based on the concept of persistence and exchange times if the elementary event is assumed to be associated with transport on a length scale significantly smaller than the particle size.
Polydispersity effect on solid-fluid transition in hard sphere systems
Nogawa, T.
2010-02-01
The solid-fluid transition of the hard elastic particle system with size polydispersity is studied by molecular dynamics simulations. Using nonequilibrium relaxation from the mixed initial condition we determines the melting point where the first order transition between the solid, fcc crystal, and fluid states occurs. It is found that the density gap between the bistable states decreases with increasing the strength of the polydispersity and continuously approaches to zero at the critical point. © 2010.
Ustinov, E. A.
2017-01-01
The paper aims at a comparison of techniques based on the kinetic Monte Carlo (kMC) and the conventional Metropolis Monte Carlo (MC) methods as applied to the hard-sphere (HS) fluid and solid. In the case of the kMC, an alternative representation of the chemical potential is explored [E. A. Ustinov and D. D. Do, J. Colloid Interface Sci. 366, 216 (2012)], which does not require any external procedure like the Widom test particle insertion method. A direct evaluation of the chemical potential of the fluid and solid without thermodynamic integration is achieved by molecular simulation in an elongated box with an external potential imposed on the system in order to reduce the particle density in the vicinity of the box ends. The existence of rarefied zones allows one to determine the chemical potential of the crystalline phase and substantially increases its accuracy for the disordered dense phase in the central zone of the simulation box. This method is applicable to both the Metropolis MC and the kMC, but in the latter case, the chemical potential is determined with higher accuracy at the same conditions and the number of MC steps. Thermodynamic functions of the disordered fluid and crystalline face-centered cubic (FCC) phase for the hard-sphere system have been evaluated with the kinetic MC and the standard MC coupled with the Widom procedure over a wide range of density. The melting transition parameters have been determined by the point of intersection of the pressure-chemical potential curves for the disordered HS fluid and FCC crystal using the Gibbs-Duhem equation as a constraint. A detailed thermodynamic analysis of the hard-sphere fluid has provided a rigorous verification of the approach, which can be extended to more complex systems.
Long-range weight functions in fundamental measure theory of the non-uniform hard-sphere fluid
Hansen-Goos, Hendrik
2016-06-01
We introduce long-range weight functions to the framework of fundamental measure theory (FMT) of the non-uniform, single-component hard-sphere fluid. While the range of the usual weight functions is equal to the hard-sphere radius R, the modified weight functions have range 3R. Based on the augmented FMT, we calculate the radial distribution function g(r) up to second order in the density within Percus’ test particle theory. Consistency of the compressibility and virial routes on this level allows us to determine the free parameter γ of the theory. As a side result, we obtain a value for the fourth virial coefficient B 4 which deviates by only 0.01% from the exact result. The augmented FMT is tested for the dense fluid by comparing results for g(r) calculated via the test particle route to existing results from molecular dynamics simulations. The agreement at large distances (r > 6R) is significantly improved when the FMT with long-range weight functions is used. In order to improve agreement close to contact (r = 2R) we construct a free energy which is based on the accurate Carnahan-Starling equation of state, rather than the Percus-Yevick compressibility equation underlying standard FMT.
Gazzillo, Domenico; Giacometti, Achille
2004-03-08
We discuss structural and thermodynamical properties of Baxter's adhesive hard sphere model within a class of closures which includes the Percus-Yevick (PY) one. The common feature of all these closures is to have a direct correlation function vanishing beyond a certain range, each closure being identified by a different approximation within the original square-well region. This allows a common analytical solution of the Ornstein-Zernike integral equation, with the cavity function playing a privileged role. A careful analytical treatment of the equation of state is reported. Numerical comparison with Monte Carlo simulations shows that the PY approximation lies between simpler closures, which may yield less accurate predictions but are easily extensible to multicomponent fluids, and more sophisticate closures which give more precise predictions but can hardly be extended to mixtures. In regimes typical for colloidal and protein solutions, however, it is found that the perturbative closures, even when limited to first order, produce satisfactory results.
Institute of Scientific and Technical Information of China (English)
S. B. Khasare
2012-01-01
The present work uses the concept of a scaled particle along with the perturbation and variation approach,to develop an equation of state (EOS) for a mixture of hard sphere (HS),Lennard-Jones (LJ) fluids.A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture,with R as a variable.The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m.For m =0.75 and m =0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively.
Jiang, Hao; Adidharma, Hertanto
2014-11-07
The thermodynamic modeling of flexible charged hard-sphere chains representing polyampholyte or polyelectrolyte molecules in solution is considered. The excess Helmholtz energy and osmotic coefficients of solutions containing short polyampholyte and the osmotic coefficients of solutions containing short polyelectrolytes are determined by performing canonical and isobaric-isothermal Monte Carlo simulations. A new equation of state based on the thermodynamic perturbation theory is also proposed for flexible charged hard-sphere chains. For the modeling of such chains, the use of solely the structure information of monomer fluid for calculating the chain contribution is found to be insufficient and more detailed structure information must therefore be considered. Two approaches, i.e., the dimer and dimer-monomer approaches, are explored to obtain the contribution of the chain formation to the Helmholtz energy. By comparing with the simulation results, the equation of state with either the dimer or dimer-monomer approach accurately predicts the excess Helmholtz energy and osmotic coefficients of polyampholyte and polyelectrolyte solutions except at very low density. It also well captures the effect of temperature on the thermodynamic properties of these solutions.
Institute of Scientific and Technical Information of China (English)
YU Yang-Xin; WU Jian-Zhong; YOU Feng-Qi; GAO Guang-Hua
2005-01-01
@@ An extended test-particle method is used to predict the inter- and intramolecular correlation functions of freely jointed hard-sphere-Yukawa-chain fluids by calculating the segmental density distributions around a fixed seg ment. The underlying density functional theory for chain fluids is based on a modified fundamental measure theory for the hard-sphere repulsive and a mean-field approximation for attraction between different segments.The calculated intra- and inter-molecular distribution functions agree well with the results from Monte Carlo simulations, better than those from alternative approaches.
Román, F L; White, J A; González, A; Velasco, S
2006-04-21
We examine the microscopic structure of a hard-sphere fluid confined to a small cylindrical pore by means of Monte Carlo simulation. In order to analyze finite-size effects, the simulations are carried out in the framework of different statistical mechanics ensembles. We find that the size effects are specially relevant in the canonical ensemble where noticeable differences are found with the results in the grand canonical ensemble (GCE) and the isothermal isobaric ensemble (IIE) which, in most situations, remain very close to the infinite system results. A customary series expansion in terms of fluctuations of either the number of particles (GCE) or the inverse volume (IIE) allows us to connect with the results of the canonical ensemble.
Sesé, Luis M
2012-06-28
A systematic study of the direct computation of the isothermal compressibility of normal quantum fluids is presented by analyzing the solving of the Ornstein-Zernike integral (OZ2) equation for the pair correlations between the path-integral necklace centroids. A number of issues related to the accuracy that can be achieved via this sort of procedure have been addressed, paying particular attention to the finite-N effects and to the definition of significant error bars for the estimates of isothermal compressibilities. Extensive path-integral Monte Carlo computations for the quantum hard-sphere fluid (QHS) have been performed in the (N, V, T) ensemble under temperature and density conditions for which dispersion effects dominate the quantum behavior. These computations have served to obtain the centroid correlations, which have been processed further via the numerical solving of the OZ2 equation. To do so, Baxter-Dixon-Hutchinson's variational procedure, complemented with Baumketner-Hiwatari's grand-canonical corrections, has been used. The virial equation of state has also been obtained and several comparisons between different versions of the QHS equation of state have been made. The results show the reliability of the procedure based on isothermal compressibilities discussed herein, which can then be regarded as a useful and quick means of obtaining the equation of state for fluids under quantum conditions involving strong repulsive interactions.
Santos, Andrés; Yuste, Santos B; López de Haro, Mariano
2005-12-15
The contact values g(sigma,sigma') of the radial distribution functions of a fluid of (additive) hard spheres with a given size distribution f(sigma) are considered. A "universality" assumption is introduced, according to which, at a given packing fraction eta,g(sigma,sigma')=G(z(sigma,sigma')), where G is a common function independent of the number of components (either finite or infinite) and z(sigma,sigma')=[2sigmasigma'/(sigma+sigma')]mu2/mu3 is a dimensionless parameter, mu n being the nth moment of the diameter distribution. A cubic form proposal for the z dependence of G is made and known exact consistency conditions for the point particle and equal size limits, as well as between two different routes to compute the pressure of the system in the presence of a hard wall, are used to express Gz in terms of the radial distribution at contact of the one-component system. For polydisperse systems we compare the contact values of the wall-particle correlation function and the compressibility factor with those obtained from recent Monte Carlo simulations.
Kinetic theory of hard spheres
Beijeren, H. van; Ernst, M.H.
1979-01-01
Kinetic equations for the hard-sphere system are derived by diagrammatic techniques. A linear equation is obtained for the one-particle-one particle equilibrium time correlation function and a nonlinear equation for the one-particle distribution function in nonequilibrium. Both equations are nonloca
Tsekov, R
2014-01-01
The finite size effect of electron and nucleus is accounted for in the model of atom. Due to their hard sphere repulsion the energy of the 1s orbital decreases and the corrections amount up to 8 % in Uranium. Several models for boundary conditions on the atomic nucleus surface are discussed as well.
Reiss, Howard; Manzanares, José A.
2016-09-01
Using several theoretical toolsldots (i) the nucleation theorem, (ii) an equivalent cavity, (iii) the reversible work of adding a cavity to an open hard sphere system, and (iv) the theory of "stability"... the authors estimated the density at which the hard sphere freezing transition occurs. No direct involvement of the equilibrium solid phase is involved. The reduced density \\uppi a^3ρ _f/6 (where a is the hard sphere diameter and ρ _f is the actual density at which freezing occurs) is found to be 0.4937 while the value obtained by computer simulation is 0.494. The agreement is good, but the new method still contains some approximation. However, the approximation is based on the idea that at a density just below ρ _f the fluid adopts a distorted structure resembling the solid, but different enough so that long-range order vanishes. Initial loss of stability may not be involved in every fluid-solid transition, but it may be an early step in the hard sphere and related systems.
Flexible equation of state for a hard sphere and Lennard–Jones fluid near critical temperature
Indian Academy of Sciences (India)
S B Khasare
2014-12-01
Author uses the condition in terms of contact point radial distribution function $G(, (_c, ))$ containing the self-consistent function $(_c, )$ and condition of continuity at /2 = contact point, to determine equation of state, (EoS). Different EoSs in terms of built-in parameter, , can be obtained with a suitable choice of $(_c, )$ and the present EoSs have less r.m.s. deviation than Barker–Henderson BH2 for LJ fluids, and results are much closer to molecular dynamics (MD) simulations than expectations and reproduce the existing simulation data and present EoS for LJ potential, with the help of a set of minimum single-scaled parameter, $a_0(_c, )$ for a given reduced temperature, $T^* = (1/ )$= 1.4, 2, 3, 4, 5, 6. It has been found that parameter = 1.059128388 can be used to fix up the critical temperature parameter c = 1.3120(7) to that of a computer simulation result.
Hard sphere packings within cylinders.
Fu, Lin; Steinhardt, William; Zhao, Hao; Socolar, Joshua E S; Charbonneau, Patrick
2016-03-07
Arrangements of identical hard spheres confined to a cylinder with hard walls have been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest configurations, called close packings, of hard spheres of diameter σ in a cylinder of diameter D is a purely geometric problem that grows increasingly complex as D/σ increases, and little is thus known about the regime for D > 2.873σ. In this work, we extend the identification of close packings up to D = 4.00σ by adapting Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (SLP) technique. We identify 17 new structures, almost all of them chiral. Beyond D ≈ 2.85σ, most of the structures consist of an outer shell and an inner core that compete for being close packed. In some cases, the shell adopts its own maximum density configuration, and the stacking of core spheres within it is quasiperiodic. In other cases, an interplay between the two components is observed, which may result in simple periodic structures. In yet other cases, the very distinction between the core and shell vanishes, resulting in more exotic packing geometries, including some that are three-dimensional extensions of structures obtained from packing hard disks in a circle.
Depletion induced demixing in polydisperse mixtures of hard spheres
Sear, RP
1998-01-01
Polydisperse mixtures are those in which components with a whole range of sizes are present. It is shown that the fluid phase of polydisperse hard spheres is thermodynamically unstable unless the density of large spheres decreases at least exponentially as their size increases. The instability is with respect to the large spheres crystallising out into multiple solid phases.
Hvozd, Taras V; Kalyuzhnyi, Yurij V
2017-02-15
We have studied the phase behavior of polydisperse Yukawa hard-sphere fluid confined in random porous media using extension and combination of high temperature approximation and scaled particle theory. The porous media are represented by the matrix of randomly placed hard-sphere obstacles. Due to the confinement, polydispersity effects are substantially enhanced. At an intermediate degree of fluid polydispersity and low density of the matrix, we observe two-phase coexistence with two critical points, and cloud and shadow curves forming closed loops of ellipsoidal shape. With the increase of the matrix density and the constant degree of polydispersity, these two critical points merge and disappear, and at lower temperatures the system fractionates into three coexisting phases. A similar phase behavior was observed in the absence of the porous media caused, however, by the increase of the polydispersity.
Thermodynamic signature of the dynamic glass transition in hard spheres
Hermes, M|info:eu-repo/dai/nl/304829854; Dijkstra, M.|info:eu-repo/dai/nl/123538807
2010-01-01
We use extensive event-driven molecular dynamics simulations to study the thermodynamic, structural and dynamic properties of hard-sphere glasses. We determine the equation of state of the metastable fluid branch for hard spheres with a size polydispersity of 10%. Our results show a clear jump in
Germain, Ph; Amokrane, S
2007-09-01
Motivated by recent experimental results on model binary colloidal mixtures, especially for the glass transition, we investigate the phase diagram of two models of asymmetric binary mixtures: the hard sphere and the Asakura-Oosawa mixtures. This includes the binodals and the glass transition line, computed in the effective one-component representation using the corresponding potentials of mean force at infinite dilution. The reference hypernetted chain approximation is used for computing the static properties and the glass transition line is computed in the mode coupling approximation. The similarities and the differences between the two models are discussed for different size ratios. It is shown that while both models follow a universal behavior at large asymmetry, the hard sphere mixture model leads to more original results at moderate size ratio. These results show that a modeling beyond generic effective potentials might be necessary for an appropriate description of the complete phase diagram.
Institute of Scientific and Technical Information of China (English)
Limin Wang; Guofeng Zhou; Xiaowei Wang; Qingang Xiong; Wei Ge
2010-01-01
A coupled numerical method for the direct numerical simulation of particle-fluid systems is formulated and implemented,resolving an order of magnitude smaller than particle size.The particle motion is described by the time-driven hard-sphere model,while the hydrodynamic equations governing fluid flow are solved by the lattice Boltzmann method(LBM).Particle-fluid coupling is realized by an immersed boundary method(IBM),which considers the effect of boundary on surrounding fluid as a restoring force added to the governing equations of the fluid.The proposed scheme is validated in the classical flow-around-cylinder simulations,and preliminary application of this scheme to fluidization is reported,demonstrating it to be a promising computational strategy for better understanding complex behavior in particle-fluid systems.
Close packing density of polydisperse hard spheres.
Farr, Robert S; Groot, Robert D
2009-12-28
The most efficient way to pack equally sized spheres isotropically in three dimensions is known as the random close packed state, which provides a starting point for many approximations in physics and engineering. However, the particle size distribution of a real granular material is never monodisperse. Here we present a simple but accurate approximation for the random close packing density of hard spheres of any size distribution based upon a mapping onto a one-dimensional problem. To test this theory we performed extensive simulations for mixtures of elastic spheres with hydrodynamic friction. The simulations show a general (but weak) dependence of the final (essentially hard sphere) packing density on fluid viscosity and on particle size but this can be eliminated by choosing a specific relation between mass and particle size, making the random close packed volume fraction well defined. Our theory agrees well with the simulations for bidisperse, tridisperse, and log-normal distributions and correctly reproduces the exact limits for large size ratios.
Multidensity integral-equation theory for short diblock hard-sphere-sticky-hard-sphere chains.
Wu, Ning; Chiew, Y C
2010-04-01
The multidensity Ornstein-Zernike integral equation theory is applied to study a simple model of hard sphere/sticky hard sphere diblock chains. The multidensity integral equation formalism has been successfully used to model the equilibrium structure and thermodynamic properties of homonuclear chains and shorter dimer fluids; to our knowledge it has not been applied to model diblock chains. In this work, a diblock chain fluids is represented by an m-component equal molar mixture of hard spheres with species 1,2,...,mh and sticky hard spheres with species mh+1,mh+2,...,m. Each spherical particle has two attractive sites A and B except species 1 and m, which have only one site per particle. In the limit of complete association, this mixture yields a system of monodisperse diblock chains. A general solution of this model is obtained in the Percus-Yevick, Polymer Percus-Yevick and ideal chain approximations. Both structural and thermodynamic properties of this model are investigated. From this study, a microphase separation is predicted for relatively short diblock symmetric and asymmetric chains. This microphase separation is enhanced at lower temperature and higher density. When chain length increases, the phase transition changes from a microphase level to a macrophase level. The size of microdomain structure is found to be dependent on total chain length, relative ratio of block lengths, temperature, and density.
Directory of Open Access Journals (Sweden)
Yu.V. Kalyuzhnyi
2012-06-01
Full Text Available The liquid-gas phase diagram for polydisperse dipolar hard-sphere fluid with polydispersity in the hard-sphere size and dipolar moment is calculated using extension of the recently proposed thermodynamic perturbation theory for central force (TPT-CF associating potential. To establish the connection with the phase behavior of ferrocolloidal dispersions it is assumed that the dipole moment is proportional to the cube of the hard-sphere diameter. We present and discuss the full phase diagram, which includes cloud and shadow curves, binodals and distribution functions of the coexisting daughter phases at different degrees of the system polydispersity. In all cases studied polydispersity increases the region of the phase instability and shifts the critical point to the higher values of the temperature and density. The larger size particles always fractionate to the liquid phase and the smaller size particles tend to move to the gas phase. At relatively high values of the system polydispersity three-phase coexistence is observed.
Collision statistics in sheared inelastic hard spheres.
Bannerman, Marcus N; Green, Thomas E; Grassia, Paul; Lue, Leo
2009-04-01
The dynamics of sheared inelastic-hard-sphere systems is studied using nonequilibrium molecular-dynamics simulations and direct simulation Monte Carlo. In the molecular-dynamics simulations Lees-Edwards boundary conditions are used to impose the shear. The dimensions of the simulation box are chosen to ensure that the systems are homogeneous and that the shear is applied uniformly. Various system properties are monitored, including the one-particle velocity distribution, granular temperature, stress tensor, collision rates, and time between collisions. The one-particle velocity distribution is found to agree reasonably well with an anisotropic Gaussian distribution, with only a slight overpopulation of the high-velocity tails. The velocity distribution is strongly anisotropic, especially at lower densities and lower values of the coefficient of restitution, with the largest variance in the direction of shear. The density dependence of the compressibility factor of the sheared inelastic-hard-sphere system is quite similar to that of elastic-hard-sphere fluids. As the systems become more inelastic, the glancing collisions begin to dominate over more direct, head-on collisions. Examination of the distribution of the times between collisions indicates that the collisions experienced by the particles are strongly correlated in the highly inelastic systems. A comparison of the simulation data is made with direct Monte Carlo simulation of the Enskog equation. Results of the kinetic model of Montanero [J. Fluid Mech. 389, 391 (1999)] based on the Enskog equation are also included. In general, good agreement is found for high-density, weakly inelastic systems.
The Chiral Dipolar Hard Sphere Model.
Mazars, Martial
2009-01-01
Abstract A simple molecular model of chiral molecules is presented in this paper : the chiral dipolar hard sphere model. The discriminatory interaction between enantiomers is represented by electrostatic (or magnetic) dipoles-dipoles interactions : short ranged steric repulsion are represented by hard sphere potential and, in each molecule, two point dipoles are located inside the sphere. The model is described in detail and some of its elementary properties are given ; in particul...
Energy Technology Data Exchange (ETDEWEB)
Schaefer, B.; Lambert, S.M.; Song, Y.; Prausnitz, J.M.
1994-10-01
Goal of this work is the extension of a Perturbed-Hard-Sphere-Chain equation of state (PHSC EOS) to systems containing strong polar components. Three different types of association models (ten Brinke/Karasz, SAFI, modified Veytsman) were used to calculate the contribution of specific interactions like hydrogen bonding to thermodynamic quantities. Pure component parameters obtained from regression of temperature dependent density and vapor pressure data allow the prediction of VLE and LLE data. The results of simple fluids and polymer solutions were compared with experimental data. The SAFT and the modified Veytsman extension give similar results for pure fluids and mixtures with components of similar segment size. Differences increase with increasing difference of segment size.
The vanishing limit of the square-well fluid: the adhesive hard-sphere model as a reference system.
Largo, J; Miller, M A; Sciortino, F
2008-04-07
We report a simulation study of the gas-liquid critical point for the square-well potential, for values of well width delta as small as 0.005 times the particle diameter sigma. For small delta, the reduced second virial coefficient at the critical point B2*c is found to depend linearly on delta. The observed weak linear dependence is not sufficient to produce any significant observable effect if the critical temperature Tc is estimated via a constant B2*c assumption, due to the highly nonlinear transformation between B2*c and Tc. This explains the previously observed validity of the law of corresponding states. The critical density rho c is also found to be constant when measured in units of the cube of the average distance between two bonded particles (1+0.5 delta)sigma. The possibility of describing the delta-->0 dependence with precise functional forms provides improved accurate estimates of the critical parameters of the adhesive hard-sphere model.
Enhanced KR-Fundamental Measure Functional for Inhomogeneous Binary and Ternary Hard Sphere Mixtures
National Research Council Canada - National Science Library
Zhou, Shi-Qi (世琦 周)
2011-01-01
An enhanced KR-fundamental measure functional （FMF） is elaborated and employed to investigate binary and ternary hard sphere fluids near a planar hard wall or confined within two planar hard walls separated by certain interval...
Depletion potential in colloidal mixtures of hard spheres and platelets.
Harnau, L; Dietrich, S
2004-05-01
The depletion potential between two hard spheres in a solvent of thin hard disclike platelets is investigated by using either the Derjaguin approximation or density functional theory. Particular attention is paid to the density dependence of the depletion potential. A second-order virial approximation is applied, which yields nearly exact results for the bulk properties of the hard-platelet fluid at densities two times smaller than the density of the isotropic fluid at isotropic-nematic phase coexistence. As the platelet density increases, the attractive primary minimum of the depletion potential deepens and an additional small repulsive barrier at larger sphere separations develops. Upon decreasing the ratio of the radius of the spheres and the platelets, the primary minimum diminishes and the position of the small repulsive barrier shifts to smaller values of the sphere separation.
SURFACES OF HARD-SPHERE SYSTEMS
Directory of Open Access Journals (Sweden)
Dietrich Stoyan
2014-07-01
Full Text Available In various situations surfaces appear that are formed by systems of hard spheres. Examples are porous layers as surfaces of sand heaps and biofilms or fracture surfaces of concrete. The present paper considers models where a statistically homogeneous system of hard spheres with random radii is intersected by a plane and the surface is formed by the spheres with centers close to this plane. Formulae are derived for various characteristics of such surfaces: for the porosity profile, i.e. the local porosity in dependence on the distance from the section plane and for the geometry of the sphere caps that look above the section plane.It turns out that these characteristics only depend on the first-order characteristics of the sphere system, its sphere density and the sphere radius distribution.Comparison with empirically studied biofilms shows that the model is realistic.
Thermodynamic signature of the dynamic glass transition in hard spheres.
Hermes, Michiel; Dijkstra, Marjolein
2010-03-17
We use extensive event-driven molecular dynamics simulations to study the thermodynamic, structural and dynamic properties of hard-sphere glasses. We determine the equation of state of the metastable fluid branch for hard spheres with a size polydispersity of 10%. Our results show a clear jump in the slope of the isothermal compressibility. The observation of a thermodynamic signature at the transition from a metastable fluid to a glassy state is analogous to the abrupt change in the specific heat or thermal expansion coefficient as observed for molecular liquids at the glass transition. The dynamic glass transition becomes more pronounced and shifts to higher densities for longer equilibration times.
Point defects in hard-sphere crystals
Pronk, S.; Frenkel, D.
2001-01-01
We report numerical calculations of the concentration of interstitials in hard-sphere crystals. We find that, in a three-dimensional fcc hard-sphere crystal at the melting point, the concentration of interstitials is 2 * 10^-8. This is some three orders of magnitude lower than the concentration of vacancies. A simple, analytical estimate yields a value that is in fair agreement with the numerical results.
Macromolecule-Induced Clustering of Hard Spheres.
Chatterjee, Avik Prasun
2001-06-01
The connectivity Ornstein-Zernike formalism, together with the polymer reference interaction site model (PRISM), is employed to describe connectivity and network formation in mixtures of spheres and polymers. Results are presented for the percolation of spheres induced by both flexible coil-like and rigid rod-like linear polymers; the Percus-Yevick (PY) approximation is used throughout. Our results are compared with predictions based on the adhesive hard sphere (AHS) model, and correlations with the polymer-mediated second virial coefficient between spheres are discussed. Copyright 2001 Academic Press.
Rowlinson’s concept of an effective hard sphere diameter
Henderson, Douglas
2010-01-01
Attention is drawn to John Rowlinson’s idea that the repulsive portion of the intermolecular interaction may be replaced by a temperature-dependent hard sphere diameter. It is this approximation that made the development of perturbation theory possible for realistic fluids whose intermolecular interactions have a steep, but finite, repulsion at short separations. PMID:20953320
Rowlinson's concept of an effective hard sphere diameter.
Henderson, Douglas
2010-01-01
Attention is drawn to John Rowlinson's idea that the repulsive portion of the intermolecular interaction may be replaced by a temperature-dependent hard sphere diameter. It is this approximation that made the development of perturbation theory possible for realistic fluids whose intermolecular interactions have a steep, but finite, repulsion at short separations.
Simulating colloids with Baxter's adhesive hard sphere model
Miller, M.A.; Frenkel, D.
2004-01-01
The structure of the Baxter adhesive hard sphere fluid is examined using computer simulation. The radial distribution function (which exhibits unusual discontinuities due to the particle adhesion) and static structure factor are calculated with high accuracy over a range of conditions and compared w
Simulating colloids with Baxter's adhesive hard sphere model
Miller, M.A.; Frenkel, D.
2004-01-01
The structure of the Baxter adhesive hard sphere fluid is examined using computer simulation. The radial distribution function (which exhibits unusual discontinuities due to the particle adhesion) and static structure factor are calculated with high accuracy over a range of conditions and compared
Free volume distribution of nearly jammed hard sphere packings
Maiti, Moumita; Sastry, Srikanth
2014-07-01
We calculate the free volume distributions of nearly jammed packings of monodisperse and bidisperse hard sphere configurations. These distributions differ qualitatively from those of the fluid, displaying a power law tail at large free volumes, which constitutes a distinct signature of nearly jammed configurations, persisting for moderate degrees of decompression. We reproduce and explain the observed distribution by considering the pair correlation function within the first coordination shell for jammed hard sphere configurations. We analyze features of the equation of state near jamming, and discuss the significance of observed asphericities of the free volumes to the equation of state.
Slip and flow of hard-sphere colloidal glasses.
Ballesta, P; Besseling, R; Isa, L; Petekidis, G; Poon, W C K
2008-12-19
We study the flow of concentrated hard-sphere colloidal suspensions along smooth, nonstick walls using cone-plate rheometry and simultaneous confocal microscopy. In the glass regime, the global flow shows a transition from Herschel-Bulkley behavior at large shear rate to a characteristic Bingham slip response at small rates, absent for ergodic colloidal fluids. Imaging reveals both the "solid" microstructure during full slip and the local nature of the "slip to shear" transition. Both the local and global flow are described by a phenomenological model, and the associated Bingham slip parameters exhibit characteristic scaling with size and concentration of the hard spheres.
Theory of asymmetric nonadditive binary hard-sphere mixtures.
Roth, R; Evans, R; Louis, A A
2001-11-01
It is shown that the formal procedure of integrating out the degrees of freedom of the small spheres in a binary hard-sphere mixture works equally well for nonadditive as it does for additive mixtures. For highly asymmetric mixtures (small size ratios) the resulting effective Hamiltonian of the one-component fluid of big spheres, which consists of an infinite number of many-body interactions, should be accurately approximated by truncating after the term describing the effective pair interaction. Using a density functional treatment developed originally for additive hard-sphere mixtures the zero, one, and two-body contribution to the effective Hamiltonian are determined. It is demonstrated that even small degrees of positive or negative nonadditivity have significant effect on the shape of the depletion potential. The second virial coefficient B2, corresponding to the effective pair interaction between two big spheres, is found to be a sensitive measure of the effects of nonadditivity. The variation of B2 with the density of the small spheres shows significantly different behavior for additive, slightly positive and slightly negative nonadditive mixtures. Possible repercussions of these results for the phase behavior of binary hard-sphere mixtures are discussed and it is suggested that measurements of B2 might provide a means of determining the degree of nonadditivity in real colloidal mixtures.
Patchy sticky hard spheres: analytical study and Monte Carlo simulations.
Fantoni, Riccardo; Gazzillo, Domenico; Giacometti, Achille; Miller, Mark A; Pastore, Giorgio
2007-12-21
We consider a fluid of hard spheres bearing one or two uniform circular adhesive patches, distributed so as not to overlap. Two spheres interact via a "sticky" Baxter potential if the line joining the centers of the two spheres intersects a patch on each sphere, and via a hard sphere potential otherwise. We analyze the location of the fluid-fluid transition and of the percolation line as a function of the size of the patch (the fractional coverage of the sphere's surface) and of the number of patches within a virial expansion up to third order and within the first two terms (C0 and C1) of a class of closures Cn hinging on a density expansion of the direct correlation function. We find that the locations of the two lines depend sensitively on both the total adhesive coverage and its distribution. The treatment is almost fully analytical within the chosen approximate theory. We test our findings by means of specialized Monte Carlo simulations and find the main qualitative features of the critical behavior to be well captured in spite of the low density perturbative nature of the closure. The introduction of anisotropic attractions into a model suspension of spherical particles is a first step toward a more realistic description of globular proteins in solution.
Gazzillo, Domenico
2011-03-28
For fluids of molecules with short-ranged hard-sphere-Yukawa (HSY) interactions, it is proven that the Noro-Frenkel "extended law of corresponding states" cannot be applied down to the vanishing attraction range, since the exact HSY second virial coefficient diverges in such a limit. It is also shown that, besides Baxter's original approach, a fully correct alternative definition of "adhesive hard spheres" can be obtained by taking the vanishing-range-limit (sticky limit) not of a Yukawa tail, as is commonly done, but of a slightly different potential with a logarithmic-Yukawa attraction.
Event Driven Langevin simulations of Hard Spheres
Scala, Antonio
2011-01-01
The blossoming of interest in colloids and nano-particles has given renewed impulse to the study of hard-body systems. In particular, hard spheres have become a real test system for theories and experiments. It is therefore necessary to study the complex dynamics of such systems in presence of a solvent; disregarding hydrodynamic interactions, the simplest model is the Langevin equation. Unfortunately, standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during an integration timestep. This in not the case for hard-body systems, where there is no clearcut between the correlation time of the noise and the timescale of the interactions. Starting first from a splitting of the Fokker-Plank operator associated with the Langevin dynamics, and then from an approximation of the two-body Green's function, we introduce and test two new algorithms for the simulation of the Langevin dynamics of hard-spheres.
Cao, M; Monson, P A
2009-10-22
We present a study of the phase behavior for models of n-alkanes with chain lengths up to C(21) based on hard sphere united atom models of methyl and methylene groups, with fixed bond lengths and C-C-C bond angles. We extend earlier work on such models of shorter alkanes by allowing for gauche conformations in the chains. We focus particularly on the orientational order about the chain axes in the solid phase near the melting point, and our model shows how the loss of this orientational order leads to the formation of rotator phases. We have made extensive calculations of the thermodynamic properties of the models as well as order parameters for tracking the degree of orientational order around the chain axis. Depending on the chain length and whether the carbon number is even or odd, the model exhibits both a rotator phase and a more orientationally ordered solid phase in addition to the fluid phase. Our results indicate that the transition between the two solid phases is first-order with a small density change. The results are qualitatively similar to those seen experimentally and show that rotator phases can appear in models of alkanes without explicit treatment of attractive forces or explicit treatment of the hydrogen atoms in the chains.
Institute of Scientific and Technical Information of China (English)
周世琦
2005-01-01
A universal theoretical way is proposed which enables all of hard sphere density functional approximations (DFAs) applicable to non-hard sphere fluids.The resultant DFA by combining the universal theoretical way with any hard sphere DFAs only needs as input a second order direct correlation function (DCF) of a coexistence bulk fluid,and can be applicable to both supercitical and subcritical temperature regions.The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that so determined value of the effective hard sphere density can be universal,i.e. can be applied for any external potentials different from the single hard wall. As an illustrating example,the universal theoretical way is combined with a hard sphere BDFA to predict density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields,agreement between the present formalism predictions and the corresponding simulation data is very good or at least comparable with several previous DFT approaches. The most advantage of the present theoretical way combined with other hard sphere DFAs is discused.%提出了一个普适性的理论方案,该方案使一切硬球密度泛函近似能被扩展到非硬球流体的情形.将该普适性理论方案与任意硬球密度泛函近似结合所形成的非硬球密度泛函近似,仅仅需要共存体相流体的二阶直接相关函数作为输入,因而能用于超临界与亚临界区域的情形.其中的有效硬球密度可由硬墙Sum规则确定.结果表明,如此确定的有效硬球密度可用于任意外势情形.作为代表性的例子,我们将该普适性理论方案与一个最近提出的桥密度泛函近似结合,用以预言硬核吸引汤川势流体在几个不同的外场影响下的密度分布.此理论与相应的计算机模拟数据符合很好,或至少与以前的几个密度泛函近似相当.并讨论了该方法相比于以前的几个方法所具有的优点.
Dynamic equivalences in the hard-sphere dynamic universality class.
López-Flores, Leticia; Ruíz-Estrada, Honorina; Chávez-Páez, Martín; Medina-Noyola, Magdaleno
2013-10-01
We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, α-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. Finally, we verify another more recently proposed dynamic equivalence, this time between the long-time dynamics of an atomic liquid and its corresponding Brownian fluid (i.e., the Brownian system with the same interaction potential).
Bulk and wetting phenomena in a colloidal mixture of hard spheres and platelets
Harnau, L.; Dietrich, S.
2004-01-01
Density functional theory is used to study binary colloidal fluids consisting of hard spheres and thin platelets in their bulk and near a planar hard wall. This system exhibits liquid-liquid coexistence of a phase that is rich in spheres (poor in platelets) and a phase that is poor in spheres (rich in platelets). For the mixture near a planar hard wall, we find that the phase rich in spheres wets the wall completely upon approaching the liquid demixing binodal from the sphere-poor phase, prov...
Dogic, Z.; Frenkel, D.; Fraden, S.
2000-01-01
There is increasing evidence that entropy can induce microphase separation in binary fluid mixtures interacting through hard particle potentials. One such phase consists of alternating two-dimensional liquidlike layers of rods and spheres. We study the transition from a uniform miscible state to
Depletion potential in hard-sphere mixtures: theory and applications
Roth; Evans; Dietrich
2000-10-01
We present a versatile density functional approach (DFT) for calculating the depletion potential in general fluid mixtures. For the standard situation of a single big particle immersed in a sea of small particles near a fixed object, the system is regarded as an inhomogeneous binary mixture of big and small particles in the external field of the fixed object, and the limit of vanishing density of the big species, rho(b)-->0, is taken explicitly. In this limit our approach requires only the equilibrium density profile of a one-component fluid of small particles in the field of the fixed object, and a knowledge of the density independent weight functions which characterize the mixture functional. Thus, for a big particle near a planar wall or a cylinder or another fixed big particle, the relevant density profiles are functions of a single variable, which avoids the numerical complications inherent in brute force DFT. We implement our approach for additive hard-sphere mixtures, comparing our results with computer simulations for the depletion potential of a big sphere of radius R(b) in a sea of small spheres of radius R(s) near (i) a planar hard wall, and (ii) another big sphere. In both cases our results are accurate for size ratios s=R(s)/R(b) as small as 0.1, and for packing fractions of the small spheres eta(s) as large as 0.3; these are the most extreme situations for which reliable simulation data are currently available. Our approach satisfies several consistency requirements, and the resulting depletion potentials incorporate the correct damped oscillatory decay at large separations of the big particles or of the big particle and the wall. By investigating the depletion potential for high size asymmetries we assess the regime of validity of the well-known Derjaguin approximation for hard-sphere mixtures and argue that this fails, even for very small size ratios s, for all but the smallest values of eta(s) where the depletion potential reduces to the Asakura
Phase diagram of highly asymmetric binary hard-sphere mixtures.
Dijkstra, M; van Roij, R; Evans, R
1999-05-01
We study the phase behavior and structure of highly asymmetric binary hard-sphere mixtures. By first integrating out the degrees of freedom of the small spheres in the partition function we derive a formal expression for the effective Hamiltonian of the large spheres. Then using an explicit pairwise (depletion) potential approximation to this effective Hamiltonian in computer simulations, we determine fluid-solid coexistence for size ratios q=0.033, 0.05, 0.1, 0.2, and 1.0. The resulting two-phase region becomes very broad in packing fractions of the large spheres as q becomes very small. We find a stable, isostructural solid-solid transition for q0 the phase diagram mimics that of the sticky-sphere system. As expected, the radial distribution function g(r) and the structure factor S(k) of the effective one-component system show no sharp signature of the onset of the freezing transition and we find that at most points on the fluid-solid boundary the value of S(k) at its first peak is much lower than the value given by the Hansen-Verlet freezing criterion. Direct simulations of the true binary mixture of hard spheres were performed for q > or =0.05 in order to test the predictions from the effective Hamiltonian. For those packing fractions of the small spheres where direct simulations are possible, we find remarkably good agreement between the phase boundaries calculated from the two approaches-even up to the symmetric limit q=1 and for very high packings of the large spheres, where the solid-solid transition occurs. In both limits one might expect that an approximation which neglects higher-body terms should fail, but our results support the notion that the main features of the phase equilibria of asymmetric binary hard-sphere mixtures are accounted for by the effective pairwise depletion potential description. We also compare our results with those of other theoretical treatments and experiments on colloidal hard-sphere mixtures.
Extended hard-sphere model and collisions of cohesive particles.
Kosinski, Pawel; Hoffmann, Alex C
2011-09-01
In two earlier papers the present authors modified a standard hard-sphere particle-wall and particle-particle collision model to account for the presence of adhesive or cohesive interaction between the colliding particles: the problem is of importance for modeling particle-fluid flow using the Lagrangian approach. This technique, which involves a direct numerical simulation of such flows, is gaining increasing popularity for simulating, e.g., dust transport, flows of nanofluids and grains in planetary rings. The main objective of the previous papers was to formally extend the impulse-based hard-sphere model, while suggestions for quantifications of the adhesive or cohesive interaction were made. This present paper gives an improved quantification of the adhesive and cohesive interactions for use in the extended hard-sphere model for cases where the surfaces of the colliding bodies are "dry," e.g., there is no liquid-bridge formation between the colliding bodies. This quantification is based on the Johnson-Kendall-Roberts (JKR) analysis of collision dynamics but includes, in addition, dissipative forces using a soft-sphere modeling technique. In this way the cohesive impulse, required for the hard-sphere model, is calculated together with other parameters, namely the collision duration and the restitution coefficient. Finally a dimensional analysis technique is applied to fit an analytical expression to the results for the cohesive impulse that can be used in the extended hard-sphere model. At the end of the paper we show some simulation results in order to illustrate the model.
Fundamental measure theory for hard-sphere mixtures: a review.
Roth, Roland
2010-02-17
Hard-sphere systems are one of the fundamental model systems of statistical physics and represent an important reference system for molecular or colloidal systems with soft repulsive or attractive interactions in addition to hard-core repulsion at short distances. Density functional theory for classical systems, as one of the core theoretical approaches of statistical physics of fluids and solids, has to be able to treat such an important system successfully and accurately. Fundamental measure theory is up to date the most successful and most accurate density functional theory for hard-sphere mixtures. Since its introduction fundamental measure theory has been applied to many problems, tested against computer simulations, and further developed in many respects. The literature on fundamental measure theory is already large and is growing fast. This review aims to provide a starting point for readers new to fundamental measure theory and an overview of important developments.
Simulations of driven overdamped frictionless hard spheres
Lerner, Edan; Düring, Gustavo; Wyart, Matthieu
2013-03-01
We introduce an event-driven simulation scheme for overdamped dynamics of frictionless hard spheres subjected to external forces, neglecting hydrodynamic interactions. Our event-driven approach is based on an exact equation of motion which relates the driving force to the resulting velocities through the geometric information characterizing the underlying network of contacts between the hard spheres. Our method allows for a robust extraction of the instantaneous coordination of the particles as well as contact force statistics and dynamics, under any chosen driving force, in addition to shear flow and compression. It can also be used for generating high-precision jammed packings under shear, compression, or both. We present a number of additional applications of our method.
Structure of crystals of hard colloidal spheres
Energy Technology Data Exchange (ETDEWEB)
Pusey, P.N.; van Megen, W.; Bartlett, P.; Ackerson, B.J.; Rarity, J.G.; Underwood, S.M. (Royal Signals and Radar Establishment, Malvern, WR14 3PS, United Kingsom (GB) Department of Applied Physics, Royal Melbourne Institute of Technology, Melbourne, Victoria, Australia School of Chemistry, Bristol University, Bristol, BS8 1TS, United Kingdom Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078)
1989-12-18
We report light-scattering measurements of powder diffraction patterns of crystals of essentially hard colloidal spheres. These are consistent with structures formed by stacking close-packed planes of particles in a sequence of permitted lateral positions, {ital A},{ital B},{ital C}, which shows a high degree of randomness. Crystals grown slowly, while still containing many stacking faults, show a tendency towards face-centered-cubic packing: possible explanations for this observation are discussed.
Dogic; Frenkel; Fraden
2000-09-01
There is increasing evidence that entropy can induce microphase separation in binary fluid mixtures interacting through hard particle potentials. One such phase consists of alternating two-dimensional liquidlike layers of rods and spheres. We study the transition from a uniform miscible state to this ordered state using computer simulations, and compare results to experiments and theory. We conclude the following: (1) There is stable entropy driven microphase separation in mixtures of parallel rods and spheres. (2) Adding spheres smaller than the rod length decreases the total volume fraction needed for the formation of a layered phase, and therefore small spheres effectively stabilize the layered phase; the opposite is true for large spheres. (3) The degree of this stabilization increases with increasing rod length.
Fractional Boundaries for Fluid Spheres
Bayin, S; Krisch, J P; Bayin, Selcuk; Krisch, Jean P.
2006-01-01
A single Israel layer can be created when two metrics adjoin with no continuous metric derivative across the boundary. The properties of the layer depend only on the two metrics it separates. By using a fractional derivative match, a family of Israel layers can be created between the same two metrics. The family is indexed by the order of the fractional derivative. The method is applied to Tolman IV and V interiors and a Schwarzschild vacuum exterior. The method creates new ranges of modeling parameters for fluid spheres. A thin shell analysis clarifies pressure/tension in the family of boundary layers.
Hard spheres at a planar hard wall: Simulations and density functional theory
Directory of Open Access Journals (Sweden)
R.L. Davidchack
2016-03-01
Full Text Available Hard spheres are a central and important model reference system for both homogeneous and inhomogeneous fluid systems. In this paper we present new high-precision molecular-dynamics computer simulations for a hard sphere fluid at a planar hard wall. For this system we present benchmark data for the density profile ρ(z at various bulk densities, the wall surface free energy γ, the excess adsorption Γ, and the excess volume v_{ex}, which is closely related to Γ. We compare all benchmark quantities with predictions from state-of-the-art classical density functional theory calculations within the framework of fundamental measure theory. While we find overall good agreement between computer simulations and theory, significant deviations appear at sufficiently high bulk densities.
High-order virial coefficients and equation of state for hard sphere and hard disk systems.
Hu, Jiawen; Yu, Yang-Xin
2009-11-07
A very simple and accurate approach is proposed to predict the high-order virial coefficients of hard spheres and hard disks. In the approach, the nth virial coefficient B(n) is expressed as the sum of n(D-1) and a remainder, where D is the spatial dimension of the system. When n > or = 3, the remainders of the virials can be accurately expressed with Padé-type functions of n. The maximum deviations of predicted B(5)-B(10) for the two systems are only 0.0209%-0.0044% and 0.0390%-0.0525%, respectively, which are much better than the numerous existing approaches. The virial equation based on the predicted virials diverges when packing fraction eta = 1. With the predicted virials, the compressibility factors of hard sphere system can be predicted very accurately in the whole stable fluid region, and those in the metastable fluid region can also be well predicted up to eta = 0.545. The compressibility factors of hard disk fluid can be predicted very accurately up to eta = 0.63. The simulated B(7) and B(10) for hard spheres are found to be inconsistent with the other known virials and therefore they are modified as 53.2467 and 105.042, respectively.
Phase equilibria in polydisperse nonadditive hard-sphere systems.
