Tracer diffusion in hard sphere fluids from molecular to hydrodynamic regimes

• Published in: The Journal of chemical physics 2006-11, Vol.125 (20), p.204502-204502-10
• Main Authors: Sokolovskii, R. O., Thachuk, M., Patey, G. N.
• Format: Article
• Language: English
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.2397074

Molecular dynamics is employed to investigate tracer diffusion in hard sphere fluids. Reduced densities ( ρ * = ρ σ 3 , σ is the diameter of bath fluid particles) ranging from 0.02 to 0.52 and tracers ranging in diameter from 0.125 σ to 16 σ 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.