scholarly journals The Divergence of the Viscosity of a Fluid of Hard Spheres as an Indicator for the Fluid-Solid Phase Transition

1987 ◽  
Vol 42 (3) ◽  
pp. 231-235
Author(s):  
Hyearn-Maw Koo ◽  
Siegfried Hess
Keyword(s):  
Hard Sphere ◽  
Solid Phase ◽  
Hard Spheres ◽  
Pair Correlation ◽  
Transition Density ◽  
Colloidal Dispersions ◽  
Number Density ◽  
Relative Pair ◽  
Hard Sphere Fluid ◽  
Solid Phase Transition

Solution of the Kirkwood-Smoluchowski equation for a hard sphere fluid yields an expression for the viscosity which shows a dramatic pretransitional increase and a divergence at a number density close to that one observed in computer simulations and in colloidal dispersions. The value for the transition density stems from a boundary condition at the surface of the hard sphere in the configurational relative pair-space and makes use of the density dependence of the pair-correlation function and of its derivative at the point of contact.

New bounds on the sedimentation velocity for hard, charged and adhesive hard-sphere colloids

2011 ◽  
Vol 667 ◽  
pp. 403-425 ◽  
Author(s):  
W. TODD GILLELAND ◽  
SALVATORE TORQUATO ◽  
WILLIAM B. RUSSEL
Keyword(s):  
Brownian Motion ◽  
Upper Bound ◽  
Hard Sphere ◽  
Large Scale ◽  
Hard Spheres ◽  
Colloidal Dispersions ◽  
Sedimentation Velocity ◽  
Close Packing ◽  
Interparticle Potential ◽  
Equilibrium Microstructure

The sedimentation velocity of colloidal dispersions is known from experiment and theory at dilute concentrations to be quite sensitive to the interparticle potential with attractions/repulsions increasing/decreasing the rate significantly at intermediate volume fractions. Since the differences necessarily disappear at close packing, this implies a substantial maximum in the rate for attractions. This paper describes the derivation of a robust upper bound on the velocity that reflects these trends quantitatively and motivates wider application of a simple theory formulated for hard spheres. The treatment pertains to sedimentation velocities slow enough that Brownian motion sustains an equilibrium microstructure without large-scale inhomogeneities in density.

scholarly journals BEHAVIOR OF THE CONFINED HARD-SPHERE FLUID WITHIN NANOSLITS: A FUNDAMENTAL-MEASURE DENSITY-FUNCTIONAL THEORY STUDY

2008 ◽  
Vol 07 (04n05) ◽  
pp. 245-253 ◽  
Author(s):  
MOHAMMAD KAMALVAND ◽  
TAHMINEH (EZZAT) KESHAVARZI ◽  
G. ALI MANSOORI
Keyword(s):  
Density Functional Theory ◽  
Density Profile ◽  
Hard Sphere ◽  
Density Functional ◽  
Hard Spheres ◽  
Calculated Data ◽  
Computational Procedure ◽  
Functional Theory ◽  
Hard Sphere Fluid ◽  
Wide Range

A property of central interest for theoretical study of nanoconfined fluids is the density distribution of molecules. The density profile of the hard-sphere fluids confined within nanoslit pores is a key quantity for understanding the configurational behavior of confined real molecules. In this report, we produce the density profile of the hard-sphere fluid confined within nanoslit pores using the fundamental-measure density-functional theory (FM-DFT). FM-DFT is a powerful approach to studying the structure and the phase behavior of nanoconfined fluids. We report the computational procedure and the calculated data for nanoslits with different widths and for a wide range of hard-sphere fluid densities. The high accuracy of the resulting density profiles and optimum grid-size values in numerical integration are verified. The data reveal a number of interesting features of hard spheres in nanoslits, which are different from the bulk hard-sphere systems. These data are also useful for a variety of purposes, including obtaining the shear stress, thermal conductivity, adsorption, solvation forces, free volume and prediction of phase transitions.