Paricaud, Patrice
2008-08-01
Colloidal particles naturally exhibit a size polydispersity that can greatly influence their phase behavior in solution. Nonadditive hard-sphere (NAHS) mixtures are simple and well-suited model systems to represent phase transitions in colloid systems. Here, we propose an analytical equation of state (EOS) for NAHS fluid mixtures, which can be straightforwardly applied to polydisperse systems. For positive values of the nonadditivity parameter Delta the model gives accurate predictions of the simulated fluid-fluid coexistence curves and compressibility factors. NPT Monte Carlo simulations of the mixing properties of the NAHS symmetric binary mixture with Delta>0 are reported. It is shown that the enthalpy of mixing is largely positive and overcomes the positive entropy of mixing when the pressure is increased, leading to a fluid-fluid phase transition with a lower critical solution pressure. Phase equilibria in polydisperse systems are predicted with the model by using the density moment formalism [P. Sollich, Adv. Chem. Phys. 116, 265 (2001)]. We present predictions of the cloud and shadow curves for polydisperse NAHS systems composed of monodisperse spheres and polydisperse colloid particles. A fixed nonadditivity parameter Delta > 0 is assumed between the monodisperse and polydisperse spheres, and a Schulz distribution is used to represent the size polydispersity. Polydispersity is found to increase the extent of the immiscibility region. The predicted cloud and shadow curves depend dramatically on the upper cutoff diameter sigmac of the Schulz distribution, and three-phase equilibria can occur for large values of sigmac.
Thermodynamic properties of lattice hard-sphere models.
Panagiotopoulos, A Z
2005-09-08
Thermodynamic properties of several lattice hard-sphere models were obtained from grand canonical histogram- reweighting Monte Carlo simulations. Sphere centers occupy positions on a simple cubic lattice of unit spacing and exclude neighboring sites up to a distance sigma. The nearestneighbor exclusion model, sigma = radical2, was previously found to have a second-order transition. Models with integer values of sigma = 1 or 2 do not have any transitions. Models with sigma = radical3 and sigma = 3 have weak first-order fluid-solid transitions while those with sigma = 2 radical2, 2 radical3, and 3 radical2 have strong fluid-solid transitions. Pressure, chemical potential, and density are reported for all models and compared to the results for the continuum, theoretical predictions, and prior simulations when available.
Bulk and wetting phenomena in a colloidal mixture of hard spheres and platelets.
Harnau, L; Dietrich, S
2005-01-01
Density functional theory is used to study binary colloidal fluids consisting of hard spheres and thin platelets in their bulk and near a planar hard wall. This system exhibits liquid-liquid coexistence of a phase that is rich in spheres (poor in platelets) and a phase that is poor in spheres (rich in platelets). For the mixture near a planar hard wall, we find that the phase rich in spheres wets the wall completely upon approaching the liquid demixing binodal from the sphere-poor phase, provided the concentration of the platelets is smaller than a threshold value which marks a first-order wetting transition at coexistence. No layering transitions are found, in contrast to recent studies on binary mixtures of spheres and nonadsorbing polymers or thin hard rods.
Fernández Tejero, Carlos; Cuesta, J. A.
1993-01-01
We apply the differential formulation of the generalized effective liquid approximation to the study of hard-sphere and hard-disk freezing. We show that the thermodynamic properties of the solid phase are rather insensitive to the compressibility factor of the fluid phase used to map the solid onto the effective liquid. The solid-fluid coexistence data instead are quite dependent on the equation of state describing the fluid phase. Very accurate results, as compared with the simulation data, ...
Passive and active microrheology of hard-sphere colloids.
Wilson, L G; Harrison, A W; Schofield, A B; Arlt, J; Poon, W C K
2009-03-26
We performed passive and active microrheology using probe particles in a bath of well-characterized, model hard-sphere colloids in the fluid state over the whole range of volume fractions below the glass transition. The probe and bath particles have nearly the same size. Passive tracking of probe particles yields short-time self-diffusion coefficients. Comparison with literature data demonstrates that the interaction between probe and bath particles is hard-sphere-like. The short-time diffusivities yield one set of microviscosities as a function of volume fraction, which agrees with previous macrorheological measurements of the high-frequency viscosity of hard-sphere colloids. Using optical tweezers, we measure the force on a trapped probe particle as the rest of the sample is translated at constant velocity. This yields a second set of microviscosities at high Péclet numbers. These agree with previous macrorheological measurements of the high-shear viscosity of similar colloids, at shear-rates below the onset of shear-thickening.
Replica exchange Monte Carlo applied to hard spheres.
Odriozola, Gerardo
2009-10-14
In this work a replica exchange Monte Carlo scheme which considers an extended isobaric-isothermal ensemble with respect to pressure is applied to study hard spheres (HSs). The idea behind the proposal is expanding volume instead of increasing temperature to let crowded systems characterized by dominant repulsive interactions to unblock, and so, to produce sampling from disjoint configurations. The method produces, in a single parallel run, the complete HS equation of state. Thus, the first order fluid-solid transition is captured. The obtained results well agree with previous calculations. This approach seems particularly useful to treat purely entropy-driven systems such as hard body and nonadditive hard mixtures, where temperature plays a trivial role.
Packing Effect of Excluded Volume on Hard-Sphere Colloids
Institute of Scientific and Technical Information of China (English)
肖长明; 金国钧; 马余强
2001-01-01
We apply the principle of maximum entropy to consider the excluded volume effect on the phase separation of binary mixtures consisting of hard spheres with two different diameters. We show that a critical volume fraction of hard spheres exists locating the packing of large spheres. In particular, through numerical calculation, we have found that the critical volume fraction becomes lower when the ratio α = σ1/σ2 of large-to-small sphere diameters increases, but becomes higher when the ratio of the large sphere volume fraction to the total volume fraction of large and small spheres increases.
De Gennes Narrowing and Hard-Sphere Approach.
Sobolev, Oleg
2016-09-22
The energy width Δω of the quasielastic coherent dynamic structure factor S(Q, ω) for a simple liquid exhibits the oscillating dependence on wavenumber Q with the sharp minimum at Qmax corresponding to the maximum of the structure factor S(Q). The only known expression for Δω(Q) was derived for a dense hard-sphere (HS) fluid (Cohen et al., Phys. Rev. Lett. 1987, 59, 2872). Though this expression has been frequently used for the analysis of the experimental data obtained for liquid metals, until now, it has never been tested against a true HS fluid. A test performed by means of HS molecular dynamic simulations reveals a considerable discrepancy between the simulations results and the examined model. The main output of the analysis is the finding that the ΔωHS(Q) behavior is defined in terms of the average cage size, ⟨Lc⟩, rather than of the HS diameter, σHS. The simulated ΔωHS(Q) has been compared with the results for the soft-spherical potential. The microscopic dynamics of the soft-sphere fluid shows significant difference in comparison to the HS system. Nevertheless, the diffusive mobility of soft spheres can be characterized within the HS approximation using an effective diameter, σeff, and this parameter can be found from Δω(Q) at Q ≈ Qmax. A similar result has been obtained for the neutron scattering data measured for liquid Rb.
Theory of asymmetric non-additive binary hard-sphere mixtures
Roth, R.; Evans, R.; Louis, A. A.
2001-01-01
We show that the formal procedure of integrating out the degrees of freedom of the small spheres in a binary hard-sphere mixture works equally well for non-additive as it does for additive mixtures. For highly asymmetric mixtures (small size ratios) the resulting effective Hamiltonian of the one-component fluid of big spheres, which consists of an infinite number of many-body interactions, should be accurately approximated by truncating after the term describing the effective pair interaction...
Thermodynamic instabilities of a binary mixture of sticky hard spheres.
Fantoni, Riccardo; Gazzillo, Domenico; Giacometti, Achille
2005-07-01
The thermodynamic instabilities of a binary mixture of sticky hard spheres (SHS) in the modified mean spherical approximation (mMSA) and the Percus-Yevick (PY) approximation are investigated using an approach devised by Chen and Forstmann [corrected] [J. Chem. Phys. [corrected] 97, 3696 (1992)]. This scheme hinges on a diagonalization of the matrix of second functional derivatives of the grand canonical potential with respect to the particle density fluctuations. The zeroes of the smallest eigenvalue and the direction of the relative eigenvector characterize the instability uniquely. We explicitly compute three different classes of examples. For a symmetrical binary mixture, analytical calculations, both for mMSA and for PY, predict that when the strength of adhesiveness between like particles is smaller than the one between unlike particles, only a pure condensation spinodal exists; in the opposite regime, a pure demixing spinodal appears at high densities. We then compare the mMSA and PY results for a mixture where like particles interact as hard spheres (HS) and unlike particles as SHS, and for a mixture of HS in a SHS fluid. In these cases, even though the mMSA and PY spinodals are quantitatively and qualitatively very different from each other, we prove that they have the same kind of instabilities. Finally, we study the mMSA solution for five different mixtures obtained by setting the stickiness parameters equal to five different functions of the hard sphere diameters. We find that four of the five mixtures exhibit very different type of instabilities. Our results are expected to provide a further step toward a more thoughtful application of SHS models to colloidal fluids.
When mixtures of hard-sphere-like colloids do not behave as mixtures of hard spheres.
Germain, Ph; Malherbe, J G; Amokrane, S
2004-10-01
The validity of the concept of "hard-sphere-like" particles for mixtures of colloids is questioned from a theoretical point of view. This concerns the class of pseudobinary mixtures in which the nonsteric interactions between the colloids are "residual" (with very small range and moderate strength). It is shown that contrary to common expectation, such interactions may have unexpected consequences on the theoretical phase diagram. The distinction between this situation and true solute-solvent mixtures is emphasized.
Phase behavior and structure of binary hard-sphere mixtures
Dijkstra, Marjolein; Roij, R. van; Evans, R.
1998-01-01
By integrating out the degrees of freedom of the small spheres in a binary mixture of large and small hard spheres, we derive an explicit effective Hamiltonian for the large spheres. Using the two-body (depletion potential) contribution to this effective Hamiltonian in simulations, we find stable
Xu, Wen-Sheng; Sun, Zhao-Yan; An, Li-Jia
2011-01-01
We report a molecular dynamics study of crystallization in highly asymmetric binary hard-sphere mixtures, in which the large spheres can form a crystal phase while the small ones remain disordered during the crystallization process of the large spheres. By taking advantage of assisting crystal nucleation with a patterned substrate, direct evidence is presented that there is a close link between the diffusive redistribution of the small spheres and the crystal formation of the large spheres. A...
Direct measurement of thermodynamic properties of colloidal hard spheres
Dullens, R.P.A.; Kegel, W.K.; Aarts, D.G.A.L.
2008-01-01
Recently, we have shown how to measure thermodynamic properties of colloidal hard sphere suspensions by microscopy [Dullens et al. (2006) PNAS 103, 529]. Here, we give full experimental details on how to acquire three dimensional snapshots of a colloidal hard sphere suspension over a wide range of d
Population annealing simulations of a binary hard-sphere mixture
Callaham, Jared; Machta, Jonathan
2017-06-01
Population annealing is a sequential Monte Carlo scheme well suited to simulating equilibrium states of systems with rough free energy landscapes. Here we use population annealing to study a binary mixture of hard spheres. Population annealing is a parallel version of simulated annealing with an extra resampling step that ensures that a population of replicas of the system represents the equilibrium ensemble at every packing fraction in an annealing schedule. The algorithm and its equilibration properties are described, and results are presented for a glass-forming fluid composed of a 50/50 mixture of hard spheres with diameter ratio of 1.4:1. For this system, we obtain precise results for the equation of state in the glassy regime up to packing fractions φ ≈0.60 and study deviations from the Boublik-Mansoori-Carnahan-Starling-Leland equation of state. For higher packing fractions, the algorithm falls out of equilibrium and a free volume fit predicts jamming at packing fraction φ ≈0.667 . We conclude that population annealing is an effective tool for studying equilibrium glassy fluids and the jamming transition.
The influence of third-order interactions on the density profile of associating hard spheres
Henderson, D.; Sokolowski, S.; Zagorski, R.; Trokhymchuk, A.
Canonical ensemble Monte Carlo simulations and the non-uniform Percus-Yevick (NPY) equation for the local density are used to study the influence of surface mediated thirdorder interactions on the adsorption of associating hard spheres on a hard wall. A comparison of the NPY density profiles with the computer simulations data indicates that this approximation predicts the fluid structure reasonably well.
Wu, Liang; Malijevský, Alexandr; Jackson, George; Müller, Erich A; Avendaño, Carlos
2015-07-28
We study the structure and fluid-phase behaviour of binary mixtures of hard spheres (HSs) and hard spherocylinders (HSCs) in isotropic and nematic states using the NPnAT ensemble Monte Carlo (MC) approach in which the normal component of the pressure tensor is fixed in a system confined between two hard walls. The method allows one to estimate the location of the isotropic-nematic phase transition and to observe the asymmetry in the composition between the coexisting phases, with the expected enhancement of the HSC concentration in the nematic phase. This is in stark contrast with the previously reported MC simulations where a conventional isotropic NPT ensemble was used. We further compare the simulation results with the theoretical predictions of two analytic theories that extend the original Parsons-Lee theory using the one-fluid and the many-fluid approximations [Malijevský et al., J. Chem. Phys. 129, 144504 (2008)]. In the one-fluid version of the theory, the properties of the mixture are related to an effective one-component HS system, while in the many-fluid theory, the components of the mixtures are represented as separate effective HS particles. The comparison reveals that both the one- and the many-fluid approaches provide a reasonably accurate quantitative description of the mixture including the predictions of the isotropic-nematic phase boundary and degree of orientational order of the HSC-HS mixture.
Jadrich, Ryan; Schweizer, Kenneth S.
2013-08-01
Building on the equation-of-state theory of Paper I, we construct a new thermodynamically consistent integral equation theory for the equilibrium pair structure of 3-dimensional monodisperse hard spheres applicable up to the jamming transition. The approach is built on a two Yukawa generalized mean spherical approximation closure for the direct correlation function (DCF) beyond contact that reproduces the exact contact value of the pair correlation function and isothermal compressibility. The detailed construction of the DCF is guided by the desire to capture its distinctive features as jamming is approached. Comparison of the theory with jamming limit simulations reveals good agreement for many, but not all, of the key features of the pair correlation function. The theory is more accurate in Fourier space where predictions for the structure factor and DCF are accurate over a wide range of wavevectors from significantly below the first cage peak to very high wavevectors. New features of the equilibrium pair structure are predicted for packing fractions below jamming but well above crystallization. For example, the oscillatory DCF decays very slowly at large wavevectors for high packing fractions as a consequence of the unusual structure of the radial distribution function at small separations. The structural theory is used as input to the nonlinear Langevin equation theory of activated dynamics, and calculations of the alpha relaxation time based on single particle hopping are compared to recent colloid experiments and simulations at very high volume fractions.
Modelling anisotropic fluid spheres in general relativity
Boonserm, Petarpa; Visser, Matt
2015-01-01
We argue that an arbitrary general relativistic anisotropic fluid sphere, (spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully modelled by suitable linear combinations of quite ordinary classical matter: an isotropic perfect fluid, a classical electromagnetic field, and a classical (minimally coupled) scalar field. While the most general decomposition is not unique, a preferred minimal decomposition can be constructed that is unique. We show how the classical energy conditions for the anisotropic fluid sphere can be related to energy conditions for the isotropic perfect fluid, electromagnetic field, and scalar field components of the model. Furthermore we show how this decomposition relates to the distribution of electric charge density and scalar charge density throughout the model that is used to mimic the anisotropic fluid sphere. Consequently, we can build physically reasonable matter models for almost any spherically symmetric spacetime.
Eckert, Thomas; Richtering, Walter
2008-09-28
The colloidal phase behavior, structure factors, short-time collective diffusion coefficients, and hydrodynamic interactions of concentrated poly(N-isopropylacryamide) (PNiPAM) microgels in dimethylformamide suspensions were measured with simultaneous static and dynamic three-dimensional cross-correlated light scattering. The data are interpreted through comparison with hard sphere theory. The fluid-crystal transition and the static structure factors can be described consistently by the hard sphere approximation. On the other hand, collective diffusion and hydrodynamic interaction cannot be described satisfactorily by the hard sphere model. The microgel structure is different from hard spheres, as the cross-link density decreases with the distance from the particle center leading to a "fuzzy" particle surface with dangling polymer chains. These seem to affect the hydrodynamic interaction much more as compared to direct thermodynamic interaction.
Alternative fundamental measure theory for additive hard sphere mixtures.
Malijevský, Alexandr
2006-11-21
The purpose of this short paper is to present an alternative fundamental measure theory (FMT) for hard sphere mixtures. Keeping the main features of the original Rosenfeld's FMT [Phys. Rev. Lett. 63, 980 (1989)] and using the dimensional and the low-density limit conditions a new functional is derived incorporating Boublik's multicomponent extension [Mol. Phys. 59, 371 (1986)] of highly accurate Kolafa's equation of state for pure hard spheres. We test the theory for pure hard spheres and hard sphere mixtures near a planar hard wall and compare the results with the original Rosenfeld's FMT and one of its modifications and with new very accurate simulation data. The test reveals an excellent agreement between the results based on the alternative FMT and simulation data for density profile near a contact and some improvement over the original Rosenfeld's FMT and its modification at the contact region.
Clustering and gelation of hard spheres induced by the Pickering effect
Fortini, Andrea
2012-04-01
A mixture of hard-sphere particles and model emulsion droplets is studied with a Brownian dynamics simulation. We find that the addition of nonwetting emulsion droplets to a suspension of pure hard spheres can lead to both gas-liquid and fluid-solid phase separations. Furthermore, we find a stable fluid of hard-sphere clusters. The stability is due to the saturation of the attraction that occurs when the surface of the droplets is completely covered with colloidal particles. At larger emulsion droplet densities a percolation transition is observed. The resulting networks of colloidal particles show dynamical and mechanical properties typical of a colloidal gel. The results of the model are in good qualitative agreement with recent experimental findings [E. Koos and N. Willenbacher, ScienceSCIEAS0036-807510.1126/science.1199243 331, 897 (2011)] in a mixture of colloidal particles and two immiscible fluids.
Oettel, M; Dorosz, S; Berghoff, M; Nestler, B; Schilling, T
2012-08-01
In materials science the phase-field crystal approach has become popular to model crystallization processes. Phase-field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase-field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three-dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a second-order Taylor expansion thereof, and a minimal phase-field crystal model. We have computed coexistence densities, vacancy concentrations in the crystalline phase, interfacial tensions, and interfacial order parameter profiles, and we compare these quantities to simulation results. We also suggest a procedure to fit the free parameters of the phase-field crystal model. Thereby it turns out that the order parameter of the phase-field crystal model is more consistent with a smeared density field (shifted and rescaled) than with the shifted and rescaled density itself. In brief, we conclude that fundamental measure theory is very accurate and can serve as a benchmark for the other theories. Taylor expansion strongly affects free energies, surface tensions, and vacancy concentrations. Furthermore it is phenomenologically misleading to interpret the phase-field crystal model as stemming directly from Taylor-expanded density functional theory.
Self-diffusion in liquid gallium and hard sphere model
Directory of Open Access Journals (Sweden)
Blagoveshchenskii Nikolay
2015-01-01
Full Text Available Incoherent and coherent components of quasielastic neutron scattering have been studied in the temperature range of T = 313 K – 793 K aiming to explore the applicability limits of the hard-sphere approach for the microscopic dynamics of liquid gallium, which is usually considered as a non-hard-sphere system. It was found that the non-hard-sphere effects come into play at the distances shorter than the average interatomic distance. The longer range diffusive dynamics of liquid Ga is dominated by the repulsive forces between the atoms.
Binary hard-sphere mixtures within spherical pores
Kim, S C; Lee, C H
1999-01-01
The free-energy model, which is based on the fundamental geometric measures of the particles, has been employed to investigate the structural properties of nonuniform hard-sphere mixtures within spherical pores. Monte Carlo simulation has been performed to calculate the density profiles of hard-sphere mixtures confined in spherical pores, and the simulation has been compared with the calculated results. Comparisons between the theoretical results and the simulation data have shown that the free-energy model demonstrates reliable accuracy and reproduces the simulation data accurately even for larger size ratios of hard spheres.
On the relation between virial coefficients and the close-packing of hard disks and hard spheres.
Maestre, Miguel Angel G; Santos, Andrés; Robles, Miguel; de Haro, Mariano López
2011-02-28
The question of whether the known virial coefficients are enough to determine the packing fraction η(∞) at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Padé approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that η(∞) is equal to the maximum packing fraction corresponding to an ordered crystalline structure.
Levesque, Maximilien; Borgis, Daniel; 10.1063/1.4734009
2012-01-01
Hard-sphere mixtures provide one a solvable reference system that can be used to improve the density functional theory of realistic molecular fluids. We show how the Kierlik-Rosinberg's scalar version of the fundamental measure density functional theory of hard spheres [Phys. Rev. A, {\\bf 42}, 3382 (1990)], which presents computational advantages with respect to the original Rosenfeld's vectorial formulation or its extensions, can be implemented and minimized in three dimensions to describe fluid mixtures in complex environments. This implementation is used as a basis for defining a molecular density functional theory of water around molecular hydrophobic solutes of arbitrary shape.
Levesque, Maximilien; Vuilleumier, Rodolphe; Borgis, Daniel
2012-07-21
Hard-sphere mixtures provide one a solvable reference system that can be used to improve the density functional theory of realistic molecular fluids. We show how the Kierlik-Rosinberg's scalar version of the fundamental measure density functional theory of hard spheres [E. Kierlik and M. L. Rosinberg, Phys. Rev. A 42, 3382 (1990)], which presents computational advantages with respect to the original Rosenfeld's vectorial formulation or its extensions, can be implemented and minimized in three dimensions to describe fluid mixtures in complex environments. This implementation is used as a basis for defining a molecular density functional theory of water around molecular hydrophobic solutes of arbitrary shape.
Crystallization kinetics of polydisperse colloidal hard spheres. II. Binary mixtures.
Martin, S; Bryant, G; van Megen, W
2005-02-01
In this paper we present measurements of the crystallization kinetics of binary mixtures of two different sized hard sphere particles. The growth of the Bragg reflections over time were analyzed to yield the crystallite scattering vector, the total amount of crystal, and the average linear crystal size. It was observed that a particle size distribution skewed to higher sized particles has a less detrimental effect on the crystal structure than a skew to smaller sized particles. In the latter case we observe that initial crystallite growth occurs at only a small number of sites, with further crystallization sites developing at later times. Based on these measurements we elaborate further on the previously proposed growth mechanism whereby crystallization occurs in conjunction with a local fractionation process in the fluid, which significantly affects the kinetic growth of crystallites in polydisperse systems.
Molecular Thermodynamics of Charged Hard-Dumbbell Fluids
Institute of Scientific and Technical Information of China (English)
秦原; 刘洪来; 胡英
2001-01-01
Chemical potentials of charged hard-dumbbell fluids are obtained by Monte Carlo simulations using Widom's test-particle method, corresponding compressibility factors are achieved by integration of chemical potentials at different densities. A molecular thermodynamic model is also developed for these charged hard-dumbbell fluids where the residual Helmholtz function is composed of two terms: a reference term responsible for the charged hard spheres and a bonding contribution measuring the sticky interactions between positive and negative hard ions.Model predictions are in good agreement with simulation results.
López de Haro, Mariano; Tejero, Carlos F; Santos, Andrés
2013-04-28
The problem of demixing in a binary fluid mixture of highly asymmetric additive hard spheres is revisited. A comparison is presented between the results derived previously using truncated virial expansions for three finite size ratios with those that one obtains with the same approach in the extreme case in which one of the components consists of point particles. Since this latter system is known not to exhibit fluid-fluid segregation, the similarity observed for the behavior of the critical constants arising in the truncated series in all instances, while not being conclusive, may cast serious doubts as to the actual existence of a demixing fluid-fluid transition in disparate-sized binary additive hard-sphere mixtures.
Demixing in binary mixtures of apolar and dipolar hard spheres.
Almarza, N G; Lomba, E; Martín, C; Gallardo, A
2008-12-21
We study the demixing transition of mixtures of equal size hard spheres and dipolar hard spheres using computer simulation and integral equation theories. Calculations are carried out at constant pressure, and it is found that there is a strong correlation between the total density and the composition. The critical temperature and the critical total density are found to increase with pressure. The critical mole fraction of the dipolar component on the contrary decreases as pressure is augmented. These qualitative trends are reproduced by the theoretical approaches that on the other hand overestimate by far the value of the critical temperature. Interestingly, the critical parameters for the liquid-vapor equilibrium extrapolated from the mixture results in the limit of vanishing neutral hard sphere concentration agree rather well with recent estimates based on the extrapolation of charged hard dumbbell phase equilibria when dumbbell elongation shrinks to zero [G. Ganzenmuller and P. J. Camp, J. Chem. Phys. 126, 191104 (2007)].
Radial distribution function for hard spheres in fractal dimensions. A heuristic approximation
Santos, Andrés
2016-01-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension $d$ ($1 \\leq d \\leq 3$) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for fractal dimension [M. Heinen et al., Phys. Rev. Lett. \\textbf{115}, 097801 (2015)], a good agreement being observed.
The interplay of sedimentation and crystallization in hard-sphere suspensions
Russo, J.; Maggs, A.C.; Bonn, D.; Tanaka, H.
2013-01-01
We study crystal nucleation under the influence of sedimentation in a model of colloidal hard spheres via Brownian dynamics simulations. We introduce two external fields acting on the colloidal fluid: a uniform gravitational field (body force), and a surface field imposed by pinning a layer of equil
The isotropic-nematic phase transition of tangent hard-sphere chain fluids—Pure components
Van Westen, T.; Oyarzun, B.; Vlugt, T.J.H.; Gross, J.
2013-01-01
An extension of Onsager's second virial theory is developed to describe the isotropic-nematic phase transition of tangent hard-sphere chain fluids. Flexibility is introduced by the rod-coil model. The effect of chain-flexibility on the second virial coefficient is described using an accurate, analyt
Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres
Santos, A.; Yuste, S.B.; Lopèz de Haro, M.; Odriozola, G.; Ogarko, V.
2014-01-01
A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction ϕJ of the polydisperse system as a simple function of M1M3/M22, where Mk is the kth
Phonon contribution to the entropy of hard-sphere crystals.
Elser, Veit
2014-05-01
Comparing the entropies of hard spheres in the limit of close packing, for different stacking sequences of the hexagonal layers, has been a challenge because the differences are so small. Here we present a method based on a "sticky-sphere" model by which the system interpolates between hard spheres in one limit and a harmonic crystal in the other. For the fcc and hcp stackings we have calculated the entropy difference in the harmonic (sticky) limit, as well as the differences in the free energy change upon removing the stickiness in the model. The former, or phonon entropy, accounts for most of the entropy difference. Our value for the net entropy difference, Δs = 0.001164(8)k(B) per sphere, is in excellent agreement with the best previous estimate by Mau and Huse [Phys. Rev. E 59, 4396 (1999)].
Note: Sound velocity of a soft sphere model near the fluid-solid phase transition.
Khrapak, Sergey A
2016-03-28
The quasilocalized charge approximation is applied to estimate the sound velocity of simple soft sphere fluid with the repulsive inverse-power-law interaction. The obtained results are discussed in the context of the sound velocity of the hard-sphere system and of liquid metals at the melting temperature.
Brownian versus Newtonian devitrification of hard-sphere glasses
Montero de Hijes, Pablo; Rosales-Pelaez, Pablo; Valeriani, Chantal; Pusey, Peter N.; Sanz, Eduardo
2017-08-01
In a recent molecular dynamics simulation work it has been shown that glasses composed of hard spheres crystallize via cooperative, stochastic particle displacements called avalanches [E. Sanz et al., Proc. Natl. Acad. Sci. USA 111, 75 (2014), 10.1073/pnas.1308338110]. In this Rapid Communication we investigate if such a devitrification mechanism is also present when the dynamics is Brownian rather than Newtonian. The research is motivated in part by the fact that colloidal suspensions, an experimental realization of hard-sphere systems, undergo Brownian motion. We find that Brownian hard-sphere glasses do crystallize via avalanches with very similar characteristics to those found in the Newtonian case. We briefly discuss the implications of these findings for experiments on colloids.
New phase for one-component hard spheres.
Wu, Guang-Wen; Sadus, Richard J
2004-06-22
A completely new phase for one-component hard spheres is reported in an unexpected region of the phase diagram. The new phase is observed at compressibility factors intermediate between the solid and the metastable branches. It can be obtained from either Monte Carlo simulations alone or a combination of Monte Carlo and molecular dynamics calculations. An analysis of the intermediate scattering function data shows that the new phase is in a stable equilibrium. Radial distribution function data, configurational snapshots, bond order parameters, and translational order parameters obtained from molecular simulations indicate that the new phase is significantly different from the isotropic liquid, metastable, or crystalline phases traditionally observed in hard sphere systems. This result significantly changes our previous understanding of the behavior of hard spheres. (c) 2004 American Institute of Physics.
Investigating hard sphere interactions through spin echo scattering angle measurement
Washington, Adam
Spin Echo Scattering Angle Measurement (SESAME) allows neutron scattering instruments to perform real space measurements on large micron scale samples by encoding the scattering angle into the neutron's spin state via Larmor precession. I have built a SESAME instrument at the Low Energy Neutron Source. I have also assisted in the construction of a modular SESAME instrument on the ASTERIX beamline at Los Alamos National lab. The ability to tune these instruments has been proved mathematically and optimized and automated experimentally. Practical limits of the SESAME technique with respect to polarization analyzers, neutron spectra, Larmor elements, and data analysis were investigated. The SESAME technique was used to examine the interaction of hard spheres under depletion. Poly(methyl methacrylate) spheres suspended in decalin had previously been studied as a hard sphere solution. The interparticle correlations between the spheres were found to match the Percus-Yevick closure, as had been previously seen in dynamical light scattering experiments. To expand beyond pure hard spheres, 900kDa polystyrene was added to the solution in concentrations of less than 1% by mass. The steric effects of the polystyrene were expected to produce a short-range, attractive, "sticky" potential. Experiment showed, however, that the "sticky" potential was not a stable state and that the spheres would eventually form long range aggregates.
Hydration entropy change from the hard sphere model.
Graziano, Giuseppe; Lee, Byungkook
2002-12-10
The gas to liquid transfer entropy change for a pure non-polar liquid can be calculated quite accurately using a hard sphere model that obeys the Carnahan-Starling equation of state. The same procedure fails to produce a reasonable value for hydrogen bonding liquids such as water, methanol and ethanol. However, the size of the molecules increases when the hydrogen bonds are turned off to produce the hard sphere system and the volume packing density rises. We show here that the hard sphere system that has this increased packing density reproduces the experimental transfer entropy values rather well. The gas to water transfer entropy values for small non-polar hydrocarbons is also not reproduced by a hard sphere model, whether one uses the normal (2.8 A diameter) or the increased (3.2 A) size for water. At least part of the reason that the hard sphere model with 2.8 A size water produces too small entropy change is that the size of water is too small for a system without hydrogen bonds. The reason that the 3.2 A model also produces too small entropy values is that this is an overly crowded system and that the free volume introduced in the system by the addition of a solute molecule produces too much of a relief to this crowding. A hard sphere model, in which the free volume increase is limited by requiring that the average surface-to-surface distance between the solute and water molecules is the same as that between the increased-size water molecules, does approximately reproduce the experimental hydration entropy values.
Solid-solid transition of the size-polydisperse hard-sphere system
Yang, Mingcheng; Ma, Hongru
2008-01-01
The solid-solid coexistence of a polydisperse hard sphere system is studied by using the Monte Carlo simulation. The results show that for large enough polydispersity the solid-solid coexistence state is more stable than the single-phase solid. The two coexisting solids have different composition distributions but the same crystal structure. Moreover, there is evidence that the solid-solid transition terminates in a critical point as in the case of the fluid-fluid transition.
A generalized hard-sphere model for Monte Carlo simulation
Hassan, H. A.; Hash, David B.
1993-01-01
A new molecular model, called the generalized hard-sphere, or GHS model, is introduced. This model contains, as a special case, the variable hard-sphere model of Bird (1981) and is capable of reproducing all of the analytic viscosity coefficients available in the literature that are derived for a variety of interaction potentials incorporating attraction and repulsion. In addition, a new procedure for determining interaction potentials in a gas mixture is outlined. Expressions needed for implementing the new model in the direct simulation Monte Carlo methods are derived. This development makes it possible to employ interaction models that have the same level of complexity as used in Navier-Stokes calculations.
Oversteegen, S M; Lekkerkerker, H N W
2004-02-01
Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc concentrations in systems now experimentally available. The gas-liquid equilibrium of the spheres becomes stable at comparable size ratios as with bimodal mixtures of spheres or mixtures of rods and spheres. Introducing finite thickness of the platelets gives rise to a significant lowering of the fluid branch of the binodal. Copyright 2004 American Institute of Physics
Crystallizing hard-sphere glasses by doping with active particles.
Ni, Ran; Cohen Stuart, Martien A; Dijkstra, Marjolein; Bolhuis, Peter G
2014-09-21
Crystallization and vitrification are two different routes to form a solid. Normally these two processes suppress each other, with the glass transition preventing crystallization at high density (or low temperature). This is even true for systems of colloidal hard spheres, which are commonly used as building blocks for novel functional materials with potential applications, e.g. photonic crystals. By performing Brownian dynamics simulations of glassy systems consisting of mixtures of active and passive hard spheres, we show that the crystallization of such hard-sphere glasses can be dramatically promoted by doping the system with small amounts of active particles. Surprisingly, even hard-sphere glasses of packing fraction up to ϕ = 0.635 crystallize, which is around 0.5% below the random close packing at ϕ ≃ 0.64. Our results suggest a novel way of fabricating crystalline materials from (colloidal) glasses. This is particularly important for materials that get easily kinetically trapped in glassy states, and the crystal nucleation hardly occurs.
Microstructure and macroscopic properties of polydisperse systems of hard spheres
Ogarko, Vitaliy Anatolyevich
2014-01-01
This dissertation describes an investigation of systems of polydisperse smooth hard spheres. This includes the development of a fast contact detection algorithm for computer modelling, the development of macroscopic constitutive laws that are based on microscopic features such as the moments of the
Hard sphere colloidal dispersions: Mechanical relaxation pertaining to thermodynamic forces
Mellema, J.; Kruif, de C.G.; Blom, C.; Vrij, A.
1987-01-01
The complex viscosity of sterically stabilized (hard) silica spheres in cyclohexane has been measured between 80 Hz and 170 kHz with torsion pendulums and a nickel tube resonator. The observed relaxation behaviour can be attributed to the interplay of hydrodynamic and thermodynamic forces. The valid
Self-assembly in colloidal hard-sphere systems
Filion, L.C.
2011-01-01
In this thesis, we examine the phase behaviour and nucleation in a variety of hard-sphere systems. In Chapter 1 we present a short introduction and describe some of the simulation techniques used in this thesis. One of the main difficulties in predicting the phase behaviour in colloidal, atomic and
Transport properties of the Fermi hard-sphere system
Mecca, Angela; Benhar, Omar; Polls, Artur
2015-01-01
The transport properties of neutron star matter play an important role in a variety of astrophysical processes. We report the results of a calculation of the shear viscosity and thermal conductivity coefficients of the hard-sphere fermion system of degeneracy $\
Simulation of the adhesive-hard-sphere model
Kranendonk, W.G.T.; Frenkel, D.
1988-01-01
Monte Carlo simulations of the three-dimensional sticky-hard-sphere system are presented. A new modified Monte Carlo algorithm has been developed which makes it possible to explore the phase diagram for a large region of both the packing fraction and the stickiness parameter t. The phase diagram is
A New Perturbed Hard-Sphere Equation of State
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A new equation of state based on hard-sphere perturbed theory was developed. This equation combined the CS repulsive term and Guo-Du attractive term. Parameters of 38 substances were estimated, the pressure-volume-temperature properties were calculated and compared with two other equations. The results show that this equation is more accurate.
Crystallizing hard-sphere glasses by doping with active particles
Ni, Ran; Cohen Stuart, M.A.; Dijkstra, M.; Bolhuis, P.G.
2014-01-01
Crystallization and vitrification are two different routes to form a solid. Normally these two processes suppress each other, with the glass transition preventing crystallization at high density (or low temperature). This is even true for systems of colloidal hard spheres, which are commonly used as
Self-assembly in colloidal hard-sphere systems
Filion, L.C.|info:eu-repo/dai/nl/326823484
2011-01-01
In this thesis, we examine the phase behaviour and nucleation in a variety of hard-sphere systems. In Chapter 1 we present a short introduction and describe some of the simulation techniques used in this thesis. One of the main difficulties in predicting the phase behaviour in colloidal, atomic and
Microscopic Hydrodynamic Modes in a Binary Hard Sphere Mixture
Reichl, L. E.; Gust, Erich D.
2017-07-01
We derive analytic microscopic expressions for the shear viscosity, the speed of sound, and the decay rates of the hydrodynamic modes in a hard sphere binary gas mixture directly from the spectral properties of coupled Boltzmann equations. We show that the analytic expressions give good agreement with experimental viscosity data and to the results of light scattering experiments on noble gas binary mixtures.
Microstructure and macroscopic properties of polydisperse systems of hard spheres
Ogarko, V.
2014-01-01
This dissertation describes an investigation of systems of polydisperse smooth hard spheres. This includes the development of a fast contact detection algorithm for computer modelling, the development of macroscopic constitutive laws that are based on microscopic features such as the moments of the
Probing the evolution and morphology of hard carbon spheres
Energy Technology Data Exchange (ETDEWEB)
Pol, Vilas G.; Wen, Jianguo; Lau, Kah Chun; Callear, Samantha; Bowron, Daniel T.; Lin, Chi-Kai; Deshmukh, Sanket A.; Sankaranarayanan, Subramanian; Curtiss, Larry A.; David, William; Miller, Dean J.; Thackeray, Michael M.
2014-03-01
Monodispersed hard carbon spheres can be synthesized quickly and reproducibly by autogenic reactions of hydrocarbon precursors, notably polyethylene (including plastic waste), at high temperature and pressure. The carbon microparticles formed by this reaction have a unique spherical architecture, with a dominant internal nanometer layered motif, and they exhibit diamond-like hardness and electrochemical properties similar to graphite. In the present study, in-situ monitoring by X-ray diffraction along with electron microscopy, Raman spectroscopy, neutron pair-distribution function analysis, and computational modeling has been used to elucidate the morphology and evolution of the carbon spheres that form from the autogenic reaction of polyethylene at high temperature and pressure. A mechanism is proposed on how polyethylene evolves from a linear chain-based material to a layered carbon motif. Heating the spheres to 2400-2800 °C under inert conditions increases their graphitic character, particularly at the surface, which enhances their electrochemical and tribological properties.
A CONTINUUM HARD-SPHERE MODEL OF PROTEIN ADSORPTION.
Finch, Craig; Clarke, Thomas; Hickman, James J
2013-07-01
Protein adsorption plays a significant role in biological phenomena such as cell-surface interactions and the coagulation of blood. Two-dimensional random sequential adsorption (RSA) models are widely used to model the adsorption of proteins on solid surfaces. Continuum equations have been developed so that the results of RSA simulations can be used to predict the kinetics of adsorption. Recently, Brownian dynamics simulations have become popular for modeling protein adsorption. In this work a continuum model was developed to allow the results from a Brownian dynamics simulation to be used as the boundary condition in a computational fluid dynamics (CFD) simulation. Brownian dynamics simulations were used to model the diffusive transport of hard-sphere particles in a liquid and the adsorption of the particles onto a solid surface. The configuration of the adsorbed particles was analyzed to quantify the chemical potential near the surface, which was found to be a function of the distance from the surface and the fractional surface coverage. The near-surface chemical potential was used to derive a continuum model of adsorption that incorporates the results from the Brownian dynamics simulations. The equations of the continuum model were discretized and coupled to a CFD simulation of diffusive transport to the surface. The kinetics of adsorption predicted by the continuum model closely matched the results from the Brownian dynamics simulation. This new model allows the results from mesoscale simulations to be incorporated into micro- or macro-scale CFD transport simulations of protein adsorption in practical devices.
First-order layering and critical wetting transitions in nonadditive hard-sphere mixtures.
Hopkins, Paul; Schmidt, Matthias
2011-05-01
Using fundamental-measure density functional theory we investigate entropic wetting in an asymmetric binary mixture of hard spheres with positive nonadditivity. We consider a general planar hard wall, where preferential adsorption is induced by a difference in closest approach of the different species and the wall. Close to bulk fluid-fluid coexistence, the phase rich in the minority component adsorbs either through a series of first-order layering transitions, where an increasing number of liquid layers adsorbs sequentially, or via a critical wetting transition, where a thick film grows continuously.
Transport properties of highly asymmetric hard-sphere mixtures.
Bannerman, Marcus N; Lue, Leo
2009-04-28
The static and dynamic properties of binary mixtures of hard spheres with a diameter ratio of sigma(B)/sigma(A)=0.1 and a mass ratio of m(B)/m(A)=0.001 are investigated using event driven molecular dynamics. The contact values of the pair correlation functions are found to compare favorably with recently proposed theoretical expressions. The transport coefficients of the mixture, determined from simulation, are compared to the predictions of the revised Enskog theory using both a third-order Sonine expansion and direct simulation Monte Carlo. Overall, the Enskog theory provides a fairly good description of the simulation data, with the exception of systems at the smallest mole fraction of larger spheres (x(A)=0.01) examined. A "fines effect" was observed at higher packing fractions, where adding smaller spheres to a system of large spheres decreases the viscosity of the mixture; this effect is not captured by the Enskog theory.
Bond-orientational analysis of hard-disk and hard-sphere structures.
Senthil Kumar, V; Kumaran, V
2006-05-28
We report the bond-orientational analysis results for the thermodynamic, random, and homogeneously sheared inelastic structures of hard-disks and hard-spheres. The thermodynamic structures show a sharp rise in the order across the freezing transition. The random structures show the absence of crystallization. The homogeneously sheared structures get ordered at a packing fraction higher than the thermodynamic freezing packing fraction, due to the suppression of crystal nucleation. On shear ordering, strings of close-packed hard-disks in two dimensions and close-packed layers of hard-spheres in three dimensions, oriented along the velocity direction, slide past each other. Such a flow creates a considerable amount of fourfold order in two dimensions and body-centered-tetragonal (bct) structure in three dimensions. These transitions are the flow analogs of the martensitic transformations occurring in metals due to the stresses induced by a rapid quench. In hard-disk structures, using the bond-orientational analysis we show the presence of fourfold order. In sheared inelastic hard-sphere structures, even though the global bond-orientational analysis shows that the system is highly ordered, a third-order rotational invariant analysis shows that only about 40% of the spheres have face-centered-cubic (fcc) order, even in the dense and near-elastic limits, clearly indicating the coexistence of multiple crystalline orders. When layers of close-packed spheres slide past each other, in addition to the bct structure, the hexagonal-close-packed (hcp) structure is formed due to the random stacking faults. Using the Honeycutt-Andersen pair analysis and an analysis based on the 14-faceted polyhedra having six quadrilateral and eight hexagonal faces, we show the presence of bct and hcp signatures in shear ordered inelastic hard-spheres. Thus, our analysis shows that the dense sheared inelastic hard-spheres have a mixture of fcc, bct, and hcp structures.
A Monte Carlo study of the freezing transition of hard spheres.
Nayhouse, Michael; Amlani, Ankur M; Orkoulas, G
2011-08-17
A simulation method for fluid-solid transitions, which is based on a modification of the constrained cell model of Hoover and Ree, is developed and tested on a system of hard spheres. In the fully occupied constrained cell model, each particle is confined in its own Wigner-Seitz cell. Constant-pressure simulations of the constrained cell model for a system of hard spheres indicate a point of mechanical instability at a density which is about 64% of the density at the close packed limit. Below that point, the solid is mechanically unstable since without the confinement imposed by the cell walls it will disintegrate to a disordered, fluid-like phase. Hoover and Ree proposed a modified cell model by introducing an external field of variable strength. High values of the external field variable favor configurations with one particle per cell and thus stabilize the solid phase. In this work, the modified cell model of a hard-sphere system is simulated under constant-pressure conditions using tempering and histogram reweighting techniques. The simulations indicate that as the strength of the field is reduced, the transition from the solid to the fluid phase is continuous below the mechanical instability point and discontinuous above. The fluid-solid transition of the hard-sphere system is determined by analyzing the field-induced fluid-solid transition of the modified cell model in the limit in which the external field vanishes. The coexistence pressure and densities are obtained through finite-size scaling techniques and are in good accord with previous estimates.
New interior solution describing relativistic fluid sphere
Indian Academy of Sciences (India)
KSH NEWTON SINGH; NARENDRA PRADHAN; NEERAJ PANT
2017-08-01
Anewexact solution of embedding class I is presented for a relativistic anisotropicmassive fluid sphere. The new exact solution satisfies Karmarkar condition, is well-behaved in all respects, and therefore is suitable for the modelling of superdense stars. Consequently, using this solution, we have studied in detail two compact stars, namely, XTE J1739-289 (strange star 1.51$M_{\\odot}$, 10.9 km) and PSR J1614-2230 (neutron star 1.97$M_{\\odot}$, 14 km). The solution also satisfies all energy conditions with the compactness parameter lying within the Buchdahl limit.
Fluid of fused spheres as a model for protein solution
Directory of Open Access Journals (Sweden)
M. Kastelic
2016-03-01
Full Text Available In this work we examine thermodynamics of fluid with "molecules" represented by two fused hard spheres, decorated by the attractive square-well sites. Interactions between these sites are of short-range and cause association between the fused-sphere particles. The model can be used to study the non-spherical (or dimerized proteins in solution. Thermodynamic quantities of the system are calculated using a modification of Wertheim's thermodynamic perturbation theory and the results compared with new Monte Carlo simulations under isobaric-isothermal conditions. In particular, we are interested in the liquid-liquid phase separation in such systems. The model fluid serves to evaluate the effect of the shape of the molecules, changing from spherical to more elongated (two fused spheres ones. The results indicate that the effect of the non-spherical shape is to reduce the critical density and temperature. This finding is consistent with experimental observations for the antibodies of non-spherical shape.
