A Thermodynamically-Consistent Non-Ideal Stochastic Hard-Sphere Fluid

TL;DR

This paper introduces a grid-free, thermodynamically consistent stochastic simulation method for dense fluids, accurately capturing microscopic and hydrodynamic behaviors, and validated through theoretical and particle-based comparisons.

Contribution

It develops the Isotropic DSMC algorithm with non-ideal collision rules, creating a thermodynamically consistent stochastic fluid model that matches deterministic systems and hydrodynamic theories.

Findings

The SHSD fluid matches the structure factor and compressibility of real dense fluids.

Transport coefficients from kinetic theory agree with particle simulations.

Velocity autocorrelation exhibits long-time tails consistent with hydrodynamics.

Abstract

A grid-free variant of the Direct Simulation Monte Carlo (DSMC) method is proposed, named the Isotropic DSMC (I-DSMC) method, that is suitable for simulating dense fluid flows at molecular scales. The I-DSMC algorithm eliminates all grid artifacts from the traditional DSMC algorithm; it is Galilean invariant and microscopically isotropic. The stochastic collision rules in I-DSMC are modified to yield a non-ideal structure factor that gives consistent compressibility, as first proposed in [Phys. Rev. Lett. 101:075902 (2008)]. The resulting Stochastic Hard Sphere Dynamics (SHSD) fluid is empirically shown to be thermodynamically identical to a deterministic Hamiltonian system of penetrable spheres interacting with a linear core pair potential, well-described by the hypernetted chain (HNC) approximation. We apply a stochastic Enskog kinetic theory for the SHSD fluid to obtain estimates for the transport coefficients that are in excellent agreement with particle simulations over a wide range of densities and collision rates. The fluctuating hydrodynamic behavior of the SHSD fluid is verified by comparing its dynamic structure factor against theory based on the Landau-Lifshitz Navier-Stokes equations. We also study the Brownian motion of a nano-particle suspended in an SHSD fluid and find a long-time power-law tail in its velocity autocorrelation function consistent with hydrodynamic theory and molecular dynamics calculations.