The direct correlation functions and bridge functions for hard spheres near a large hard sphere

Douglas Henderson; Kwong‐yu Chan; Léo Degrève

doi:10.1063/1.468324

Low Density Density Derivative of the Self-Correlation Function of a Hard Sphere Gas

Canadian Journal of Physics ◽

10.1139/p74-121 ◽

1974 ◽

Vol 52 (10) ◽

pp. 902-916

Author(s):

D. G. Blair ◽

N. K. Pope

Keyword(s):

Correlation Functions ◽

Hard Sphere ◽

Hard Spheres ◽

Time Model ◽

Direct Derivation ◽

Linearized Boltzmann Equation ◽

Langevin Diffusion ◽

Classical Gas ◽

Density Derivative ◽

Derivatives Of

For the classical gas of hard spheres, exact expressions are derived for [∂Is(r,t)/∂n]n = 0, [∂Is(q,t)/∂n]n = 0, and [∂Ss(q,ω)/∂n]n = 0, the density derivatives of the Van Hove self-correlation functions. The relationships between the direct derivation using the activity expansion, and the derivations based on the generalized kinetic equation and the linearized Boltzmann equation are discussed. Properties of these density derivatives and of the corresponding self-correlation functions, as given by the first two terms of the density expansion, are discussed in detail. The expressions are compared with the hard sphere results of Desai and Nelkin. of Sears and of Mazenko et al.; and also with the predictions of the single relaxation time model and the Langevin diffusion model.

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Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc2009510 ◽

2010 ◽

Vol 75 (3) ◽

pp. 359-369 ◽

Cited By ~ 6

Author(s):

Mariano López De Haro ◽

Anatol Malijevský ◽

Stanislav Labík

Keyword(s):

Equation Of State ◽

Binary Mixtures ◽

Hard Sphere ◽

Hard Spheres ◽

Virial Coefficients ◽

Fluid Mixture ◽

Binary Fluid ◽

Virial Series ◽

Consolute Point ◽

Critical Constants

Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

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On the calculation of equilibrium time correlation functions in hard-sphere fluids

Journal of Statistical Physics ◽

10.1007/bf01023481 ◽

1989 ◽

Vol 54 (1-2) ◽

pp. 273-313 ◽

Cited By ~ 9

Author(s):

I. M. de Schepper ◽

E. G. D. Cohen ◽

B. Kamgar-Parsi

Keyword(s):

Correlation Functions ◽

Hard Sphere ◽

Time Correlation ◽

Time Correlation Functions ◽

Equilibrium Time

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Correlation functions in quantum hard-sphere fluids at short times or high frequencies, and high-energy neutron scattering

Physical Review B ◽

10.1103/physrevb.30.1266 ◽

1984 ◽

Vol 30 (3) ◽

pp. 1266-1281 ◽

Cited By ~ 20

Author(s):

T. R. Kirkpatrick

Keyword(s):

Neutron Scattering ◽

Correlation Functions ◽

Hard Sphere ◽

High Energy ◽

High Frequencies ◽

High Energy Neutron ◽

Energy Neutron ◽

Short Times

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Event-Driven Molecular Dynamics Simulation of Hard-Sphere Gas Flows in Microchannels

Mathematical Problems in Engineering ◽

10.1155/2015/842837 ◽

2015 ◽

Vol 2015 ◽

pp. 1-12 ◽

Cited By ~ 8

Author(s):

Volkan Ramazan Akkaya ◽

Ilyas Kandemir

Keyword(s):

Molecular Dynamics ◽

Hard Sphere ◽

Stokes Equations ◽

Hard Spheres ◽

Flow Characteristics ◽

Dynamics Simulation ◽

Navier Stokes ◽

Gas Flows ◽

Linearized Boltzmann Equation ◽

Event Driven

Classical solution of Navier-Stokes equations with nonslip boundary condition leads to inaccurate predictions of flow characteristics of rarefied gases confined in micro/nanochannels. Therefore, molecular interaction based simulations are often used to properly express velocity and temperature slips at high Knudsen numbers (Kn) seen at dilute gases or narrow channels. In this study, an event-driven molecular dynamics (EDMD) simulation is proposed to estimate properties of hard-sphere gas flows. Considering molecules as hard-spheres, trajectories of the molecules, collision partners, corresponding interaction times, and postcollision velocities are computed deterministically using discrete interaction potentials. On the other hand, boundary interactions are handled stochastically. Added to that, in order to create a pressure gradient along the channel, an implicit treatment for flow boundaries is adapted for EDMD simulations. Shear-Driven (Couette) and Pressure-Driven flows for various channel configurations are simulated to demonstrate the validity of suggested treatment. Results agree well with DSMC method and solution of linearized Boltzmann equation. At low Kn, EDMD produces similar velocity profiles with Navier-Stokes (N-S) equations and slip boundary conditions, but as Kn increases, N-S slip models overestimate slip velocities.

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

Journal of Fluid Mechanics ◽

10.1017/s0022112010004490 ◽

2011 ◽

Vol 667 ◽

pp. 403-425 ◽

Cited By ~ 10

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.

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