Shock Waves in Dense Hard Disk Fluids
Sirmas, Nick; Tudorache, Marion; Barahona, Javier; Radulescu, Matei I.
2011-01-01
Media composed of colliding hard disks (2D) or hard spheres (3D) serve as good approximations for the collective hydrodynamic description of gases, liquids and granular media. In the present study, the compressible hydrodynamics and shock dynamics are studied for a two-dimensional hard-disk medium at both the continuum and discrete particle level descriptions. For the continuum description, closed form analytical expressions for the inviscid hydrodynamic description, shock Hugoniot, isentropi...
Stability of LS and LS2 crystal structures in binary mixtures of hard and charged spheres.
Hynninen, A-P; Filion, L; Dijkstra, M
2009-08-14
We study by computer simulations the stability of various crystal structures in a binary mixture of large and small spheres interacting either with a hard sphere or a screened-Coulomb potential. In the case of hard-core systems, we consider structures that have atomic prototypes CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se and the Laves phases (MgCu2, MgNi2, and MgZn2) as well as a structure with space group symmetry 74. By utilizing Monte Carlo simulations to calculate Gibbs free energies, we determine composition versus pressure and constant volume phase diagrams for diameter ratios of q=0.74, 0.76, 0.8, 0.82, 0.84, and 0.85 for the small and large spheres. For diameter ratios 0.76 mixture. By extrapolating to the thermodynamic limit, we show that the MgZn2 structure is the most stable one of the Laves structures. We also calculate phase diagrams for equally and oppositely charged spheres for size ratio of 0.73 taking into consideration the Laves phases and CsCl. In the case of equally charged spheres, we find a pocket of stable Laves phases, while in the case of oppositely charged spheres, Laves phases are found to be metastable with respect to the CsCl and fluid phases.
Demixing can occur in binary hard-sphere mixtures with negative nonadditivity.
Santos, A; López de Haro, M
2005-07-01
A binary fluid mixture of nonadditive hard spheres characterized by a size ratio gamma = sigma(2)/sigma(1) infinity) a demixing transition with a critical consolute point at a packing fraction scaling as eta approximately d2(-d) is found, even for slightly negative nonadditivity, if Delta >-1/8 (ln gamma)(2). Arguments concerning the stability of the demixing with respect to freezing are provided.
Complex oscillatory yielding of model hard-sphere glasses.
Koumakis, N; Brady, J F; Petekidis, G
2013-04-26
The yielding behavior of hard sphere glasses under large-amplitude oscillatory shear has been studied by probing the interplay of Brownian motion and shear-induced diffusion at varying oscillation frequencies. Stress, structure and dynamics are followed by experimental rheology and Browian dynamics simulations. Brownian-motion-assisted cage escape dominates at low frequencies while escape through shear-induced collisions at high ones, both related with a yielding peak in G''. At intermediate frequencies a novel, for hard sphere glasses, double peak in G'' is revealed reflecting both mechanisms. At high frequencies and strain amplitudes a persistent structural anisotropy causes a stress drop within the cycle after strain reversal, while higher stress harmonics are minimized at certain strain amplitudes indicating an apparent harmonic response.
Frustrated spin model as a hard-sphere liquid.
Mostovoy, M V; Khomskii, D I; Knoester, J; Prokof'ev, N V
2003-04-11
We show that one-dimensional topological objects (kinks) are natural degrees of freedom for an antiferromagnetic Ising model on a triangular lattice. Its ground states and the coexistence of spin ordering with an extensive zero-temperature entropy can easily be understood in terms of kinks forming a hard-sphere liquid. Using this picture we explain effects of quantum spin dynamics on that frustrated model, which we also study numerically.
Nested sampling for materials: the case of hard spheres
Partay, Livia B.; Bartok, Albert P.; Csanyi, Gabor
2012-01-01
The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by studying the three dimensional hard sphere model. Having obtained the partition function, we show how easy it is to calculate the compressibility and the free energy as functions of the packing fraction and local order, verifying that the transition to cryst...
Collective excitations in soft-sphere fluids.
Bryk, Taras; Gorelli, Federico; Ruocco, Giancarlo; Santoro, Mario; Scopigno, Tullio
2014-10-01
Despite that the thermodynamic distinction between a liquid and the corresponding gas ceases to exist at the critical point, it has been recently shown that reminiscence of gaslike and liquidlike behavior can be identified in the supercritical fluid region, encoded in the behavior of hypersonic waves dispersion. By using a combination of molecular dynamics simulations and calculations within the approach of generalized collective modes, we provide an accurate determination of the dispersion of longitudinal and transverse collective excitations in soft-sphere fluids. Specifically, we address the decreasing rigidity upon density reduction along an isothermal line, showing that the positive sound dispersion, an excess of sound velocity over the hydrodynamic limit typical for dense liquids, displays a nonmonotonic density dependence strictly correlated to that of thermal diffusivity and kinematic viscosity. This allows rationalizing recent observation parting the supercritical state based on the Widom line, i.e., the extension of the coexistence line. Remarkably, we show here that the extremals of transport properties such as thermal diffusivity and kinematic viscosity provide a robust definition for the boundary between liquidlike and gaslike regions, even in those systems without a liquid-gas binodal line. Finally, we discuss these findings in comparison with recent results for Lennard-Jones model fluid and with the notion of the "rigid-nonrigid" fluid separation lines.
Dynamical study of a polydisperse hard-sphere system
Nogawa, Tomoaki
2010-08-10
We study the interplay between the fluid-crystal transition and the glass transition of elastic sphere system with polydispersity using nonequilibrium molecular dynamics simulations. It is found that the end point of the crystal-fluid transition line, which corresponds to the critical polydispersity above which the crystal state is unstable, is on the glass transition line. This means that crystal and fluid states at the melting point becomes less distinguishable as polydispersity increases and finally they become identical state, i.e., marginal glass state, at critical polydispersity. © 2010 The American Physical Society.
Jover, J; Haslam, A J; Galindo, A; Jackson, G; Müller, E A
2012-10-14
We present a continuous pseudo-hard-sphere potential based on a cut-and-shifted Mie (generalized Lennard-Jones) potential with exponents (50, 49). Using this potential one can mimic the volumetric, structural, and dynamic properties of the discontinuous hard-sphere potential over the whole fluid range. The continuous pseudo potential has the advantage that it may be incorporated directly into off-the-shelf molecular-dynamics code, allowing the user to capitalise on existing hardware and software advances. Simulation results for the compressibility factor of the fluid and solid phases of our pseudo hard spheres are presented and compared both to the Carnahan-Starling equation of state of the fluid and published data, the differences being indistinguishable within simulation uncertainty. The specific form of the potential is employed to simulate flexible chains formed from these pseudo hard spheres at contact (pearl-necklace model) for m(c) = 4, 5, 7, 8, 16, 20, 100, 201, and 500 monomer segments. The compressibility factor of the chains per unit of monomer, m(c), approaches a limiting value at reasonably small values, m(c) hard spheres, with diameter ratios of 3:1, 5:1, 20:1 over the whole composition range.
Bulk fluid phase behaviour of colloidal platelet-sphere and platelet-polymer mixtures.
de las Heras, Daniel; Schmidt, Matthias
2013-04-13
Using a geometry-based fundamental measure density functional theory, we calculate bulk fluid phase diagrams of colloidal mixtures of vanishingly thin hard circular platelets and hard spheres. We find isotropic-nematic phase separation, with strong broadening of the biphasic region, upon increasing the pressure. In mixtures with large size ratio of platelet and sphere diameters, there is also demixing between two nematic phases with differing platelet concentrations. We formulate a fundamental measure density functional for mixtures of colloidal platelets and freely overlapping spheres, which represent ideal polymers, and use it to obtain phase diagrams. We find that, for low platelet-polymer size ratio, in addition to isotropic-nematic and nematic-nematic phase coexistence, platelet-polymer mixtures also display isotropic-isotropic demixing. By contrast, we do not find isotropic-isotropic demixing in hard-core platelet-sphere mixtures for the size ratios considered.
Mitarai, Namiko; Nakanishi, Hiizu
2002-01-01
Dynamical behavior of steady granular flow is investigated numerically in the inelastic hard sphere limit of the soft sphere model. We find distinctively different limiting behaviors for the two flow regimes, i.e., the collisional flow and the frictional flow. In the collisional flow, the hard sphere limit is straightforward; the number of collisions per particle per unit time converges to a finite value and the total contact time fraction with other particles goes to zero. For the frictional...
Paricaud, P
2015-07-28
A simple modification of the Boublík-Mansoori-Carnahan-Starling-Leland equation of state is proposed for an application to the metastable disordered region. The new model has a positive pole at the jamming limit and can accurately describe the molecular simulation data of pure hard in the stable fluid region and along the metastable branch. The new model has also been applied to binary mixtures hard spheres, and an excellent description of the fluid and metastable branches can be obtained by adjusting the jamming packing fraction. The new model for hard sphere mixtures can be used as the repulsive term of equations of state for real fluids. In this case, the modified equations of state give very similar predictions of thermodynamic properties as the original models, and one can remove the multiple liquid density roots observed for some versions of the Statistical Associating Fluid Theory (SAFT) at low temperature without any modification of the dispersion term.
Energy Technology Data Exchange (ETDEWEB)
Paricaud, P. [Unité de Chimie et Procédés, ENSTA-ParisTech, Université Paris-Saclay, 828 Boulevard des Maréchaux, 91762 Palaiseau cedex (France)
2015-07-28
A simple modification of the Boublík-Mansoori-Carnahan-Starling-Leland equation of state is proposed for an application to the metastable disordered region. The new model has a positive pole at the jamming limit and can accurately describe the molecular simulation data of pure hard in the stable fluid region and along the metastable branch. The new model has also been applied to binary mixtures hard spheres, and an excellent description of the fluid and metastable branches can be obtained by adjusting the jamming packing fraction. The new model for hard sphere mixtures can be used as the repulsive term of equations of state for real fluids. In this case, the modified equations of state give very similar predictions of thermodynamic properties as the original models, and one can remove the multiple liquid density roots observed for some versions of the Statistical Associating Fluid Theory (SAFT) at low temperature without any modification of the dispersion term.
Physics of Hard Spheres Experiment: Significant and Quantitative Findings Made
Doherty, Michael P.
2000-01-01
Direct examination of atomic interactions is difficult. One powerful approach to visualizing atomic interactions is to study near-index-matched colloidal dispersions of microscopic plastic spheres, which can be probed by visible light. Such spheres interact through hydrodynamic and Brownian forces, but they feel no direct force before an infinite repulsion at contact. Through the microgravity flight of the Physics of Hard Spheres Experiment (PHaSE), researchers have sought a more complete understanding of the entropically driven disorder-order transition in hard-sphere colloidal dispersions. The experiment was conceived by Professors Paul M. Chaikin and William B. Russel of Princeton University. Microgravity was required because, on Earth, index-matched colloidal dispersions often cannot be density matched, resulting in significant settling over the crystallization period. This settling makes them a poor model of the equilibrium atomic system, where the effect of gravity is truly negligible. For this purpose, a customized light-scattering instrument was designed, built, and flown by the NASA Glenn Research Center at Lewis Field on the space shuttle (shuttle missions STS 83 and STS 94). This instrument performed both static and dynamic light scattering, with sample oscillation for determining rheological properties. Scattered light from a 532- nm laser was recorded either by a 10-bit charge-coupled discharge (CCD) camera from a concentric screen covering angles of 0 to 60 or by sensitive avalanche photodiode detectors, which convert the photons into binary data from which two correlators compute autocorrelation functions. The sample cell was driven by a direct-current servomotor to allow sinusoidal oscillation for the measurement of rheological properties. Significant microgravity research findings include the observation of beautiful dendritic crystals, the crystallization of a "glassy phase" sample in microgravity that did not crystallize for over 1 year in 1g
Extension of the hard-sphere particle-wall collision model to account for particle deposition.
Kosinski, Pawel; Hoffmann, Alex C
2009-06-01
Numerical simulations of flows of fluids with granular materials using the Eulerian-Lagrangian approach involve the problem of modeling of collisions: both between the particles and particles with walls. One of the most popular techniques is the hard-sphere model. This model, however, has a major drawback in that it does not take into account cohesive or adhesive forces. In this paper we develop an extension to a well-known hard-sphere model for modeling particle-wall interactions, making it possible to account for adhesion. The model is able to account for virtually any physical interaction, such as van der Waals forces or liquid bridging. In this paper we focus on the derivation of the new model and we show some computational results.
Chemical-potential route: a hidden Percus-Yevick equation of state for hard spheres.
Santos, Andrés
2012-09-21
The chemical potential of a hard-sphere fluid can be expressed in terms of the contact value of the radial distribution function of a solute particle with a diameter varying from zero to that of the solvent particles. Exploiting the explicit knowledge of such a contact value within the Percus-Yevick theory, and using standard thermodynamic relations, a hitherto unknown Percus-Yevick equation of state, p/ρk(B)T = -(9/η) ln(1-η)-(16-31η)/2(1-η)(2), is unveiled. This equation of state turns out to be better than the one obtained from the conventional virial route. Interpolations between the chemical-potential and compressibility routes are shown to be more accurate than the widely used Carnahan-Starling equation of state. The extension to polydisperse hard-sphere systems is also presented.
Improved model for mixtures of polymers and hard spheres
D'Adamo, Giuseppe; Pelissetto, Andrea
2016-12-01
Extensive Monte Carlo simulations are used to investigate how model systems of mixtures of polymers and hard spheres approach the scaling limit. We represent polymers as lattice random walks of length L with an energy penalty w for each intersection (Domb-Joyce model), interacting with hard spheres of radius R c via a hard-core pair potential of range {{R}\\text{mon}}+{{R}c} , where R mon is identified as the monomer radius. We show that the mixed polymer-colloid interaction gives rise to new confluent corrections. The leading ones scale as {{L}-ν} , where ν ≈ 0.588 is the usual Flory exponent. Finally, we determine optimal values of the model parameters w and R mon that guarantee the absence of the two leading confluent corrections. This improved model shows a significantly faster convergence to the asymptotic limit L\\to ∞ and is amenable for extensive and accurate numerical simulations at finite density, with only a limited computational effort.
Depletion potentials in colloidal mixtures of hard spheres and rods.
Li, Weihua; Yang, Tao; Ma, Hong-ru
2008-01-28
The depletion potential between a hard sphere and a planar hard wall, or two hard spheres, imposed by suspended rigid spherocylindrical rods is computed by the acceptance ratio method through the application of Monte Carlo simulation. The accurate results and ideal-gas approximation results of the depletion potential are determined with the acceptance ratio method in our simulations. For comparison, the depletion potentials are also studied by using both the density functional theory and Derjaguin approximations. The density profile as a function of positions and orientations of rods, used in the density functional theory, is calculated by Monte Carlo simulation. The potential obtained by the acceptance ratio method is in good agreement with that of density functional theory under the ideal-gas approximation. The comparison between our results and those of other theories suggests that the acceptance ratio method is the only efficient method used to compute the depletion potential induced by nonspherical colloids with the volume fraction beyond the ideal-gas approximation.
Transport properties of the Fermi hard-sphere system
Energy Technology Data Exchange (ETDEWEB)
Mecca, Angela; Lovato, Alessandro; Benhar, Omar; Polls, Artur
2016-03-01
The transport properties of neutron star matter play an important role in many astrophysical processes. We report the results of a calculation of the shear viscosity and thermal conductivity coefficients of the hard-sphere fermion system of degeneracy ν = 2, that can be regarded as a model of pure neutron matter. Our approach is based on the effective interaction obtained from the formalism of correlated basis functions and the cluster expansion technique. The resulting transport coefficients show a strong sensitivity to the quasiparticle effective mass, reflecting the effect of second-order contributions to the self-energy that are not taken into account in nuclear matter studies available in the literature.
Hard-sphere interactions in velocity-jump models
Franz, Benjamin; Taylor-King, Jake P.; Yates, Christian; Erban, Radek
2016-07-01
Group-level behavior of particles undergoing a velocity-jump process with hard-sphere interactions is investigated. We derive N -particle transport equations that include the possibility of collisions between particles and apply different approximation techniques to get expressions for the dependence of the collective diffusion coefficient on the number of particles and their diameter. The derived approximations are compared with numerical results obtained from individual-based simulations. The theoretical results compare well with Monte Carlo simulations providing the excluded-volume fraction is small.
Hard-sphere interactions in velocity jump models
Franz, Benjamin; Yates, Christian; Erban, Radek
2014-01-01
Group-level behaviour of particles undergoing a velocity jump process with hard-sphere interactions is investigated. We derive $N$-particle transport equations that include the possibility of collisions between particles and apply different approximation techniques to get expressions for the dependence of the collective diffusion coefficient on the number of particles and their diameter. The derived approximations are compared with numerical results obtained from individual-based simulations. The theoretical results compare well with Monte Carlo simulations providing the excluded volume fraction is small.
Statistical mechanics of two hard spheres in a box.
Uranagase, Masayuki; Munakata, Toyonori
2006-12-01
We investigate some statistical mechanical properties of a system consisting of two hard spheres in a D-dimensional rectangular box (D=1, 2, ...). We give a theoretical method for computing a configurational partition function Zc,D of this system and compare the equation of state obtained from Zc,D with molecular dynamics simulations. Especially in D=3, we give a fully analytic expression for the pressure which turns out to have one or more negative compressibility regions when the box size is small.
Density functional for ternary non-additive hard sphere mixtures.
Schmidt, Matthias
2011-10-19
Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data. © 2011 IOP Publishing Ltd
Theory of amorphous packings of binary mixtures of hard spheres.
Biazzo, Indaco; Caltagirone, Francesco; Parisi, Giorgio; Zamponi, Francesco
2009-05-15
We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical protocols can be identified with the infinite pressure limit of long-lived metastable glassy states. We test this assumption against numerical and experimental data and show that the theory correctly reproduces the variation with mixture composition of structural observables, such as the total packing fraction and the partial coordination numbers.
Hard Sphere Diffusion Behaviour of Polymer Translocating through Interacting Pores
Institute of Scientific and Technical Information of China (English)
SUN Li-Zhen; LUO Meng-Bo
2008-01-01
The translocation of polymer chain through a small pore from a high concentration side (cis side) to a low concentration side (trans side) is simulated by using Monte Carlo technique. The effect of the polymer-pore interaction on the translocation is studied. We find a special interaction at which the decay of the number of polymer chain, N, at the cis side obeys Fick's law, i.e. N decreases exponentially with time. The behaviour is analogous to the diffusion of hard sphere.
Simple liquids’ quasiuniversality and the hard-sphere paradigm
DEFF Research Database (Denmark)
Dyre, Jeppe C.
2016-01-01
This topical review discusses the quasiuniversality of simple liquids' structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues...... that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field....
The hard-sphere model of strongly interacting fermion systems
Mecca, Angela
2016-01-01
The formalism based on Correlated Basis Functions (CBF) and the cluster-expansion technique has been recently employed to derive an effective interaction from a realistic nuclear Hamiltonian. One of the main objectives of the work described in this Thesis is establishing the accuracy of this novel approach--that allows to combine the flexibility of perturbation theory in the basis of eigenstates of the noninteracting system with a realistic description of short-range correlations in coordinate space--by focusing on the hard-sphere fermion system. As a first application of the formalism, the quasiparticle properties of hard spheres of degeneracy four have been determined from the two-point Green's function. The calculation has been performed carrying out a perturbative expansion of the self-energy, up to the second order in the CBF effective interaction. The main results of this study are the momentum distributions, the quasiparticle spectra and their description in terms of effective mass. The investigation o...
Assembly of body-centered cubic crystals in hard spheres.
Xu, W-S; Sun, Z-Y; An, L-J
2011-05-01
We investigate the crystallization of monodisperse hard spheres confined by two square patterned substrates (possessing the basic character of the body-centered cubic (bcc) crystal structure) at varying substrate separations via molecular dynamics simulation. Through slowly increasing the density of the system, we find that crystallization under the influence of square patterned substrates can set in at lower densities compared with the homogeneous crystallization. As the substrate separation decreases, the density, where crystallization occurs (i.e., pressure drops), becomes small. Moreover, two distinct regimes are identified in the plane of bcc particle fraction and density for the separation range investigated. For large substrate separations, the bcc particle fraction displays a local maximum as the density is increased, and the resulting formed crystals have a polycrystalline structure. However, and more importantly, another situation emerges for small substrate separations: the capillary effects (stemming from the presence of two substrates) overwhelm the bulk driving forces (stemming from the spontaneous thermal fluctuations in the bulk) during the densification, eventually resulting in the formation of a defect-free bcc crystal (unstable with respect to the bulk hard-sphere crystals) by using two square patterned substrates.
Crystallization and dynamical arrest of attractive hard spheres.
Babu, Sujin; Gimel, Jean-Christophe; Nicolai, Taco
2009-02-14
Crystallization of hard spheres interacting with a square well potential was investigated by numerical simulations using so-called Brownian cluster dynamics. The phase diagram was determined over a broad range of volume fractions. The crystallization rate was studied as a function of the interaction strength expressed in terms of the second virial coefficient. For volume fractions below about 0.3 the rate was found to increase abruptly with increasing attraction at the binodal of the metastable liquid-liquid phase separation. The rate increased until a maximum was reached after which it decreased with a power law dependence on the second virial coefficient. Above a critical percolation concentration, a transient system spanning network of connected particles was formed. Crystals were formed initially as part of the network, but eventually crystallization led to the breakup of the network. The lifetime of the transient gels increased very rapidly over a small range of interaction energies. Weak attraction destabilized the so-called repulsive crystals formed in pure hard sphere systems and shifted the coexistence line to higher volume fractions. Stronger attraction led to the formation of a denser, so-called attractive, crystalline phase. Nucleation of attractive crystals in the repulsive crystalline phase was observed close to the transition.
Analytic studies of the hard dumbell fluid
Morriss, G. P.; Cummings, P. T.
A closed form analytic theory for the structure of the hard dumbell fluid is introduced and evaluated. It is found to be comparable in accuracy to the reference interaction site approximation (RISA) of Chandler and Andersen.
Second virial coefficient at the critical point in a fluid of colloidal spheres plus depletants.
Tuinier, Remco; Feenstra, Maartje S
2014-11-11
Vliegenthart-Lekkerkerker (VL) criterion B2 = -6vc for second virial coefficient B2 at the critical (colloidal) gas-liquid point is considered for a mixture of spheres with volume vc plus depletants. For the onset of fluid-phase instability, the VL criterion holds for a wide range of shapes of direct attractive forces between hard-core spheres (Vliegenthart, G. A.; Lekkerkerker, H. N. W. J. Chem. Phys. 2000, 112, 5364). In the case of long-ranged attractions imposed indirectly via depletants, it is found that the VL relation fails. Instead, B2/vc at the critical point depends strongly on the sphere/depletant size ratio. By making the hard spheres sticky, we find that B2 moves gradually toward the VL criterion upon increasing the stickiness.
Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres.
Santos, Andrés; Yuste, Santos B; López de Haro, Mariano; Odriozola, Gerardo; Ogarko, Vitaliy
2014-04-01
A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction ϕJ of the polydisperse system as a simple function of M1M3/M22, where Mk is the kth moment of the size distribution. An analysis of experimental and simulation data of ϕJ for a large number of different mixtures shows a remarkable general agreement with the theoretical estimate. To give extra support to the procedure, simulation data for seventeen mixtures in the high-density region are used to infer the equation of state of the pure hard-sphere system in the metastable region. An excellent collapse of the inferred curves up to the glass transition and a significant narrowing of the different out-of-equilibrium glass branches all the way to jamming are observed. Thus, the present approach provides an extremely simple criterion to unify in a common framework and to give coherence to data coming from very different polydisperse hard-sphere mixtures.
Shear viscosity of hard chain fluids through molecular dynamics simulation techniques
Directory of Open Access Journals (Sweden)
Ratanapisit, J.
2005-07-01
Full Text Available In this paper, we represent the viscosity of hard chain fluids. This study was initiated with an investigation of the equilibrium molecular dynamic simulations of pure hard-sphere molecules. The natural extension of that work was to hard chain fluids. The hard chain model is one in which each molecule is represented as a chain of freely jointed hard spheres that interact on a site-site basis. The major use of the results from this study lie in the future development of a transport perturbation theory in which the hard chain serves as the reference. Our results show agreement to within the combined uncertainties with the previous studies. Comparisons have also been made to a modified Enskog theory. Results show the failure of the Enskog theory to predict the high density viscosity and that the theory fails more rapidly with density as the chain length increases. We attribute this to a failure of the molecular chaos assumption used in the Enskog theory. Further comparisons are made to real fluids using the SAFT-MET and TRAPP approaches. As expected, the hard sphere model is not appropriate to estimate properties of real fluids. However, the hard sphere model provides the good starting point to serve as the reference basis to study chain molecule systems.
Chemical-Potential Route: A Hidden Percus-Yevick Equation of State for Hard Spheres
Santos, Andrés
2012-01-01
The chemical potential of a hard-sphere fluid can be expressed in terms of the contact value of the radial distribution function of a solute particle with a diameter varying from zero to that of the solvent particles. Exploiting the explicit knowledge of such a contact value within the Percus--Yevick (PY) theory, and using standard thermodynamic relations, a hitherto unknown PY equation of state, $p/\\rho k_BT=-(9/\\eta)\\ln(1-\\eta)-(16-31\\eta)/2(1-\\eta)^2$, is unveiled. This equation of state t...
Detecting Phase Boundaries in Hard-Sphere Suspensions
McDowell, Mark; Rogers, Richard B.; Gray, Elizabeth
2009-01-01
A special image-data-processing technique has been developed for use in experiments that involve observation, via optical microscopes equipped with electronic cameras, of moving boundaries between the colloidal-solid and colloidal-liquid phases of colloidal suspensions of monodisperse hard spheres. During an experiment, it is necessary to adjust the position of a microscope to keep the phase boundary within view. A boundary typically moves at a speed of the order of microns per hour. Because an experiment can last days or even weeks, it is impractical to require human intervention to keep the phase boundary in view. The present image-data-processing technique yields results within a computation time short enough to enable generation of automated-microscope-positioning commands to track the moving phase boundary
Shear Yielding and Shear Jamming of Dense Hard Sphere Glasses
Urbani, Pierfrancesco; Zamponi, Francesco
2017-01-01
We investigate the response of dense hard sphere glasses to a shear strain in a wide range of pressures ranging from the glass transition to the infinite-pressure jamming point. The phase diagram in the density-shear strain plane is calculated analytically using the mean-field infinite-dimensional solution. We find that just above the glass transition, the glass generically yields at a finite shear strain. The yielding transition in the mean-field picture is a spinodal point in presence of disorder. At higher densities, instead, we find that the glass generically jams at a finite shear strain: the jamming transition prevents yielding. The shear yielding and shear jamming lines merge in a critical point, close to which the system yields at extremely large shear stress. Around this point, highly nontrivial yielding dynamics, characterized by system-spanning disordered fractures, is expected.
Nested sampling for materials: The case of hard spheres
Pártay, Lívia B.; Bartók, Albert P.; Csányi, Gábor
2014-02-01
The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by studying the three-dimensional hard-sphere model. Having obtained the partition function, we show how easy it is to calculate the compressibility and the free energy as functions of the packing fraction and local order, verifying that the transition to crystallinity has a very small barrier, and that the entropic contribution of jammed states to the free energy is negligible for packing fractions above the phase transition. We quantify the previously proposed schematic phase diagram and estimate the extent of the region of jammed states. We find that within our samples, the maximally random jammed configuration is surprisingly disordered.
Hard sphere crystal nucleation and growth near large spherical impurities
de Villeneuve, V. W. A.; Verboekend, D.; Dullens, R. P. A.; Aarts, D. G. A. L.; Kegel, W. K.; Lekkerkerker, H. N. W.
2005-11-01
We report how large spherical impurities affect the nucleation and growth of hard sphere colloidal crystals. Both the impurities and the colloids are fluorescently labelled polymethylmetacrylate particles and are dispersed in an optically and density matching solvent mixture. Crystal growth, initiated either at the impurity surface, or at the sample bottom, was studied by imaging sequences of two-dimensional xy-slices in the plane of the impurity's centre of mass with a laser scanning confocal microscope. At least two factors determine whether a large impurity can function as a seed for heterogeneous nucleation: timescales and impurity curvature. The curvature needs to be sufficiently low for crystal nuclei to form on the impurity surface. If bulk crystal growth has already approached the impurity, bulk growth is dominant over growth of crystallites on the impurity surface. Such surface crystallites eventually reorient to adapt to the overall bulk crystal symmetry.
Sun, Jiu-Xun; Wu, Qiang; Cai, Ling-Cang; Jin, Ke
2013-11-01
A universal cubic equation of state (UC EOS) is proposed based on a modification of the virial Percus-Yevick (PY) integral equation EOS for hard-sphere fluid. The UC EOS is extended to multi-component hard-sphere mixtures based on a modification of Lebowitz solution of PY equation for hard-sphere mixtures. And expressions of the radial distribution functions at contact (RDFC) are improved with the form as simple as the original one. The numerical results for the compressibility factor and RDFC are in good agreement with the simulation results. The average errors of the compressibility factor relative to MC data are 3.40%, 1.84% and 0.92% for CP3P, BMCSL equations and UC EOS, respectively. The UC EOS is a unique cubic one with satisfactory precision among many EOSs in the literature both for pure and mixture fluids of hard spheres.
Shock Waves in Dense Hard Disk Fluids
Sirmas, Nick; Barahona, Javier; Radulescu, Matei I
2011-01-01
Media composed of colliding hard disks (2D) or hard spheres (3D) serve as good approximations for the collective hydrodynamic description of gases, liquids and granular media. In the present study, the compressible hydrodynamics and shock dynamics are studied for a two-dimensional hard-disk medium at both the continuum and discrete particle level descriptions. For the continuum description, closed form analytical expressions for the inviscid hydrodynamic description, shock Hugoniot, isentropic exponent and shock jump conditions were obtained using the Helfand equation of state. The closed-form analytical solutions permitted us to gain physical insight on the role of the material's density on its compressibility, i.e. how the medium compresses under mechanical loadings and sustains wave motion. Furthermore, the predictions were found in excellent agreement with calculations using the Event Driven Molecular Dynamic method involving 30,000 particles over the entire range of compressibility spanning the dilute id...
Mitarai, Namiko; Nakanishi, Hiizu
2003-02-01
Dynamical behavior of steady granular flow is investigated numerically in the inelastic hard-sphere limit of the soft-sphere model. We find distinctively different limiting behaviors for the two flow regimes, i.e., the collisional flow and the frictional flow. In the collisional flow, the hard-sphere limit is straightforward; the number of collisions per particle per unit time converges to a finite value and the total contact time fraction with other particles goes to zero. For the frictional flow, however, we demonstrate that the collision rate diverges as the power of the particle stiffness so that the time fraction of the multiple contacts remains finite even in the hard-sphere limit, although the contact time fraction for the binary collisions tends to zero.
Decay of correlation functions in hard-sphere mixtures: structural crossover.
Grodon, C; Dijkstra, M; Evans, R; Roth, R
2004-10-22
We investigate the decay of pair correlation functions in a homogeneous (bulk) binary mixture of hard spheres. At a given state point the asymptotic decay r-->infinity of all three correlation functions is governed by a common exponential decay length and a common wavelength of oscillations. Provided the mixture is sufficiently asymmetric, size ratios q less than or approximately 0.7, we find that the common wavelength reflects either the size of the small or that of the big spheres. By analyzing the (complex) poles of the partial structure factors we find a sharp structural crossover line in the phase diagram. On one side of this line the common wavelength is approximately the diameter of the smaller sized spheres whereas on the other side it is approximately the diameter of the bigger ones; the wavelength of the longest ranged oscillations changes discontinuously at the structural crossover line. Using density functional theory and Monte Carlo simulations we show that structural crossover also manifests itself in the intermediate range behavior of the pair correlation functions and we comment on the relevance of this observation for real (colloidal) mixtures. In highly asymmetric mixtures, q< or =0.1, where there is metastable fluid-fluid transition, we find a Fisher-Widom line with two branches. This line separates a region of the phase diagram where the decay of pair correlations is oscillatory from one in which it is monotonic. (c) 2004 American Institute of Physics.
Analytical expressions for the fourth virial coefficient of a hard-sphere mixture.
Labík, Stanislav; Kolafa, Jirí
2009-11-01
A method of numerical calculation of the fourth virial coefficients of the mixture of additive hard spheres is proposed. The results are compared with an exact analytical formula for the fourth partial virial coefficient B4[1] (i.e., three spheres of diameters sigma1 and one sphere of diameter sigma2) and a semiempirical expression for B4[2] (i.e., two spheres of each kind). It is shown that the first formula is nonanalytic and the implication to the equations of state for hard-sphere mixtures is discussed.
Rodríguez-López, Tonalli; Moreno-Razo, J. Antonio; del Río, Fernando
2013-03-01
In this work, we explore transport properties of a special type of repulsive spheres that exhibit remarkable scaling of their thermodynamic properties. In order to accomplish that we propose a new way to derive and express effective hard-sphere diameters for transport properties of simple fluids. The procedure relies on mapping the system's transport properties, in the low density limit, to the hard-sphere fluid. We have chosen a set of soft-sphere systems characterised by a well-defined variation of their softness. These systems represent an extension of the repulsive Lennard-Jones potential widely used in statistical mechanics of fluids and are an accurate representation of the effective repulsive potentials of real systems. The self-diffusion coefficient of the soft-sphere fluids is obtained by equilibrium molecular dynamics. The soft-sphere collision integrals of different systems are shown to follow quite simple relationships between each other. These collision integrals are incorporated, through the definition of the effective hard-sphere diameter, in the resulting equation for the self-diffusion coefficient. The approach followed exhibits a density rescaling that leads to a single master curve for all systems and temperatures. The scaling is carried through to the level of the mean-squared displacement.
Edison, John R.; Dasgupta, Tonnishtha; Dijkstra, Marjolein
2016-08-01
We study the phase behaviour of a binary mixture of colloidal hard spheres and freely jointed chains of beads using Monte Carlo simulations. Recently Panagiotopoulos and co-workers predicted [Nat. Commun. 5, 4472 (2014)] that the hexagonal close packed (HCP) structure of hard spheres can be stabilized in such a mixture due to the interplay between polymer and the void structure in the crystal phase. Their predictions were based on estimates of the free-energy penalty for adding a single hard polymer chain in the HCP and the competing face centered cubic (FCC) phase. Here we calculate the phase diagram using free-energy calculations of the full binary mixture and find a broad fluid-solid coexistence region and a metastable gas-liquid coexistence region. For the colloid-monomer size ratio considered in this work, we find that the HCP phase is only stable in a small window at relatively high polymer reservoir packing fractions, where the coexisting HCP phase is nearly close packed. Additionally we investigate the structure and dynamic behaviour of these mixtures.
Hard-sphere kinetic models for inert and reactive mixtures
Polewczak, Jacek
2016-10-01
I consider stochastic variants of a simple reacting sphere (SRS) kinetic model (Xystris and Dahler 1978 J. Chem. Phys. 68 387-401, Qin and Dahler 1995 J. Chem. Phys. 103 725-50, Dahler and Qin 2003 J. Chem. Phys. 118 8396-404) for dense reacting mixtures. In contrast to the line-of-center models of chemical reactive models, in the SRS kinetic model, the microscopic reversibility (detailed balance) can be easily shown to be satisfied, and thus all mathematical aspects of the model can be fully justified. In the SRS model, the molecules behave as if they were single mass points with two internal states. Collisions may alter the internal states of the molecules, and this occurs when the kinetic energy associated with the reactive motion exceeds the activation energy. Reactive and non-reactive collision events are considered to be hard sphere-like. I consider a four component mixture A, B, A *, B *, in which the chemical reactions are of the type A+B\\rightleftharpoons {{A}\\ast}+{{B}\\ast} , with A * and B * being distinct species from A and B. This work extends the joined works with George Stell to the kinetic models of dense inert and reactive mixtures. The idea of introducing smearing-type effect in the collisional process results in a new class of stochastic kinetic models for both inert and reactive mixtures. In this paper the important new mathematical properties of such systems of kinetic equations are proven. The new results for stochastic revised Enskog system for inert mixtures are also provided.
Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers
Sear, Richard P.
2002-01-01
A simple analytic theory for mixtures of hard spheres and larger polymers with excluded volume interactions is developed. The mixture is shown to exhibit extensive immiscibility. For large polymers with strong excluded volume interactions, the density of monomers at the critical point for demixing decreases as one over the square root of the length of the polymer, while the density of spheres tends to a constant. This is very different to the behaviour of mixtures of hard spheres and ideal po...
Depletion effects in smectic phases of hard-rod-hard-sphere mixtures.
Martínez-Ratón, Y; Cinacchi, G; Velasco, E; Mederos, L
2006-10-01
It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen-orientation approximation. These results are discussed in terms of the tau parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for tau, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a fundamental-measure density-functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the tau parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard-rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, d, in contrast to Onsager approximation, which predicts tau approximately d (3). Based on both this result and the Percus-Yevick approximation for the direct correlation function for a hard-sphere binary mixture in the same limit of infinite asymmetry, we speculate that, for
Equation of state and critical point behavior of hard-core double-Yukawa fluids.
Montes, J; Robles, M; López de Haro, M
2016-02-28
A theoretical study on the equation of state and the critical point behavior of hard-core double-Yukawa fluids is presented. Thermodynamic perturbation theory, restricted to first order in the inverse temperature and having the hard-sphere fluid as the reference system, is used to derive a relatively simple analytical equation of state of hard-core multi-Yukawa fluids. Using such an equation of state, the compressibility factor and phase behavior of six representative hard-core double-Yukawa fluids are examined and compared with available simulation results. The effect of varying the parameters of the hard-core double-Yukawa intermolecular potential on the location of the critical point is also analyzed using different perspectives. The relevance of this analysis for fluids whose molecules interact with realistic potentials is also pointed out.
Equation of state and critical point behavior of hard-core double-Yukawa fluids
Montes, J.; Robles, M.; López de Haro, M.
2016-02-01
A theoretical study on the equation of state and the critical point behavior of hard-core double-Yukawa fluids is presented. Thermodynamic perturbation theory, restricted to first order in the inverse temperature and having the hard-sphere fluid as the reference system, is used to derive a relatively simple analytical equation of state of hard-core multi-Yukawa fluids. Using such an equation of state, the compressibility factor and phase behavior of six representative hard-core double-Yukawa fluids are examined and compared with available simulation results. The effect of varying the parameters of the hard-core double-Yukawa intermolecular potential on the location of the critical point is also analyzed using different perspectives. The relevance of this analysis for fluids whose molecules interact with realistic potentials is also pointed out.
Avazpour, A; Avazpour, L
2010-12-28
This article applies the density functional theory to confined liquid crystals, comprised of ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The extended restricted orientation model proposed by Moradi and co-workers [J. Phys.: Condens. Matter 17, 5625 (2005)] is used to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the optimized sum of Percus-Yevick and Roth DCF for hard spheres; the anisotropy introduced by means of the closest approach parameter, the expression proposed by Marko [Physica B 392, 242 (2007)] for DCF of HGO, and hard ellipsoids were used. In this study we extend an our previous work [Phys. Rev. E 72, 061706 (2005)] on the anchoring behavior of hard particle liquid crystal model, by studying the effect of changing the particle-substrate contact function instead of hard needle-wall potentials. We use the two particle-surface potentials: the HGO-sphere and the HGO-surface potentials. The average number density and order parameter profiles of a confined HGO fluid are obtained using the two particle-wall potentials. For bulk isotropic liquid, the results are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 71, 021705 (2005)]. Also, for the bulk nematic phase, the theory gives the correct density profile and order parameter between the walls.
Avalanches mediate crystallization in a hard-sphere glass.
Sanz, Eduardo; Valeriani, Chantal; Zaccarelli, Emanuela; Poon, Wilson C K; Cates, Michael E; Pusey, Peter N
2014-01-07
By molecular-dynamics simulations, we have studied the devitrification (or crystallization) of aged hard-sphere glasses. First, we find that the dynamics of the particles are intermittent: Quiescent periods, when the particles simply "rattle" in their nearest-neighbor cages, are interrupted by abrupt "avalanches," where a subset of particles undergo large rearrangements. Second, we find that crystallization is associated with these avalanches but that the connection is not straightforward. The amount of crystal in the system increases during an avalanche, but most of the particles that become crystalline are different from those involved in the avalanche. Third, the occurrence of the avalanches is a largely stochastic process. Randomizing the velocities of the particles at any time during the simulation leads to a different subsequent series of avalanches. The spatial distribution of avalanching particles appears random, although correlations are found among avalanche initiation events. By contrast, we find that crystallization tends to take place in regions that already show incipient local order.
Statistical measure of complexity of hard-sphere gas: applications to nuclear matter
Moustakidis, Ch. C.; Chatzisavvas, K. Ch.; Nikolaidis, N. S.; Panos, C. P.
2010-01-01
We apply the statistical measure of complexity, introduced by L\\'{o}pez-Ruiz, Mancini and Calbet to a hard-sphere dilute Fermi gas whose particles interact via a repulsive hard-core potential. We employ the momentum distribution of this system to calculate the information entropy, the disequilibrium and the statistical complexity. We examine possible connections between the particle correlations and energy of the system with those information and complexity measures. The hard-sphere model ser...
Squeeze flow of a Carreau fluid during sphere impact
Uddin, J.
2012-07-19
We present results from a combined numerical and experimental investigation into the squeeze flow induced when a solid sphere impacts onto a thin, ultra-viscous film of non-Newtonian fluid. We examine both the sphere motion through the liquid as well as the fluid flow field in the region directly beneath the sphere during approach to a solid plate. In the experiments we use silicone oil as the model fluid, which is well-described by the Carreau model. We use high-speed imaging and particle tracking to achieve flow visualisation within the film itself and derive the corresponding velocity fields. We show that the radial velocity either diverges as the gap between the sphere and the wall diminishes (Z tip → 0) or that it reaches a maximum value and then decays rapidly to zero as the sphere comes to rest at a non-zero distance (Z tip = Z min ) away from the wall. The horizontal shear rate is calculated and is responsible for significant viscosity reduction during the approach of the sphere. Our model of this flow, based on lubrication theory, is solved numerically and compared to experimental trials. We show that our model is able to correctly describe the physical features of the flow observed in the experiments.
Gazzillo, Domenico; Giacometti, Achille; Fantoni, Riccardo; Sollich, Peter
2006-11-01
We investigate the dependence of the stickiness parameters tij=1/(12tauij)--where the tauij are the conventional Baxter parameters--on the solute diameters sigmai and sigmaj in multicomponent sticky hard sphere (SHS) models for fluid mixtures of mesoscopic neutral particles. A variety of simple but realistic interaction potentials, utilized in the literature to model short-ranged attractions present in real solutions of colloids or reverse micelles, is reviewed. We consider: (i) van der Waals attractions, (ii) hard-sphere-depletion forces, (iii) polymer-coated colloids, and (iv) solvation effects (in particular hydrophobic bonding and attractions between reverse micelles of water-in-oil microemulsions). We map each of these potentials onto an equivalent SHS model by requiring the equality of the second virial coefficients. The main finding is that, for most of the potentials considered, the size-dependence of tij(T,sigmai,sigmaj) can be approximated by essentially the same expression, i.e., a simple polynomial in the variable sigmaisigmaj/sigmaij2, with coefficients depending on the temperature T, or--for depletion interactions--on the packing fraction eta0 of the depletant particles.
Communication: Dynamical density functional theory for dense suspensions of colloidal hard spheres.
Stopper, Daniel; Roth, Roland; Hansen-Goos, Hendrik
2015-11-14
We study structural relaxation of colloidal hard spheres undergoing Brownian motion using dynamical density functional theory. Contrary to the partial linearization route [D. Stopper et al., Phys. Rev. E 92, 022151 (2015)] which amounts to using different free energy functionals for the self and distinct part of the van Hove function G(r, t), we put forward a unified description employing a single functional for both components. To this end, interactions within the self part are removed via the zero-dimensional limit of the functional with a quenched self component. In addition, we make use of a theoretical result for the long-time mobility in hard-sphere suspensions, which we adapt to the inhomogeneous fluid. Our results for G(r, t) are in excellent agreement with numerical simulations even in the dense liquid phase. In particular, our theory accurately yields the crossover from free diffusion at short times to the slower long-time diffusion in a crowded environment.
Viehman, Douglas C; Schweizer, Kenneth S
2008-02-28
Naive mode coupling theory (NMCT) and the nonlinear stochastic Langevin equation theory of activated dynamics have been generalized to mixtures of spherical particles. Two types of ideal nonergodicity transitions are predicted corresponding to localization of both, or only one, species. The NMCT transition signals a dynamical crossover to activated barrier hopping dynamics. For binary mixtures of equal diameter hard and attractive spheres, a mixture composition sensitive "glass-melting" type of phenomenon is predicted at high total packing fractions and weak attractions. As the total packing fraction decreases, a transition to partial localization occurs corresponding to the coexistence of a tightly localized sticky species in a gel-like state with a fluid of hard spheres. Complex behavior of the localization lengths and shear moduli exist because of the competition between excluded volume caging forces and attraction-induced physical bond formation between sticky particles. Beyond the NMCT transition, a two-dimensional nonequilibrium free energy surface emerges, which quantifies cooperative activated motions. The barrier locations and heights are sensitive to the relative amplitude of the cooperative displacements of the different species.
