Self-Consistent Multiscale Modeling in the Presence of Inhomogeneous Fields

Molecular dynamics (MD) simulations of a Lennard-Jones fluid in an inhomogeneous external field generate steady-state profiles of density and pressure with nanoscopic heterogeneities. The continuum level of mass, momentum, and energy transport balances is capable of reproducing the MD profiles only when the equation of state for pressure as a function of density is extracted directly from the molecular level of description. We show that the density profile resulting from simulation is consistent with both a molecular-level theoretical prediction from statistical mechanics as well as the solution of the continuum-level set of differential equations describing the conservation of mass and momentum. 1. Introduction. The principles of conservation of mass, momentum, and en- ergy in classical systems are equally valid at both the continuum and the molecular levels. At the continuum level, the density and velocity distributions are given by solutions of partial differential equations (PDEs) describing the mass and momentum balances. It is sufficient for the purposes of this work to limit the investigation to single-component fluids in an isothermal system. Therefore, the relevant continuum equations are a mass balance (1), ∂ρ ∂t = −∇ · (ρv), (1a)