Diffusion of particles in simple fluids: A joint theory of kinetics and hydrodynamics

TL;DR

This paper develops an analytical theory for particle diffusion in simple fluids, incorporating hydrodynamics and ring-collision effects, validated by molecular dynamics simulations across a wide density range.

Contribution

It provides a comprehensive analytical solution for velocity autocorrelation and diffusion constants, extending hydrodynamics to all time scales and including ring-collision effects.

Findings

Analytical expressions match simulations up to high densities.

Hydrodynamics significantly influence diffusion over the entire time range.

Ring-collision effects are crucial for accurate diffusion modeling.

Abstract

The particle diffusion in a fluid is a classical topic that dates back to more than one century ago. However, a full solution to this issue still lacks. In this work the velocity autocorrelation function and the diffusion constant are derived analytically, and the hydrodynamics effect on the particle diffusion is analyzed in detail. Unlike previous studies, the ring-collision effect is exhaustively considered in our treatment, and the hydrodynamics approach is extended to the whole time range. Large scale molecular dynamics simulations for the hard-disk fluid show that our analytical results are valid up to the density close to the crystallization point.