Tunable long range forces mediated by self-propelled colloidal hard spheres
Ni, R.; Cohen Stuart, M.A.; Bolhuis, P.G.
2015-01-01
Using Brownian dynamics simulations, we systematically study the effective interaction between two parallel hard walls in a 2D suspension of self-propelled (active) colloidal hard spheres, and we find that the effective force between two hard walls can be tuned from a long range repulsion into a lon
Enhanced KR-Fundamental Measure Functional for Inhomogeneous Binary and Ternary Hard Sphere Mixtures
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi
2011-01-01
An enhanced KR-fundarnentai measure functional (FMF) is elaborated and employed to investigate binary and ternary hard sphere fluids near a planar hard wall or confined within two planar hard wails separated by certain interval.The present enhanced KR-FMF incorporates respectively, for aim of comparison, a recent 3rd-order expansion equation of state (EOS) and a Boublik's extension of Kolafa's EOS for HS mixtures.It is indicated that the two versions of the EOS lead to, in the framework of the enhanced KR-FMF, similar density profiles, but the 3rd-order EOS is more consistent with an exact scaled particle theory (SPT) relation than the BK EOS.Extensive comparison between the enhanced KR-FMF-3rd-order EOS predictions and corresponding density profiles produced in different periods indicates the excellent performance of the present enhanced KR-FMF-3rd-order EOS in comparison with other available density functional approximations (DFAs).There are two anomalous situations from whose density profiles all DFAs studied deviate significantly; however, subsequent new computer simulation results for state conditions similar to the two anomalous situations are in very excellent agreement with the present enhanced KR-FMF-3rd-order EOS.The present paper indicates that (i) the validity of the “naive” substitution elaborated in the present paper and peculiar to the original KR-FMF is still in operation even if inhomogeneous mixtures are being dealt with; (ii) the high accuracy and seff-consistency of the third order EOS seem to allow for application of the KR-FMF-third order EOS to more severe state conditions; and (iii) the “naive” substitution enables very easy the combination of the original KR-FMF with future's more accurate but potentially more complicated EOS of hard sphere mixtures.
Rescaled density expansions and demixing in hard-sphere binary mixtures.
López de Haro, M; Tejero, C F
2004-10-08
The demixing transition of a binary fluid mixture of additive hard spheres is analyzed for different size asymmetries by starting from the exact low-density expansion of the pressure. Already within the second virial approximation the fluid separates into two phases of different composition with a lower consolute critical point. By successively incorporating the third, fourth, and fifth virial coefficients, the critical consolute point moves to higher values of the pressure and to lower values of the partial number fraction of the large spheres. When the exact low-density expansion of the pressure is rescaled to higher densities as in the Percus-Yevick theory, by adding more exact virial coefficients a different qualitative movement of the critical consolute point in the phase diagram is found. It is argued that the Percus-Yevick factor appearing in many empirical equations of state for the mixture has a deep influence on the location of the critical consolute point, so that the resulting phase diagram for a prescribed equation has to be taken with caution.
The unsteady motion of a sphere in a viscoelastic fluid
DEFF Research Database (Denmark)
Becker, L.E.; McKinley, G. H.; Rasmussen, Henrik K.
1994-01-01
The motion of a sphere accelerating from rest along the center line of a cylindrical tube filled with a polyisobutylene (PIB) Boger fluid is examined both experimentally, using a digital imaging system, and numerically via a Lagrangian finite element method for single and multimode Oldroyd models...
Avvisati, Guido; Dasgupta, Tonnishtha; Dijkstra, Marjolein
2017-08-22
Colloidal photonic crystals display peculiar optical properties that make them particularly suitable for application in different fields. However, the low packing fraction of the targeted structures usually poses a real challenge in the fabrication stage. Here, we propose a route to colloidal photonic crystals via a binary mixture of hard tetramers and hard spheres. By combining theory and computer simulations, we calculate the phase diagram as well as the stacking diagram of the mixture and show that a colloidal analogue of the MgCu2 Laves phase-which can serve as a precursor of a photonic band-gap structure-is a thermodynamically stable phase in a large region of the phase diagram. Our findings show a relatively large coexistence region between the fluid and the Laves phase, which is potentially accessible by experiments. Furthermore, we determine the sedimentation behavior of the suggested mixture, by identifying several stacking sequences in the sediment. Our work uncovers a self-assembly path toward a photonic structure with a band gap in the visible region.
2017-01-01
Colloidal photonic crystals display peculiar optical properties that make them particularly suitable for application in different fields. However, the low packing fraction of the targeted structures usually poses a real challenge in the fabrication stage. Here, we propose a route to colloidal photonic crystals via a binary mixture of hard tetramers and hard spheres. By combining theory and computer simulations, we calculate the phase diagram as well as the stacking diagram of the mixture and show that a colloidal analogue of the MgCu2 Laves phase—which can serve as a precursor of a photonic band-gap structure—is a thermodynamically stable phase in a large region of the phase diagram. Our findings show a relatively large coexistence region between the fluid and the Laves phase, which is potentially accessible by experiments. Furthermore, we determine the sedimentation behavior of the suggested mixture, by identifying several stacking sequences in the sediment. Our work uncovers a self-assembly path toward a photonic structure with a band gap in the visible region. PMID:28787126
The early crystal nucleation process in hard spheres shows synchronised ordering and densification
Berryman, Joshua T.; Anwar, Muhammad; Dorosz, Sven; Schilling, Tanja
2016-12-01
We investigate the early part of the crystal nucleation process in the hard sphere fluid using data produced by computer simulation. We find that hexagonal order manifests continuously in the overcompressed liquid, beginning approximately one diffusion time before the appearance of the first "solid-like" particle of the nucleating cluster, and that a collective influx of particles towards the nucleation site occurs simultaneously to the ordering process: the density increases leading to nucleation are generated by the same individual particle displacements as the increases in order. We rule out the presence of qualitative differences in the early nucleation process between medium and low overcompressions and also provide evidence against any separation of translational and orientational order on the relevant lengthscales.
Three Semi-empirical Analytic Expressions for the Radial Distribution Function of Hard Spheres
Institute of Scientific and Technical Information of China (English)
SUN Jiu-Xun; CAI Ling-Cang; WU Qiang; JING Fu-Qian
2004-01-01
Three simple analytic expressions satisfying the limitation condition at low densities for the radial distribution function of hard spheres are developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan-Starling equation of state. The simplicity and precision for these expressions are superior to the well-known Percus-Yevick expression. The coefficients contained in these expressions have been determined by fitting the Monte Carlo data for the first coordination shell, and by fitting both the Monte Carlo data and the numerical results of PercusYevick expression for the second coordination shell. One of the expressions has been applied to develop an analytic equation of state for the square-well fluid, and the numerical results are in good agreement with the computer simulation data.
Experimental observation of structural crossover in binary mixtures of colloidal hard spheres.
Baumgartl, Jörg; Dullens, Roel P A; Dijkstra, Marjolein; Roth, Roland; Bechinger, Clemens
2007-05-11
Using confocal microscopy, we investigate the structure of binary mixtures of colloidal hard spheres with size ratio q=0.61. As a function of the packing fraction of the two particle species, we observe a marked change of the dominant wavelength in the pair-correlation function. This behavior is in excellent agreement with a recently predicted structural crossover in such mixtures. In addition, the repercussions of structural crossover on the real-space structure of a binary fluid are analyzed. We suggest a relation between crossover and the lateral extension of networks containing only equally-sized particles that are connected by nearest-neighbor bonds. This is supported by Monte Carlo simulations which are performed at different packing fractions and size ratios.
Apparent wall-slip of colloidal hard-sphere suspensions in microchannel flow
Ghosh, Somnath; van den Ende, Henricus T.M.; Mugele, Friedrich Gunther; Duits, Michael H.G.
2016-01-01
We investigated the dependence of the apparent slip length (β) on the particle concentration for suspensions of colloidal hard spheres flowing through microchannels with smooth walls. Hydrostatic pressure was used to pump monodisperse suspensions of 1 μm silica spheres in water–glycerol mixture thro
Direct simulation of diatomic gases using the generalized hard sphere model
Hash, D. B.; Hassan, H. A.
1993-01-01
The generalized hard sphere model which incorporates the effects of attraction and repulsion is used to predict flow measurements in tests involving extremely low freestream temperatures. For the two cases considered, a Mach 26 nitrogen shock and a Mach 20 nitrogen flow over a flat place, only rotational excitation is deemed important, and appropriate modifications for the Borgnakke-Larsen procedure are developed. In general, for the cases considered, the present model performed better than the variable hard sphere model.
Simulating asymmetric colloidal mixture with adhesive hard sphere model.
Jamnik, A
2008-06-21
Monte Carlo simulation and Percus-Yevick (PY) theory are used to investigate the structural properties of a two-component system of the Baxter adhesive fluids with the size asymmetry of the particles of both components mimicking an asymmetric binary colloidal mixture. The radial distribution functions for all possible species pairs, g(11)(r), g(22)(r), and g(12)(r), exhibit discontinuities at the interparticle distances corresponding to certain combinations of n and m values (n and m being integers) in the sum nsigma(1)+msigma(2) (sigma(1) and sigma(2) being the hard-core diameters of individual components) as a consequence of the impulse character of 1-1, 2-2, and 1-2 attractive interactions. In contrast to the PY theory, which predicts the delta function peaks in the shape of g(ij)(r) only at the distances which are the multiple of the molecular sizes corresponding to different linear structures of successively connected particles, the simulation results reveal additional peaks at intermediate distances originating from the formation of rigid clusters of various geometries.
Theoretical Investigation of Uniform and Non-uniform Penetrable Sphere Fluid
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi
2006-01-01
A bridge function approximation is proposed for a single-component fluid consisting of penetrable sphere interacting via a potential that remains finite and constant for center-center distance smaller than the particle diameter and is zero otherwise. The radial distribution function from the Ornstein-Zernike integral equation combined with the present bridge function approximation is in satisfactory agreement with the corresponding simulation data for all of the investigated state points. The presently calculated excess Helmholtz free energy respectively based on virial route and compressibility route is highly self-consistent, and is in very good agreement with simulational results for the case of low temperatures. The present bridge function approximation, combined with the bridge density functional approximation,can reproduce very accurately density profiles of the penetrable sphere fluid confined in a hard spherical cavity for all the cases where simulational results are available.
Bommineni, Praveen Kumar; Punnathanam, Sudeep N.
2017-08-01
Co-crystal formation from fluid-mixtures is quite common in a large number of systems. The simplest systems that show co-crystal (also called substitutionally ordered solids) formation are binary hard sphere mixtures. In this work, we study the nucleation of AB2 type solid compounds using Monte Carlo molecular simulations in binary hard sphere mixtures with the size ratio of 0.55. The conditions chosen for the study lie in the region where nucleation of an AB2 type solid competes with that of a pure A solid with a face-centered-cubic structure. The fluid phase composition is kept equal to that of the AB2 type solid. The nucleation free-energy barriers are computed using the seeding technique of Sanz et al. [J. Am. Chem. Soc. 135, 15008 (2013)]. Our simulation results show that the nucleation of the AB2 type solid is favored even under conditions where the pure A solid is more stable. This is primarily due to the similarity in the composition of the fluid phase and the AB2 type solid which in turn leads to much lower interfacial tension between the crystal nucleus and the fluid phase. This system is an example of how the fluid phase composition affects the structure of the nucleating solid phase during crystallization and has relevance to crystal polymorphism during crystallization processes.
Hard, charged spheres in spherical pores. Grand canonical ensemble Monte Carlo calculations
DEFF Research Database (Denmark)
Sloth, Peter; Sørensen, T. S.
1992-01-01
A model consisting of hard charged spheres inside hard spherical pores is investigated by grand canonical ensemble Monte Carlo calculations. It is found that the mean ionic density profiles in the pores are almost the same when the wall of the pore is moderately charged as when it is uncharged...
Solano-Altamirano, J M; Goldman, Saul
2015-12-01
We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another.
Statistical measure of complexity of hard-sphere gas: applications to nuclear matter
Moustakidis, Ch C; Nikolaidis, N S; Panos, C P
2010-01-01
We apply the statistical measure of complexity, introduced by L\\'{o}pez-Ruiz, Mancini and Calbet to a hard-sphere dilute Fermi gas whose particles interact via a repulsive hard-core potential. We employ the momentum distribution of this system to calculate the information entropy, the disequilibrium and the statistical complexity. We examine possible connections between the particle correlations and energy of the system with those information and complexity measures. The hard-sphere model serves as a test bed for concepts about complexity.
Malijevský, Alexandr; Jackson, George; Varga, Szabolcs
2008-10-14
The extension of Onsager's second-virial theory [L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949)] for the orientational ordering of hard rods to mixtures of nonspherical hard bodies with finite length-to-breadth ratios is examined using the decoupling approximations of Parsons [Phys. Rev. A 19, 1225 (1979)] and Lee [J. Chem. Phys. 86, 6567 (1987); 89, 7036 (1988)]. Invariably the extension of the Parsons-Lee (PL) theory to mixtures has in the past involved a van der Waals one-fluid treatment in which the properties of the mixture are approximated by those of a reference one-component hard-sphere fluid with an effective diameter which depends on the composition of the mixture and the molecular parameters of the various components; commonly this is achieved by equating the molecular volumes of the effective hard sphere and of the components in the mixture and is referred to as the PL theory of mixtures. It is well known that a one-fluid treatment is not the most appropriate for the description of the thermodynamic properties of isotropic fluids, and inadequacies are often rectified with a many-fluid (MF) theory. Here, we examine MF theories which are developed from the virial theorem and the virial expansion of the Helmholtz free energy of anisotropic fluid mixtures. The use of the decoupling approximation of the pair distribution function at the level of a multicomponent hard-sphere reference system leads to our MF Parsons (MFP) theory of anisotropic mixtures. Alternatively the mapping of the virial coefficients of the hard-body mixtures onto those of equivalent hard-sphere systems leads to our MF Lee (MFL) theory. The description of the isotropic-nematic phase behavior of binary mixtures of hard Gaussian overlap particles is used to assess the adequacy of the four different theories, namely, the original second-virial theory of Onsager, the usual PL one-fluid theory, and the MF theories based on the Lee (MFL) and Parsons (MFP) approaches. A comparison with the
Anisotropic fluid spheres of embedding class one using Karmarkar condition
Energy Technology Data Exchange (ETDEWEB)
Maurya, S.K. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Maharaj, S.D. [School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, Private Bag X54001, Durban (South Africa)
2017-05-15
We obtain a new anisotropic solution for spherically symmetric spacetimes by analyzing the Karmarkar embedding condition. For this purpose we construct a suitable form of one of the gravitational potentials to obtain a closed form solution. This form of the remaining gravitational potential allows us to solve the embedding equation and integrate the field equations. The resulting new anisotropic solution is well behaved, which can be utilized to construct realistic static fluid spheres. Also we estimated the masses and radii of fluid spheres for LMC X-4, EXO 1785-248, PSR J1903+327 and 4U 1820-30 by using observational data set values. The masses and radii obtained show that our anisotropic solution can represent fluid spheres to a very good degree of accuracy. The physical validity of the solution depends on the parameter values of a, b and c. The solution is well behaved for the wide range of parameters values 0.00393 ≤ a ≤ 0.0055, 0.0002 ≤ b ≤ 0.0025 and 0.0107 ≤ c ≤ 0.0155. The range of corresponding physical parameters for the different compact stars are 0.3266 ≤ v{sub r0} ≤ 0.3708, 0.1583 ≤ v{sub t0} ≤ 0.2558, 0.3256 ≤ z{sub s} ≤ 0.4450 and 4.3587 ≤ Γ{sub 0} ≤ 5.6462. (orig.)
Mimicking static anisotropic fluid spheres in general relativity
Boonserm, Petarpa; Ngampitipan, Tritos; Visser, Matt
2016-11-01
We argue that an arbitrary general relativistic static anisotropic fluid sphere, (static and spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully mimicked by suitable linear combinations of theoretically attractive and quite simple classical matter: a classical (charged) isotropic perfect fluid, a classical electromagnetic field and a classical (minimally coupled) scalar field. While the most general decomposition is not unique, a preferred minimal decomposition can be constructed that is unique. We show how the classical energy conditions for the anisotropic fluid sphere can be related to energy conditions for the isotropic perfect fluid, electromagnetic field, and scalar field components of the model. Furthermore, we show how this decomposition relates to the distribution of both electric charge density and scalar charge density throughout the model. The generalized TOV equation implies that the perfect fluid component in this model is automatically in internal equilibrium, with pressure forces, electric forces, and scalar forces balancing the gravitational pseudo-force. Consequently, we can build theoretically attractive matter models that can be used to mimic almost any static spherically symmetric spacetime.
Brouwers, H J H
2007-10-01
The geometrical stability of the three lattices of the cubic crystal system, viz. face-centered cubic (fcc), body-centered cubic (bcc), and simple cubic (sc), consisting of bimodal discrete hard spheres, and the transition to amorphous packing is studied. First, the random close packing (rcp) fraction of binary mixtures of amorphously packed spheres is recapitulated. Next, the packing of a binary mixture of hard spheres in randomly disordered cubic structures is analyzed, resulting in original analytical expressions for the unit cell volume and the packing fraction, and which are also valid for the other five crystal systems. The bimodal fcc lattice parameter appears to be in close agreement with empirical hard sphere data from literature, and this parameter could be used to distinguish the size mismatch effect from all other effects in distorted binary lattices of materials. Here, as a first model application, bimodal amorphous and crystalline fcc/bcc packing fractions are combined, yielding the optimum packing configuration, which depends on mixture composition and diameter ratio only. Maps of the closest packing mode are established and applied to colloidal mixtures of polydisperse spheres and to binary alloys of bcc, fcc, and hcp metals. The extensive comparison between the analytical expressions derived here and the published numerical and empirical data yields good agreement. Hence, it is seen that basic space-filling theories on "simple" noninteracting hard spheres are a valuable tool for the study of crystalline materials.
Brouwers, H. J. H.
2007-10-01
The geometrical stability of the three lattices of the cubic crystal system, viz. face-centered cubic (fcc), body-centered cubic (bcc), and simple cubic (sc), consisting of bimodal discrete hard spheres, and the transition to amorphous packing is studied. First, the random close packing (rcp) fraction of binary mixtures of amorphously packed spheres is recapitulated. Next, the packing of a binary mixture of hard spheres in randomly disordered cubic structures is analyzed, resulting in original analytical expressions for the unit cell volume and the packing fraction, and which are also valid for the other five crystal systems. The bimodal fcc lattice parameter appears to be in close agreement with empirical hard sphere data from literature, and this parameter could be used to distinguish the size mismatch effect from all other effects in distorted binary lattices of materials. Here, as a first model application, bimodal amorphous and crystalline fcc/bcc packing fractions are combined, yielding the optimum packing configuration, which depends on mixture composition and diameter ratio only. Maps of the closest packing mode are established and applied to colloidal mixtures of polydisperse spheres and to binary alloys of bcc, fcc, and hcp metals. The extensive comparison between the analytical expressions derived here and the published numerical and empirical data yields good agreement. Hence, it is seen that basic space-filling theories on “simple” noninteracting hard spheres are a valuable tool for the study of crystalline materials.
Shells of charge: a density functional theory for charged hard spheres.
Roth, Roland; Gillespie, Dirk
2016-06-22
A functional for the electrostatic excess free-energy for charged, hard sphere fluids is proposed. The functional is derived from two complementary, but equivalent, interpretations of the mean spherical approximation (MSA). The first combines fundamental measure theory (FMT) from hard-core interactions with the idea that MSA can be interpreted in terms of the interaction spherical shells of charge. This formulation gives the free-energy density as a function of weighted densities. When all the ions have the same size, the functional adopts an FMT-like form. The second in effect 'functionalizes' the derivation of MSA; that is, it generalizes the MSA as a functional-based version of MSA (fMSA). This formulation defines the free-energy density as a function of a position-dependent MSA screening parameter and the weighted densities of the FMT approach. This FMT/fMSA functional is shown to give accurate density profiles, as compared to Monte Carlo simulations, under a wide range of ion concentrations, size asymmetries, and valences.
Shells of charge: a density functional theory for charged hard spheres
Roth, Roland; Gillespie, Dirk
2016-06-01
A functional for the electrostatic excess free-energy for charged, hard sphere fluids is proposed. The functional is derived from two complementary, but equivalent, interpretations of the mean spherical approximation (MSA). The first combines fundamental measure theory (FMT) from hard-core interactions with the idea that MSA can be interpreted in terms of the interaction spherical shells of charge. This formulation gives the free-energy density as a function of weighted densities. When all the ions have the same size, the functional adopts an FMT-like form. The second in effect ‘functionalizes’ the derivation of MSA; that is, it generalizes the MSA as a functional-based version of MSA (fMSA). This formulation defines the free-energy density as a function of a position-dependent MSA screening parameter and the weighted densities of the FMT approach. This FMT/fMSA functional is shown to give accurate density profiles, as compared to Monte Carlo simulations, under a wide range of ion concentrations, size asymmetries, and valences.
Ashton, Douglas J; Wilding, Nigel B; Roth, Roland; Evans, Robert
2011-12-01
We report a detailed study, using state-of-the-art simulation and theoretical methods, of the effective (depletion) potential between a pair of big hard spheres immersed in a reservoir of much smaller hard spheres, the size disparity being measured by the ratio of diameters q ≡ σ(s)/σ(b). Small particles are treated grand canonically, their influence being parameterized in terms of their packing fraction in the reservoir η(s)(r). Two Monte Carlo simulation schemes--the geometrical cluster algorithm, and staged particle insertion--are deployed to obtain accurate depletion potentials for a number of combinations of q ≤ 0.1 and η(s)(r). After applying corrections for simulation finite-size effects, the depletion potentials are compared with the prediction of new density functional theory (DFT) calculations based on the insertion trick using the Rosenfeld functional and several subsequent modifications. While agreement between the DFT and simulation is generally good, significant discrepancies are evident at the largest reservoir packing fraction accessible to our simulation methods, namely, η(s)(r) = 0.35. These discrepancies are, however, small compared to those between simulation and the much poorer predictions of the Derjaguin approximation at this η(s)(r). The recently proposed morphometric approximation performs better than Derjaguin but is somewhat poorer than DFT for the size ratios and small-sphere packing fractions that we consider. The effective potentials from simulation, DFT, and the morphometric approximation were used to compute the second virial coefficient B(2) as a function of η(s)(r). Comparison of the results enables an assessment of the extent to which DFT can be expected to correctly predict the propensity toward fluid-fluid phase separation in additive binary hard-sphere mixtures with q ≤ 0.1. In all, the new simulation results provide a fully quantitative benchmark for assessing the relative accuracy of theoretical approaches for
Hard-sphere perturbation theory for a model of liquid Ga.
Tsai, K H; Wu, Ten-Ming
2008-07-14
Investigating thermodynamic properties of a model for liquid Ga, we have extended the application of the hard-sphere (HS) perturbation theory to an interatomic pair potential that possesses a soft repulsive core and a long-range oscillatory part. The model is interesting for displaying a discontinuous jump on the main-peak position of the radial distribution function at some critical density. At densities less than this critical value, the effective HS diameter of the model, estimated by the variational HS perturbation theory, has a substantial reduction with increasing density. Thus, the density dependence of the packing fraction of the HS reference fluid has an anomalous behavior, with a negative slope, within a density region below the critical density. By adding a correction term originally proposed by Mon to remedy the inherent deficiency of the HS perturbation theory, the extended Mansoori-Canfield/Rasaiah-Stell theory [J. Chem. Phys. 120, 4844 (2004)] very accurately predicts the Helmholtz free energy and entropy of the model, including an excess entropy anomaly. Almost occurring in the same density region, the excess entropy anomaly is found to be associated with the anomalous packing faction of the HS fluid.
Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers.
Sear, Richard P
2002-11-01
A simple analytic theory for mixtures of hard spheres and larger polymers with excluded volume interactions is developed. The mixture is shown to exhibit extensive immiscibility. For large polymers with strong excluded volume interactions, the density of monomers at the critical point for demixing decreases as one over the square root of the length of the polymer, while the density of spheres tends to a constant. This is very different from the behavior of mixtures of hard spheres and ideal polymers, these mixtures, although even less miscible than those with polymers with excluded volume interactions, have a much higher polymer density at the critical point of demixing. The theory applies to the complete range of mixtures of spheres with flexible polymers, from those with strong excluded volume interactions to ideal polymers.
Geometrical characteristics of the enlarged fused hard sphere models of simple molecules.
Boublík, Tomas
2005-10-20
The enlarged fused hard sphere model represents a compromise between fused hard sphere- and hard convex body models of repulsive interactions of nonspherical molecules. Geometric functionals of the enlarged fused hard sphere models, i.e., the hard body volume, surface area, and "mean radius" for 25 molecules of the linear and approximately planar shapes (cycloalkanes and aromatic compounds), neopentane and cyclohexane were determined from the bond lengths and bond angles and expressed in the dimensionless form. The hard sphere diameters, first approximated by the values found from the correlation of the second virial coefficients, were then adjusted to heats of vaporization of the studied compounds. Parameters of nonsphericity and molar volumes, evaluated from these characteristics, are compared with parameters of modern semiempirical equations of state (BACK, BACKONE, SAFT). The calculated geometric quantities for a series of compounds make it possible to improve methods of determining the characteristic parameters of the modern semiempirical equations of state, as well as those from the perturbation approaches.
Hansen-Goos, Hendrik; Roth, Roland
2006-04-21
We introduce an expansion of the equation of state for additive hard-sphere mixtures in powers of the total packing fraction with coefficients which depend on a set of weighted densities used in scaled particle theory and fundamental measure theory. We demand that the mixture equation of state recovers the quasiexact Carnahan-Starling [J. Chem. Phys. 51, 635 (1969)] result in the case of a one-component fluid and show from thermodynamic considerations and consistency with an exact scaled particle relation that the first and second orders of the expansion lead unambiguously to the Boublik-Mansoori-Carnahan-Starling-Leland [J. Chem. Phys. 53, 471 (1970); J. Chem. Phys. 54, 1523 (1971)] equation and the extended Carnahan-Starling equation introduced by Santos et al. [Mol. Phys. 96, 1 (1999)]. In the third order of the expansion, our approach allows us to define a new equation of state for hard-sphere mixtures which we find to be more accurate than the former equations when compared to available computer simulation data for binary and ternary mixtures. Using the new mixture equation of state, we calculate expressions for the surface tension and excess adsorption of the one-component fluid at a planar hard wall and compare its predictions to available simulation data.
Small-angle scattering from precipitates: Analysis by use of a polydisperse hard-sphere model
DEFF Research Database (Denmark)
Pedersen, J.S.
1993-01-01
A general polydisperse hard-sphere model for analyzing small-angle-scattering data from spherical precipitates in alloys is presented. In the model the size distribution is chosen as a Weibull density distribution and the hard-sphere interaction radius is taken as being proportional to the radius...... very good fits to the experimental data and the results are in agreement with a Li content of 25% in the precipitates. The concentration of Li in the matrix is also in good agreement with the phase diagram of Al-Li found in the literature. Results from the application of a monodisperse hard-sphere...... of the precipitates. The Weibull distribution is monomodal, and depending on the parameters describing the distribution, it can skew to either side. Small-angle x-ray- and neutron-scattering data, taken from the literature, from spherical delta' precipitates in Al-Li alloys have been analyzed with the model. It gives...
Franke, Markus; Golde, Sebastian; Schöpe, Hans Joachim
2014-08-07
We investigated the process of vitrification and crystallization in a model system of colloidal hard spheres. The kinetics of the solidification process was measured using time resolved static light scattering, while the time evolution of the dynamic properties was determined using time resolved dynamic light scattering. By performing further analysis we confirm that solidification of hard sphere colloids is mediated by precursors. Analyzing the dynamic properties we can show that the long time dynamics and thus the shear rigidity of the metastable melt is highly correlated with the number density of solid clusters (precursors) nucleated. In crystallization these objects convert into highly ordered crystals whereas in the case of vitrification this conversion is blocked and the system is (temporarily) locked in the metastable precursor state. From the early stages of solidification one cannot clearly conclude whether the melt will crystallize or vitrify. Furthermore our data suggests that colloidal hard sphere glasses can crystallize via homogeneous nucleation.
Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension
Urrutia, Ignacio; Szybisz, Leszek
2010-03-01
This work is devoted to the exact statistical mechanics treatment of simple inhomogeneous few-body systems. The system of two hard spheres (HSs) confined in a hard spherical pore is systematically analyzed in terms of its dimensionality D. The canonical partition function and the one- and two-body distribution functions are analytically evaluated and a scheme of iterative construction of the D +1 system properties is presented. We analyze in detail both the effect of high confinement, when particles become caged, and the low density limit. Other confinement situations are also studied analytically and several relations between the two HSs in a spherical pore, two sticked HSs in a spherical pore, and two HSs on a spherical surface partition functions are traced. These relations make meaningful the limiting caging and low density behavior. Turning to the system of two HSs in a spherical pore, we also analytically evaluate the pressure tensor. The thermodynamic properties of the system are discussed. To accomplish this statement we purposely focus in the overall characteristics of the inhomogeneous fluid system, instead of concentrate in the peculiarities of a few-body system. Hence, we analyze the equation of state, the pressure at the wall, and the fluid-substrate surface tension. The consequences of new results about the spherically confined system of two HSs in D dimension on the confined many HS system are investigated. New constant coefficients involved in the low density limit properties of the open and closed systems of many HS in a spherical pore are obtained for arbitrary D. The complementary system of many HS which surrounds a HS (a cavity inside of a bulk HS system) is also discussed.
Kernels of the linear Boltzmann equation for spherical particles and rough hard sphere particles.
Khurana, Saheba; Thachuk, Mark
2013-10-28
Kernels for the collision integral of the linear Boltzmann equation are presented for several cases. First, a rigorous and complete derivation of the velocity kernel for spherical particles is given, along with reductions to the smooth, rigid sphere case. This combines and extends various derivations for this kernel which have appeared previously in the literature. In addition, the analogous kernel is derived for the rough hard sphere model, for which a dependence upon both velocity and angular velocity is required. This model can account for exchange between translational and rotational degrees of freedom. Finally, an approximation to the exact rough hard sphere kernel is presented which averages over the rotational degrees of freedom in the system. This results in a kernel depending only upon velocities which retains a memory of the exchange with rotational states. This kernel tends towards the smooth hard sphere kernel in the limit when translational-rotational energy exchange is attenuated. Comparisons are made between the smooth and approximate rough hard sphere kernels, including their dependence upon velocity and their eigenvalues.
Stochastic interactions of two Brownian hard spheres in the presence of depletants
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Karzar-Jeddi, Mehdi; Fan, Tai-Hsi, E-mail: thfan@engr.uconn.edu [Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut 06269-3139 (United States); Tuinier, Remco [Van' t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Department of Chemistry, Utrecht University, Padualaan 8, 3584 CH, Utrecht (Netherlands); DSM ChemTech R and D, P.O. Box 18, 6160 MD Geleen (Netherlands); Taniguchi, Takashi [Graduate School of Engineering, Kyoto University Katsura Campus, Nishikyo-ku, Kyoto 615-8510 (Japan)
2014-06-07
A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions.
Statistical properties of two interacting soft spheres in a hard spherical pore
Kim, Soon-Chul
2015-06-01
The structure and thermodynamics of two soft spheres, whose interactions include the soft repulsion and attraction, confined in a hard spherical pore have been considered. The exact partition function, one-body density, and equation of state have been obtained using the Fourier transform method. The pore-size and potential dependence of the structural and thermodynamic properties have been investigated. The two penetrable square-well spheres shows a negative compressibility of the van der Waals type, which imitates the phase transition of many particle system. The van der Waals instability for two penetrable square-well spheres has been studied.
Equation of state of non-additive $d$-dimensional hard-sphere mixtures
Santos, A.; de Haro, M. Lopez; Yuste, S. B.
2004-01-01
An equation of state for a multicomponent mixture of non-additive hard spheres in $d$ dimensions is proposed. It yields a rather simple density dependence and constitutes a natural extension of the equation of state for additive hard spheres proposed by us [A. Santos, S. B. Yuste, and M. L\\'opez de Haro, Mol. Phys. 96, 1 (1999)]. The proposal relies on the known exact second and third virial coefficients and requires as input the compressibility factor of the one-component system. A compariso...
van der Waals-Tonks-type equations of state for hard-hypersphere fluids in four and five dimensions.
Wang, Xian-Zhi
2004-04-15
Recently, we developed accurate van der Waals-Tonks-type equations of state for hard-disk and hard-sphere fluids by using the known virial coefficients. In this paper, we derive the van der Waals-Tonks-type equations of state. We further apply these equations of state to hard-hypersphere fluids in four and five dimensions. In the low-density fluid regime, these equations of state are in good agreement with the simulation results and existing equations of state.
Towards an analytical theory for charged hard spheres
Blum, L.; D.V.P.Veloz
2007-01-01
Ion mixtures require an exclusion core to avoid collapse. The Debye Hueckel theory, where ions are point charges, is accurate only in the limit of infinite dilution. The MSA is the embedding of hard cores into DH, is valid for higher densities. In the MSA the properties of any ionic mixture can be represented by a single screening parameter $\\Gamma$. For equal ionic size restricted model is obtained from the Debye parameter $\\kappa$. This one parameter representation (BIMSA) is valid for comp...
Radial distribution function of penetrable sphere fluids to the second order in density.
Santos, Andrés; Malijevský, Alexandr
2007-02-01
The simplest bounded potential is that of penetrable spheres, which takes a positive finite value epsilon if the two spheres are overlapped, being zero otherwise. In this paper we derive the cavity function to second order in density and the fourth virial coefficient as functions of T* identical with k(B)T/epsilon (where k(B is the Boltzmann constant and T is the temperature) for penetrable sphere fluids. The expressions are exact, except for the function represented by an elementary diagram inside the core, which is approximated by a polynomial form in excellent agreement with accurate results obtained by Monte Carlo integration. Comparison with the hypernetted-chain (HNC) and Percus-Yevick (PY) theories shows that the latter is better than the former for T* hard sphere limit), the PY solution is not accurate inside the overlapping region, where no practical cancellation of the neglected diagrams takes place. The exact fourth virial coefficient is positive for T* compressibility route is the best one for T* or similar to 0.7.
Statistical Mechanics of Two Hard Spheres in a Spherical Pore, Exact Analytic Results in D Dimension
Urrutia, Ignacio; Szybisz, Leszek
2009-01-01
This work is devoted to the exact statistical mechanics treatment of simple inhomogeneous few-body systems. The system of two Hard Spheres (HS) confined in a hard spherical pore is systematically analyzed in terms of its dimensionality >. The canonical partition function, and the one- and two-body distribution functions are analytically evaluated and a scheme of iterative construction of the system properties is presented. We analyse in detail both the effect of high confinement, when particl...
Mixtures of Hard Ellipsoids and Spheres: Stability of the Nematic Phase
Alvarez, Carlos E.; Mazars, Martial
2014-01-01
The stability of liquid crystal phases in presence of small amount of non-mesogenic impurities is of general interest for a large spectrum of technological applications and in the theories of binary mixtures. Starting from the known phase diagram of the hard ellipsoids systems, we propose a simple model and method to explore the stability of the nematic phase in presence of small impurities represented by hard spheres. The study is performed in the isobaric ensemble with Monte Carlo simulations.
Excluded-volume effects in the diffusion of hard spheres
Bruna, Maria
2012-01-03
Excluded-volume effects can play an important role in determining transport properties in diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two or three dimensions is considered systematically using the method of matched asymptotic expansions. The result is a nonlinear diffusion equation for the one-particle distribution function, with excluded-volume effects enhancing the overall collective diffusion rate. An expression for the effective (collective) diffusion coefficient is obtained. Stochastic simulations of the full particle system are shown to compare well with the solution of this equation for two examples. © 2012 American Physical Society.
Fluid-fluid versus fluid-solid demixing in mixtures of parallel hard hypercubes
Lafuente, Luis; Martínez-Ratón, Yuri
2011-02-01
It is well known that increase of the spatial dimensionality enhances the fluid-fluid demixing of a binary mixture of hard hyperspheres, i.e. the demixing occurs for lower mixture size asymmetry as compared to the three-dimensional case. However, according to simulations, in the latter dimension the fluid-fluid demixing is metastable with respect to the fluid-solid transition. According to the results obtained from approximations to the equation of state of hard hyperspheres in higher dimensions, the fluid-fluid demixing might become stable for high enough dimension. However, this conclusion is rather speculative since none of these works have taken into account the stability of the crystalline phase (by a minimization of a given density functional, by spinodal calculations or by MC simulations). Of course, the lack of results is justified by the difficulty of performing density functional calculations or simulations in high dimensions and, in particular, for highly asymmetric binary mixtures. In the present work, we will take advantage of a well tested theoretical tool, namely the fundamental measure density functional theory for parallel hard hypercubes (in the continuum and in the hypercubic lattice). With this, we have calculated the fluid-fluid and fluid-solid spinodals for different spatial dimensions. We have obtained, no matter what the dimensionality, the mixture size asymmetry or the polydispersity (included as a bimodal distribution function centered around the asymmetric edge lengths), that the fluid-fluid critical point is always located above the fluid-solid spinodal. In conclusion, these results point to the existence of demixing between at least one solid phase rich in large particles and one fluid phase rich in small ones, preempting a fluid-fluid demixing, independently of the spatial dimension or the polydispersity.
Solid–liquid interfacial free energy of small colloidal hard-sphere crystals
Cacciuto, A.; Auer, S.; Frenkel, D.
2003-01-01
Using free-energy calculations on small crystalline clusters, we estimate the free-energy density γSL for the solid–liquid equimolar interface of a system of hard-sphere colloids. By studying the behavior of a crystallite at coexistence, we determine the dependence of γSL on the radius of curvature
Brouwers, H.J.H.
2008-01-01
In a previous paper analytical equations were derived for the packing fraction of crystalline structures consisting of bimodal randomly placed hard spheres H. J. H. Brouwers, Phys. Rev. E 76, 041304 2007. The bimodal packing fraction was derived for the three crystalline cubic systems: viz., face-ce
Brouwers, H.J.H.
2007-01-01
The geometrical stability of the three lattices of the cubic crystal system, viz. face-centered cubic (fcc), body-centered cubic (bcc), and simple cubic (sc), consisting of bimodal discrete hard spheres, and the transition to amorphous packing is studied. First, the random close packing (rcp) fracti
Hilhorst, J.; Wolters, J. R.; Petukhov, A.V.
2010-01-01
Hard sphere crystal growth is a delicate interplay between kinetics and thermodynamics, where the former is commonly thought to favour a random hexagonal close packed structure and the latter leads to a face centered cubic crystal. In this article, we discuss the influence of slanted stacking faults
Chaudhari, Mangesh I.; Holleran, Sinead A.; Ashbaugh, Henry S.; Pratt, Lawrence R.
2013-01-01
The osmotic second virial coefficients, B2, for atomic-sized hard spheres in water are attractive (B2 statistical mechanical theory. These results constitute an initial step toward detailed molecular theory of additional intermolecular interaction features, specifically, attractive interactions associated with hydrophobic solutes. PMID:24297918
Note: equation of state and the freezing point in the hard-sphere model.
Robles, Miguel; López de Haro, Mariano; Santos, Andrés
2014-04-07
The merits of different analytical equations of state for the hard-sphere system with respect to the recently computed high-accuracy value of the freezing-point packing fraction are assessed. It is found that the Carnahan-Starling-Kolafa and the branch-point approximant equations of state yield the best performance.
Vrij, A.
1982-01-01
The usefulness of the hard-sphere model in characterizing polydispersity in concentrated colloidal solutions is stressed. A recently derived equation for (∂ρi/∂μj)μ is used to give a simpler route for application to light scattering and sedimentation in multicomponent and polydisperse systems. Some
Ikuta, Daijo; Kono, Yoshio; Shen, Guoyin
2016-10-01
The structure of liquid aluminum is measured up to 6.9 GPa and 1773 K using a multi-angle energy-dispersive X-ray diffraction method in a Paris-Edinburgh press. The effect of pressure and temperature on the structure and density of liquid aluminum is analyzed by means of the hard sphere model. Peak positions in the structure factor of liquid aluminum show a nearly constant value with varying temperatures at ˜1-2 GPa and slightly change with varying pressures up to 6.9 GPa at 1173-1773 K. In contrast, the height of the first peak in the structure factor significantly changes with varying pressures and temperatures. Hard sphere model analysis shows that the structure of liquid aluminum in the pressure-temperature range of this study is controlled mostly by the packing fraction with only a minor change in hard sphere diameters. The obtained packing fractions and hard sphere diameters are used to calculate densities of liquid aluminum at high pressure-temperature conditions.
Monte Carlo simulations of in-plane stacking disorder in hard-sphere crystals
Miedema, P.S.; de Villeneuve, V.W.A.; Petukhov, A.V.
2008-01-01
On-lattice Monte Carlo simulations of colloidal random-stacking hard-sphere colloidal crystals are presented. The model yields close-packed crystals with random-stacking hexagonal structure. We find a significant amount of in-plane stacking disorder, which slowly anneals in the course of the simulat
Experimental Investigation of Fully Plastic Contact of a Sphere Against a Hard Flat
Jamari, J.; Schipper, D.J.
2006-01-01
In this paper we report the experimental investigation to evaluate the published models for the contact of a deformable sphere against a hard flat in the fully plastic contact regime. A new measurement method has been used to measure the contact area. The behavior of the mean contact pressure and th
Direct observation of dynamical heterogeneities in colloidal hard-sphere suspensions
Kegel, W.K.; Blaaderen, A. van
2000-01-01
The real-space dynamics in a model system of colloidal hard spheres was studied by means of time-resolved ßuorescence confocal scanning microscopy. Direct experimental evidence for the presence of dynamical heterogeneities in a dense liquid was obtained from an analysis of particle trajectories in t
Brouwers, Jos
2007-01-01
The geometrical stability of the three lattices of the cubic crystal system, viz. face-centered cubic (fcc), body-centered cubic (bcc), and simple cubic (sc), consisting of bimodal discrete hard spheres, and the transition to amorphous packing is studied. First, the random close packing (rcp)
Interpretation of the complex viscosity of dense hard-sphere dispersions
Mellema, J.; Werff, van der J.C.; Blom, C.; Kruif, de C.G.
1989-01-01
The complex viscosity of dense hard-sphere dispersions has been determined recently over a large frequency range. If conceived as a homogeneous system with continuously distributed elasticity and viscosity, the complex viscosity can be described theoretically with a constant relaxation strength and
Large difference in the elastic properties of fcc and hcp hard-sphere crystals
Pronk, S.; Frenkel, D.
2003-01-01
We report a numerical calculation of the elastic constants of the fcc and hcp crystal phases of monodisperse hard-sphere colloids. Surprisingly, some of these elastic constants are very different (up to 20%), even though the free-energy, pressure, and bulk compressibility of the two crystal structur
Ashton, D J; Sánchez-Gil, V; Wilding, N B
2013-10-14
We investigate Monte Carlo simulation strategies for determining the effective ("depletion") potential between a pair of hard spheres immersed in a dense sea of much smaller hard spheres. Two routes to the depletion potential are considered. The first is based on estimates of the insertion probability of one big sphere in the presence of the other; we describe and compare three such methods. The second route exploits collective (cluster) updating to sample the depletion potential as a function of the separation of the big particles; we describe two such methods. For both routes, we find that the sampling efficiency at high densities of small particles can be enhanced considerably by exploiting "geometrical shortcuts" that focus the computational effort on a subset of small particles. All the methods we describe are readily extendable to particles interacting via arbitrary potentials.
Kinetic Theory of a Confined Quasi-Two-Dimensional Gas of Hard Spheres
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J. Javier Brey
2017-02-01
Full Text Available The dynamics of a system of hard spheres enclosed between two parallel plates separated a distance smaller than two particle diameters is described at the level of kinetic theory. The interest focuses on the behavior of the quasi-two-dimensional fluid seen when looking at the system from above or below. In the first part, a collisional model for the effective two-dimensional dynamics is analyzed. Although it is able to describe quite well the homogeneous evolution observed in the experiments, it is shown that it fails to predict the existence of non-equilibrium phase transitions, and in particular, the bimodal regime exhibited by the real system. A critical revision analysis of the model is presented , and as a starting point to get a more accurate description, the Boltzmann equation for the quasi-two-dimensional gas has been derived. In the elastic case, the solutions of the equation verify an H-theorem implying a monotonic tendency to a non-uniform steady state. As an example of application of the kinetic equation, here the evolution equations for the vertical and horizontal temperatures of the system are derived in the homogeneous approximation, and the results compared with molecular dynamics simulation results.
Doubled heterogeneous crystal nucleation in sediments of hard sphere binary-mass mixtures.
