A thermodynamically consistent non-ideal stochastic hard-sphere fluid

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 fluidflows at molecular scales. The I-DSMC algorithm eliminates all grid artifacts from thetraditional DSMC algorithm; it is Galilean invariant and microscopically isotropic. Thestochastic collision rules in I-DSMC are modified to yield a non-ideal structure factor thatgives consistent compressibility, as first proposed by Donev et al (2008 Phys. Rev. Lett. 101 075902). The resulting stochastic hard-sphere dynamics (SHSD) fluid is empiricallyfound to have the same pair correlation function as a deterministic Hamiltonian system ofpenetrable spheres interacting with a linear core pair potential, well described by thehypernetted chain (HNC) approximation. We apply a stochastic Enskog kinetic theory tothe SHSD fluid to obtain estimates for the transport coefficients that are in excellentagreement with particle simulations over a wide range of densities and collision rates. Thefluctuating hydrodynamic behavior of the SHSD fluid is verified by comparing itsdynamic structure factor against theory based on the Landau–Lifshitz Navier–Stokesequations. We also study the Brownian motion of a nanoparticle suspended in anSHSD fluid and find a long-time power-law tail in its velocity autocorrelationfunction consistent with hydrodynamic theory and molecular dynamics calculations.