Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics

TL;DR

This paper develops a systematic coarse-grained model for nanoparticle dynamics in a fluid, deriving stochastic equations from microscopic principles and linking them to fluctuating hydrodynamics for efficient simulations.

Contribution

It introduces a new coarse-graining approach that derives stochastic differential equations directly from microscopic dynamics, connecting particle-level details with mesoscopic fluctuating hydrodynamics.

Findings

Derived stochastic ODEs consistent with SPDEs for nanoparticle-fluid systems.

Provided explicit microscopic expressions for model coefficients.

Enabled efficient simulation of nanocolloidal suspensions using combined MD and FEM methods.

Abstract

We derive a coarse-grained description of the dynamics of a nanoparticle immersed in an isothermal simple fluid by performing a systematic coarse graining of the underlying microscopic dynamics. As coarse-grained or relevant variables we select the position of the nanoparticle and the \emph{total} mass and momentum density field of the fluid, which are locally conserved slow variables because they are defined to include the contribution of the nanoparticle. The theory of coarse graining based on the Zwanzing projection operator leads us to a system of stochastic \emph{ordinary} differential equations (SODEs) that are closed in the relevant variables. We demonstrate that our discrete coarse-grained equations are consistent with a Petrov-Galerkin finite-element discretization of a system of formal stochastic \emph{partial} differential equations (SPDEs) which resemble previously-used phenomenological models based on fluctuating hydrodynamics. Under suitable approximations we obtain \emph{closed} approximations of the coarse-grained dynamics in a manner which gives them a clear physical interpretation, and provides \emph{explicit} microscopic expressions for all of the coefficients appearing in the closure. Our work leads to a model for dilute nanocolloidal suspensions that can be simulated effectively using feasibly short molecular dynamics simulations as input to a FEM fluctuating hydrodynamic solver.