Löwen, Hartmut; Allahyarov, Elshad
2011-10-07
Crystallization during the sedimentation process of a binary colloidal hard spheres mixture is explored by Brownian dynamics computer simulations. The two species are different in buoyant mass but have the same interaction diameter. Starting from a completely mixed system in a finite container, gravity is suddenly turned on, and the crystallization process in the sample is monitored. If the Peclet numbers of the two species are both not too large, crystalline layers are formed at the bottom of the cell. The composition of lighter particles in the sedimented crystal is non-monotonic in the altitude: it is first increasing, then decreasing, and then increasing again. If one Peclet number is large and the other is small, we observe the occurrence of a doubled heterogeneous crystal nucleation process. First, crystalline layers are formed at the bottom container wall which are separated from an amorphous sediment. At the amorphous-fluid interface, a secondary crystal nucleation of layers is identified. This doubled heterogeneous nucleation can be verified in real-space experiments on colloidal mixtures. © 2011 American Institute of Physics
Towards an analytical theory for charged hard spheres
Directory of Open Access Journals (Sweden)
L.Blum
2007-09-01
Full Text Available Ion mixtures require an exclusion core to avoid collapse. The Debye Hueckel (DH theory, where ions are point charges, is accurate only in the limit of infinite dilution. The mean spherical approximation (MSA is the embedding of hard cores into DH, and is valid for higher densities. The properties of any ionic mixture can be represented by the single screening parameter Γ which for the equal ionic size restricted model is obtained from the Debye parameter κ. This Γ representation, the binding mean spherical approximation (BIMSA, is also valid for complex/associating systems, such as the general n-polyelectrolytes. The BIMSA is the only theory that satisfies the infinite dilution limit of the DH theory for any chain length. Furthermore, the contact pair distribution function calculated from our theory agrees with the Monte Carlo of Bresmeea. (Phys. Rev. E, 1995, 51, 289.
Eldridge, M.D.; Madden, P.A.; Frenkel, D.
1993-01-01
The thermodynamic stability of the binary hard-sphere AB2 superlattice structure has been confirmed by means of computer simulations. This is consistent with the results of experimental studies of suspensions of hard-sphere colloidal particles. A fit of the Helmholtz free energy surface for the regi
Isotropic-nematic phase equilibria of hard-sphere chain fluids—Pure components and binary mixtures
Oyarzun, B.; Van Westen, T.; Vlugt, T.J.H.
2015-01-01
The isotropic-nematic phase equilibria of linear hard-sphere chains and binary mixtures of them are obtained from Monte Carlo simulations. In addition, the infinite dilution solubility of hard spheres in the coexisting isotropic and nematic phases is determined. Phase equilibria calculations are
Hard sphere-like glass transition in eye lens α-crystallin solutions.
Foffi, Giuseppe; Savin, Gabriela; Bucciarelli, Saskia; Dorsaz, Nicolas; Thurston, George M; Stradner, Anna; Schurtenberger, Peter
2014-11-25
We study the equilibrium liquid structure and dynamics of dilute and concentrated bovine eye lens α-crystallin solutions, using small-angle X-ray scattering, static and dynamic light scattering, viscometry, molecular dynamics simulations, and mode-coupling theory. We find that a polydisperse Percus-Yevick hard-sphere liquid-structure model accurately reproduces both static light scattering data and small-angle X-ray scattering liquid structure data from α-crystallin solutions over an extended range of protein concentrations up to 290 mg/mL or 49% vol fraction and up to ca. 330 mg/mL for static light scattering. The measured dynamic light scattering and viscosity properties are also consistent with those of hard-sphere colloids and show power laws characteristic of an approach toward a glass transition at α-crystallin volume fractions near 58%. Dynamic light scattering at a volume fraction beyond the glass transition indicates formation of an arrested state. We further perform event-driven molecular dynamics simulations of polydisperse hard-sphere systems and use mode-coupling theory to compare the measured dynamic power laws with those of hard-sphere models. The static and dynamic data, simulations, and analysis show that aqueous eye lens α-crystallin solutions exhibit a glass transition at high concentrations that is similar to those found in hard-sphere colloidal systems. The α-crystallin glass transition could have implications for the molecular basis of presbyopia and the kinetics of molecular change during cataractogenesis.
Density functional theory for colloidal mixtures of hard platelets, rods, and spheres.
Esztermann, Ansgar; Reich, Hendrik; Schmidt, Matthias
2006-01-01
A geometry-based density-functional theory is presented for mixtures of hard spheres, hard needles, and hard platelets; both the needles and platelets are taken to be of vanishing thickness. Geometrical weight functions that are characteristic for each species are given, and it is shown how convolutions of pairs of weight functions recover each Mayer bond of the ternary mixture and hence ensure the correct second virial expansion of the excess free-energy functional. The case of sphere-platelet overlap relies on the same approximation as does Rosenfeld's functional for strictly two-dimensional hard disks. We explicitly control contributions to the excess free energy that are of third order in density. Analytic expressions relevant for the application of the theory to states with planar translational and cylindrical rotational symmetry--e.g., to describe behavior at planar smooth walls--are given. For binary sphere-platelet mixtures, in the appropriate limit of small platelet densities, the theory differs from that used in a recent treatment [L. Harnau and S. Dietrich, Phys. Rev. E 71, 011504 (2004)]. As a test case of our approach we consider the isotropic-nematic bulk transition of pure hard platelets, which we find to be weakly first order, with values for the coexistence densities and the nematic order parameter that compare well with simulation results.
Lekkerkerker, H. N. W.; Oversteegen, S.M.
2004-01-01
Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc concentrations in systems now experimentally available. The gas–liquid equilibrium of the spheres becomes stable at comparable size ratios as with bimodal mixtures of spheres or mixtures of rods and ...
Energy Technology Data Exchange (ETDEWEB)
2017-02-24
The GIBS software program is a Grand Canonical Monte Carlo (GCMC) simulation program (written in C++) that can be used for 1) computing the excess chemical potential of ions and the mean activity coefficients of salts in homogeneous electrolyte solutions; and, 2) for computing the distribution of ions around fixed macromolecules such as, nucleic acids and proteins. The solvent can be represented as neutral hard spheres or as a dielectric continuum. The ions are represented as charged hard spheres that can interact via Coulomb, hard-sphere, or Lennard-Jones potentials. In addition to hard-sphere repulsions, the ions can also be made to interact with the solvent hard spheres via short-ranged attractive square-well potentials.
Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid
Institute of Scientific and Technical Information of China (English)
Zhou Shi-Qi
2008-01-01
In this work,a bridge density functional approximation(BDFA)(J.Chem.Phys.112,8079(2000))for a non-uniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa(HCRY)fluid.It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid.A new bridge functional approximation is proposed,which can accurately predict the radial distribution function of the bulk HCRY fluid.With the new bridge functional approximation and its associated bulk second order direct correlation function as input,the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields,and the theoretical predictions are in good agreement with the corresponding simulation data.The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase,and the adsorption properties of the HCRY fluid,which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail.
Virial series for fluids of hard hyperspheres in odd dimensions.
Rohrmann, René D; Robles, Miguel; López de Haro, Mariano; Santos, Andrés
2008-07-07
A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E 76, 051202 (2007)] to obtain the exact solution of the Percus-Yevick equation for a fluid of hard spheres in (odd) d dimensions is used to investigate the convergence properties of the resulting virial series. This is done both for the virial and compressibility routes, in which the virial coefficients B(j) are expressed in terms of the solution of a set of (d-1)/2 coupled algebraic equations which become nonlinear for d>/=5. Results have been derived up to d=13. A confirmation of the alternating character of the series for d>/=5, due to the existence of a branch point on the negative real axis, is found and the radius of convergence is explicitly determined for each dimension. The resulting scaled density per dimension 2eta(1/d), where eta is the packing fraction, is wholly consistent with the limiting value of 1 for d-->infinity. Finally, the values for B(j) predicted by the virial and compressibility routes in the Percus-Yevick approximation are compared with the known exact values [N. Clisby and B. M. McCoy, J. Stat. Phys. 122, 15 (2006)].
Largo, Julio; Wilding, Nigel B
2006-03-01
We report a Monte Carlo simulation study of the properties of highly asymmetric binary hard-sphere mixtures. This system is treated within an effective fluid approximation in which the large particles interact through a depletion potential [R. Roth, Phys. Rev. E 62 5360 (2000)] designed to capture the effects of a virtual sea of small particles. We generalize this depletion potential to include the effects of explicit size dispersity in the large particles and consider the case in which the particle diameters are distributed according to a Schulz form having a degree of polydispersity 14%. The resulting alteration (with respect to the monodisperse limit) of the metastable fluid-fluid critical point parameters is determined for two values of the ratio of the diameters of the small and large particles: q(triple bond)sigma(s)/(-)sigma(b)=0.1 and q=0.05. We find that the inclusion of polydispersity moves the critical point to lower reservoir volume fractions of the small particles and high volume fractions of the large ones. The estimated critical point parameters are found to be in good agreement with those predicted by a generalized corresponding states argument which provides a link to the known critical adhesion parameter of the adhesive hard-sphere model. Finite-size scaling estimates of the cluster percolation line in the one phase fluid region indicate that inclusion of polydispersity moves the critical point deeper into the percolating regime. This suggests that phase separation is more likely to be preempted by dynamical arrest in polydisperse systems.
Liouvillian integrability of gravitating static isothermal fluid spheres
Iacono, Roberto; Llibre, Jaume
2014-10-01
We examine the integrability properties of the Einstein field equations for static, spherically symmetric fluid spheres, complemented with an isothermal equation of state, ρ = np. In this case, Einstein's equations can be reduced to a nonlinear, autonomous second order ordinary differential equation (ODE) for m/R (m is the mass inside the radius R) that has been solved analytically only for n = -1 and n = -3, yielding the cosmological solutions by De Sitter and Einstein, respectively, and for n = -5, case for which the solution can be derived from the De Sitter's one using a symmetry of Einstein's equations. The solutions for these three cases are of Liouvillian type, since they can be expressed in terms of elementary functions. Here, we address the question of whether Liouvillian solutions can be obtained for other values of n. To do so, we transform the second order equation into an equivalent autonomous Lotka-Volterra quadratic polynomial differential system in {R}^2, and characterize the Liouvillian integrability of this system using Darboux theory. We find that the Lotka-Volterra system possesses Liouvillian first integrals for n = -1, -3, -5, which descend from the existence of invariant algebraic curves of degree one, and for n = -6, a new solvable case, associated to an invariant algebraic curve of higher degree (second). For any other value of n, eventual first integrals of the Lotka-Volterra system, and consequently of the second order ODE for the mass function must be non-Liouvillian. This makes the existence of other solutions of the isothermal fluid sphere problem with a Liouvillian metric quite unlikely.
Liouvillian integrability of gravitating static isothermal fluid spheres
Energy Technology Data Exchange (ETDEWEB)
Iacono, Roberto, E-mail: roberto.iacono@enea.it [ENEA-C. R. Casaccia, Via Anguillarese 301, 00123 Roma (Italy); Llibre, Jaume, E-mail: jllibre@mat.uab.cat [Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia (Spain)
2014-10-01
We examine the integrability properties of the Einstein field equations for static, spherically symmetric fluid spheres, complemented with an isothermal equation of state, ρ = np. In this case, Einstein's equations can be reduced to a nonlinear, autonomous second order ordinary differential equation (ODE) for m/R (m is the mass inside the radius R) that has been solved analytically only for n = -1 and n = -3, yielding the cosmological solutions by De Sitter and Einstein, respectively, and for n = -5, case for which the solution can be derived from the De Sitter's one using a symmetry of Einstein's equations. The solutions for these three cases are of Liouvillian type, since they can be expressed in terms of elementary functions. Here, we address the question of whether Liouvillian solutions can be obtained for other values of n. To do so, we transform the second order equation into an equivalent autonomous Lotka–Volterra quadratic polynomial differential system in R² and characterize the Liouvillian integrability of this system using Darboux theory. We find that the Lotka–Volterra system possesses Liouvillian first integrals for n = -1, -3, -5, which descend from the existence of invariant algebraic curves of degree one, and for n = -6, a new solvable case, associated to an invariant algebraic curve of higher degree (second). For any other value of n, eventual first integrals of the Lotka–Volterra system, and consequently of the second order ODE for the mass function must be non-Liouvillian. This makes the existence of other solutions of the isothermal fluid sphere problem with a Liouvillian metric quite unlikely.
Chung, S.; Malherbe, J. G.; Amokrane, S.
2015-11-01
We study by Monte Carlo simulation the model of a binary mixture of neutral and dipolar hard spheres confined between two widely separated planar walls and subjected to a uniform external field. The goal is to investigate the structural response and the phase transitions of a fluid of hard-sphere-like colloids dispersed in a low-permittivity solvent under the combined effect of geometrical confinement and applied field. In a wide slab, the direction of the field, either normal or perpendicular to the walls, remains one of the most important factors that govern the response of the mixture: in normal field, a wide variety of structural effects are evidenced, including partial wetting or drying of the wall; in parallel field, phase separation is favoured with a specific population of the region close to the wall and a clear separation of the two species. These results suggest possible means to modulate the response of the confined fluid for specific needs.
Itami, Toshio; Mizuno, Akitoshi; Masaki, Tadahiko; 伊丹 俊夫; 水野 章敏; 正木 匡彦
2001-01-01
In the hard sphere model, the hard sphere diameter is the only and important parameter. The empirical relation, the Protopapas et al.'s relation, was employed for the temperature dependence of hard sphere diameter, which is indispensable to reproduce the temperature dependence of physical quantities. In this study, the detailed comparison was performed between the Protopapas et al.'s equation and the temperature dependence of hard sphere diameter determined by the refined theories of liquids....
Mendoza, Carlos I; Santamaría-Holek, I
2009-01-28
We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as the integration variable implicitly considers interactions between the spheres of the same recursive stage. The final expression for the viscosity scales with this effective volume fraction, which allows constructing a master curve that contains all the experimental situations considered. The agreement of our expression for the viscosity with experiments at low- and high-shear rates and in the high-frequency limit is remarkable for all volume fractions.
Cuetos, Alejandro; Martínez-Haya, Bruno; Lago, Santiago; Rull, Luis F
2007-06-01
Parsons-Lee and Onsager theories are formulated for the isotropic-nematic transition in a binary mixture of hard rods and hard spheres. Results for the phase coexistence and for the equation of state in both phases for mixtures with different relative sizes and composition are presented. The two theories explain correctly the general behavior observed in experiments and computer simulations for these fluids. In particular, the theory accounts for the destabilization of the nematic phase when spherical or globular macromolecules are added to a system of rodlike colloids, and the entrance of the system into a demixed regime at high volume fractions of the spherical particles. Upon demixing a nematic state rich in rods coexists in equilibrium with an isotropic state much more diluted in the rodlike component. Onsager theory fails on quantitative grounds for aspect ratios of the rodlike molecules smaller than 100, and in the cases where the molar fractions of spheres becomes close to unity. On the contrary, the Parsons-Lee approximation remains accurate down to aspect ratios as small as 5. The spinodal analysis indicates that the isotropic-isotropic and nematic-nematic coexistences become feasible for sufficiently large spheres and long rods, respectively. The latter type of coexistence interferes partially with the isotropic-nematic coexistence regime of interest to the present work. Overall, the study serves to rationalize and control key aspects of the behavior of these binary nematogenic colloidal systems, which can be tuned with an appropriate choice of the relative size and molar fractions of the particles.
Thorneywork, Alice L; Roth, Roland; Aarts, Dirk G A L; Dullens, Roel P A
2014-04-28
Two-dimensional hard disks are a fundamentally important many-body model system in classical statistical mechanics. Despite their significance, a comprehensive experimental data set for two-dimensional single component and binary hard disks is lacking. Here, we present a direct comparison between the full set of radial distribution functions and the contact values of a two-dimensional binary colloidal hard sphere model system and those calculated using fundamental measure theory. We find excellent quantitative agreement between our experimental data and theoretical predictions for both single component and binary hard disk systems. Our results provide a unique and fully quantitative mapping between experiments and theory, which is crucial in establishing the fundamental link between structure and dynamics in simple liquids and glass forming systems.
Study of the Motion of a Vertically Falling Sphere in a Viscous Fluid
Soares, A. A.; Caramelo, L.; Andrade, M. A. P. M.
2012-01-01
This paper aims at contributing to a better understanding of the motion of spherical particles in viscous fluids. The classical problem of spheres falling through viscous fluids for small Reynolds numbers was solved taking into account the effects of added mass. The analytical solution for the motion of a falling sphere, from the beginning to the…
Institute of Scientific and Technical Information of China (English)
AN Xi-Zhong
2007-01-01
The crystallization, corresponding to the fcc structure (with packing density p ≈ 0.74), of smooth equal hard spheres under batch-wised feeding and three-dimensional interval vibration is numerically obtained by using the discrete element method. The numerical experiment shows that the ordered packing can be realized by proper control of the dynamic parameters such as batch of each feeding § and vibration amplitude A. The radial distribution function and force network are used to characterize the ordered structure. The defect formed during vibrated packing is characterized as well The results in our work fill the gap of getting packing density between random close packing and fcc packing in phase diagram which provides an effective way of theoretically investigating the complex process and mechanism of hard sphere crystallization and its dynamics.
Equation of state of nonadditive d-dimensional hard-sphere mixtures.
Santos, A; López de Haro, M; Yuste, S B
2005-01-08
An equation of state for a multicomponent mixture of nonadditive hard spheres in d dimensions is proposed. It yields a rather simple density dependence and constitutes a natural extension of the equation of state for additive hard spheres proposed by us [A. Santos, S. B. Yuste, and M. Lopez de Haro, Mol. Phys. 96, 1 (1999)]. The proposal relies on the known exact second and third virial coefficients and requires as input the compressibility factor of the one-component system. A comparison is carried out both with another recent theoretical proposal based on a similar philosophy and with the available exact results and simulation data in d=1, 2, and 3. Good general agreement with the reported values of the virial coefficients and of the compressibility factor of binary mixtures is observed, especially for high asymmetries and/or positive nonadditivities. 2005 American Institute of Physics.
Physical viability of fluid spheres satisfying the Karmarkar condition
Singha, Ksh Newton; Govenderc, M
2016-01-01
We obtain a new solution of the TOV-equation for an anisotropic fluid distribution by imposing the Karmarkar condition. In order to close the system of equations we postulate an interesting form for the grr gravitational potential which allows us to solve for gtt metric component via the Karmarkar condition. We demonstrate that the new interior solution has well-behaved physical attributes and can be utilized to model relativistic static fluid spheres. By using observational data sets for the radii and mass-to-radius relations for compact stars such as 4U 1538-52, LMC X-4 and PSR J1614- 2230 we show that our solution describes these objects to a very good degree of accuracy. The physical plausibility of the solution depends on a parameter $c$ for a particular star. For 4U 1538-52 the solution behaves well for $0.1574 \\le c \\le 0.46$ which corresponds to $1 \\ge v^2_{r0} \\ge 0:13$, $0.91 \\ge v^2_{t0}\\ge 0.04$ and $17.8 \\ge \\Gamma_0 \\ge 3.8$. For LMC X-4 the solution behaves well for $0.1235 \\le c \\le 0.35$ whic...
Magnetic separation of micro-spheres from viscous biological fluids.
Chen, Haitao; Kaminski, Michael D; Caviness, Patricia L; Liu, Xianqiao; Dhar, Promila; Torno, Michael; Rosengart, Axel J
2007-02-21
A magnetically based detoxification system is being developed as a therapeutic tool for selective and rapid removal of biohazards, i.e. chemicals and radioactive substances, from human blood. One of the key components of this system is a portable magnetic separator capable of separating polymer-based magnetic nano/micro-spheres from arterial blood flow in an ex vivo unit. The magnetic separator consists of an array of alternating and parallel capillary tubing and magnetizable wires, which is exposed to an applied magnetic field created by two parallel permanent magnets such that the magnetic field is perpendicular to both the wires and the fluid flow. In this paper, the performance of this separator was evaluated via preliminary in vitro flow experiments using a separator unit consisting of single capillary glass tubing and two metal wires. Pure water, ethylene glycol-water solution (v:v=39:61 and v:v=49:51) and human whole blood were used as the fluids. The results showed that when the viscosity increased from 1.0 cp to 3.0 cp, the capture efficiency (CE) decreased from 90% to 56%. However, it is still feasible to obtain >90% CE in blood flow if the separator design is optimized to create higher magnetic gradients and magnetic fields in the separation area.
Tracking three-phase coexistences in binary mixtures of hard plates and spheres
Aliabadi, Roohollah; Moradi, Mahmood; Varga, Szabolcs
2016-02-01
The stability of demixing phase transition in binary mixtures of hard plates (with thickness L and diameter D) and hard spheres (with diameter σ) is studied by means of Parsons-Lee theory. The isotropic-isotropic demixing, which is found in mixtures of large spheres and small plates, is very likely to be pre-empted by crystallization. In contrast, the nematic-nematic demixing, which is obtained in mixtures of large plates and small spheres, can be stabilized at low diameter ratios (σ/D) and aspect ratios (L/D). At intermediate values of σ/D, where the sizes of the components are similar, neither the isotropic-isotropic nor the nematic-nematic demixing can be stabilized, but a very strong fractionation takes place between a plate rich nematic and a sphere rich isotropic phases. Our results show that the excluded volume interactions are capable alone to explain the experimental observation of the nematic-nematic demixing, but they fail in the description of isotropic-isotropic one [M. Chen et al., Soft Matter 11, 5775 (2015)].
Analytic methods for the Percus-Yevick hard sphere correlation functions
Directory of Open Access Journals (Sweden)
D. Henderson
2009-01-01
Full Text Available The Percus-Yevick theory for hard spheres provides simple accurate expressions for the correlation functions that have proven exceptionally useful. A summary of the author's lecture notes concerning three methods of obtaining these functions are presented. These notes are original only in part. However, they contain some helpful steps and simplifications. The purpose of this paper is to make these notes more widely available.
Thermodynamic scaling law for the diffusion coefficient in hard-sphere system
Bomont, Jean-Marc; Bretonnet, Jean-Louis
2015-02-01
Two scaling laws are investigated, which are devoted to link the diffusion coefficient to the thermodynamic properties for the athermal hard-sphere system, over the wide range of packing fraction covering the stable and metastable regimes. It is found that the most relevant control parameter is not the excess entropy, but the compressibility factor, i.e. the logarithm derivative of the excess entropy with respect to the packing fraction.
A two-stage approach to relaxation in billiard systems of locally confined hard spheres.
Gaspard, Pierre; Gilbert, Thomas
2012-06-01
We consider the three-dimensional dynamics of systems of many interacting hard spheres, each individually confined to a dispersive environment, and show that the macroscopic limit of such systems is characterized by a coefficient of heat conduction whose value reduces to a dimensional formula in the limit of vanishingly small rate of interaction. It is argued that this limit arises from an effective loss of memory. Similarities with the diffusion of a tagged particle in binary mixtures are emphasized.
Duignan, Timothy T.; Baer, Marcel D.; Schenter, Gregory K.; Mundy, Chistopher J.
2017-10-01
Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. Here, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecular dynamics simulation and isolate the effects of charge and cavitation, comparing to the Born (linear response) model. We show that using uncorrected Ewald summation leads to unphysical values for the single ion solvation free energy and that charging free energies for cations are approximately linear as a function of charge but that there is a small non-linearity for small anions. The charge hydration asymmetry for hard spheres, determined with quantum mechanics, is much larger than for the analogous real ions. This suggests that real ions, particularly anions, are significantly more complex than simple charged hard spheres, a commonly employed representation.
Flow of power-law fluids in fixed beds of cylinders or spheres
Singh, John P.
2012-10-29
An ensemble average of the equations of motion for a Newtonian fluid over particle configurations in a dilute fixed bed of spheres or cylinders yields Brinkman\\'s equations of motion, where the disturbance velocity produced by a test particle is influenced by the Newtonian fluid stress and a body force representing the linear drag on the surrounding particles. We consider a similar analysis for a power-law fluid where the stress τ is related to the rate of strain e by τ = 2m en-1e, where m and n are constants. In this case, the ensemble-averaged momentum equation includes a body force resulting from the nonlinear drag exerted on the surrounding particles, a power-law stress associated with the disturbance velocity of the test particle, and a stress term that is linear with respect to the test particle\\'s disturbance velocity. The latter term results from the interaction of the test particle\\'s velocity disturbance with the random straining motions produced by the neighbouring particles and is important only in shear-thickening fluids where the velocity disturbances of the particles are long-ranged. The solutions to these equations using scaling analyses for dilute beds and numerical simulations using the finite element method are presented. We show that the drag force acting on a particle in a fixed bed can be written as a function of a particle-concentration-dependent length scale at which the fluid velocity disturbance produced by a particle is modified by hydrodynamic interactions with its neighbours. This is also true of the drag on a particle in a periodic array where the length scale is the lattice spacing. The effects of particle interactions on the drag in dilute arrays (periodic or random) of cylinders and spheres in shear-thickening fluids is dramatic, where it arrests the algebraic growth of the disturbance velocity with radial position when n≥ 1 for cylinders and n≥ 2 for spheres. For concentrated random arrays of particles, we adopt an
DEFF Research Database (Denmark)
Valiente, Manuel
2012-01-01
We prove the equivalence between the hard-sphere Bose gas and a system with momentum-dependent zero-range interactions in one spatial dimension, which we call extended hard-sphere Bose gas. The two-body interaction in the latter model has the advantage of being a regular pseudopotential. The most......, identified with the hard-sphere diameter only when it is positive. We are then able to obtain, directly in the thermodynamic limit, the ground-state energy of the strongly repulsive Lieb-Liniger gas and, more importantly, the energy of the lowest-lying super Tonks-Girardeau gas state with finite, strongly...... attractive interactions, in perturbation theory from the novel extended hard-sphere Bose gas....
Hopkins, Paul; Fortini, Andrea; Archer, Andrew J; Schmidt, Matthias
2010-12-14
We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self " component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.
Directory of Open Access Journals (Sweden)
Lin Wang
2016-01-01
Full Text Available Quantitative characterization on the topological and metrical properties of radical subunits (polyhedra for two new ternary hard sphere crystals was studied. These two ideal crystalline structures are numerically constructed by filling small and medium spheres into interstices (corresponding to regular tetrahedral and octahedral pores of perfect face centered cubic (FCC and hexagonal close packed (HCP crystals formed by the packing of large spheres. Topological properties such as face number, edge number, vertex number of each radical polyhedron (RP, edge number of each RP face and metrical properties such as volume, surface area, total perimeter and pore volume of each RP, area and perimeter of each RP face were analyzed and compared. The results show that even though the overall packing densities for FCC and HCP ternary crystals are the same, different characteristics of radical polyhedra for corresponding spheres in these two crystals can be identified. That is, in the former structure RPs are more symmetric than those in the latter; the orientations of corresponding RP in the latter are twice as many as that in the former. Moreover, RP topological and metrical properties in the HCP ternary crystal are much more complicated than those in the FCC ternary crystal. These differences imply the structure and property differences of these two ternary crystals. Analyses of RPs provide intensive understanding of pores in the structure.
Wang, Lin; An, Xizhong; Wang, Defeng; Qian, Quan
2016-01-01
Quantitative characterization on the topological and metrical properties of radical subunits (polyhedra) for two new ternary hard sphere crystals was studied. These two ideal crystalline structures are numerically constructed by filling small and medium spheres into interstices (corresponding to regular tetrahedral and octahedral pores) of perfect face centered cubic (FCC) and hexagonal close packed (HCP) crystals formed by the packing of large spheres. Topological properties such as face number, edge number, vertex number of each radical polyhedron (RP), edge number of each RP face and metrical properties such as volume, surface area, total perimeter and pore volume of each RP, area and perimeter of each RP face were analyzed and compared. The results show that even though the overall packing densities for FCC and HCP ternary crystals are the same, different characteristics of radical polyhedra for corresponding spheres in these two crystals can be identified. That is, in the former structure RPs are more symmetric than those in the latter; the orientations of corresponding RP in the latter are twice as many as that in the former. Moreover, RP topological and metrical properties in the HCP ternary crystal are much more complicated than those in the FCC ternary crystal. These differences imply the structure and property differences of these two ternary crystals. Analyses of RPs provide intensive understanding of pores in the structure.
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Caillol, Jean-Michel, E-mail: Jean-Michel.Caillol@th.u-psud.fr [University of Paris-Sud, CNRS, LPT, UMR 8627, Orsay F-91405 (France)
2015-04-21
We present two methods for solving the electrostatics of point charges and multipoles on the surface of a sphere, i.e., in the space S{sub 2}, with applications to numerical simulations of two-dimensional (2D) polar fluids. In the first approach, point charges are associated with uniform neutralizing backgrounds to form neutral pseudo-charges, while in the second, one instead considers bi-charges, i.e., dumbells of antipodal point charges of opposite signs. We establish the expressions of the electric potentials of pseudo- and bi-charges as isotropic solutions of the Laplace-Beltrami equation in S{sub 2}. A multipolar expansion of pseudo- and bi-charge potentials leads to the electric potentials of mono- and bi-multipoles, respectively. These potentials constitute non-isotropic solutions of the Laplace-Beltrami equation, the general solution of which in spherical coordinates is recast under a new appealing form. We then focus on the case of mono- and bi-dipoles and build the theory of dielectric media in S{sub 2}. We notably obtain the expression of the static dielectric constant of a uniform isotropic polar fluid living in S{sub 2} in terms of the polarization fluctuations of subdomains of S{sub 2}. We also derive the long range behavior of the equilibrium pair correlation function under the assumption that it is governed by macroscopic electrostatics. These theoretical developments find their application in Monte Carlo simulations of the 2D fluid of dipolar hard spheres. Some preliminary numerical experiments are discussed with a special emphasis on finite size effects, a careful study of the thermodynamic limit, and a check of the theoretical predictions for the asymptotic behavior of the pair correlation function.
Granular mixtures modeled as elastic hard spheres subject to a drag force.
Vega Reyes, Francisco; Garzó, Vicente; Santos, Andrés
2007-06-01
Granular gaseous mixtures under rapid flow conditions are usually modeled as a multicomponent system of smooth inelastic hard disks (two dimensions) or spheres (three dimensions) with constant coefficients of normal restitution alpha{ij}. In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard disks or spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. For each collision term ij, the model has two parameters: a dimensionless factor beta{ij} modifying the collision rate of the elastic hard spheres, and the drag coefficient zeta{ij}. Both parameters are determined by requiring that the model reproduces the collisional transfers of momentum and energy of the true inelastic Boltzmann operator, yielding beta{ij}=(1+alpha{ij})2 and zeta{ij} proportional, variant1-alpha{ij}/{2}, where the proportionality constant is a function of the partial densities, velocities, and temperatures of species i and j. The Navier-Stokes transport coefficients for a binary mixture are obtained from the model by application of the Chapman-Enskog method. The three coefficients associated with the mass flux are the same as those obtained from the inelastic Boltzmann equation, while the remaining four transport coefficients show a general good agreement, especially in the case of the thermal conductivity. The discrepancies between both descriptions are seen to be similar to those found for monocomponent gases. Finally, the approximate decomposition of the inelastic Boltzmann collision operator is exploited to construct a model kinetic equation for granular mixtures as a direct extension of a known kinetic model for elastic collisions.
Brouwers, H J H
2008-07-01
In a previous paper analytical equations were derived for the packing fraction of crystalline structures consisting of bimodal randomly placed hard spheres [H. J. H. Brouwers, Phys. Rev. E 76, 041304 (2007)]. The bimodal packing fraction was derived for the three crystalline cubic systems: viz., face-centered cubic, body-centered cubic, and simple cubic. These three equations appeared also to be applicable to all 14 Bravais lattices. Here it is demonstrated, accounting for the number of distorted bonds in the building blocks and using graph theory, that one general packing equation can be derived, valid again for all lattices. This expression is validated and applied to the process of amorphization.
Event-chain Monte Carlo algorithms for hard-sphere systems.
Bernard, Etienne P; Krauth, Werner; Wilson, David B
2009-11-01
In this paper we present the event-chain algorithms, which are fast Markov-chain Monte Carlo methods for hard spheres and related systems. In a single move of these rejection-free methods, an arbitrarily long chain of particles is displaced, and long-range coherent motion can be induced. Numerical simulations show that event-chain algorithms clearly outperform the conventional Metropolis method. Irreversible versions of the algorithms, which violate detailed balance, improve the speed of the method even further. We also compare our method with a recent implementations of the molecular-dynamics algorithm.
Monte Carlo simulations of in-plane stacking disorder in hard-sphere crystals.
Miedema, P S; de Villeneuve, V W A; Petukhov, A V
2008-01-01
On-lattice Monte Carlo simulations of colloidal random-stacking hard-sphere colloidal crystals are presented. The model yields close-packed crystals with random-stacking hexagonal structure. We find a significant amount of in-plane stacking disorder, which slowly anneals in the course of the simulation. The in-plane stacking disorder leads to lateral broadening of the stacking-disorder-induced Bragg rods. It is found that not only the scattering intensity, but also the width is modulated along the Bragg rods.
Ising low-temperature polynomials and hard-sphere gases on cubic lattices of general dimension
Butera, P
2015-01-01
We derive and analyze the low-activity and low-density expansions of the pressure for the model of a hard-sphere gas on cubic lattices of general dimension $d$, through the 13th order. These calculations are based on our recent extension to dimension d of the low-temperature expansions for the specific free-energy of the spin-1/2 Ising models subject to a uniform magnetic field on the (hyper-)simple-cubic lattices. Estimates of the model parameters are given also for some other lattices
Phase behavior of polyampholytes from charged hard-sphere chain model.
Jiang, Jianwen; Feng, Jian; Liu, Honglai; Hu, Ying
2006-04-14
A molecular thermodynamic theory is developed for polyampholytes from the coarse-grained charged hard-sphere chain model. The phase behavior of polyampholytes with variations in sequence and chain length is satisfactorily predicted by the theory, consistent with simulation results and experimental observations. At a fixed chain length, the phase envelope expands as the sequence of charge distribution becomes less random. With increasing chain length, the phase envelope expands for diblock and random polyampholytes, but shrinks for zwitterionic polyampholytes. The predicted critical temperature, density, and pressure exhibit scaling relations with chain length for all the three (diblock, random, and zwitterionic) polyampholytes.
Equivalence of glass transition and colloidal glass transition in the hard-sphere limit.
Xu, Ning; Haxton, Thomas K; Liu, Andrea J; Nagel, Sidney R
2009-12-11
We show that the slowing of the dynamics in simulations of several model glass-forming liquids is equivalent to the hard-sphere glass transition in the low-pressure limit. In this limit, we find universal behavior of the relaxation time by collapsing molecular-dynamics data for all systems studied onto a single curve as a function of T/p, the ratio of the temperature to the pressure. At higher pressures, there are deviations from this universal behavior that depend on the interparticle potential, implying that additional physical processes must enter into the dynamics of glass formation.
Structure of Some 4f Rare Earth Liquid Metals - A Charged Hard Sphere Approach
Institute of Scientific and Technical Information of China (English)
P.B. Thakor; P.N. Gajjar; A.R. Jani
2006-01-01
A well-established pseodopotential is used to study the structure of some 4f rare earth liquid metals (Ce,Pr, Eu, Gd, Tb, and Yb). The structure factor S(q), pair distribution function g(r), interatomic distance r1, and coordination number n1 are calculated using Charged Hard Sphere (CHS) reference system. To introduce the exchange and correlation effects, the local field correction due to Sarkar et al. (S) is applied. The present investigation is successful in generating the structural information of Ce, Pr, Eu, Gd, Tb, and Yb 4f rare earth liquid metals.
Scattering for mixtures of hard spheres: comparison of total scattering intensities with model.
Anderson, B J; Gopalakrishnan, V; Ramakrishnan, S; Zukoski, C F
2006-03-01
The angular dependence of the intensity of x-rays scattered from binary and ternary hard sphere mixtures is investigated and compared to the predictions of two scattering models. Mixture ratio and total volume fraction dependent effects are investigated for size ratios equal to 0.51 and 0.22. Comparisons of model predictions with experimental results indicate the significant impact of the role of particle size distributions in interpreting the angular dependence of the scattering at wave vectors probing density fluctuations intermediate between the sizes of the particles in the mixture.
Lekkerkerker, H.N.W.; Oversteegen, S.M.
2004-01-01
Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc co
Lekkerkerker, H.N.W.; Oversteegen, S.M.
2004-01-01
Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc
Hard, soft, and sticky spheres for dynamical studies of disordered colloidal packings
Gratale, Matthew Daniel
This thesis describes experiments which explore the role of interparticle interactions as a means to alter, and control, the properties of dense colloidal packings. The first set of experiments studied phonon modes in two-dimensional colloidal crystals composed of soft microgel particles with hard polystyrene particle dopants distributed randomly on the triangular lattice. By mixing hard and soft spheres we obtain close-packed lattices of spheres with random bond strength disorder, textit{i.e.,} the effective springs coupling nearest-neighbors are either very stiff, very soft, or of intermediate stiffness. Video microscopy, particle tracking, and covariance matrix techniques are employed to derive the phonon modes of the corresponding ``shadow'' crystals, thereby enabling us to study how bond strength disorder affects vibrational properties. Hard and soft particles participate equally in low frequency phonon modes, and the samples exhibit Debye-like density of states behavior characteristic of crystals at low frequency. For mid- and high-frequency phonons, the relative participation of hard versus soft particles in each mode is found to vary systematically with dopant concentration. The second set of experiments investigated depletion interaction potentials between micron-size colloidal particles induced by nanometer-scale micelles composed of the surfactant hexaethylene glycol monododecyl ether (C12E6). The strength and range of the depletion interaction is revealed to arise from variations in shape anisotropy of the rod-like surfactant micelles. This shape anisotropy increases with increasing sample temperature. By fitting the colloidal interaction potentials to theoretical models, we extract the rod-like micelle length and shape anisotropy as a function of temperature. This work introduces micelle shape anisotropy as a means to control interparticle interactions in colloidal suspensions, and shows how interparticle depletion potentials of micron-scale objects
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi
2005-01-01
The accuracy of hard core attractive Yukawa (HCAY) potential and adhesive hard sphere (AH) potential in representing the structure factor of short range square well potential and Asakura and Oosawa (AO) depletion potential is examined by comparing theoretical predictions with the existing simulation data and the present numerical results from the non-linear optimized random phase approximation closure for Ornstein-Zernike equation. For the case of square-well (SW) potential, it is shown that the structure factor of HCAY potential based on a recently proposed semi-analytical expression for the radial distribution function can describe the structure factor of SW potential with reduced well width λ≤ 2 only if the reduced contact potential βesw ≤ 0.25, while the analytical expression for the structure factor of AH potential under Percus-Yevick (PY) approximation completely fails for the case of λ＞ 1.2. For the case of AO depletion potential, the domain of validity of both HCAY potential and AH potential is complementary. With the above analysis and considering the solid-liquid transition of the AH potential with an adhesive parameter τ below 1.31 cannot be predicted by modified weighted density approximation, the role played by the HCAY potential about the mapping manipulation should not be ignored.
带电硬哑铃流体的分子热力学%Molecular Thermodynamics of Charged Hard-Dumbbell Fluids
Institute of Scientific and Technical Information of China (English)
秦原; 刘洪来; 胡英
2001-01-01
Chemical potentials of charged hard-dumbbell fluids are obtained by Monte Carlo simulations using Widom's test-particle method, corresponding compressibility factors are achieved by integration of chemical potentials at different densities. A molecular thermodynamic model is also developed for these charged hard-dumbbell fluids where the residual Helmholtz function is composed of two terms: a reference term responsible for the charged hard spheres and a bonding contribution measuring the sticky interactions between positive and negative hard ions.Model predictions are in good agreement with simulation results.``
Alavi, Farzad; Feyzi, Farzaneh
2013-01-14
Radial and triplet correlation functions of the reference hard sphere system are determined at several solid densities by canonical Monte Carlo (MC) simulations. These customized data are used to extend the second order thermodynamic perturbation theory (TPT) to the solid phase of flexible hard chain systems. In order to test the accuracy of the TPT equation of state (EOS) for hard chains, MC simulations are carried out for systems of chain length 4 to 15. Several simulations are performed in the isobaric-isothermal ensemble to obtain the high-density EOS of hard chains in the fluid and solid phases. To determine solid-fluid equilibrium (SFE), Helmholtz free energies of solid crystals at a reference density are determined in a series of canonical MC simulations. As the chain length increases, asymptotic behaviors are observed in the coexistence pressure and densities of fluid and solid phases. It is found that the accuracy of TPT for EOS and SFE in systems of hard chains greatly improves by extending it to second order.
System of elastic hard spheres which mimics the transport properties of a granular gas.
Santos, Andrés; Astillero, Antonio
2005-09-01
The prototype model of a fluidized granular system is a gas of inelastic hard spheres (IHS) with a constant coefficient of normal restitution alpha. Using a kinetic theory description we investigate the two basic ingredients that a model of elastic hard spheres (EHS) must have in order to mimic the most relevant transport properties of the underlying IHS gas. First, the EHS gas is assumed to be subject to the action of an effective drag force with a friction constant equal to half the cooling rate of the IHS gas, the latter being evaluated in the local equilibrium approximation for simplicity. Second, the collision rate of the EHS gas is reduced by a factor (1/2)(1+alpha), relative to that of the IHS gas. Comparison between the respective Navier-Stokes transport coefficients shows that the EHS model reproduces almost perfectly the self-diffusion coefficient and reasonably well the two transport coefficients defining the heat flux, the shear viscosity being reproduced within a deviation less than 14% (for alpha > or = 0.5). Moreover, the EHS model is seen to agree with the fundamental collision integrals of inelastic mixtures and dense gases. The approximate equivalence between IHS and EHS is used to propose kinetic models for inelastic collisions as simple extensions of known kinetic models for elastic collisions.
Fundamental measure density functional theory study of hard spheres solid-liquid interface
Warshavsky, Vadim
2005-03-01
Interfacial free energy is an important characteristic of solid-liquid interface as it is one of the crucial parameters in many formula of interface thermodynamics such the nucleation theory. Previously different aspects of crystal-melt interfaces were intensively studied with simulations [1,2,3], but theoretical studies with Density Functional Theories (DFT) are inconclusive [4,5]. In this report the structure of hard spheres fcc crystal-melt interfaces and the anisotropy of the interfacial free energies are studied using the Rosenfeld's Fundamental Measure DFT as such a functional leads to reliable coexistence results not only for the hard sphere system but also for the Lennard-Jones systems [6]. The parameters of interfacial density profile were calculated by a proper minimization procedure. For the equilibrium density profile the interfacial free energies were compared with simulation results. 1. R.L.Davidchak and B.B.Laird, Phys.Rev.Lett., 85, 4751(2000). 2. J.J. Hoyt, M. Asta and A. Karma, Phys.Rev.Lett., 86, 5530 (2001). 3. J.R.Morris and X.Song, J.Chem.Phys., 119, 3920 (2003). 4. W.A.Curtin, Phys.Rev.B, 39, 6775(1989). 5. R.Ohnesorge, H.Lowen, and H.Wagner, Phys.Rev.E, 50, 4801 (1994). 6. V.Warshavsky and X.Song, Phys.Rev.E, 69, 061113 (2004).
Physics of Hard Sphere Experiment: Scattering, Rheology and Microscopy Study of Colloidal Particles
Cheng, Z.-D.; Zhu, J.; Phan, S.-E.; Russel, W. B.; Chaikin, P. M.; Meyer, W. V.
2002-01-01
The Physics of Hard Sphere Experiment has two incarnations: the first as a scattering and rheology experiment on STS-83 and STS-94 and the second as a microscopy experiment to be performed in the future on LMM on the space station. Here we describe some of the quantitative and qualitative results from previous flights on the dynamics of crystallization in microgravity and especially the observed interaction of growing crystallites in the coexistance regime. To clarify rheological measurements we also present ground based experiments on the low shear rate viscosity and diffusion coefficient of several hard sphere experiments at high volume fraction. We also show how these experiments will be performed with confocal microscopy and laser tweezers in our lab and as preparation for the phAse II experiments on LMM. One of the main aims of the microscopy study will be the control of colloidal samples using an array of applied fields with an eye toward colloidal architectures. Temperature gradients, electric field gradients, laser tweezers and a variety of switchable imposed surface patterns are used toward this control.
Sedov, I A; Magsumov, T I
2015-07-16
Thermodynamic solvation properties of mixtures of water with tetrahydrofuran at 298 K are studied. The Gibbs free energies and enthalpies of solvation of n-octane and toluene are determined experimentally. For molecular dynamics simulations of the binary solvent, we have modified a TraPPE-UA model for tetrahydrofuran and combined it with the SPC/E potential for water. The excess thermodynamic functions of neon, xenon, and hard spheres with two different radii are calculated using the particle insertion method. Simulated and real systems share the same characteristic trends for the thermodynamic functions. A maximum is present on dependencies of the enthalpy of solvation from the composition of solvent at 70-90 mol % water, making it higher than in both of the cosolvents. It is caused by a high enthalpy of cavity formation in the mixtures rich with water due to solvent reorganization around the cavity, which is shown by calculation of the enthalpy of solvation of hard spheres. Addition of relatively small amounts of tetrahydrofuran to water effectively suppresses the hydrophobic effect, leading to a quick increase of both the entropy and enthalpy of cavity formation and solvation of low polar molecules.
Short-time diffusion in concentrated bidisperse hard-sphere suspensions.
Wang, Mu; Heinen, Marco; Brady, John F
2015-02-14
Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method [Physica A 120, 388-410 (1983); 126, 349-370 (1984)]. Two species of hard spheres are suspended in an overdamped viscous solvent that mediates the salient hydrodynamic interactions among all particles. In a comprehensive parameter scan that covers various packing fractions and suspension compositions, we employ numerically accurate SD simulations to compute the initial diffusive relaxation of density modulations at the Brownian time scale, quantified by the partial hydrodynamic functions. A revised version of Beenakker and Mazur's δγ-scheme for monodisperse suspensions is found to exhibit surprisingly good accuracy, when simple rescaling laws are invoked in its application to mixtures. The so-modified δγ scheme predicts hydrodynamic functions in very good agreement with our SD simulation results, for all densities from the very dilute limit up to packing fractions as high as 40%.