Statistical Geometry and Cavity Correlations in the Hard Sphere Fluid

2008 ◽  
Vol 73 (3) ◽  
pp. 344-357 ◽  
Author(s):  
Robin J. Speedy ◽  
Richard K. Bowles
Keyword(s):  
Computer Simulation ◽  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Sphere Diameter ◽  
Statistical Geometry ◽  
Empirical Expression ◽  
Hard Sphere Fluid ◽  
A Site ◽  
Exact Relations

The statistical geometry of a system of hard spheres is discussed in terms of the volumes Vj that lie with a sphere diameter, σ, of exactly j sphere centres. A site that has no sphere centre within σ is called a cavity site. We focus on the probability n00(r) that two sites separated by r are both cavity sites. n00(0), n00(σ), and the limiting slope (d ln n00(r)/dr)r=0, are all known in terms of the thermodynamic properties. The Vj and n00(r) are measured by computer simulation and an empirical expression, which satisfies the known exact relations, is shown to represent n00(r) precisely in the range 0 ≤ r ≤ σ.

Decay of pair correlation functions

1977 ◽  
Vol 55 (9) ◽  
pp. 761-766 ◽  
Author(s):  
Yoshio Tago ◽  
William R. Smith
Keyword(s):  
Correlation Function ◽  
Correlation Length ◽  
Correlation Functions ◽  
Pair Correlation Function ◽  
Hard Sphere ◽  
Pair Correlation ◽  
Direct Correlation Function ◽  
Pair Correlation Functions ◽  
Hard Sphere Fluid

The decay equation, which determines the correlation length and the period of the pair correlation function of a fluid at large distances, is discussed using the Ornstein–Zernike equation when the direct correlation function vanishes rapidly at large distances. The decay equation is solved numerically using the exact hard sphere and sticky hard sphere fluid results from the Percus–Yevick approximation. In the case of the hard sphere fluid, oscillatory decay is always obtained. For the sticky hard sphere fluid, we obtain a locus both in the pressure–temperature plane and the density–temperature plane such that the decay is monotonic inside and oscillatory outside the locus.

Fluid-Solid Phase Transition of a Hard-Sphere Bose System

1971 ◽  
Vol 3 (2) ◽  
pp. 776-780 ◽  
Author(s):  
Jean-Pierre Hansen ◽  
Dominique Levesque ◽  
Daniel Schiff
Keyword(s):  
Phase Transition ◽  
Hard Sphere ◽  
Solid Phase ◽  
Bose System ◽  
Solid Phase Transition

scholarly journals Statistical mechanics of hard spheres: the scaled particle theory of the hard sphere fluid revisited

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Bruno Baeyens
Keyword(s):  
Equation Of State ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Virial Coefficients ◽  
Scaled Particle Theory ◽  
Particle Theory ◽  
Simulation Data ◽  
Hard Sphere Fluid ◽  
Two Parameters ◽  
Compressibility Factors

The aim of this paper is to exhaust the possibilities offered by the scaled particle theory as far as possible and to confirm the reliability of the virial coefficients found in the literature, especially the estimated ones: B i for i > 11. In a previous article (J.Math.Phys.36,201,1995) a theoretical equation of state for the hard sphere fluid was derived making use of the ideas of the so called scaled particle theory which has been developed by Reiss et al.(J.Chem.Phys.31,369,1959). It contains two parameters which could be calculated. The equation of state agrees with the simulation data up to high densities, where the fluid is metastable. The derivation was besed on a generalized series expansion. The virial coefficients B 2 , B 3 and B 4 are exactly reproduced and B 5 , B 6 and B 7 to within small deviations, but the higher ones up to B 18 are systematically and significantly smaller than the values found in the literature. The scaled particle theory yields a number of equations of which only four were used. In this paper we make use of seven equations to calculate the compressibility factors of the fluid. They agree with the simulation data slightly better than those yielded by the old equation. Moreover, the differences between the calculated virial coefficients B i and those found in the literature up to B 18 are very small (less than 4 percent).

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