Tracer diffusion in hard sphere fluids from molecular to hydrodynamic regimes

Abstract

Molecular dynamics is employed to investigate tracer diffusion in hard sphere fluids. Reduced densities (rho*=rhosigma(3), sigma is the diameter of bath fluid particles) ranging from 0.02 to 0.52 and tracers ranging in diameter from 0.125sigma to 16sigma are considered. Finite-size effects are found to pose a significant problem and can lead to seriously underestimated tracer diffusion constants even in systems that are very large by simulation standards. It is shown that this can be overcome by applying a simple extrapolation formula that is linear in the reciprocal cell length L(-1), allowing us to obtain infinite-volume estimates of the diffusion constant for all tracer sizes. For higher densities, the range of tracer diameters considered spans diffusion behavior from molecular to hydrodynamic regimes. In the hydrodynamic limit our extrapolated results are clearly consistent with the theoretically expected slip boundary conditions, whereas the underestimated values obtained without extrapolation could easily be interpreted as approaching the stick limit. It is shown that simply adding the Enskog and hydrodynamic contributions gives a reasonable qualitative description of the diffusion behavior but tends to overestimate the diffusion constant. We propose another expression that fits the simulation results for all densities and tracer diameters.

Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass asymmetry

“…The dynamic properties of binary fluid systems where one particle species differs from the other only in size, mass or both of these parameters have been the subject of a large number of studies during the last years [1,2,3,4,5,6,7,8,9,10,11,12]. The increasing interest is, on the one hand, due to the fact that such systems serve as simple models for colloids and micellar solutions, which are of prime importance in many scientific areas such as biology or biochemistry, on the other hand it is sparked by the rapidly growing capabilities of modern computer hardware which allows us to investigate parameter ranges and system sizes that were not accessible before.…”

A Perturbation Theory for Friction of a Large Particle Immersed in a Binary Solvent

“…This fundamental phenomenon is of interest to many researchers of biology as well as physics [1][2][3][4][5][6][7][8]. In particular, one cannot disregard the friction from solvent particles when considering the dynamical functions of biomolecules [7].…”

“…To study the effect, many microscopic theories were previously developed [12,13]. When the solute particle is large, however, the theories are not suitable because of a finite-size effect [5]. We avoid this difficulty by employing a perturbation expansion, assuming that the ratio between the radii of the solvent and solute particles is a small perturbation parameter.…”

Test of Stokes-Einstein Formula for a Tracer in a Large System by Molecular Dynamics Simulation

“…He concluded that for σ 2 /σ 1 > 1 the SE prediction is not valid for mass ratios 1/16 ≤ m 2 / m 1 ≤ 50, and that for σ 2 /σ 1 > 2 and for m 2 /m 1 < 1 the SE regime is reached for smaller densities than for the same system but m 2 /m 1 > 1. The test of SE formula for the size ratio or the mass ratio of the tracer was further discussed by Sokolovskii et al 8 for hard sphere fluids, by Cappelezzo et al 9 for Lennard-Jones (LJ) fluids, by Funazukuri et al 10 for supercritical and liquid conditions, and by Harris 11 for LJ, molecular, and ionic liquids.…”

“…A time dependent friction coefficient ζ(t) is defined from the force autocorrelation function by 19 (8) and through the Laplace transforms of the projected and unprojected force autocorrelation functions, [14][15][16] in t space, the following relation is obtained .…”