Transport coefficients for relativistic gas mixtures of hard-sphere particles
Kremer, Gilberto M.; Moratto, Valdemar
2017-04-01
In the present work, we calculate the transport coefficients for a relativistic binary mixture of diluted gases of hard-sphere particles. The gas mixture under consideration is studied within the relativistic Boltzmann equation in the presence of a gravitational field described by the isotropic Schwarzschild metric. We obtain the linear constitutive equations for the thermodynamic fluxes. The driving forces for the fluxes of particles and heat will appear with terms proportional to the gradient of gravitational potential. We discuss the consequences of the gravitational dependence on the driving forces. We obtain general integral expressions for the transport coefficients and evaluate them by assuming a hard-sphere interaction amongst the particles when they collide and not very disparate masses and diameters of the particles of each species. The obtained results are expressed in terms of their temperature dependence through the relativistic parameter which gives the ratio of the rest energy of the particles and the thermal energy of the gas mixture. Plots are given to analyze the behavior of the transport coefficients with respect to the temperature when small variations in masses and diameters of the particles of the species are present. We also analyze for each coefficient the corresponding limits to a single gas so the non-relativistic and ultra-relativistic limiting cases are recovered as well. Furthermore, we show that the transport coefficients have a dependence on the gravitational field.
Solubilities of Solutes in Ionic Liquids from a SimplePerturbed-Hard-Sphere Theory
Energy Technology Data Exchange (ETDEWEB)
Qin, Yuan; Prausnitz, John M.
2005-09-20
In recent years, several publications have provided solubilities of ordinary gases and liquids in ionic liquids. This work reports an initial attempt to correlate the experimental data using a perturbed-hard-sphere theory; the perturbation is based on well-known molecular physics when the solution is considered as a dielectric continuum. For this correlation, the most important input parameters are hard-sphere diameters of the solute and of the cation and anion that constitute the ionic liquid. In addition, the correlation uses the solvent density and the solute's polarizability and dipole and quadrupole moments, if any. Dispersion-energy parameters are obtained from global correlation of solubility data. Results are given for twenty solutes in several ionic liquids at normal temperatures; in addition, some results are given for gases in two molten salts at very high temperatures. Because the theory used here is much simplified, and because experimental uncertainties (especially for gaseous solutes) are often large, the accuracy of the correlation presented here is not high; in general, predicted solubilities (Henry's constants) agree with experiment to within roughly {+-} 70%. As more reliable experimental data become available, modifications in the characterizing parameters are likely to improve accuracy. Nevertheless, even in its present form, the correlation may be useful for solvent screening in engineering design.
Sun, Jiu-Xun; Jin, Ke; Cai, Ling-Cang; Wu, Qiang
2014-08-01
The equation of state (EOS) for hard-sphere fluid derived from compressibility routes of Percus-Yevick theory (PYC) is extended. The two parameters are determined by fitting well-known virial coefficients of pure fluid. The extended cubic EOS can be directly extended to multi-component mixtures, merely demanding the EOS of mixtures also is cubic and combining two physical conditions for the radial distribution functions at contact (RDFC) of mixtures. The calculated virial coefficients of pure fluid and predicted compressibility factors and RDFC for both pure fluid and mixtures are excellent as compared with the simulation data. The values of RDFC for mixtures with extremely large size ratio 10 are far better than the BGHLL expressions in literature.
Felderhof, B U
2016-01-01
Swimming at small Reynolds number of a linear assembly of identical spheres immersed in a viscous fluid is studied on the basis of a set of equations of motion for the individual spheres. The motion of the spheres is caused by actuating forces and forces derived from a direct interaction potential, as well as hydrodynamic forces exerted by the fluid as frictional and added mass hydrodynamic interactions. The swimming velocity is deduced from the momentum balance equation for the assembly of spheres, and the mean power required during a period is calculated from an instantaneous power equation. Expressions are derived for the mean swimming velocity and the mean power, valid to second order in the amplitude of displacements from the relative equilibrium positions. Hence these quantities can be evaluated in terms of prescribed periodic displacements. Explicit calculations are performed for a linear chain of three identical spheres.
Statistical Mechanics Approach for Uniform and Non-uniform Fluid with Hard Core and Interaction Tail
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi; CHEN Hong; LING Si-Li; XIANG Xian-Wei; ZHANG Xiao-Qi
2003-01-01
One recently proposed self-consistent hard sphere bridge functional was combined with an exponential function exp(-cr) and a re-normalized indirect correlation function to construct the bridge function for fluid with hard core and interaction tail. In the present approach, the adjustable parameter α was determined by the thermodynamic consistency realized on the compressibility modulus, the re-normalization of the indirect correlation function was realized by a modified Mayer function with the interaction potential replaced by the perturbative part of the interaction potential. As an example, the present bridge function was combined with the Ornstein-Zernike (OZ) equation to predict structure and thermodynamics properties in very good agreement with the simulation data available for Lennard-Jones (L J). Based on the universality principle of the free energy density functional and the test particle trick, the numerical solution of the OZ equation was employed to construct the first order direct correlation function of the non-uniform fluid as a functional of the density distribution by means of the indirect correlation function. In the framework of the density functional theory, the numerically obtained functional predicted the density distribution of LJ fluid confined in two planar hard walls that is in good agreement with the simulation data.
Lukšič, Miha; Hribar-Lee, Barbara; Vlachy, Vojko; Pizio, O
2012-12-28
The canonical Monte Carlo computer simulations and integral equation theory were applied to examine the structural and thermodynamic properties of a mixture of ions and a core-softened fluid molecules. The positive and negative ions forming a +1:-1 salt were modeled as charged hard spheres, immersed in the dielectric medium. It was shown previously that the core-softened fluid under study is characterized by a set of structural, thermodynamic, and dynamic anomalies. The principal objective of this work was to elucidate how the presence of ions alters this behavior. The structural properties of the mixtures are discussed in terms of the pair distribution functions; in addition, the pair contribution to the excess entropy was calculated. Thermodynamic properties are investigated by using the dependencies of energy and compressibility factor on density, composition of the mixture, and reduced temperature. The heat capacity was also evaluated. Our principal findings concern the description of structural anomalies in the mixture, the dependence of the temperature of maximum density on the ionic concentration, and establishing the regions delimiting the structural and thermodynamic anomalies of the model mixture.
Rovibrationally Inelastic Atom-Molecule Collision Cross Sections from a Hard Sphere Model
Lashner, Jacob; Stewart, Brian
2016-05-01
Hard-shell models have long been used to elucidate the principal features of molecular energy transfer and exchange reaction in the A + BC system. Nevertheless, no three-dimensional hard-shell calculation of inelastic collision cross sections has been reported. This work aims to fill that void. A particular motivation comes from our experimental results, which show the importance of equatorial impacts in the vibrational excitation process. Working with the simple hard-sphere model, we incorporated secondary impacts, defined as those in which A strikes C after striking B. Such collisions are important in systems such as Li2 - X, in which vibrational energy transfer occurs principally through side impacts. We discuss the complexity this adds to the model and present fully three-dimensional cross sections for rovibrational excitation of an initially stationary molecule in the homonuclear A + B2 system, examining the cross section as a function of the masses and radii of the atoms. We show how the features in the cross section evolve as these parameters are varied and calculate the contribution of secondary (near-equatorial) impacts to the dynamics. We compare with recent measurements in our laboratory and with the results of quasiclassical trajectories.
Communication: Fundamental measure theory for hard disks: fluid and solid.
Roth, Roland; Mecke, Klaus; Oettel, Martin
2012-02-28
Two-dimensional hard-particle systems are rather easy to simulate but surprisingly difficult to treat by theory. Despite their importance from both theoretical and experimental points of view, theoretical approaches are usually qualitative or at best semi-quantitative. Here, we present a density functional theory based on the ideas of fundamental measure theory for two-dimensional hard-disk mixtures, which allows for the first time an accurate description of the structure of the dense fluid and the equation of state for the solid phase within the framework of density functional theory. The properties of the solid phase are obtained by freely minimizing the functional.
Indian Academy of Sciences (India)
Vimla Vyas
2008-04-01
Speeds of sound and densities of three ternary liquid systems namely, toluene + -heptane + -hexane (I), cyclohexane + -heptane + -hexane (II) and -hexane + - heptane + -decane (III) have been measured as a function of the composition at 298.15 K at atmospheric pressure. The experimental isothermal compressibility has been evaluated from measured values of speeds of sound and density. The isothermal compressibility of these mixtures has also been computed theoretically using different models for hard sphere equations of state and Flory's statistical theory. Computed values of isothermal compressibility have been compared with experimental findings. A satisfactory agreement has been observed. The superiority of Flory's statistical theory has been established quite reasonably over hard sphere models.
Thermal properties of an impurity immersed in a granular gas of rough hard spheres
Directory of Open Access Journals (Sweden)
Vega Reyes Francisco
2017-01-01
Full Text Available We study in this work the dynamics of a granular impurity immersed in a low-density granular gas of identical particles. For description of the kinetics of the granular gas and the impurity particles we use the rough hard sphere collisional model. We take into account the effects of non-conservation of energy upon particle collision. We find an (approximate analytical solution of the pertinent kinetic equations for the single-particle velocity distribution functions that reproduces reasonably well the properties of translational/rotational energy non-equipartition. We assess the accuracy of the theoretical solution by comparing with computer simulations. For this, we use two independent computer data sets, from molecular dynamics (MD and from Direct Simulation Monte Carlo method (DSMC. Both approach well, with different degrees, the kinetic theory within a reasonable range of parameter values.
Thermal properties of an impurity immersed in a granular gas of rough hard spheres
Vega Reyes, Francisco; Lasanta, Antonio; Santos, Andrés; Garzó, Vicente
2017-06-01
We study in this work the dynamics of a granular impurity immersed in a low-density granular gas of identical particles. For description of the kinetics of the granular gas and the impurity particles we use the rough hard sphere collisional model. We take into account the effects of non-conservation of energy upon particle collision. We find an (approximate) analytical solution of the pertinent kinetic equations for the single-particle velocity distribution functions that reproduces reasonably well the properties of translational/rotational energy non-equipartition. We assess the accuracy of the theoretical solution by comparing with computer simulations. For this, we use two independent computer data sets, from molecular dynamics (MD) and from Direct Simulation Monte Carlo method (DSMC). Both approach well, with different degrees, the kinetic theory within a reasonable range of parameter values.
Polydisperse hard spheres: crystallization kinetics in small systems and role of local structure
Campo, Matteo; Speck, Thomas
2016-08-01
We study numerically the crystallization of a hard-sphere mixture with 8% polydispersity. Although often used as a model glass former, for small system sizes we observe crystallization in molecular dynamics simulations. This opens the possibility to study the competition between crystallization and structural relaxation of the melt, which typically is out of reach due to the disparate timescales. We quantify the dependence of relaxation and crystallization times on density and system size. For one density and system size we perform a detailed committor analysis to investigate the suitability of local structures as order parameters to describe the crystallization process. We find that local structures are strongly correlated with generic bond order and add little information to the reaction coordinate.
Correlation between dynamical and structural heterogeneities in colloidal hard-sphere suspensions
Golde, Sebastian; Palberg, Thomas; Schöpe, Hans Joachim
2016-07-01
Dynamical and structural heterogeneities have long been thought to play a key role in a unified picture of solidification in view of the two competitive processes of crystallization and vitrification. Here, we study these heterogeneities by means of a combination of dynamic and static light-scattering techniques applied to the simplest model system exhibiting crystallization and vitrification: the colloidal hard-sphere system. Our method enables us to quantify and correlate the temporal evolution of the amount of ordered clusters (precursors) and the amount of slow particles. Our analysis shows that their temporal evolutions are closely related and that there is an intimate link between structural and dynamic heterogeneities, crystal nucleation and the non-crystallization transition.
The relationship between efficient packing and glass-forming ability in hard-sphere systems
Zhang, Kai
2014-03-01
When supercooled liquids are rapidly quenched at rates R exceeding a critical value Rc, they avoid crystallization and form amorphous solids, such as bulk metallic glasses (BMGs). However, engineering applications of BMGs are often limited by the high cost of the constituent elements and their small casting thickness. Thus, we seek to design particular alloys with controllable stoichiometry and maximal critical cooling rate Rc. We perform numerical simulations to compress binary hard-sphere mixtures into glasses as a function of the particle size ratio and stoichiometry. We measure the packing fraction and local structural order for each glass to determine the critical compression rate. We find that large packing fraction differences between the crystalline and amorphous states implies poor glass forming ability, whereas small packing fraction differences yield better glass-formers. In addition, we show that an abundance of icosahedral order in amorphous packings enhances the glass forming ability of the mixtures. NSF MRSEC DMR-1119826, DMR-1006537, CBET-0968013.
Electro-Optomechanical Transduction & Quantum Hard-Sphere Model for Dissipative Rydberg-EIT Media
DEFF Research Database (Denmark)
Zeuthen, Emil
transduction functionality into the well-established framework of electrical engineering, thereby facilitating its implementation in potential applications such as nuclear magnetic resonance imaging and radio astronomy. We consider such optomechanical sensing of weak electrical signals and discuss how...... the equivalent circuit formalism can be used to optimize the electrical circuit design. We also discuss the parameter requirements for transducing microwave photons in the quantum regime. Part II: Effective photon-photon interactions can be engineered by combining long-range Rydberg interactions between atoms....... We introduce a new approach to analyzing this challenging many-body problem in the limit of large optical depth per blockade radius. The idea is to separate the single-polariton EIT physics from the Rydberg-Rydberg interactions in a serialized manner while using a hard-sphere model for the latter...
Equation of state for classical hard-particlelike fluids
Edgal, U. F.; Boukahil, A.; Huber, D. L.
1995-09-01
We extend earlier studies of the equation of state of classical hard-particle fluids to potentials where there is an attractive tail in addition to a repulsive hard core. Like the earlier work, the approach is based on the arbitrary point, nearest-neighbor probability density function. In the high temperature (hard-particle) limit, a parametrization of the integrated distribution is introduced. By matching the parameters against the coefficients in a seven-term virial expansion, we obtain an equation of state that is in excellent agreement with the results from Monte Carlo, molecular dynamics calculations in both two and three dimensions. The theory is extended to finite temperatures by treating deviations from the hard-particle limit as small corrections that can be evaluated using hard-particle distribution functions. A comparison is made with the results from a five-term finite temperature virial expansion for a three-dimensional hard-particle system with a square well attractive potential.
Random-close packing limits for monodisperse and polydisperse hard spheres.
Baranau, Vasili; Tallarek, Ulrich
2014-06-07
We investigate how the densities of inherent structures, which we refer to as the closest jammed configurations, are distributed for packings of 10(4) frictionless hard spheres. A computational algorithm is introduced to generate closest jammed configurations and determine corresponding densities. Closest jamming densities for monodisperse packings generated with high compression rates using Lubachevsky-Stillinger and force-biased algorithms are distributed in a narrow density range from φ = 0.634-0.636 to φ≈ 0.64; closest jamming densities for monodisperse packings generated with low compression rates converge to φ≈ 0.65 and grow rapidly when crystallization starts with very low compression rates. We interpret φ≈ 0.64 as the random-close packing (RCP) limit and φ≈ 0.65 as a lower bound of the glass close packing (GCP) limit, whereas φ = 0.634-0.636 is attributed to another characteristic (lowest typical, LT) density φLT. The three characteristic densities φLT, φRCP, and φGCP are determined for polydisperse packings with log-normal sphere radii distributions.
Motions in binary mixtures of hard colloidal spheres: melting of the glass.
Williams, S R; van Megen, W
2001-10-01
Dynamic light-scattering experiments are performed on binary mixtures of hard-sphere-like colloidal suspensions with a size ratio of 0.6. The optical properties of the particles are such that the relative contrast of the two species is very sensitive to temperature, a feature that is exploited to obtain the three partial coherent intermediate scattering functions. The glass transition is identified by the onset of structural arrest, or arrest of the alpha process, on the time scale of the experiment. This is observed in a one-component suspension at a packing fraction of 0.575. The intermediate scattering functions measured on the mixtures quantify how, on introduction of the smaller spheres, the alpha process is released, i.e., how the glass melts. Increasing the fraction of smaller particles causes the alpha process to speed up but, at a given wave vector, also incurs a change to its amplitude in proportion to the change in the (partial) structure factor.
Slow Rotation of a Sphere with Source at its Centre in a Viscous Fluid
Indian Academy of Sciences (India)
Sunil Datta; Deepak Kumar Srivastava
2000-02-01
In this note, the problem of a sphere carrying a fluid source at its centre and rotating with slow uniform angular velocity about a diameter is studied. The analysis reveals that only the azimuthal component of velocity exists and is seen that the effect of the source is to decrease it. Also, the couple on the sphere is found to decrease on account of the source.
Qiao, Yu; Liu, Xuejiao; Chen, Minxin; Lu, Benzhuo
2016-04-01
The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model (Borukhov et al. in Phys Rev Lett 79:435-438, 1997; Kilic et al. in Phys Rev E 75:021502, 2007; Lu and Zhou in Biophys J 100:2475-2485, 2011; Liu and Eisenberg in J Chem Phys 141:22D532, 2014) has a very similar form to one term of the LHS model, but LHSPNP has more additional terms accounting for size effects. Equation of state for one component homogeneous fluid is studied for the local hard sphere approximation of FMT and is proved to be exact for the first two virial coefficients, while the previous size modified model only presents the first virial coefficient accurately. To investigate the effects of LHS model and the competitions among different counterion species, numerical experiments are performed for the traditional PNP model, the LHSPNP model, the previous size modified PNP (SMPNP) model and the Monte Carlo simulation. It's observed that in steady state the LHSPNP results are quite different from the PNP results, but are close to the SMPNP results under a wide range of boundary conditions. Besides, in both
Mathematical problems of the dynamics of incompressible fluid on a rotating sphere
Skiba, Yuri N
2017-01-01
This book presents selected mathematical problems involving the dynamics of a two-dimensional viscous and ideal incompressible fluid on a rotating sphere. In this case, the fluid motion is completely governed by the barotropic vorticity equation (BVE), and the viscosity term in the vorticity equation is taken in its general form, which contains the derivative of real degree of the spherical Laplace operator. This work builds a bridge between basic concepts and concrete outcomes by pursuing a rich combination of theoretical, analytical and numerical approaches, and is recommended for specialists developing mathematical methods for application to problems in physics, hydrodynamics, meteorology and geophysics, as well for upper undergraduate or graduate students in the areas of dynamics of incompressible fluid on a rotating sphere, theory of functions on a sphere, and flow stability.
The complete T-->V,R energy conversion in three-body collisions within the hard sphere model.
Azriel, Vladimir M; Rusin, Lev Yu; Sevryuk, Mikhail B
2005-02-15
It is shown that in hard sphere (impulsive) collisions of atoms with diatomic molecules, complete conversion of the collision energy into the internal energy of the diatomic partner is possible for any number of impacts between the elastic balls representing the particles. The corresponding collision geometries and relations between the masses of the particles are described in detail.
Ni, R.; Smallenburg, F.; Filion, L.C.; Dijkstra, M.
2011-01-01
We study crystal nucleation in a binary mixture of hard spheres and investigate the composition and size of the (non)critical clusters using Monte Carlo simulations. In order to study nucleation of a crystal phase in computer simulations, a one-dimensional order parameter is usually defined to ident
Filion, L.C.; Hermes, M; Ni, R.; Dijkstra, M.
2010-01-01
Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett–Chandlertype the
Sushko, N; van der Schoot, P
2005-01-01
As is well known, hard-sphere crystals of the fcc and hcp type differ very little in their thermodynamic properties. Nonetheless, recent computer simulations by Pronk and Frenkel indicate that the elastic response to mechanical deformation of these two types of crystal are quite different [S. Pronk
Lamperski, Stanisław; Sosnowska, Joanna; Bhuiyan, Lutful Bari; Henderson, Douglas
2014-01-07
Even though ionic liquids are composed of nonspherical ions, it is shown here that the general features of the capacitance of an electrical double layer can be obtained using a charged hard sphere model. We have shown in our earlier studies that at high electrolyte concentrations or large magnitudes of the electrode charge density the fact that the ions have a finite size, and are not point ions, cause the capacitance near the potential of zero charge to increase and change from a minimum to a maximum as the ionic concentration is increased and to decrease as the magnitude of the electrode charge density increases. Here, we show that the asymmetry of the capacitance of an ionic liquid can be explained qualitatively by using spherical ions of different size without attempting to introduce the ionic shape in a detailed manner. This means that the general features of the capacitance of the double layer of an ionic liquid can be studied without using a complex model, although the study of the density or charge profiles of an ionic fluid would require one. However, this is often unnecessary in the analysis of many experiments.
VISCOUS FORCES BETWEEN TWO SPHERES COLLIDING THROUGH INTERSTITIAL POWER-LAW FLUID
Institute of Scientific and Technical Information of China (English)
Yong; Xu; Hongyan; Li; Wenbin; Huang
2005-01-01
Interaction between two spheres with an interstitial fluid is essential in Discrete Element modeling for simulating the behaviors of ‘wet' particulate materials. In this paper the interaction between two spheres with an interstitial Power-law fluid was approximately resolved as normal and tangential interactive models respectively, for which the governing equations were simplified on the basis of Reynolds approximation. These equations were then solved analytically together with the boundary conditions to obtain the pressure distributions for each individual model, and event ually solutions of the viscous squeeze force and the tangential viscous resistance were obtained, which provide a set of solutions for implementing into DEM code or other purposes.
SQUEEZE FLOW OF A SECOND-ORDER FLUID BETWEEN TWO PARALLEL DISKS OR TWO SPHERES
Institute of Scientific and Technical Information of China (English)
徐春晖; 黄文彬; 徐泳
2004-01-01
The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.
Elusiveness of Fluid-Fluid Demixing in Additive Hard-Core Mixtures
Lafuente, Luis; Cuesta, José A.
2002-09-01
The conjecture that when an additive hard-core mixture phase separates when one of the phases is spatially ordered, well supported by considerable evidence, is in contradiction with some simulations of a binary mixture of hard cubes on cubic lattices. By extending Rosenfeld's fundamental measure theory to lattice models we show that the phase behavior of this mixture is far more complex than simulations show, exhibiting regions of stability of several smectic, columnar, and solid phases, but no fluid-fluid demixing. A comparison with the simulations show that they are, in fact, compatible with a fluid-columnar demixing transition, thus bringing this model into the same demixing scheme as the rest of additive hard-core mixtures.
Conformal anisotropic relativistic charged fluid spheres with a linear equation of state
Esculpi, M.; Alomá, E.
2010-06-01
We obtain two new families of compact solutions for a spherically symmetric distribution of matter consisting of an electrically charged anisotropic fluid sphere joined to the Reissner-Nordstrom static solution through a zero pressure surface. The static inner region also admits a one parameter group of conformal motions. First, to study the effect of the anisotropy in the sense of the pressures of the charged fluid, besides assuming a linear equation of state to hold for the fluid, we consider the tangential pressure p ⊥ to be proportional to the radial pressure p r , the proportionality factor C measuring the grade of anisotropy. We analyze the resulting charge distribution and the features of the obtained family of solutions. These families of solutions reproduce for the value C=1, the conformal isotropic solution for quark stars, previously obtained by Mak and Harko. The second family of solutions is obtained assuming the electrical charge inside the sphere to be a known function of the radial coordinate. The allowed values of the parameters pertained to these solutions are constrained by the physical conditions imposed. We study the effect of anisotropy in the allowed compactness ratios and in the values of the charge. The Glazer’s pulsation equation for isotropic charged spheres is extended to the case of anisotropic and charged fluid spheres in order to study the behavior of the solutions under linear adiabatic radial oscillations. These solutions could model some stage of the evolution of strange quark matter fluid stars.
Institute of Scientific and Technical Information of China (English)
付东
2004-01-01
An analytical equation of state (EOS) for hard core Asakura-Oosawa (AO) fluid is established by combining the AO potential, the first-order perturbation theory and the radial distribution function (RDF) for the hard sphere fluid. The phase equilibria are studied by using the renormalization-group (RG) theory. The obtained results agree well with the simulation data. Investigation shows that the attractive range parameter plays an important role in the phase equilibria for AO fluid.
Floating and Sinking of a Pair of Spheres at a Liquid-Fluid Interface.
Cooray, Himantha; Cicuta, Pietro; Vella, Dominic
2017-02-14
Spheres floating at liquid-fluid interfaces cause interfacial deformations such that their weight is balanced by the resultant forces of surface tension and hydrostatic pressure while also satisfying a contact angle condition. Determining the meniscus shape around several floating spheres is a complicated problem because the vertical locations of the spheres and the horizontal projections of the three-phase contact lines are not known a priori. Here, a new computational algorithm is developed to simultaneously satisfy the nonlinear Laplace-Young equation for the meniscus shape, the vertical force balance, and the geometric properties of the spheres. We implement this algorithm to find the shape of the interface around a pair of floating spheres and the horizontal force required to keep them at a fixed center-center separation. Our numerical simulations show that the ability of a pair of spheres to float (rather than sink) depends on their separation. Similar to previous work on horizontal cylinders, sinking may be induced at close range for small spheres that float when isolated. However, we also discover a new and unexpected behavior: at intermediate inter-particle distances, spheres that would sink in isolation can float as a pair. This effect is more pronounced for spheres of radius comparable to the capillary length, suggesting that this effect is a result of hydrostatic pressure, rather than surface tension. An approximate solution confirms these phenomena and shows that the mechanism is indeed the increased supporting force provided by the hydrostatic pressure. Finally, the horizontal force of capillary attraction between the spheres is calculated using the results of the numerical simulations. These results show that the classic linear superposition approximation (due to Nicolson) can lose its validity for relatively heavy particles at close range.
Optical measurements of pore geometry and fluid velocity in a bed of irregularly packed spheres
Huang, Alice Y. L.; Huang, Michelle Y. F.; Capart, Hervé; Chen, Rong-Her
2008-08-01
Imaging methods are proposed for the characterisation of liquid flows through transparent porous media of matched refractive index. The methods are based on the analysis of laser-illuminated slices, and specialized for the case in which the porous medium is composed of irregularly packed spheres. They include algorithms for the reconstruction of the three-dimensional (3D) sphere arrangement based on a laser scan of the packed bed, particle tracking velocimetry applied to the motions of micro-tracers in a laser-illuminated plane, and techniques for the co-registration of geometry and velocity measurements acquired from different slices. The methods are applied to a cylindrical flow cell filled with mono-sized spheres and operated at Reynolds number Re = 28. The data produced include the full 3D geometry of the packed spheres assembly, the 2D fluid velocity field in the axial centre-plane of the flow cell, and the corresponding porosity and velocity distributions.
Integrable cases of gravitating static isothermal fluid spheres
Ivanov, B V
2002-01-01
It is shown that different approaches towards the solution of the Einstein equations for a static spherically symmetric perfect fluid with a gamma-law equation of state lead to an Abel differential equation of the second kind. Its only integrable cases at present are flat spacetime, de Sitter solution and its Buchdahl transform, Einstein static universe and the Klein-Tolman solution.
Energy Technology Data Exchange (ETDEWEB)
Radiom, Milad, E-mail: milad.radiom@unige.ch; Ducker, William, E-mail: wducker@vt.edu [Department of Chemical Engineering, Virginia Tech, Blacksburg, Virginia 24060 (United States); Robbins, Brian; Paul, Mark [Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia 24060 (United States)
2015-02-15
The hydrodynamic interaction of two closely spaced micron-scale spheres undergoing Brownian motion was measured as a function of their separation. Each sphere was attached to the distal end of a different atomic force microscopy cantilever, placing each sphere in a stiff one-dimensional potential (0.08 Nm{sup −1}) with a high frequency of thermal oscillations (resonance at 4 kHz). As a result, the sphere’s inertial and restoring forces were significant when compared to the force due to viscous drag. We explored interparticle gap regions where there was overlap between the two Stokes layers surrounding each sphere. Our experimental measurements are the first of their kind in this parameter regime. The high frequency of oscillation of the spheres means that an analysis of the fluid dynamics would include the effects of fluid inertia, as described by the unsteady Stokes equation. However, we find that, for interparticle separations less than twice the thickness of the wake of the unsteady viscous boundary layer (the Stokes layer), the hydrodynamic interaction between the Brownian particles is well-approximated by analytical expressions that neglect the inertia of the fluid. This is because elevated frictional forces at narrow gaps dominate fluid inertial effects. The significance is that interparticle collisions and concentrated suspensions at this condition can be modeled without the need to incorporate fluid inertia. We suggest a way to predict when fluid inertial effects can be ignored by including the gap-width dependence into the frequency number. We also show that low frequency number analysis can be used to determine the microrheology of mixtures at interfaces.
Acharya, A.; Maaskant, P.
1978-01-01
In this work, measurement of the flow field around a rotating sphere has been used to obtain the material parameters of a second-order Rivlin-Ericksen fluid. Experiments were carried out with a Laser-Doppler anemometer to obtain the velocity distribution and usingGiesekus' analysis, the material par
Goussev, Arseni; Dorfman, J. Robert
2006-01-01
We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision expansions we provide a first-principle analytical calculation of the time-dependent autocorrelation function for the wave packet in the high-energy diffraction regime, in which the particle's de Broglie wave length, while being small compared to the size of the ...
Goussev, Arseni; Dorfman, J R
2006-07-01
We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision expansions we provide a first-principle analytical calculation of the time-dependent autocorrelation function for the wave packet in the high-energy diffraction regime, in which the particle's de Broglie wavelength, while being small compared to the size of the scatterers, is large enough to prevent the formation of geometric shadow over distances of the order of the particle's free flight path. The hard-disk or hard-sphere scattering system must be sufficiently dilute in order for this high-energy diffraction regime to be achievable. Apart from the overall exponential decay, the autocorrelation function exhibits a generally complicated sequence of relatively strong peaks corresponding to partial revivals of the wave packet. Both the exponential decay (or escape) rate and the revival peak structure are predominantly determined by the underlying classical dynamics. A relation between the escape rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the counterpart classical system, previously known for hard-disk billiards, is strengthened by generalization to three spatial dimensions. The results of the quantum mechanical calculation of the time-dependent autocorrelation function agree with predictions of the semiclassical periodic orbit theory.
Flow of a viscous nematic fluid around a sphere
Gómez-González, Manuel
2013-01-01
We analyze the creeping flow generated by a spherical particle moving through a viscous fluid with nematic directional order, in which momentum diffusivity is anisotropic and which opposes resistance to bending. Specifically, we provide closed-form analytical expressions for the response function, i.e. the equivalent to Stokes's drag formula for nematic fluids. Particular attention is given to the rotationally pseudo-isotropic condition defined by zero resistance to bending, and to the strain pseudo-isotropic condition defined by isotropic momentum diffusivity. We find the former to be consistent with the rheology of biopolymer networks and the latter to be closer to the rheology of nematic liquid crystals. These "pure" anisotropic conditions are used to benchmark existing particle tracking microrheology methods that provide effective directional viscosities by applying Stokes's drag law separately in different directions. We find that the effective viscosity approach is phenomenologically justified in rotati...
Lechman, Jeremy; Pierce, Flint
2012-02-01
Diffusive transport is a ubiquitous process that is typically understood in terms of a classical random walk of non-interacting particles. Here we present the results for a model of hard-sphere colloids in a Newtonian incompressible solvent at various volume fractions below the ordering transition (˜50%). We numerically simulate the colloidal systems via Fast Lubrication Dynamics -- a Brownian Dynamics approach with corrected mean-field hydrodynamic interactions. Colloid-colloid interactions are also included so that we effectively solve a system of interacting Langevin equations. The results of the simulations are analyzed in terms of the diffusion coefficient as a function of time with the early and late time diffusion coefficients comparing well with experimental results. An interpretation of the full time dependent behavior of the diffusion coefficient and mean-squared displacement is given in terms of a continuous time random walk. Therefore, the deterministic, continuum diffusion equation which arises from the discrete, interacting random walkers is presented. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Assembly of vorticity-aligned hard-sphere colloidal strings in a simple shear flow
Cheng, X.
2011-12-23
Colloidal suspensions self-assemble into equilibrium structures ranging from face- and body-centered cubic crystals to binary ionic crystals, and even kagome lattices. When driven out of equilibrium by hydrodynamic interactions, even more diverse structures can be accessed. However, mechanisms underlying out-of-equilibrium assembly are much less understood, though such processes are clearly relevant in many natural and industrial systems. Even in the simple case of hard-sphere colloidal particles under shear, there are conflicting predictions about whether particles link up into string-like structures along the shear flow direction. Here, using confocal microscopy, we measure the shear-induced suspension structure. Surprisingly, rather than flow-aligned strings, we observe log-rolling strings of particles normal to the plane of shear. By employing Stokesian dynamics simulations, we address the mechanism leading to this out-of-equilibrium structure and show that it emerges from a delicate balance between hydrodynamic and interparticle interactions. These results demonstrate a method for assembling large-scale particle structures using shear flows.
Improvement and extension of the generalized hard-sphere reaction probability model.
Schübler, M A; Petkow, D; Herdrich, G
2012-04-01
The GHS (Generalized Hard Sphere)-based standard reaction probability model commonly used in probabilistic particle methods is evaluated. We show that the original model has no general validity with respect to the molecular reaction. Mathematical consistency exists only for reactions with vanishing activation energy. For small energies close to the activation threshold the individual reaction probability for the special case of associative ionization of atomic nitrogen diverges. This makes the model extremely expensive, and nonphysical. An improved model is derived, and its implementation is verified on basis of the aforementioned reaction. Both models converge to the same value at large energies. The relative error of the original model with respect to the new model is independent of the particle pairing and, hence, of the reaction type. The error is smaller than 1% for collision energies in excess of 200 times the activation energy. For typical simulation problems like atmospheric high-enthalpy entry flows (assuming heavy-particle temperatures on the order of 10000 K) the relative error is in the order of 10(5)%.
A Fokker-Planck model of hard sphere gases based on H-theorem
Gorji, M. Hossein; Torillhon, Manuel
2016-11-01
It has been shown recently that the Fokker-Planck kinetic model can be employed as an approximation of the Boltzmann equation for rarefied gas flow simulations [4, 5, 10]. Similar to the direct simulation Monte-Carlo (DSMC), the Fokker-Planck solution algorithm is based on the particle Monte-Carlo representation of the distribution function. Yet opposed to DSMC, here the particles evolve along independent stochastic paths where no collisions need to be resolved. This leads to significant computational advantages over DSMC, considering small Knudsen numbers [10]. The original Fokker-Planck model (FP) for rarefied gas flow simulations was devised according to the Maxwell type pseudo-molecules [4, 5]. In this paper a consistent Fokker-Planck equation is derived based on the Boltzmann collision integrals and maximum entropy distribution. Therefore the resulting model fulfills the H-theorem and leads to correct relaxation of velocity moments up to heat fluxes consistent with hard sphere interactions. For assessment of the model, simulations are performed for Mach 5 flow around a vertical plate using both Fokker-Planck and DSMC simulations. Compared to the original FP model, significant improvements are achieved at high Mach flows.
Demixing and confinement of non-additive hard-sphere mixtures in slit pores.
Almarza, N G; Martín, C; Lomba, E; Bores, C
2015-01-07
Using Monte Carlo simulation, we study the influence of geometric confinement on demixing for a series of symmetric non-additive hard spheres mixtures confined in slit pores. We consider both a wide range of positive non-additivities and a series of pore widths, ranging from the pure two dimensional limit to a large pore width where results are close to the bulk three dimensional case. Critical parameters are extracted by means of finite size analysis. As a general trend, we find that for this particular case in which demixing is induced by volume effects, the critical demixing densities (and pressures) increase due to confinement between neutral walls, following the expected behavior for phase equilibria of systems confined by pure repulsive walls: i.e., confinement generally enhances miscibility. However, a non-monotonous dependence of the critical pressure and density with pore size is found for small non-additivities. In this latter case, it turns out that an otherwise stable bulk mixture can be unexpectedly forced to demix by simple geometric confinement when the pore width decreases down to approximately one and a half molecular diameters.
Single file and normal dual mode diffusion in highly confined hard sphere mixtures under flow.
Wanasundara, Surajith N; Spiteri, Raymond J; Bowles, Richard K
2012-09-14
We use Monte Carlo simulations to study the dual-mode diffusion regime of binary and tertiary mixtures of hard spheres confined in narrow cylindrical pores under the influence of an imposed flow. The flow is introduced to the dynamics by adding a small bias directed along the long axis of the pore to the random displacement of each Monte Carlo move. As a result, the motion of the particles in all the components is dominated by a drift velocity that causes the mean squared displacements to increase quadratically in the long time limit. However, an analysis of the mean squared displacements at intermediate time scales shows that components of the mixture above and below their passing thresholds still exhibit behaviors consistent with normal and single-file diffusion, respectively. The difference between the mean squared displacements of the various components is shown to go though a maximum, suggesting there may be an optimal pore diameter for the separation of mixtures exhibiting dual-mode diffusion.
Hudson, Toby S; Harrowell, Peter
2011-05-18
Algorithms to search for crystal structures that optimize some extensive property (energy, volume, etc) typically make use of random particle reorganizations in the context of one or more numerical techniques such as simulated annealing, genetic algorithms or biased random walks, applied to the coordinates of every particle in the unit cell, together with the cell angles and lengths. In this paper we describe the restriction of such searches to predefined isopointal sets, breaking the problem into countable sub-problems which exploit crystal symmetries to reduce the dimensionality of the search space. Applying this method to the search for maximally packed mixtures of hard spheres of two sizes, we demonstrate that the densest packed structures can be identified by searches within a couple of isopointal sets. For the A(2)B system, the densest known packings over the entire tested range 0.2 < r(A)/r(B) < 2.5, including some improvements on previous optima, can all be identified by searches within a single isopointal set. In the case of the AB composition, searches of two isopointal sets generate the densest packed structures over the radius ratio range 0.2 < r(A)/r(B) < 5.0.
Cooperative activated dynamics in dense mixtures of hard and sticky spheres.
Viehman, Douglas C; Schweizer, Kenneth S
2008-11-01
The coupled activated dynamics in dense mixtures of repulsive and sticky hard spheres is studied using stochastic nonlinear Langevin equation theory. The effective free energy surface, barriers, saddle point trajectories, and mean first passage times depend in a rich manner on mixture composition, (high) total volume fraction, and attractive interaction strength. In general, there are three types of saddle point trajectories or relaxation pathways: a pure sticky or pure repulsive particle displacement keeping the other species localized, and a cooperative motion involving repulsive and attractive particle displacements. The barrier for activated hopping usually increases with the ratio of sticky to repulsive particle displacement. However, at intermediate values of the displacement ratio it can attain a broad plateau value, and can even exhibit a local maximum, and hence nonmonotonic behavior, at high sticky particle mixture compositions if the attraction strength is modest. The mean first passage, or hopping, times are computed using multidimensional Kramers theory. In most cases the hopping time trends reflect the behavior of the barrier height, especially as the sticky particle attraction strengths become large. However, there are dramatic exceptions associated with cooperative repulsive and attractive particle trajectories where the barriers are high but a greatly enhanced number of such trajectories exist near the saddle point.
Virrueta, A.; Gaines, J.; O'Hern, C. S.; Regan, L.
2015-03-01
Current research in the O'Hern and Regan laboratories focuses on the development of hard-sphere models with stereochemical constraints for protein structure prediction as an alternative to molecular dynamics methods that utilize knowledge-based corrections in their force-fields. Beginning with simple hydrophobic dipeptides like valine, leucine, and isoleucine, we have shown that our model is able to reproduce the side-chain dihedral angle distributions derived from sets of high-resolution protein crystal structures. However, methionine remains an exception - our model yields a chi-3 side-chain dihedral angle distribution that is relatively uniform from 60 to 300 degrees, while the observed distribution displays peaks at 60, 180, and 300 degrees. Our goal is to resolve this discrepancy by considering clashes with neighboring residues, and averaging the reduced distribution of allowable methionine structures taken from a set of crystallized proteins. We will also re-evaluate the electron density maps from which these protein structures are derived to ensure that the methionines and their local environments are correctly modeled. This work will ultimately serve as a tool for computing side-chain entropy and protein stability. A. V. is supported by an NSF Graduate Research Fellowship and a Ford Foundation Fellowship. J. G. is supported by NIH training Grant NIH-5T15LM007056-28.
Gelation and state diagram for a model nanoparticle system with adhesive hard sphere interactions
Wagner, Norman; Aaron, Eberle
2012-02-01
We provide the first comprehensive state diagram of thermoreversible gelation in a model nanoparticle system from dilute concentrations to the attractive driven glass. We show the temperature dependence of the interparticle potential is related to a surface molecular phase transition of the brush layer using neutron reflectivity (NR) and small-angle neutron scattering (SANS) [1]. We establish the temperature dependence of the interparticle potential using SANS, dynamic light scattering (DLS), and rheology. The potential parameters extracted from SANS suggest that, for this system, gelation is an extension of the Mode Coupling Theory (MCT) attractive driven glass line (ADG) to lower volume fractions and follows the percolation transition. Below the critical concentration, gelation proceeds without competition for phase separation [2]. These results are used to develop a complete state diagram for the sticky hard sphere reference system. [4pt] [1] A.P.R. Eberle, N.J. Wagner, B. Akgun, S.K. Satija, Langmuir 26 3003 (2010).[0pt] [2] A.P.R. Eberle, N.J. Wagner, R. Castaneda-Priego, Phys. Rev. Let. 105704 (2011).
Fingering induced by a solid sphere impact to viscous fluid
Katsuragi, H
2014-01-01
The number of splashed fingers generated by a solid projectile's impact onto a viscous liquid layer is experimentally studied. A steel sphere is dropped onto a viscous liquid pool. Then, a fingering instability occurs around the crater's rim, depending on the experimental conditions such as projectile's inertia and the viscosity of the target liquid. When the impact inertia is not sufficient, any fingering structure cannot be observed. Contrastively, if the impact inertia is too much, the random splashing is induced and the counting of fingers becomes difficult. The clear fingering instability is observable in between these two regimes. The number of fingers $N$ is counted by using high-speed video data. The scaling of $N$ is discussed on the basis of dimensionless numbers. By assuming Rayleigh-Taylor instability, scaling laws for $N$ can be derived using Reynolds number $Re$, Weber number $We$, and Froude number $Fr$. Particularly, the scaling $N=(\\rho_r Fr)^{1/4}We^{1/2}/3^{3/4}$ is obtained for the gravity...
Fingering induced by a solid sphere impact to viscous fluid
Directory of Open Access Journals (Sweden)
Katsuragi Hiroaki
2015-01-01
Full Text Available The number of splashed fingers generated by a solid projectile’s impact onto a viscous liquid layer is experimentally studied. A steel sphere is dropped onto a viscous liquid pool. Then, a fingering instability occurs around the crater’s rim, depending on the experimental conditions such as projectile’s inertia and the viscosity of the target liquid. When the impact inertia is not sufficient, any fingering structure cannot be observed. Contrastively, if the impact inertia is too much, the random splashing is induced and the counting of fingers becomes difficult. The clear fingering instability is observable in between these two regimes. The number of fingers N is counted by using high-speed video data. The scaling of N is discussed on the basis of dimensionless numbers. By assuming Rayleigh-Taylor instability, scaling laws for N can be derived using Reynolds number Re, Weber number We, and Froude number Fr. Particularly, the scaling N = (ρrFr1/4We1/2/33/4 is obtained for the gravity-dominant cratering regime, where ρr is the density ratio between a projectile and a target. Although the experimental data considerably scatters, the scaling law is consistent with the global trend of the data behavior. Using one of the scaling laws, planetary nano crater’s rim structure is also evaluated.
Radiating fluid spheres in the effective variables approximation
Barreto, W; Martínez, H
2002-01-01
We study the evolution of spherically symmetric radiating fluid distributions using the effective variables method, implemented {\\it ab initio} in Schwarzschild coordinates. To illustrate the procedure and to establish some comparison with the original method, we integrate numerically the set of equations at the surface for two different models. The first model is derived from the Schwarzschild interior solution. The second model is inspired in the Tolman VI solution.
Structure and thermodynamics of hard-core Yukawa fluids: thermodynamic perturbation approaches.
Kim, Eun-Young; Kim, Soon-Chul; Seong, Baek-Seok
2011-07-21
The thermodynamic perturbation theories, which are based on the power series of a coupling constant (λ-expansion), have been proposed for studying the structural and thermodynamic properties of a hard-core Yukawa (HCY) fluid: one (A1-approximation) is the perturbation theory based on the hard-sphere repulsion as a reference system. The other (A2-approximation) is the perturbation theory based on the reference system which incorporates both the repulsive and short-range attractive interactions. The first-order mean-spherical approximation (FMSA) provided by Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] has been employed for investigating the thermodynamic properties of a HCY fluid using the alternative method via the direct correlation function. The calculated results show that (i) the A1 and A2 approximations are in excellent agreements with previous computer simulation results in the literature and compare with the semi-empirical works of Shukla including the higher-order free energy terms, (ii) the A1 and A2 approximations are better than the FMSA and the mean-spherical approximation, (iii) the A2-approximation compares with the A1-approximation, even though the perturbation effect of an A2-approximation is much smaller than that of an A1-approximation, and that (iv) the FMSA study is particularly of advantage in providing the structure and thermodynamics in a simple and analytic manner.
New Virial Equation of State for Hard-Disk Fluids
Tian, Jianxiang; Mulero, A
2016-01-01
Although many equations of state of hard-disk fluids have been proposed, none is capable of reproducing the currently calculated or estimated values of the first eighteen virial coefficients at the same time as giving very good accuracy when compared with computer simulation values for the compressibility factor over the whole fluid range. A new virial-based expression is here proposed which achieves these aims. For that, we use the fact that the currently accepted estimated values for the highest virial coefficients behave linearly with their order, and also that virial coefficients must have a limiting behaviour that permits the closest packing limit in the compressibility factor to be also adequately reproduced.
Hydrodynamic interactions between two equally sized spheres in viscoelastic fluids in shear flow.
