A Novel Monte Carlo Approach to the Dynamics of Fluids --- Single Particle Diffusion, Correlation Functions and Phase Ordering of Binary Fluids

TL;DR

This paper introduces a new Monte Carlo method to simulate the late-time dynamics of 2D hard sphere fluids, analyzing particle diffusion, correlation functions, and phase separation behaviors.

Contribution

A novel Monte Carlo scheme for studying fluid dynamics, capable of handling particle interactions and adaptable to three dimensions.

Findings

Velocity autocorrelation function exhibits a long-time $t^{-1}$ tail.

Domain size $R(t)$ grows as $t^{1/2}$ in high viscosity fluids.

Crossover to $t^{2/3}$ growth in low viscosity fluids.

Abstract

We propose a new Monte Carlo scheme to study the late-time dynamics of a 2-dim hard sphere fluid, modeled by a tethered network of hard spheres. Fluidity is simulated by breaking and reattaching the flexible tethers. We study the diffusion of a tagged particle, and show that the velocity autocorrelation function has a long-time $t^{-1}$ tail. We investigate the dynamics of phase separation of a binary fluid at late times, and show that the domain size $R(t)$ grows as $t^{1/2}$ for high viscosity fluids with a crossover to $t^{2/3}$ for low viscosity fluids. Our scheme can accomodate particles interacting with a pair potential $V(r)$,and modified to study dynamics of fluids in three dimensions.