Snijkers, Frank; Pasquino, Rossana; Vermant, Jan
2013-05-14
The effect of using a viscoelastic suspending medium on the in-plane hydrodynamic interaction between two equally sized spheres in shear flow is studied experimentally to understand flow-induced assembly behavior (i.e., string formation). A counterrotating device equipped with a Couette geometry is used together with quantitative videomicroscopy. To evaluate the effects of differences in rheological properties of the suspending media, fluids have been selected that highlight specific constitutive features. These include a reference Newtonian fluid (N), a constant-viscosity, high-elasticity Boger fluid (BF), a wormlike micellar surfactant solution with a single dominant relaxation time (WMS), and a broad spectrum shear-thinning elastic polymer solution (ST). As expected, the trajectories are symmetric in the Newtonian fluid. In the BF, the midpoints of the spheres are observed to remain in the same plane before and after the interaction, as in the Newtonian fluid, although the path lines are in this case no longer symmetric. Interactions in the ST and WMS are highly asymmetric. Two fundamentally different kinds of path lines are observed in the WMS and ST: reversing and open trajectories. The type of trajectory depends on the initial configuration of the spheres with respect to each other and on the shear rate. On the basis of the obtained results, shear-thinning of the viscosity seems to be the key rheological parameter that determines the overall nature of the interactions, rather than the relative magnitude of the normal stress differences.
On two-parameter equations of state and the limitations of a hard sphere Peng-Robinson equation
Harmens, A.; Jeremiah, Dawn E.
Simple two-parameter equations of state are exceptionally effective for calculations on systems of small, uncomplicated molecules. They are therefore extremely useful for vapour-liquid equilibrium calculations in cryogenic and light hydrocarbon process design. In a search for further improvement three two-parameter equations of state with a co-volume repulsion term and three with a hard sphere repulsion term have been investigated. Their characteristic constants at the critical point have been compared. The procedure for fitting the two parameters to empirical data in the subcritical region was analysed. A perturbed hard sphere equation with a Peng-Robinson attraction term was shown to be unsuitable for application over a wide range of p, T conditions. A similar equation with a Redlich-Kwong attraction term gives good service in the cryogenic range.
Ayadim, A; Amokrane, S
2010-01-27
The accuracy of the structural data obtained from the recently proposed generalization to non-additive hard-spheres (Schmidt 2004 J. Phys.: Condens. Matter 16 L351) of Rosenfeld's functional is investigated. The radial distribution functions computed from the direct correlation functions generated by the functional, through the Ornstein-Zernike equations, are compared with those obtained from the density profile equations in the test-particle limit, without and with test-particle consistency. The differences between these routes and the role of the optimization of the parameters of the reference system when the functional is used to obtain the reference bridge functional are discussed in the case of symmetric binary mixtures of non-additive hard-spheres. The case of highly asymmetric mixtures is finally briefly discussed.
T.V. Hvozd; Y.V. Kalyuzhnyi
2016-01-01
Phase behavior of the Yukawa hard-sphere polydisperse mixture with high degree of polydispersity is studied using high temperature approximation (HTA) and mean spherical approximation (MSA). We have extended and applied the scheme developed to calculate the phase diagrams of polydisperse mixtures described by the truncatable free energy models, i.e., the models with Helmholtz free energy defined by the finite number of the moments of the species distribution function. At high degree of polydi...
Atkinson, Steven; Stillinger, Frank H.; Torquato, Salvatore
2016-09-01
The nonequilibrium process by which hard-particle systems may be compressed into disordered, jammed states has received much attention because of its wide utility in describing a broad class of amorphous materials. While dynamical signatures are known to precede jamming, the task of identifying static structural signatures indicating the onset of jamming have proven more elusive. The observation that compressing hard-particle packings towards jamming is accompanied by an anomalous suppression of density fluctuations (termed "hyperuniformity") has paved the way for the analysis of jamming as an "inverted critical point" in which the direct correlation function c (r ) , rather than the total correlation function h (r ) , diverges. We expand on the notion that c (r ) provides both universal and protocol-specific information as packings approach jamming. By considering the degree and position of singularities (discontinuities in the n th derivative) as well as how they are changed by the convolutions found in the Ornstein-Zernike equation, we establish quantitative statements about the structure of c (r ) with regards to singularities it inherits from h (r ) . These relations provide a concrete means of identifying features that must be expressed in c (r ) if one hopes to reproduce various details in the pair correlation function accurately and provide stringent tests on the associated numerics. We also analyze the evolution of systems of three-dimensional monodisperse hard spheres of diameter D as they approach ordered and disordered jammed configurations. For the latter, we use the Lubachevsky-Stillinger (LS) molecular dynamics and Torquato-Jiao (TJ) sequential linear programming algorithms, which both generate disordered packings, but can show perceptible structural differences. We identify a short-ranged scaling c (r )∝-1 /r as r →0 that accompanies the formation of the delta function at c (D ) that indicates the formation of contacts in all cases, and show
Zhou, Alice Qinhua; O'Hern, Corey S; Regan, Lynne
2014-10-01
The side-chain dihedral angle distributions of all amino acids have been measured from myriad high-resolution protein crystal structures. However, we do not yet know the dominant interactions that determine these distributions. Here, we explore to what extent the defining features of the side-chain dihedral angle distributions of different amino acids can be captured by a simple physical model. We find that a hard-sphere model for a dipeptide mimetic that includes only steric interactions plus stereochemical constraints is able to recapitulate the key features of the back-bone dependent observed amino acid side-chain dihedral angle distributions of Ser, Cys, Thr, Val, Ile, Leu, Phe, Tyr, and Trp. We find that for certain amino acids, performing the calculations with the amino acid of interest in the central position of a short α-helical segment improves the match between the predicted and observed distributions. We also identify the atomic interactions that give rise to the differences between the predicted distributions for the hard-sphere model of the dipeptide and that of the α-helical segment. Finally, we point out a case where the hard-sphere plus stereochemical constraint model is insufficient to recapitulate the observed side-chain dihedral angle distribution, namely the distribution P(χ₃) for Met.
Zhang, Kai; Smith, W. Wendell; Wang, Minglei; Liu, Yanhui; Schroers, Jan; Shattuck, Mark D.; O'Hern, Corey S.
2014-09-01
We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate R, size ratio α, and number fraction xS of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate Rc, below which jammed hard-sphere packings begin to form "random crystal" structures with defects. We find that for systems with α ≳0.8 that do not demix, Rc decreases strongly with ΔϕJ, as Rc˜exp(-1/ΔϕJ2), where ΔϕJ is the difference between the average packing fraction of the amorphous packings and random crystal structures at Rc. Systems with α ≲0.8 partially demix, which promotes crystallization, but we still find a strong correlation between Rc and ΔϕJ. We show that known metal-metal BMGs occur in the regions of the α and xS parameter space with the lowest values of Rc for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing α to increase packing efficiency, while maximizing α to prevent demixing.
Zhang, Kai; Smith, W Wendell; Wang, Minglei; Liu, Yanhui; Schroers, Jan; Shattuck, Mark D; O'Hern, Corey S
2014-09-01
We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate R, size ratio α, and number fraction x(S) of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate R(c), below which jammed hard-sphere packings begin to form "random crystal" structures with defects. We find that for systems with α≳0.8 that do not demix, R(c) decreases strongly with Δϕ(J), as R(c)∼exp(-1/Δϕ(J)(2)), where Δϕ(J) is the difference between the average packing fraction of the amorphous packings and random crystal structures at R(c). Systems with α≲0.8 partially demix, which promotes crystallization, but we still find a strong correlation between R(c) and Δϕ(J). We show that known metal-metal BMGs occur in the regions of the α and x(S) parameter space with the lowest values of R(c) for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing α to increase packing efficiency, while maximizing α to prevent demixing.
Casimir micro-sphere diclusters and three-body effects in fluids
Varela, Jaime; McCauley, Alexander P; Johnson, Steven G
2010-01-01
Our previous article [Phys. Rev. Lett. 104, 060401 (2010)] predicted that Casimir forces induced by the material-dispersion properties of certain dielectrics can give rise to stable configurations of objects. This phenomenon was illustrated via a dicluster configuration of non-touching objects consisting of two spheres immersed in a fluid and suspended against gravity above a plate. Here, we examine these predictions from the perspective of a practical experiment and consider the influence of non-additive, three-body, and nonzero-temperature effects on the stability of the two spheres. We conclude that the presence of Brownian motion reduces the set of experimentally realizable silicon/teflon spherical diclusters to those consisting of layered micro-spheres, such as the hollow- core (spherical shells) considered here.
A note on the breathing mode of an elastic sphere in Newtonian and complex fluids
Galstyan, Vahe; Stone, Howard A
2015-01-01
Experiments on the acoustic vibrations of elastic nanostructures in fluid media have been used to study the mechanical properties of materials, as well as for mechanical and biological sensing. The medium surrounding the nanostructure is typically modeled as a Newtonian fluid. A recent experiment however suggested that high-frequency longitudinal vibration of bipyramidal nanoparticles could trigger a viscoelastic response in water-glycerol mixtures [M. Pelton et al., "Viscoelastic flows in simple liquids generated by vibrating nanostructures," Phys. Rev. Lett. 111, 244502 (2013)]. Motivated by these experimental studies, we first revisit a classical continuum mechanics problem of the purely radial vibration of an elastic sphere, also called the breathing mode, in a compressible viscous fluid, and then extend our analysis to a viscoelastic medium using the Maxwell fluid model. The effects of fluid compressibility and viscoelasticity are discussed. Although in the case of longitudinal vibration of bipyramidal n...
Analytical solution for the lubrication force between two spheres in a bi-viscous fluid
Vázquez-Quesada, A.; Ellero, M.
2016-07-01
An analytical solution for the calculation of the normal lubrication force acting between two moving spheres embedded in a shear-thinning fluid represented by a bi-viscous model is provided. The resulting force between the suspended spheres exhibits a consistent transition between the Newtonian constant-viscosity limits and it reduces to the well-known standard Newtonian lubrication theory for viscosity-ratio approaching one. Effects of several physical parameters of the theory are analyzed under relevant physical conditions, i.e., for a prototypical case of two non-colloidal spheres immersed in a non-Newtonian fluid with rheology parameterized by a bi-viscosity model. Topological results for high/low-viscosity regions in the gap between spheres are also analyzed in detail showing a rich phenomenology. The presented model enables the extension of lubrication dynamics for suspensions interacting with non-Newtonian matrices and provides a clean theoretical framework for new numerical computations of flow of dense complex particulate systems.
Swimming of a sphere in a viscous incompressible fluid with inertia
Felderhof, B U
2015-01-01
The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier-Stokes equations. The mean swimming velocity and the mean rate of dissipation are expressed as quadratic forms in term of the surface displacements. With a choice of a basis set of modes the quadratic forms correspond to two hermitian matrices. Optimization of the mean swimming velocity for given rate of dissipation requires the solution of a generalized eigenvalue problem involving the two matrices. It is found for surface modulations of low multipole order that the optimal swimming efficiency depends in intricate fashion on a dimensionless scale number involving the radius of the sphere, the period of the cycle, and the kinematic viscosity of the fluid.
Zhou, Shiqi
2011-12-01
Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT) is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426) 1st-order high temperature series expansion (HTSE) TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861), have some serious shortcomings: (i) the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii) the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE) and a non hard sphere (HS) perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i) we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii) We give a quantitative analysis on why convergence
Directory of Open Access Journals (Sweden)
Shiqi Zhou
2011-12-01
Full Text Available Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426 1st-order high temperature series expansion (HTSE TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861, have some serious shortcomings: (i the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE and a non hard sphere (HS perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii We give a quantitative analysis on why
Dynamical stability of fluid spheres in spacetimes with a nonzero cosmological constant
Hledik, Stanislav; Mrazova, Kristina
2016-01-01
The Sturm-Liouville eigenvalue equation for eigenmodes of the radial oscillations is determined for spherically symmetric perfect fluid configurations in spacetimes with a nonzero cosmological constant and applied in the cases of configurations with uniform distribution of energy density and polytropic spheres. It is shown that a repulsive cosmological constant rises the critical adiabatic index and decreases the critical radius under which the dynamical instability occurs.
Yamagata, Atsushi
1994-01-01
We perform the Monte Carlo simulations of the hard-sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion. The critical activity is estimated, $z_{\\rm c} = 1.0588 \\pm 0.0003$. Using a relation between the hard-sphere lattice gas and the antiferromagnetic Ising model in an external magnetic field, we conclude that there is no re-entrant phase transition of the latter on the simple cubic lattice.
The rising motion of spheres in structured fluids with yield stress
Mirzaagha, S.; Pasquino, R.; Iuliano, E.; D'Avino, G.; Zonfrilli, F.; Guida, V.; Grizzuti, N.
2017-09-01
The rising of spherical bodies in structured fluids with yield stress is studied. The system is a suspension of hydrogenated castor oil colloidal fibers in a surfactant micellar solution. The fiber network confers to the fluid a viscoelastic behavior, with a well-defined yield stress, which increases with increasing fiber concentration. Various fluids with different fiber contents are prepared and rheologically characterized. A home-made time-lapse photography setup is used to monitor the time evolution position of the spherical particles, and the rising motion of both hollow spheres and air bubbles, in the diameter range 65-550 μm, is measured. The experiments last as long as several weeks, corresponding to significantly low measured velocities. Finite element simulations are performed to support the experimental data, assuming both interfacial slip and no slip conditions. The fluid dynamic phenomenon is studied and discussed in terms of dimensionless numbers, such as yield ratio, Bingham number, and Stokes drag coefficient. The results are novel for the system (suspending medium and hollow spheres) and for the covered Bingham number range, which is extended over three orders of magnitude in comparison with already available literature results. Our values provide quantitative data of the mechanical properties (i.e., yield stress value) at very low shear rates, in a prohibitive range for a traditional rheometer, and agree with the macroscopic rheological response. Moreover, the important role of the power law index n of the Herschel-Bulkley model, used to fit the data, has been highlighted. Our results, based on a Bingham-like fluid, are compared with the experimental data already available with Carbopol, treated as a Herschel Bulkley fluid with n = 0.5. The results could have important implications in the fabric and personal care detergency, a technological area where many fluids have composition and show rheological properties similar to those considered in the
López-Sánchez, Erik; Estrada-Álvarez, César D; Pérez-Ángel, Gabriel; Méndez-Alcaraz, José Miguel; González-Mozuelos, Pedro; Castañeda-Priego, Ramón
2013-09-14
Asymmetric binary mixtures of hard-spheres exhibit several interesting thermodynamic phenomena, such as multiple kinds of glassy states. When the degrees of freedom of the small spheres are integrated out from the description, their effects are incorporated into an effective pair interaction between large spheres known as the depletion potential. The latter has been widely used to study both the phase behavior and dynamic arrest of the big particles. Depletion forces can be accounted for by a contraction of the description in the multicomponent Ornstein-Zernike equation [R. Castañeda-Priego, A. Rodríguez-López, and J. M. Méndez-Alcaraz, Phys. Rev. E 73, 051404 (2006)]. Within this theoretical scheme, an approximation for the difference between the effective and bare bridge functions is needed. In the limit of infinite dilution, this difference is irrelevant and the typical Asakura-Osawa depletion potential is recovered. At higher particle concentrations, however, this difference becomes important, especially where the shell of first neighbors is formed, and, as shown here, cannot be simply neglected. In this work, we use a variant of the Verlet expression for the bridge functions to highlight their importance in the calculation of the depletion potential at high densities and close to the spinodal decomposition. We demonstrate that the modified Verlet closure predicts demixing in binary mixtures of hard spheres for different size ratios and compare its predictions with both liquid state and density functional theories, computer simulations, and experiments. We also show that it provides accurate correlation functions even near the thermodynamic instability; this is explicitly corroborated with results of molecular dynamics simulations of the whole mixture. Particularly, our findings point toward a possible universal behavior of the depletion potential around the spinodal line.
Monte Carlo simulations of the solid-liquid transition in hard spheres and colloid-polymer mixtures.
Zykova-Timan, T; Horbach, J; Binder, K
2010-07-07
Monte Carlo simulations at constant pressure are performed to study coexistence and interfacial properties of the liquid-solid transition in hard spheres and in colloid-polymer mixtures. The latter system is described as a one-component Asakura-Oosawa (AO) model where the polymer's degrees of freedom are incorporated via an attractive part in the effective potential for the colloid-colloid interactions. For the considered AO model, the polymer reservoir packing fraction is eta(p) (r)=0.1 and the colloid-polymer size ratio is q[triple bond]sigma(p)/sigma=0.15 (with sigma(p) and sigma as the diameter of polymers and colloids, respectively). Inhomogeneous solid-liquid systems are prepared by placing the solid fcc phase in the middle of a rectangular simulation box, creating two interfaces with the adjoined bulk liquid. By analyzing the growth of the crystalline region at various pressures and for different system sizes, the coexistence pressure p(co) is obtained, yielding p(co)=11.576 k(B)T/sigma(3) for the hard-sphere system and p(co)=8.00 k(B)T/sigma(3) for the AO model (with k(B) as the Boltzmann constant and T as the temperature). Several order parameters are introduced to distinguish between solid and liquid phases and to describe the interfacial properties. From the capillary-wave broadening of the solid-liquid interface, the interfacial stiffness is obtained for the (100) crystalline plane, giving the values gamma approximately 0.49 k(B)T/sigma(2) for the hard-sphere system and gamma approximately 0.95 k(B)T/sigma(2) for the AO model.
Wolf, Aaron S.; Asimow, Paul D.; Stevenson, David J.
2015-08-01
We develop a new model to understand and predict the behavior of oxide and silicate melts at extreme temperatures and pressures, including deep mantle conditions like those in the early Earth magma ocean. The Coordinated Hard Sphere Mixture (CHaSM) is based on an extension of the hard sphere mixture model, accounting for the range of coordination states available to each cation in the liquid. By utilizing approximate analytic expressions for the hard sphere model, this method is capable of predicting complex liquid structure and thermodynamics while remaining computationally efficient, requiring only minutes of calculation time on standard desktop computers. This modeling framework is applied to the MgO system, where model parameters are trained on a collection of crystal polymorphs, producing realistic predictions of coordination evolution and the equation of state of MgO melt over a wide range of pressures and temperatures. We find that the typical coordination number of the Mg cation evolves continuously upward from 5.25 at 0 GPa to 8.5 at 250 GPa. The results produced by CHaSM are evaluated by comparison with predictions from published first-principles molecular dynamics calculations, indicating that CHaSM is accurately capturing the dominant physics controlling the behavior of oxide melts at high pressure. Finally, we present a simple quantitative model to explain the universality of the increasing Grüneisen parameter trend for liquids, which directly reflects their progressive evolution toward more compact solid-like structures upon compression. This general behavior is opposite that of solid materials, and produces steep adiabatic thermal profiles for silicate melts, thus playing a crucial role in magma ocean evolution.
Wolf, A. S.; Asimow, P. D.; Stevenson, D. J.
2015-12-01
Recent first-principles calculations (e.g. Stixrude, 2009; de Koker, 2013), shock-wave experiments (Mosenfelder, 2009), and diamond-anvil cell investigations (Sanloup, 2013) indicate that silicate melts undergo complex structural evolution at high pressure. The observed increase in cation-coordination (e.g. Karki, 2006; 2007) induces higher compressibilities and lower adiabatic thermal gradients in melts as compared with their solid counterparts. These properties are crucial for understanding the evolution of impact-generated magma oceans, which are dominated by the poorly understood behavior of silicates at mantle pressures and temperatures (e.g. Stixrude et al. 2009). Probing these conditions is difficult for both theory and experiment, especially given the large compositional space (MgO-SiO2-FeO-Al2O3-etc). We develop a new model to understand and predict the behavior of oxide and silicate melts at extreme P-T conditions (Wolf et al., 2015). The Coordinated Hard Sphere Mixture (CHaSM) extends the Hard Sphere mixture model, accounting for the range of coordination states for each cation in the liquid. Using approximate analytic expressions for the hard sphere model, this fast statistical method compliments classical and first-principles methods, providing accurate thermodynamic and structural property predictions for melts. This framework is applied to the MgO system, where model parameters are trained on a collection of crystal polymorphs, producing realistic predictions of coordination evolution and the equation of state of MgO melt over a wide P-T range. Typical Mg-coordination numbers are predicted to evolve continuously from 5.25 (0 GPa) to 8.5 (250 GPa), comparing favorably with first-principles Molecular Dynamics (MD) simulations. We begin extending the model to a simplified mantle chemistry using empirical potentials (generally accurate over moderate pressure ranges, compression.
Directory of Open Access Journals (Sweden)
M. Moradi
2003-06-01
Full Text Available The Helmholtz free energy and equation of the state of an fcc crystal are calculated, where the interaction between the molecules is hard sphere-Yukawa potential. Here the perturbational density functional method is used. This method is introduced by Ebner and co-workers. In this method the density functional Taylor expansion is applied for the crystal configuration up to second order. And for the uniform parts an exact expression is used. The results are compared with those obtained by Monte Carlo computer simulation. The agreement is good.
Beltrán-Heredia, Elena; Santos, Andrés
2014-04-01
The fourth virial coefficient of additive hard-sphere mixtures, as predicted by the Percus-Yevick (PY) and hypernetted-chain (HNC) theories, is derived via the compressibility, virial, and chemical-potential routes, the outcomes being compared with exact results. Except in the case of the HNC compressibility route, the other five expressions exhibit a common structure involving the first three moments of the size distribution. In both theories, the chemical-potential route is slightly better than the virial one and the best behavior is generally presented by the compressibility route. Moreover, the PY results with any of the three routes are more accurate than any of the HNC results.
Watanabe, Hiroshi; Yukawa, Satoshi; Novotny, M A; Ito, Nobuyasu
2006-08-01
We construct asymptotic arguments for the relative efficiency of rejection-free Monte Carlo (MC) methods compared to the standard MC method. We find that the efficiency is proportional to exp(constbeta) in the Ising, sqrt[beta] in the classical XY, and beta in the classical Heisenberg spin systems with inverse temperature beta, regardless of the dimension. The efficiency in hard particle systems is also obtained, and found to be proportional to (rho(cp)-rho)(-d) with the closest packing density rho(cp), density rho, and dimension d of the systems. We construct and implement a rejection-free Monte Carlo method for the hard-disk system. The RFMC has a greater computational efficiency at high densities, and the density dependence of the efficiency is as predicted by our arguments.
Fully-resolved slumping of a pile of spheres in a fluid
Wang, Yayun; Sierakowski, Adam; Prosperetti, Andrea
2015-11-01
Turbidity currents form when a particle-laden fluid propagates into the lighter clear fluid in a predominantly horizontal direction. This work studies some microscopic aspects of the phenomenon by simulating numerically the evolution of a block of several hundred spheres released from an initial roughly cubic pile resting on the bottom of a liquid pool. The motion of the particles as well as the liquid flow are fully resolved by the Physalis method. The process undergoes several stages starting with an initial inertia-dominated one and ending with viscosity-dominated flow. The effects of the particle mass on the evolution of the kinetic energy of the particles and of the fluid, on the viscous energy dissipation and on the velocity of the front of the turbidity current will be analyzed. The study of the pair distribution function and of particle triads and tetrads sheds light on the evolution of the mutual particle arrangement. Supported by NSF award No CBET 1335965.
Acoustic interaction forces and torques acting on suspended spheres in an ideal fluid
Lopes, J Henrique; Silva, G T
2014-01-01
In this paper, the acoustic interaction forces and torques exerted by an arbitrary time-harmonic wave on a set of N spheres suspended in an inviscid fluid are theoretically analyzed. In so doing, we utilize the partial-wave expansion method to solve the related multiple scattering problem. The acoustic interaction force and torque are computed for a sphere using the farfield radiation force and torque formulas. To exemplify the method, we calculate the interaction forces exerted by an external traveling and standing plane wave on an arrangement of two and three olive-oil droplets in water. The droplets radii are comparable to the wavelength (i.e. Mie scattering regime). The results show that the radiation force may considerably deviates from that exerted solely by the external incident wave. In addition, we find that acoustic interaction torques arise on the droplets when a nonsymmetric effective incident wave interacts with the droplets.
Rheology and Structure of Concentrated Suspensions of Hard Spheres. Shear Induced Particle Migration
Mills, P.; Snabre, P.
1995-10-01
The apparent shear viscosity, in the non-Brownian limit, for a homogeneous suspension of monodispersed hard spheres in systems ranging from dilute to concentrated was previously established. From an estimation of the viscous dissipation. We use the inter-particle distance dependence of the shear viscosity for determining the components of a local stress tensor associated with the transient network of particles for the volume fraction above the percolation threshold. For this purpose, we develop a model based on lubrication forces between colliding particles for coupling the particle stress tensor to the stress tensor of the suspension considered as an effective medium. In the case of non-uniform flows with low shear rate regions, it is necessary to introduce a non-local stress tensor since the stress can be directly transmitted by the network of particles over a correlation length larger than the particle diameter. This approach shows ... A partir d'une estimation de la dissipation visqueuse, nous avons précedemment évalué la viscosité apparente de cisaillement des suspensions homogènes de sphères dures monodisperses et non Browniennes dans les systèmes dilués ou concentrés. Nos utilisons la dépendance de la viscosité de cisaillement avec la distance moyenne entre les particules pour déterminer les composantes d'un tenseur local de contraintes associé à l'amas transitoire de particlues au dessus de la fraction volumique critique de percolation. Nous developpons pour cela un modèle basé sur les forces de lubrification s'exerçant au cours des collisions entre les particules afin de coupler le tenseur local de contraintes associé aux particules et le tenseur des contraintes dans la suspension assimilée à un milieu effectif. Dans le cas des écoulements non uniformes présentant des zones de faible cisaillement, il est nécessaire de considérer un tenseur non local des contraintes car les forces peuvent alors se transmettre directement à travers l
Härtel, Andreas; Kohl, Matthias; Schmiedeberg, Michael
2015-10-01
The fundamental measure approach to classical density functional theory has been shown to be a powerful tool to predict various thermodynamic properties of hard-sphere systems. We employ this approach to determine not only one-particle densities but also two-particle correlations in binary and six-component mixtures of hard spheres in the vicinity of a hard wall. The broken isotropy enables us to carefully test a large variety of theoretically predicted two-particle features by quantitatively comparing them to the results of Brownian dynamics simulations. Specifically, we determine and compare the one-particle density, the total correlation functions, their contact values, and the force distributions acting on a particle. For this purpose, we follow the compressibility route and theoretically calculate the direct correlation functions by taking functional derivatives. We usually observe an excellent agreement between theory and simulations, except for small deviations in cases where local crystal-like order sets in. Our results set the course for further investigations on the consistency of functionals as well as for structural analysis on, e.g., the primitive model. In addition, we demonstrate that due to the suppression of local crystallization, the predictions of six-component mixtures are better than those in bidisperse or monodisperse systems. Finally, we are confident that our results of the structural modulations induced by the wall lead to a deeper understanding of ordering in anisotropic systems in general, the onset of heterogeneous crystallization, caging effects, and glassy dynamics close to a wall, as well as structural properties in systems with confinement.
Results of Microgravity Fluid Dynamics Captured with the Spheres-Slosh Experiment
Lapilli, Gabriel; Kirk, Daniel Robert; Gutierrez, Hector; Schallhorn, Paul; Marsell, Brandon; Roth, Jacob; Jeffrey Moder
2015-01-01
This paper provides an overview of the SPHERES-Slosh Experiment (SSE) aboard the International Space Station (ISS) and presents on-orbit results with data analysis. In order to predict the location of the liquid propellant during all times of a spacecraft mission, engineers and mission analysts utilize Computational Fluid Dynamics (CFD). These state-of-the-art computer programs numerically solve the fluid flow equations to predict the location of the fluid at any point in time during different spacecraft maneuvers. The models and equations used by these programs have been extensively validated on the ground, but long duration data has never been acquired in a microgravity environment. The SSE aboard the ISS is designed to acquire this type of data, used by engineers on earth to validate and improve the CFD prediction models, improving the design of the next generation of space vehicles as well as the safety of current missions. The experiment makes use of two Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES) connected by a frame. In the center of the frame there is a plastic, pill shaped tank that is partially filled with green-colored water. A pair of high resolution cameras records the movement of the liquid inside the tank as the experiment maneuvers within the Japanese Experimental Module test volume. Inertial measurement units record the accelerations and rotations of the tank, making the combination of stereo imaging and inertial data the inputs for CFD model validation.
Result of Microgravity Fluid Dynamics Captured with the SPHERES-Slosh Experiment
Lapilli, Gabriel; Kirk, Daniel; Gutierrez, Hector; Schallhorn, Paul; Marsell, Brandon; Roth, Jacob; Moder, Jeffrey
2015-01-01
This paper provides an overview of the SPHERES-Slosh Experiment (SSE) aboard the International Space Station (ISS) and presents on-orbit results with data analysis. In order to predict the location of the liquid propellant during all times of a spacecraft mission, engineers and mission analysts utilize Computational Fluid Dynamics (CFD). These state-of-the-art computer programs numerically solve the fluid flow equations to predict the location of the fluid at any point in time during different spacecraft maneuvers. The models and equations used by these programs have been extensively validated on the ground, but long duration data has never been acquired in a microgravity environment. The SSE aboard the ISS is designed to acquire this type of data, used by engineers on earth to validate and improve the CFD prediction models, improving the design of the next generation of space vehicles as well as the safety of current missions. The experiment makes use of two Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES) connected by a frame. In the center of the frame there is a plastic, pill shaped tank that is partially filled with green-colored water. A pair of high resolution cameras records the movement of the liquid inside the tank as the experiment maneuvers within the Japanese Experimental Module test volume. Inertial measurement units record the accelerations and rotations of the tank, making the combination of stereo imaging and inertial data the inputs for CFD model validation.
Filion, L; Hermes, M; Ni, R; Dijkstra, M
2010-12-28
Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett-Chandler-type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and van Megen [Phys. Rev. E 55, 3054 (1997)], Sinn et al. [Prog. Colloid Polym. Sci. 118, 266 (2001)], Schätzel and Ackerson [Phys. Rev. E 48, 3766 (1993)], and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [Nature 409, 1020 (2001)]. When the rates are examined in units of the long-time diffusion coefficient, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behavior for low supersaturation. Additionally, we examined the precritical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appears independent of the simulation method, and in all cases, the nuclei contains on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles.
Evolution of fluid-like granular ejecta generated by sphere impact
Marston, Jeremy
2012-05-01
We present results from an experimental study of the speed and shape of the ejecta formed when a solid sphere impacts onto a granular bed. We use high-speed imaging at frame rates up to 100 000 f.p.s. to provide direct measurement of individual grain velocities and ejecta angles as well as the overall evolution of the granular ejecta. For larger grain sizes, the emergence velocities of the grains during the early stage flow, i.e. before the main ejecta curtain forms, increase with the kinetic energy of the impacting sphere but are inversely proportional to the time from impact. We also observe that the fastest grains, which can obtain velocities up to five times that of the impacting sphere (V g/V 0 = 5), generally emerge at the earliest times and with the lowest ejection angles. As the grain size is decreased, a more fluid-like behaviour is observed whereby the ejected material first emerges as a thin sheet of grains between the sphere and the bed surface, which is also seen when a sphere impacts a liquid pool. In this case, the sheet velocity is approximately double that of the impacting sphere (V s/V 0 = 2) and independent of the bulk packing fraction. For the finest grains we provide evidence of the existence of a vortex ring inside the ejecta curtain where grains following the air flow are entrained through the curtain. In contrast to predictions from previous studies, we find that the temporal evolution of the ejecta neck radius is not initially quadratic but rather approaches a square-root dependence on time, for the finest grains with the highest impact kinetic energy. The evolution therefore approaches that seen for the crown evolution in liquid drop impacts. By using both spherical glass beads and coarse sands, we show that the size and shape distribution are critical in determining the post-impact dynamics whereby the sands exhibit a qualitatively different response to impact, with grains ejected at lower speeds and at later times than for the glass
Hansen-Goos, Hendrik
2016-04-01
We derive an analytical equation of state for the hard-sphere fluid that is within 0.01% of computer simulations for the whole range of the stable fluid phase. In contrast, the commonly used Carnahan-Starling equation of state deviates by up to 0.3% from simulations. The derivation uses the functional form of the isothermal compressibility from the Percus-Yevick closure of the Ornstein-Zernike relation as a starting point. Two additional degrees of freedom are introduced, which are constrained by requiring the equation of state to (i) recover the exact fourth virial coefficient B4 and (ii) involve only integer coefficients on the level of the ideal gas, while providing best possible agreement with the numerical result for B5. Virial coefficients B6 to B10 obtained from the equation of state are within 0.5% of numerical computations, and coefficients B11 and B12 are within the error of numerical results. We conjecture that even higher virial coefficients are reliably predicted.
Directory of Open Access Journals (Sweden)
B. Hribar-Lee
2013-01-01
Full Text Available Very recently the effect of equisized charged hard sphere solutes in a mixture with core-softened fluid model on the structural and thermodynamic anomalies of the system has been explored in detail by using Monte Carlo simulations and integral equations theory (J. Chem. Phys., Vol. 137, 244502 (2012. Our objective of the present short work is to complement this study by considering univalent ions of unequal diameters in a mixture with the same soft-core fluid model. Specifically, we are interested in the analysis of changes of the temperature of maximum density (TMD lines with ion concentration for three model salt solutes, namely sodium chloride, potassium chloride and rubidium chloride models. We resort to Monte Carlo simulations for this purpose. Our discussion also involves the dependences of the pair contribution to excess entropy and of constant volume heat capacity on the temperature of maximum density line. Some examples of the microscopic structure of mixtures in question in terms of pair distributions functions are given in addition.
Felderhof, B U
2016-01-01
Translational and rotational swimming at small Reynolds number of a planar assembly of identical spheres immersed in an incompressible viscous fluid is studied on the basis of a set of equations of motion for the individual spheres. The motion of the spheres is caused by actuating forces and forces derived from a direct interaction potential, as well as hydrodynamic forces exerted by the fluid as frictional and added mass hydrodynamic interactions. The translational and rotational swimming velocities of the assembly are deduced from momentum and angular momentum balance equations. The mean power required during a period is calculated from an instantaneous power equation. Expressions are derived for the mean swimming velocities and the power, valid to second order in the amplitude of displacements from the relative equilibrium positions. Hence these quantities can be evaluated for prescribed periodic displacements. Explicit calculations are performed for three spheres interacting such that they form an equilat...
Gurin, Péter; Varga, Szabolcs
2013-12-28
The effect of confinement is studied on the local structure of two- and three-dimensional hard-core fluids. The hard disks are confined between two parallel lines, while the hard spheres are in a cylindrical hard pore. In both cases only nearest neighbour interactions are allowed between the particles. The vertical and longitudinal pair correlation functions are determined by means of the exact transfer-matrix method. The vertical pair correlation function indicates that the wall induced packing constraint gives rise to a zigzag (up-down sequence) shaped close packing structure in both two- and three-dimensional systems. The longitudinal pair correlation function shows that both systems transform continuously from a one-dimensional gas-like behaviour to a zigzag solid-like structure with increasing density.
Fragile-strong fluid crossover and universal relaxation times in a confined hard-disk fluid.
Yamchi, Mahdi Zaeifi; Ashwin, S S; Bowles, Richard K
2012-11-30
We show that a system of hard disks confined to a narrow channel exhibits a fragile-strong fluid crossover located at the maximum of the isobaric heat capacity and that the relaxation times for different channel widths fall onto a single master curve when rescaled by the relaxation times and temperatures of the crossover. Calculations of the configurational entropy and the inherent structure equation of state find that the crossover is related to properties of the jamming landscape for the model but that the Adam-Gibbs relation does not predict the relaxation behavior. We also show that a facilitated dynamics description of the system, where kinetically excited regions are identified with local packing arrangements of the disks, successfully describes the fragile-strong crossover.
Perturbation approach for equation of state for hard-sphere and Lennard–Jones pure ﬂuids
Indian Academy of Sciences (India)
S B Khasare; M S Deshpande
2011-06-01
In this paper we have established the equation of state (EOS) for liquids. The EOS was established for hard-sphere (HS) ﬂuid along with Lennard–Jones (LJ) ﬂuid incorporating perturbation techniques. The calculations are based on suitable axiomatic functional forms for surface tension $S_m (r )$, $r ≥ d/2$ with intermolecular separation , as a variable, and is an arbitrary real number (pole). The results for /ρ from the present EOS thus obtained are compared with Percus-Yevick (PY), scaled particle theory (SPT), and Carnahan–Starling (CS). In addition, we have found a simple EOS for the HS ﬂuid in the region which represents the simulation data accurately. It is observed that, this EOS for HS gives, PY (pressure) for = 0, CS for = 4/5, whereas for = 1 it corresponds to SPT.
Rainone, Corrado; Urbani, Pierfrancesco; Yoshino, Hajime; Zamponi, Francesco
2015-01-01
We consider the adiabatic evolution of glassy states under external perturbations. The formalism we use is very general. Here we use it for infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i.e., compression or (volume preserving) shear strain, and we compute the response of glassy states to such perturbations: pressure and shear stress. We find that both quantities overshoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. Finally, we study the stability of the glass basins towards breaking into sub-basins, corresponding to a Gardner transition. We find that close to the dynamical transition, glasses undergo a Gardner transition after an infinitesimal perturbation.
Li, Da; Xu, Hong
2015-10-01
The bulk modulus of hard sphere solids has been computed directly by constant pressure Monte-Carlo simulations, using the histogram of the volume fluctuations. In considering first the one-component system, we show that the method is accurate in a large range of pressures, including high-pressure regime. The method is then applied to a polydisperse solid with relatively low polydispersity index. For illustrative purpose, we took a three-component mixture with symmetric size-distribution, and we studied the solid phase (fcc crystal) of this system. Our results show that the equation of state is very sensitive to the polydispersity. Furthermore, in the high-pressure region, where no (accurate) analytical fit for the equation of state exists, our simulations are able to predict the bulk modulus of such systems.
Kelkar, Aniruddha V; Franses, Elias I; Corti, David S
2014-04-08
Brownian aggregation in concentrated hard-sphere dispersions is studied using models and Brownian dynamics (BD) simulations. Two new theoretical models are presented and compared to several existing approaches and BD simulation results, which serve as benchmarks. The first new model is an improvement over an existing local density approximation (LDA)-based model. The other is based on the more rigorous Fundamental measure theory (FMT) applied to the "liquid-state" dynamic density-functional theory (DDFT). Both models provide significant improvements over the classical Smoluchowski model. The predictions of the new FM-DDFT-based model for aggregation kinetics are in excellent agreement with BD simulation results for dispersions with initial particle volume fractions, ϕ, up to 0.35 (close to the hard-sphere freezing transition at ϕ = 0.494). In contrast to previous approaches, the nonideal particle diffusion effects and the initial and time-dependent short-range ordering in concentrated dispersions due to entropic packing effects are explicitly considered here, in addition to the unsteady-state effects. The greater accuracy of the FM-DDFT-based model compared to that of the LDA-based models indicates that nonlocal contributions to particle diffusion (only accounted for in the former) play important roles in aggregation. At high concentrations, the FM-DDFT-based model predicts aggregation half-times and gelation times that are up to 2 orders of magnitude shorter than those of the Smoluchowski model. Moreover, the FM-DDFT-based model predicts asymmetric cluster-cluster aggregation rate constants, at least for short times. Overall, a rigorous mechanistic understanding of the enhancement of aggregation kinetics in concentrated dispersions is provided.
Numerical simulations of granular dynamics. I. Hard-sphere discrete element method and tests
Richardson, Derek C; Murdoch, Naomi; Michel, Patrick
2013-01-01
We present a new particle-based (discrete element) numerical method for the simulation of granular dynamics, with application to motions of particles on small solar system body and planetary surfaces. The method employs the parallel N-body tree code pkdgrav to search for collisions and compute particle trajectories. Collisions are treated as instantaneous point-contact events between rigid spheres. Particle confinement is achieved by combining arbitrary combinations of four provided wall primitives, namely infinite plane, finite disk, infinite cylinder, and finite cylinder, and degenerate cases of these. Various wall movements, including translation, oscillation, and rotation, are supported. We provide full derivations of collision prediction and resolution equations for all geometries and motions. Several tests of the method are described, including a model granular "atmosphere" that achieves correct energy equipartition, and a series of tumbler simulations that show the expected transition from tumbling to ...
Dilatonic Brans-Dicke Anisotropic Collapsing Fluid Sphere And de Broglie Quantum Wave Motion
Ghaffarnejad, Hossein
2014-01-01
Two dimensional analogue of vacuum sector of the Brans Dicke gravity is used to study dynamics of anisotropic spherical symmetric perfect fluid. We solve dynamical equations and obtain internal metric of the fluid describing a stellar collapse with equation of state as $\\rho(p)=2(p-p_0^3/p^3)$ for $\\omega>>1$. We determine time dependence oscillations of particles ensemble, apparent and event horizons location where the particles same as the event horizon are trapped by the apparent horizon and they are located on back of the apparent horizon. We determine radial accelerating velocity of the particles ensemble from the phase part of the corresponding de Broglie quantum wave of the fluid sphere. A good correspondence between our classical and de Broglie quantum wave solutions are obtained by overlapping diagram of the classical solutions of relative distance of the particles, apparent and event horizons with particles ensemble density where finally the particles together with the event horizon located back of ...
Interior Solutions of Fluid Sphere in f(R,T) Gravity Admitting Conformal Killing Vectors
Zubair, M; Rahaman, F; Abbas, G
2016-01-01
We discuss the interior solutions of fluid Sphere in f(R,T) gravity admitting conformal killing vectors, where R is Ricci scalar and T is trace of energy momentum tensor. The solutions corresponding to isotropic and anisotropic configurations have been investigated explicitly. Further, the anisotropic case has been dealt by the utilization of linear equation of state. The results for both cases have been interpreted graphically. The equation of state parameter, integration constants and other parameters of the theory have been chosen to find the central density equal to standard value of central density of the compact objects. The energy conditions as well as stability of the solutions have been investigated in the background of f(R,T) gravity.
Brunet, Charles; Amokrane, Said
2011-01-01
We study by Monte Carlo simulation a binary mixture of neutral and dipolar hard-spheres with non-additive diameters. With a view to understanding the interplay between population inversion for an open pore and the demixing phase transitions, the mixture is considered in the bulk and confined between two parallel hard-walls modeling a slit pore. A uniform field is applied in the pore in order to control its composition as shown previously. The demixing lines in the bulk and in the pore are studied by the Gibbs Ensemble Monte Carlo method. The open pore-bulk mixture equilibrium is studied by a combination of canonical/grand canonical simulations. A moderate electrostatic coupling is considered for remaining close to the conditions in which a jump in the adsorption of the minority species has been observed at zero field. Demixing lines are given in the bulk and for two different pore widths in parallel and normal fields, together with population inversion paths. Similarly to the effect of geometrical confinement...
The hard ellipsoid-of-revolution fluid. I. Monte Carlo simulations - Comment
Frenkel, D; Mulder, BM
2002-01-01
We present the results of Monte Carlo simulations on a system of hard ellipsoids of revolution with length-to-breadth ratios a/b = 3, 2.75, 2, 1.25 and b/a = 3, 2.75, 2, 1.25. We identify four distinct phases, viz. isotropic fluid, nematic fluid, ordered solid and plastic solid. The coexistence poin
The hard ellipsoid-of-revolution fluid I. Monte Carlo simulations
Frenkel, D.; Mulder, B.M.
1985-01-01
We present the results of Monte Carlo simulations on a system of hard ellipsoids of revolution with length-to-breadth ratios a/b = 3, 2·75, 2, 1·25 and b/a = 3, 2·75, 2, 1·25. We identify four distinct phases, viz. isotropic fluid, nematic fluid, ordered solid and plastic solid. The coexistence poin
Tracer diffusion of hard-sphere binary mixtures under nano-confinement
Marini Bettolo Marconi, Umberto; Malgaretti, Paolo; Pagonabarraga, Ignacio
2015-11-01
The physics of diffusion phenomena in nano- and microchannels has attracted a lot of attention in recent years, due to its close connection with many technological, medical, and industrial applications. In the present paper, we employ a kinetic approach to investigate how the confinement in nanostructured geometries affects the diffusive properties of fluid mixtures and leads to the appearance of properties different from those of bulk systems. In particular, we derive an expression for the friction tensor in the case of a bulk fluid mixture confined to a narrow slit having undulated walls. The boundary roughness leads to a new mechanism for transverse diffusion and can even lead to an effective diffusion along the channel larger than the one corresponding to a planar channel of equivalent section. Finally, we discuss a reduction of the previous equation to a one dimensional effective diffusion equation in which an entropic term encapsulates the geometrical information on the channel shape.
Qiao, Yu; Chen, Minxin
2015-01-01
The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model has a very similar form to one term of the LHS model, but LHS...
Soft Dynamics simulation. 2. Elastic spheres undergoing a T(1) process in a viscous fluid.
Rognon, P; Gay, C
2009-11-01
Robust empirical constitutive laws for granular materials in air or in a viscous fluid have been expressed in terms of timescales based on the dynamics of a single particle. However, some behaviours such as viscosity bifurcation or shear localization, observed also in foams, emulsions, and block copolymer cubic phases, seem to involve other micro-timescales which may be related to the dynamics of local particle reorganizations. In the present work, we consider a T(1) process as an example of a rearrangement. Using the Soft Dynamics simulation method introduced in the first paper of this series, we describe theoretically and numerically the motion of four elastic spheres in a viscous fluid. Hydrodynamic interactions are described at the level of lubrication (Poiseuille squeezing and Couette shear flow) and the elastic deflection of the particle surface is modeled as Hertzian. The duration of the simulated T(1) process can vary substantially as a consequence of minute changes in the initial separations, consistently with predictions. For the first time, a collective behaviour is thus found to depend on a parameter other than the typical volume fraction of particles.
Stradner, Anna; Bucciarelli, Saskia; Casal, Lucia; Foffi, Giuseppe; Thurston, George; Farago, Bela; Schurtenberger, Peter
2014-03-01
The occurrence of an arrest transition in concentrated colloid suspensions and its dependence on the interaction potential is a hot topic in soft matter. Such arrest transitions can also occur in concentrated protein solutions, as they exist e.g. in biological cells or are increasingly used in pharmaceutical formulations. Here we demonstrate the applicability of concepts from colloid science to understand the dynamics of concentrated protein solutions. In this presentation we report a combination of 3D light scattering, small-angle X-ray scattering and neutron spin echo measurements to study the structural properties as well as the collective and self diffusion of proteins in highly concentrated solutions on the relevant length and time scales. We demonstrate that various arrest scenarios indeed exist for different globular proteins. The proteins chosen are different bovine lens crystallins. We report examples of hard and attractive glass transitions and arrested spinodal decomposition directly linked to the effective pair potentials determined in static scattering experiments for the different proteins. We discuss these different arrest scenarios in view of possible applications of dense protein solutions as well as in view of their possible relevance for living systems.
Direct observation in 3d of structural crossover in binary hard sphere mixtures
Statt, Antonia; Pinchaipat, Rattachai; Turci, Francesco; Evans, Robert; Royall, C. Patrick
2016-04-01
For binary fluid mixtures of spherical particles in which the two species are sufficiently different in size, the dominant wavelength of oscillations of the pair correlation functions is predicted to change from roughly the diameter of the large species to that of the small species along a sharp crossover line in the phase diagram [C. Grodon et al., J. Chem. Phys. 121, 7869 (2004)]. Using particle-resolved colloid experiments in 3d we demonstrate that crossover exists and that its location in the phase diagram is in quantitative agreement with the results of both theory and our Monte-Carlo simulations. In contrast with previous work [J. Baumgartl et al., Phys. Rev. Lett. 98, 198303 (2007)], where a correspondence was drawn between crossover and percolation of both species, in our 3d study we find that structural crossover is unrelated to percolation.
Parisi, Giorgio
In a hard spheres systems particles cannot overlap. Increasing the density we reach a point where most of the particles are blocked and the density cannot be increased any more: this is the jamming point. The jamming point separates the phase, where all the constraint can be satisfied, from an unsatifiable phase, where spheres do have to overlap. A scaling theory of the behavior around the jamming critical point has been formulated and a few critical exponents have been introduced. The exponents are apparently super-universal, as far as they do seem to be independent from the space dimensions. The mean field version of the model (i.e. the infinite dimensions limit) has been solved analytically using broken replica symmetry techniques and the computed critical exponents have been found in a remarkable agreement with three-dimensional and two-dimensional numerical results and experiments. The theory predicts in hard spheres (in glasses) a new transition (the Gardener transition) from the replica symmetric phase to the replica broken phase at high density (at low temperature), in agreement with simulations on hard sphere systems. I will briefly discuss the possible consequences of this new picture on the very low temperature behavior of glasses in the quantum regime.
Concentration profiles in the wake of a sphere buried in a granular bed through which fluid flows
Energy Technology Data Exchange (ETDEWEB)
Guedes de Carvalho, J.R.F.; Delgado, J.M.P.Q.; Alves, M.A. [Porto Univ., Dpet. de Engenharia Quimica, Faculdade de Engenharia (Portugal)
2005-07-01
The concentration distribution in the wake of a soluble sphere immersed in a granular bed of inerts has been obtained numerically, for transport by both advection and diffusion/dispersion. Fluid flow in the granular bed around the sphere was assumed to follow Darcy's law and, at each point, dispersion of solute was considered in both the cross-stream and stream-wise directions. The elliptic PDE equation, resulting from a differential material balance on the solute, has been solved numerically over a wide range of values of the relevant parameters. (authors)
Is there solid-on-solid contact in a sphere-wall collision in a viscous fluid?
Birwa, Sumit Kumar; Govindarajan, Rama; Menon, Narayanan
2016-01-01
We study experimentally the process of normal collision between a sphere falling through a viscous fluid, and a solid plate below. As has previously been discovered, there is a well-defined threshold Stokes number above which the sphere rebounds from such a collision. Our experiment tests for direct contact between the colliding bodies, and contrary to prior expectations shows that solid-on-solid contact occurs even for Stokes numbers just above the threshold for rebounding. The details of the contact mechanics depend on the surface quality of the solids, but our experiments and a model calculation indicate that such contact is generic and will occur for any realistic surface roughness.
Maximally random jamming of one-component and binary hard-disk fluids in two dimensions.
Xu, Xinliang; Rice, Stuart A
2011-02-01
We report calculations of the density of maximally random jamming of one-component and binary hard-disk fluids. The theoretical structure used provides a common framework for description of the hard-disk liquid-to-hexatic, the liquid-to-hexagonal crystal, and the liquid to maximally random jammed state transitions. Our analysis is based on locating a particular bifurcation of the solutions of the integral equation for the inhomogeneous single-particle density at the transition between different spatial structures. The bifurcation of solutions we study is initiated from the dense metastable fluid, and we associate it with the limit of stability of the fluid, which we identify with the transition from the metastable fluid to a maximally random jammed state. For the one-component hard-disk fluid the predicted packing fraction at which the metastable fluid to maximally random jammed state transition occurs is 0.84, in excellent agreement with the experimental value 0.84 ± 0.02. The corresponding analysis of the limit of stability of a binary hard-disk fluid with specified disk-diameter ratio and disk composition requires extra approximations in the representations of the direct correlation function, the equation of state, and the number of order parameters accounted for. Keeping only the order parameter identified with the largest peak in the structure factor of the highest-density regular lattice with the same disk- diameter ratio and disk composition as the binary fluid, the predicted density of maximally random jamming is found to be 0.84-0.87, depending on the equation of state used, and very weakly dependent on the ratio of disk diameters and the fluid composition, in agreement with both experimental data and computer simulation data.
Large attractive depletion interactions in soft repulsive-sphere binary mixtures.
Cinacchi, Giorgio; Martínez-Ratón, Yuri; Mederos, Luis; Navascués, Guillermo; Tani, Alessandro; Velasco, Enrique
2007-12-07
We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.
Effective Depletion Potential of Colloidal Spheres
Institute of Scientific and Technical Information of China (English)
LI Wei-Hua; MA Hong-Ru
2004-01-01
@@ A new semianalytical method, which is a combination of the density functional theory with Rosenfeld density functional and the Ornstein-Zernike equation, is proposed for the calculation of the effective depletion potentials between a pair of big spheres immersed in a small hard sphere fluid. The calculated results are almost identical to the integral equation method with the Percus-Yevick approximation, and are also in agreement well with the Monte Carlo simulation results.
Combined temperature and density series for fluid-phase properties. I. Square-well spheres
Energy Technology Data Exchange (ETDEWEB)
Elliott, J. Richard [Chemical and Biomolecular Engineering Department, The University of Akron, Akron, Ohio 44325-3906 (United States); Schultz, Andrew J.; Kofke, David A. [Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200 (United States)
2015-09-21
Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B{sub 2}(β) η + B{sub 3}(β) η{sup 2} + B{sub 4}(β) η{sup 3} + ⋯, where Z is the compressibility factor, η is the packing fraction, and the B{sub i}(β) coefficients are expanded as a power series in reciprocal temperature, β, about β = 0. The methodology is demonstrated for square-well spheres with λ = [1.2-2.0], where λ is the well diameter relative to the hard core. For this model, the B{sub i} coefficients can be expressed in closed form as a function of β, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the β series. Expanding the B{sub i} coefficients in β provides a correspondence between the power series in density (typically called the virial series) and the power series in β (typically called thermodynamic perturbation theory, TPT). The coefficients of the β series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in β. These comparisons show good agreement at first order in β, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in β. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in β appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid.
Combined temperature and density series for fluid-phase properties. I. Square-well spheres
Elliott, J. Richard; Schultz, Andrew J.; Kofke, David A.
2015-09-01
Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B2(β) η + B3(β) η2 + B4(β) η3 + ⋯, where Z is the compressibility factor, η is the packing fraction, and the Bi(β) coefficients are expanded as a power series in reciprocal temperature, β, about β = 0. The methodology is demonstrated for square-well spheres with λ = [1.2-2.0], where λ is the well diameter relative to the hard core. For this model, the Bi coefficients can be expressed in closed form as a function of β, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the β series. Expanding the Bi coefficients in β provides a correspondence between the power series in density (typically called the virial series) and the power series in β (typically called thermodynamic perturbation theory, TPT). The coefficients of the β series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in β. These comparisons show good agreement at first order in β, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in β. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in β appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid.
Energy Technology Data Exchange (ETDEWEB)
Ayadim, A; Amokrane, S [Physique des Liquides et Milieux Complexes, Faculte des Sciences et Technologie, Universite Paris-Est (Creteil), 61 Avenue du General de Gaulle, 94010 Creteil Cedex (France)
2010-01-27
The accuracy of the structural data obtained from the recently proposed generalization to non-additive hard-spheres (Schmidt 2004 J. Phys.: Condens. Matter 16 L351) of Rosenfeld's functional is investigated. The radial distribution functions computed from the direct correlation functions generated by the functional, through the Ornstein-Zernike equations, are compared with those obtained from the density profile equations in the test-particle limit, without and with test-particle consistency. The differences between these routes and the role of the optimization of the parameters of the reference system when the functional is used to obtain the reference bridge functional are discussed in the case of symmetric binary mixtures of non-additive hard-spheres. The case of highly asymmetric mixtures is finally briefly discussed.
Pizio, O; Bucior, K; Patrykiejew, A; Sokołowski, S
2005-12-01
We consider a density-functional theory to describe nonuniform fluids composed of chain molecules, containing a charged segment each, and spherical counterions. The chain molecules are modeled as freely jointed chains of hard spheres, the counterions are oppositely charged spheres of the same diameter as all segments of chain molecules. The theory is applied to study the structure of adsorbed layers, the excess adsorption isotherms, the capacitance of the double layer, and the potential of the zero charge. We show that all electric properties are strongly dependent on the length of the chain molecules. Moreover, these properties are also dependent on the position of the charged segment in the chain.
Monte Carlo study of the isotropic-nematic transition in a fluid of thin hard disk
Frenkel, D.; Eppenga, R.
1982-01-01
The first numerical determination of the thermodynamic isotropic-nematic transition in a simple three-dimensional model fluid, viz., a system of infinitely thin hard platelets, is reported. Thermodynamic properties were studied with use of the constant-pressure Monte Carlo method; Widom's particle-i
One-dimensional hard rod fluid in a disordered porous medium: scaled particle theory
Directory of Open Access Journals (Sweden)
M. Holovko
2012-06-01
Full Text Available The scaled particle theory is applied to a description of thermodynamic properties of one-dimensional hard rod fluid in disordered porous media. To this end, we extended the SPT2 approach, which had been developed previously. Analytical expressions are obtained for the chemical potential and pressure of a hard-rod fluid in hard rod and overlapping hard rod matrices. A series of new approximations for SPT2 are proposed. It is shown that apart from two well known porosities such as geometrical porosity and specific probe particle porosity, a new type of porosity defined by the maximum value of packing fraction of fluid particles in porous medium should be taken into account. The grand canonical Monte-Carlo simulations are performed to verify the accuracy of the SPT2 approach in combination with the new approximations. It is observed that the theoretical description proposed in this study essentially improves the results up to the highest values of fluid densities.
Yabunaka, Shunsuke; Onuki, Akira
2017-09-01
We study universal critical adsorption on a solid sphere and a solid cylinder in a fluid at bulk criticality, where preferential adsorption occurs. We use a local functional theory proposed by Fisher et al. [M. E. Fisher and P. G. de Gennes, C. R. Acad. Sci. Paris Ser. B 287, 207 (1978); M. E. Fisher and H. Au-Yang, Physica A 101, 255 (1980), 10.1016/0378-4371(80)90112-0]. We calculate the mean order parameter profile ψ (r ) , where r is the distance from the sphere center and the cylinder axis, respectively. The resultant differential equation for ψ (r ) is solved exactly around a sphere and numerically around a cylinder. A strong adsorption regime is realized except for very small surface field h1, where the surface order parameter ψ (a ) is determined by h1 and is independent of the radius a . If r considerably exceeds a , ψ (r ) decays as r-(1 +η ) for a sphere and r-(1 +η )/2 for a cylinder in three dimensions, where η is the critical exponent in the order parameter correlation at bulk criticality.
Felderhof, B U
2015-01-01
A mechanical model of swimming and flying in an incompressible viscous fluid is studied on the basis of assumed equations of motion. The system is modeled as an assembly of rigid spheres subject to elastic direct interactions and to periodic actuating forces which sum to zero. Hydrodynamic interactions are taken into account in the virtual mass matrix and in the friction matrix of the assembly. An equation of motion is derived for the velocity of the geometric center of the assembly. The mean power is calculated as the sum of the mean rate of dissipation and a mean energy loss which is related to the rate of change of the virtual mass. The full range of viscosity is covered, so that the theory can be applied to the flying of birds, as well as to the swimming of fish or bacteria. As an example a system of three equal spheres moving along a common axis is studied.
Computer simulation of rod-sphere mixtures
Antypov, D
2003-01-01
Results are presented from a series of simulations undertaken to investigate the effect of adding small spherical particles to a fluid of rods which would otherwise represent a liquid crystalline (LC) substance. Firstly, a bulk mixture of Hard Gaussian Overlap particles with an aspect ratio of 3:1 and hard spheres with diameters equal to the breadth of the rods is simulated at various sphere concentrations. Both mixing-demixing and isotropic-nematic transition are studied using Monte Carlo techniques. Secondly, the effect of adding Lennard-Jones particles to an LC system modelled using the well established Gay-Berne potential is investigated. These rod-sphere mixtures are simulated using both the original set of interaction parameters and a modified version of the rod-sphere potential proposed in this work. The subject of interest is the internal structure of the binary mixture and its dependence on density, temperature, concentration and various parameters characterising the intermolecular interactions. Both...
Tian, Jianxiang; Mulero, A
2016-01-01
Despite the fact that more that more than 30 analytical expressions for the equation of state of hard-disk fluids have been proposed in the literature, none of them is capable of reproducing the currently accepted numeric or estimated values for the first eighteen virial coefficients. Using the asymptotic expansion method, extended to the first ten virial coefficients for hard-disk fluids, fifty-seven new expressions for the equation of state have been studied. Of these, a new equation of state is selected which reproduces accurately all the first eighteen virial coefficients. Comparisons for the compressibility factor with computer simulations show that this new equation is as accurate as other similar expressions with the same number of parameters. Finally, the location of the poles of the 57 new equations shows that there are some particular configurations which could give both the accurate virial coefficients and the correct closest packing fraction in the future when higher virial coefficients than the t...
Mitri, F G
2016-12-01
The goal of this work is to demonstrate the emergence of a spin torque singularity (i.e. zero spin torque) and a spin rotation reversal of a small Rayleigh lipid/fat viscous fluid sphere located arbitrarily in space in the field of an acoustical Bessel vortex beam. This counter-intuitive property of negative spin torque generation suggests a direction of spin rotation in opposite handedness of the angular momentum carried by the incident beam. Such effects may open new capabilities in methods of quantitative characterization to determine physical properties such as viscosity, viscoelasticity, compressibility, stiffness, etc., and other techniques for the rotation and positioning using acoustical tractor beams and tweezers, invisibility cloaks, and acoustically-engineered composite metamaterials to name a few examples. Based on the descriptions for the velocity potential of the incident beam and the scattering coefficients of the sphere in the long-wavelength approximation limit, simplified expressions for the spin and orbital radiation torque components are derived. For beams with (positive or negative) unit topological charge (m=±1), the axial spin torque component for a Rayleigh absorptive sphere is maximal at the center of the beam, while it vanishes for |m|>1 therein. Moreover, the longitudinal orbital torque component, causing the sphere to rotate around the center of the beam is evaluated based on the mathematical decomposition using the gradient, scattering and absorption transverse radiation force vector components. It is shown that there is no contribution of the gradient transverse force to the orbital torque, which is only caused by the scattering and absorption transverse force components. Though the incident acoustical vortex beam carrying angular momentum causes the sphere to rotate in the same orbital direction of the beam handedness, it induces a spin torque singularity (i.e. zero spin torque) and subsequent sign reversal. This phenomenon of
Gaygadzhiev, Zafir; Corredig, Milena; Alexander, Marcela
2008-04-15
Understanding the underlying processes that govern interparticle interactions in colloidal systems is fundamental to predicting changes in their bulk properties. In this paper we discuss the colloidal behavior of casein micelles and protein-stabilized fat globules individually and in a mixture. The colloidal interactions were observed by transmission diffusing wave spectroscopy. The turbidity parameter, l*, and the diffusion coefficients of the samples studied were measured experimentally and compared to the theoretically calculated parameters for a hard-sphere system. The light scattering properties of casein micelles (volume fraction phi = 0.1-0.2) dispersed in milk permeate showed no deviation from the theoretically predicted model. Whey protein isolate (WPI)-stabilized emulsions (phi = 0.025-0.1) prepared either in milk permeate or in 5 mM imidazole buffer at pH 6.8 showed a behavior identical to that of the hard-sphere model. Similarly to the WPI-stabilized fat globules, the sodium caseinate (NaCas)-stabilized emulsions (phi = 0.025-0.1) prepared in milk permeate also showed resemblance to the theory. In contrast, NaCas-stabilized emulsions prepared in 5 mM imidazole buffer exhibited some discrepancy from the theoretically calculated parameters. The deviation from theory is attributed to the enhanced steric stabilization properties of these droplets in a low ionic strength environment. When recombined milks made from concentrated milk and WPI- and NaCas-stabilized droplets prepared in permeate (phi = 0.125-0.2) were studied, the experimental data showed a significant deviation from the theoretical behavior of a hard-sphere model due to mixing of two different species.
Hayashi, Tomohiko; Oshima, Hiraku; Harano, Yuichi; Kinoshita, Masahiro
2016-09-01
For neutral hard-sphere solutes, we compare the reduced density profile of water around a solute g(r), solvation free energy μ, energy U, and entropy S under the isochoric condition predicted by the two theories: dielectrically consistent reference interaction site model (DRISM) and angle-dependent integral equation (ADIE) theories. A molecular model for water pertinent to each theory is adopted. The hypernetted-chain (HNC) closure is employed in the ADIE theory, and the HNC and Kovalenko-Hirata (K-H) closures are tested in the DRISM theory. We also calculate g(r), U, S, and μ of the same solute in a hard-sphere solvent whose molecular diameter and number density are set at those of water, in which case the radial-symmetric integral equation (RSIE) theory is employed. The dependences of μ, U, and S on the excluded volume and solvent-accessible surface area are analyzed using the morphometric approach (MA). The results from the ADIE theory are in by far better agreement with those from computer simulations available for g(r), U, and μ. For the DRISM theory, g(r) in the vicinity of the solute is quite high and becomes progressively higher as the solute diameter d U increases. By contrast, for the ADIE theory, it is much lower and becomes further lower as d U increases. Due to unphysically positive U and significantly larger |S|, μ from the DRISM theory becomes too high. It is interesting that μ, U, and S from the K-H closure are worse than those from the HNC closure. Overall, the results from the DRISM theory with a molecular model for water are quite similar to those from the RSIE theory with the hard-sphere solvent. Based on the results of the MA analysis, we comparatively discuss the different theoretical methods for cases where they are applied to studies on the solvation of a protein.
Oshima, Hiraku; Kinoshita, Masahiro
2015-04-14
In earlier works, we showed that the entropic effect originating from the translational displacement of water molecules plays the pivotal role in protein folding and denaturation. The two different solvent models, hard-sphere solvent and model water, were employed in theoretical methods wherein the entropic effect was treated as an essential factor. However, there were similarities and differences in the results obtained from the two solvent models. In the present work, to unveil the physical origins of the similarities and differences, we simultaneously consider structural transition, cold denaturation, and pressure denaturation for the same protein by employing the two solvent models and considering three different thermodynamic states for each solvent model. The solvent-entropy change upon protein folding/unfolding is decomposed into the protein-solvent pair (PA) and many-body (MB) correlation components using the integral equation theories. Each component is further decomposed into the excluded-volume (EV) and solvent-accessible surface (SAS) terms by applying the morphometric approach. The four physically insightful constituents, (PA, EV), (PA, SAS), (MB, EV), and (MB, SAS), are thus obtained. Moreover, (MB, SAS) is discussed by dividing it into two factors. This all-inclusive investigation leads to the following results: (1) the protein-water many-body correlation always plays critical roles in a variety of folding/unfolding processes; (2) the hard-sphere solvent model fails when it does not correctly reproduce the protein-water many-body correlation; (3) the hard-sphere solvent model becomes problematic when the dependence of the many-body correlation on the solvent number density and temperature is essential: it is not quite suited to studies on cold and pressure denaturating of a protein; (4) when the temperature and solvent number density are limited to the ambient values, the hard-sphere solvent model is usually successful; and (5) even at the ambient
Glasslike behavior of a hard-disk fluid confined to a narrow channel
Robinson, J. F.; Godfrey, M. J.; Moore, M. A.
2016-03-01
Disks moving in a narrow channel have many features in common with the glassy behavior of hard spheres in three dimensions. In this paper we study the caging behavior of the disks that sets in at characteristic packing fraction ϕd. Four-point overlap functions similar to those studied when investigating dynamical heterogeneities have been determined from event-driven molecular dynamics simulations and the time-dependent dynamical length scale has been extracted from them. The dynamical length scale increases with time and, on the equilibration time scale, it is proportional to the static length scale associated with the zigzag ordering in the system, which grows rapidly above ϕd. The structural features responsible for the onset of caging and the glassy behavior are easy to identify as they show up in the structure factor, which we have determined exactly from the transfer-matrix approach.
Hydrodynamic Interactions between Two Equally Sized Spheres in Viscoelastic Fluids in Shear Flow
Snijkers, F.; Pasquino, R.; Vermant, J.
2013-01-01
The effect of using a viscoelastic suspending medium, on the;in-plane hydrodynamic interaction between two equally sized spheres in shear flow is studied experimentally to understand flow-induced assembly behavior (i.e., string formation). A counterrotating device equipped with a Couette geometry is
Palberg, Thomas; Wette, Patrick; Herlach, Dieter M
2016-02-01
The interfacial free energy is a central quantity in crystallization from the metastable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from these data effective nonequilibrium values for the interfacial free energy between the emerging bcc nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory (CNT). A strictly linear increase of the interfacial free energy was observed as a function of increased metastability. Here, we further analyze these data for five aqueous suspensions of charged spheres and one binary mixture. We utilize a simple extrapolation scheme and interpret our findings in view of Turnbull's empirical rule. This enables us to present the first systematic experimental estimates for a reduced interfacial free energy, σ(0,bcc), between the bcc-crystal phase and the coexisting equilibrium fluid. Values obtained for σ(0,bcc) are on the order of a few k(B)T. Their values are not correlated to any of the electrostatic interaction parameters but rather show a systematic decrease with increasing size polydispersity and a lower value for the mixture as compared to the pure components. At the same time, σ(0) also shows an approximately linear correlation to the entropy of freezing. The equilibrium interfacial free energy of strictly monodisperse charged spheres may therefore be still greater.
Murad, Mohammad Hassan
2014-01-01
In this work some families of relativistic anisotropic charged fluid spheres have been obtained by solving Einstein-Maxwell field equations with preferred form of one of the metric potentials, a suitable forms of electric charge distribution and pressure anisotropy functions. The resulting equation of state (EOS) of the matter distribution has been obtained. Physical analysis shows that the relativistic stellar structure for matter distribution obtained in this work may reasonably model an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g. electrically charged bare strange stars). These models permit a simple method of systematically fixing bounds on the maximum possible mass of cold compact electrically charged self-bound stars. It has been demonstrated numerically that the maximum compactness and mass increase in the presence of electric field and anisotropic pressures. Based on the a...
Application of a circular 2D hard-sphere microphone array for higher-order Ambisonics auralization
DEFF Research Database (Denmark)
Weller, Tobias; Favrot, Sylvain Emmanuel; Buchholz, Jörg
2011-01-01
A circular microphone array mounted on a rigid sphere was realized and its application to higherorder Ambisonics (HOA) auralization was analysed. Besides the 2D Ambisonics application this array design provides a promising basis for the development of a mixed-order Ambisonics recording system...
Effects of curing protocols on fluid kinetics and hardness of resin cements.
Svizero, Nádia da Rocha; Silva, Marília Santos; Alonso, Roberta Caroline Bruschi; Rodrigues, Flávia Pires; Hipólito, Vinícius Di; Carvalho, Ricardo Marins; D'Alpino, Paulo Henrique Perlatti
2013-01-01
The effects of polymerization protocols on water sorption/solubility, the diffusion coefficient (D), the flux (J), and the hardness (KH) of two resin cements were evaluated. The materials were manipulated and divided into three groups (n=6) according to the curing protocol: PA=photoactivation (40 s); DP=delayed photoactivation (10 min self-curing plus 40 s photoactivated); CA=chemical activation. After desiccation, the specimens were weighed, stored in water (37ºC), evaluated over 28-days, and hardness recorded. Chemical activation resulted in lower net water uptake, D, and J for RelyX ARC (RX). For Variolink II (VL), CA yielded equivalent D and lower J; however, photoactivation resulted in lower net water uptake. Hardness of VL was less affected by the water storage, irrespective of the polymerization protocol. Considering the water diffusion parameters, VL demonstrated immediate photoactivation dependence; for RX, a chemical activation. Different polymerization protocols affect the fluid kinetics and the hardness of the resin cements tested.
Löwe, H.; Picard, G.
2015-11-01
The description of snow microstructure in microwave models is often simplified to facilitate electromagnetic calculations. Within dense media radiative transfer (DMRT), the microstructure is commonly described by sticky hard spheres (SHS). An objective mapping of real snow onto SHS is however missing which prevents measured input parameters from being used for DMRT. In contrast, the microwave emission model of layered snowpacks (MEMLS) employs a conceptually different approach, based on the two-point correlation function which is accessible by tomography. Here we show the equivalence of both electromagnetic approaches by reformulating their microstructural models in a common framework. Using analytical results for the two-point correlation function of hard spheres, we show that the scattering coefficient in both models only differs by a factor which is close to unity, weakly dependent on ice volume fraction and independent of other microstructural details. Additionally, our analysis provides an objective retrieval method for the SHS parameters (diameter and stickiness) from tomography images. For a comprehensive data set we demonstrate the variability of stickiness and compare the SHS diameter to the optical equivalent diameter. Our results confirm the necessity of a large grain-size scaling when relating both diameters in the non-sticky case, as previously suggested by several authors.
Jammed lattice sphere packings
Kallus, Yoav; Marcotte, Étienne; Torquato, Salvatore
2013-01-01
We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a...
Study of sound scattering of porous spheres in fluid%流体中多孔球中的声散射研究
Institute of Scientific and Technical Information of China (English)
庄悦; 刘晓宙; 龚秀芬
2011-01-01
沙子是一种形状复杂多样的材料,在建筑材料、海底沉积物等中都是以聚集的形式存在,这样聚集的大量沙子的特性难以直观了解,为了了解这些特性,可以用声学的方法,利用沙子对声波的反射、散射信号从中了解到沙子的一些信息.本文主要从理论上研究沙子对声波的散射特性,研究流体多孔介质中的声传播,我们引入了经典的Biot理论,建立了球坐标系下的多孑球散射模型,通过多孔球界面的边界条件推导出了表示材料散射特性的散射系数矩阵,接着利用球坐标系下的散射形式函数推导出了流体多孔球的背向散射谱.理论上获得了流体多孔球的散射特性公式,用数值的方法进行对其进行了计算,采用流体多孔沙的参数值得到了背向散射谱,并讨论了不同孔隙率及沙粒半径下的背向散射情况.%Sand is a kind of complicated material with different shape and size, and it is widely used in the architectural material and it exists in the marine sediment with the clustering morphology.As the sand is always in collective form, its characteristics are hard to know directly.In order to get some properties of sand, one way is to use the acoustical method, that is, we can get some useful and relative information from the reflecting and scattering signals of sand.In this paper, we theoretically analyze the wave propagation in porous medium in fluid and the characteristics of sound scattering by sand.The classical Biot's theory is introduced and the scattering model in spherical coordinates when acoustic wave travels through porous sphere medium is built in this paper.The scattering coefficient matrix that represents the scattering characters of the materials is obtained through the boundary conditions of the interface of the porous spherical medium; the backscattering spectra of porous sphere in fluid are derived.After we theoretically deduce formula of the scattering of the porous
Effects of background rotation on a towed-sphere wake in a stably stratified fluid
Energy Technology Data Exchange (ETDEWEB)
Spedding, G.R. [Southern California Univ., Los Angeles (United States). Dept. of Aerospace and Mechanical Engineering; Fincham, A.M. [Laboratoire Coriolis, Grenoble (France). Inst. de Mechanique
1999-12-01
The wake of a towed sphere in a stable background density gradient can be considered a convenient model problem for studying the emergence and longevity of the coherent patches of alternate-signed vertical vorticity that comprise the late wake. Wake anticyclones, with sense of rotation opposite to the background rotation, were spread out over a large area, and were less strongly peaked than their cyclonic counterparts, with the magnitude of the asymmetry depending on f/N. The observed asymmetries are consistent with existing data on homogenous wake flows with rotation.
Dilatonic Brans-Dicke Anisotropic Collapsing Fluid Sphere And de Broglie Quantum Wave Motion
Ghaffarnejad, Hossein
2016-08-01
Two dimensional (2D) analogue of vacuum sector of the Brans Dicke (BD) gravity [1] is studied to obtain dynamics of anisotropic spherically symmetric perfect fluid. Our obtained static solutions behave as dark matter with state equation but in non-static regimes behave as regular perfect fluid with barotropic index ϒ > 0. Positivity property of total mass of the fluid causes that the BD parameter to be ω >2/3 and/or ω 0 the apparent horizon is covered by event horizon where the cosmic censorship hypothesis is still valid. According to the model [1], we obtain de Broglie pilot wave of our metric solution which describes particles ensemble which become distinguishable via different values of ω. Incident current density of particles ensemble on the horizons is evaluated which describe the ‘Hawking radiation’. The de Brogle-Bohm quantum potential effect is calculated also on the event (apparent) horizon which is independent (dependent) to values of ω.
Kobryn, A E; Tokarchuk, M V
1999-01-01
An Enskog-Landau kinetic equation for a many-component system of charged hard spheres is proposed. It has been obtained from the Liouville equation with modified boundary conditions by the method of nonequilibrium statistical operator. On the basis of this equation the normal solutions and transport coefficients such as bulk kappa and shear eta viscosities, thermal conductivity lambda, mutual diffusion D^{\\alpha\\beta} and thermal diffusion D_T^\\alpha have been obtained for a binary mixture in the first approximation using the Chapman-Enskog method. Numerical calculations of all transport coefficients for mixtures Ar-Kr, Ar-Xe, Kr-Xe with different concentrations of compounds have been evaluated for the cases of absence and presence of long-range Coulomb interactions. The results are compared with those obtained from other theories and experiment.
Directory of Open Access Journals (Sweden)
N.Matubayasi
2007-12-01
Full Text Available The hydration free energy of hard-sphere solute is evaluated over a wide range of size using the method of energy representation, information-theoretic approach, reference interaction site model, and scaled-particle theory. The former three are distribution function theories and the hydration free energy is formulated to reflect the solution structure through distribution functions. The presence of the volume-dependent term is pointed out for the distribution function theories, and the asymptotic behavior in the limit of large solute size is identified. It is indicated that the volume-dependent term is a key to the improvement of distribution function theories toward the application to large molecules.
(N+2)-Dimensional Anisotropic Charged Fluid Spheres with Pressure: Riccati Equation
Bijalwan, Naveen
2011-01-01
General exact (N+2)-dimensional,n>=2 solutions in general theory of relativity of Einstein-Maxwell field equations for static anisotropic spherically symmetric distribution of charged fluid are expressed in terms of radial pressure. Subsequently, metrics (e(lambda) and e(nu)), matter density and electric intensity are expressible in terms of pressure. We extend the methodology used by Bijalwan (2011a, 2011c, 2011d) for charged and anisotropic fluid. Consequently, radial pressure is found to be an invertible arbitrary function of w(c1+c2r^2), where c1 and c2(non zero) are arbitrary constants, and r is the radius of star, i.e. p=p(w) . We present a general solution for static anisotropic charged pressure fluid in terms for w. We reduce to the problem of finding solutions to anisotropic charged fluid to that of finding solutions to a Riccati equation. Also, these solutions satisfy barotropic equation of state relating the radial pressure to the energy density.
Gurin, Péter; Varga, Szabolcs
2015-06-01
We extend the transfer matrix method of one-dimensional hard core fluids placed between confining walls for that case where the particles can pass each other and at most two layers can form. We derive an eigenvalue equation for a quasi-one-dimensional system of hard squares confined between two parallel walls, where the pore width is between σ and 3σ (σ is the side length of the square). The exact equation of state and the nearest neighbor distribution functions show three different structures: a fluid phase with one layer, a fluid phase with two layers, and a solid-like structure where the fluid layers are strongly correlated. The structural transition between differently ordered fluids develops continuously with increasing density, i.e., no thermodynamic phase transition occurs. The high density structure of the system consists of clusters with two layers which are broken with particles staying in the middle of the pore.
Gurin, Péter; Varga, Szabolcs
2015-06-14
We extend the transfer matrix method of one-dimensional hard core fluids placed between confining walls for that case where the particles can pass each other and at most two layers can form. We derive an eigenvalue equation for a quasi-one-dimensional system of hard squares confined between two parallel walls, where the pore width is between σ and 3σ (σ is the side length of the square). The exact equation of state and the nearest neighbor distribution functions show three different structures: a fluid phase with one layer, a fluid phase with two layers, and a solid-like structure where the fluid layers are strongly correlated. The structural transition between differently ordered fluids develops continuously with increasing density, i.e., no thermodynamic phase transition occurs. The high density structure of the system consists of clusters with two layers which are broken with particles staying in the middle of the pore.
Energy Technology Data Exchange (ETDEWEB)
Gurin, Péter; Varga, Szabolcs [Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém H-8201 (Hungary)
2015-06-14
We extend the transfer matrix method of one-dimensional hard core fluids placed between confining walls for that case where the particles can pass each other and at most two layers can form. We derive an eigenvalue equation for a quasi-one-dimensional system of hard squares confined between two parallel walls, where the pore width is between σ and 3σ (σ is the side length of the square). The exact equation of state and the nearest neighbor distribution functions show three different structures: a fluid phase with one layer, a fluid phase with two layers, and a solid-like structure where the fluid layers are strongly correlated. The structural transition between differently ordered fluids develops continuously with increasing density, i.e., no thermodynamic phase transition occurs. The high density structure of the system consists of clusters with two layers which are broken with particles staying in the middle of the pore.
Energy Technology Data Exchange (ETDEWEB)
Murad, Mohammad Hassan [BRAC University, Department of Mathematics and Natural Sciences, Dhaka (Bangladesh); Fatema, Saba [Daffodil International University, Department of Natural Sciences, Dhaka (Bangladesh)
2015-11-15
In this work some families of relativistic anisotropic charged fluid spheres have been obtained by solving the Einstein-Maxwell field equations with a preferred form of one of the metric potentials, and suitable forms of electric charge distribution and pressure anisotropy functions. The resulting equation of state (EOS) of the matter distribution has been obtained. Physical analysis shows that the relativistic stellar structure for the matter distribution considered in this work may reasonably model an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g., electrically charged bare strange stars). Furthermore these models permit a simple method of systematically fixing bounds on the maximum possible mass of cold compact electrically charged self-bound stars. It has been demonstrated, numerically, that the maximum compactness and mass increase in the presence of an electric field and anisotropic pressures. Based on the analytic models developed in this present work, the values of some relevant physical quantities have been calculated by assuming the estimated masses and radii of some well-known potential strange star candidates like PSR J1614-2230, PSR J1903+327, Vela X-1, and 4U 1820-30. (orig.)
Two-Yukawa fluid at a hard wall: Field theory treatment
Energy Technology Data Exchange (ETDEWEB)
Kravtsiv, I.; Patsahan, T.; Holovko, M. [Institute for Condensed Matter Physics, National Academy of Sciences, 1 Svientsitskii St., 79011 Lviv (Ukraine); Caprio, D. di [Institute of Research of Chimie Paris, CNRS-Chimie ParisTech, 11 rue Pierre et Marie Curie, 75005 Paris (France)
2015-05-21
We apply a field-theoretical approach to study the structure and thermodynamics of a two-Yukawa fluid confined by a hard wall. We derive mean field equations allowing for numerical evaluation of the density profile which is compared to analytical estimations. Beyond the mean field approximation, analytical expressions for the free energy, the pressure, and the correlation function are derived. Subsequently, contributions to the density profile and the adsorption coefficient due to Gaussian fluctuations are found. Both the mean field and the fluctuation terms of the density profile are shown to satisfy the contact theorem. We further use the contact theorem to improve the Gaussian approximation for the density profile based on a better approximation for the bulk pressure. The results obtained are compared to computer simulation data.
Directory of Open Access Journals (Sweden)
R. Robinson Gnanadurai
2016-09-01
Full Text Available Hard turning with minimal fluid application is a recently developed technique to alleviate the problem associated with cutting fluid. During this process, very small quantity of cutting fluid is applied as a narrow high velocity pulsing jet at the cutting zone. As the quantity of cutting fluid is very small, some auxiliary cooling of tool using heat pipe was attempted in the present work to enhance heat dissipation and thus improving cutting performance. Heat pipe was installed in vertical position in contact with the tool for extracting more heat from the tool. The influence of heat pipe cooling of tool on the cutting performance was analyzed by Taguchi's design of experiments. It was observed that the use of heat pipe in minimal fluid application reduced cutting temperature and tool wear to a maximum of 22% and 15%, respectively, in comparison with conventional hard turning with minimal fluid application without the aid of heat pipe. It appears that heat pipe can be successively employed as a mean of cooling the tool during hard turning with minimal fluid application.
Modelling of a compact anisotropic star as an anisotropic fluid sphere in $f(T)$ gravity
Momeni, D; Qaisar, S; Zaz, Zaid; Myrzakulov, R
2016-01-01
In this paper, we have studied the new exact model of anisotropic star in $f(T)$ theory of gravity. The dynamical equations in $f(T)$ theory with the anisotropic fluid have been solved by using Krori-Barua solution. We have determined that all the obtained solutions are free from central singularity and potentially stable. The observed values of mass and radius of the different strange stars RX J 1856-37, Her X-1, and Vela X-12 have been used to calculate the values of unknown constants in Krori and Barua metric. The physical parameters like anisotropy, stability and redshift of the stars have been investigated in detail.
Wilke, Antje; Weber, Jens
2012-05-14
The preparation of ultraporous polymer resins using a straightforward hard-templating synthesis is presented. Self-assembly of silica nanospheres into densely packed glasses allows an easy preparation of templates. Polydivinylbenzene resins with surface areas of up to 1000 m(2) g(-1) are synthesized as a model system and porosity analysis reveals bimodal porosity (spherical mesopores and micropores within the pore walls). The prepared systems can be further functionalized without loss of porosity as demonstrated by sulfonation. Because of their large pore sizes (13-28 nm), they are efficient adsorbents also for large molecules. Finally, the systems can also be used as model systems for the study of the pore drying and collapse process, which is of crucial importance for any application of mesoporous polymers.
Viscosity of a nucleonic fluid
Mekjian, Aram Z
2012-01-01
The viscosity of nucleonic matter is studied both classically and in a quantum mechanical description. The collisions between particles are modeled as hard sphere scattering as a baseline for comparison and as scattering from an attractive square well potential. Properties associated with the unitary limit are developed which are shown to be approximately realized for a system of neutrons. The issue of near perfect fluid behavior of neutron matter is remarked on. Using some results from hard sphere molecular dynamics studies near perfect fluid behavior is discussed further.
Acoustic Interaction Forces and Torques Acting on Suspended Spheres in an Ideal Fluid.
Lopes, J Henrique; Azarpeyvand, Mahdi; Silva, Glauber T
2016-01-01
In this paper, the acoustic interaction forces and torques exerted by an arbitrary time-harmonic wave on a set of N objects suspended in an inviscid fluid are theoretically analyzed. We utilize the partial-wave expansion method with translational addition theorem and re-expansion of multipole series to solve the related multiple scattering problem. We show that the acoustic interaction force and torque can be obtained using the farfield radiation force and torque formulas. To exemplify the method, we calculate the interaction forces exerted by an external traveling and standing plane wave on an arrangement of two and three olive-oil droplets in water. The droplets' radii are comparable to the wavelength (i.e., Mie scattering regime). The results show that the acoustic interaction forces present an oscillatory spatial distribution which follows the pattern formed by interference between the external and rescattered waves. In addition, acoustic interaction torques arise on the absorbing droplets whenever a nonsymmetric wavefront is formed by the external and rescattered waves' interference.
Schallhorn, Paul; Roth, Jacob; Marsell, Brandon; Kirk, Daniel; Gutierrez, Hector; Saenz-Otero, Alvar; Dorney, Daniel; Moder, Jeffrey
2013-01-01
Accurate prediction of coupled fluid slosh and launch vehicle or spacecraft dynamics (e.g., nutation/precessional movement about various axes, attitude changes, ect.) requires Computational Fluid Dynamics (CFD) models calibrated with low-gravity, long duration slosh data. Recently completed investigations of reduced gravity slosh behavior have demonstrated the limitations of utilizing parabolic flights on specialized aircraft with respect to the specific objectives of the experiments. Although valuable data was collected, the benefits of longer duration low-gravity environments were clearly established. The proposed research provides the first data set from long duration tests in zero gravity that can be directly used to benchmark CFD models, including the interaction between the sloshing fluid and the tank/vehicle dynamics. To explore the coupling of liquid slosh with the motion of an unconstrained tank in microgravity, NASA's Kennedy Space Center, Launch Services Program has teamed up with the Florida Institute of Technology (FIT), Massachusetts Institute of Technology (MIT) and the NASA Game Changing Development Program (GCD) to perform a series of slosh dynamics experiments on the International Space Station using the SPHERES platform. The Synchronized Position Hold Engage Reorient Experimental Satellites (SPHERES) testbed provides a unique, free-floating instrumented platform on ISS that can be utilized in a manner that would solve many of the limitations of the current knowledge related to propellant slosh dynamics on launch vehicle and spacecraft fuel tanks. The six degree of freedom (6-DOF) motion of the SPHERES free-flyer is controlled by an array of cold-flow C02 thrusters, supplied from a built-in liquid C02 tank. These SPHERES can independently navigate and re-orient themselves within the ISS. The intent of this project is to design an externally mounted tank to be driven inside the ISS by a set of two SPHERES devices (Figure 1). The tank geometry
Phase behaviour of deionized binary mixtures of charged colloidal spheres.
Lorenz, Nina J; Schöpe, Hans Joachim; Reiber, Holger; Palberg, Thomas; Wette, Patrick; Klassen, Ina; Holland-Moritz, Dirk; Herlach, Dieter; Okubo, Tsuneo
2009-11-18
We review recent work on the phase behaviour of binary charged sphere mixtures as a function of particle concentration and composition. Both size ratios Γ and charge ratios Λ are varied over a wide range. Unlike the case for hard spheres, the long-ranged Coulomb interaction stabilizes the crystal phase at low particle concentrations and shifts the occurrence of amorphous solids to particle concentrations considerably larger than the freezing concentration. Depending on Γ and Λ, we observe upper azeotrope, spindle, lower azeotrope and eutectic types of phase diagrams, all known well from metal systems. Most solids are of body centred cubic structure. Occasionally stoichiometric compounds are formed at large particle concentrations. For very low Γ, entropic effects dominate and induce a fluid-fluid phase separation. Since for charged spheres the charge ratio Λ is also decisive for the type of phase diagram, future experiments with charge variable silica spheres are suggested.
Lin, Neil Y C; Cheng, Xiang; Cohen, Itai
2014-03-28
Using a novel biaxial confocal rheoscope, we investigate the flow of the shear induced vorticity aligned string phase [X. Cheng et al., Proc. Natl. Acad. Sci. U. S. A., 2011, 109, 63], which has a highly anisotropic microstructure. Using biaxial shear protocols we show that we have excellent control of the string phase anisotropic morphology. We choose a shear protocol that drives the system into the string phase. Subsequently, a biaxial force measurement device is used to determine the suspension rheology along both the flow and vorticity directions. We find no measurable dependence of the suspension stress response along the shear and vorticity directions due to the hydrodynamically induced string morphology. In particular, we find that the suspension's high frequency stress response is nearly identical along the two orthogonal directions. While we do observe an anisotropic stress response at lower shear frequencies associated with shear thinning, we show that this anisotropy is independent of the shear induced string structure. These results suggest that for the range of flows explored, Brownian and hydrodynamic contributions to the stress arising from the anisotropic suspension microstructure are sufficiently weak that they do not significantly contribute to the rheology. Collectively, this study presents a general and powerful approach for using biaxial confocal rheometry to elucidate the relationship between microstructure and rheology in complex fluids driven far-from-equilibrium.
Jammed lattice sphere packings.
Kallus, Yoav; Marcotte, Étienne; Torquato, Salvatore
2013-12-01
We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a model for the jamming and glass transitions that enables exploration of much higher dimensions than are usually accessible.