A Numerical Model for Brownian Particles Fluctuating in Incompressible Fluids

TL;DR

This paper introduces a numerical method that accurately models the combined effects of thermal fluctuations and hydrodynamic interactions on Brownian particles in incompressible fluids, validated against theoretical predictions.

Contribution

The paper presents a novel numerical approach that simultaneously incorporates thermal fluctuations and hydrodynamic interactions for Brownian particles in fluids.

Findings

The method accurately reproduces the fluctuation-dissipation theorem for single particles.

Simulations of particle dispersions and polymer chains demonstrate the method's applicability.

Results show consistent particle dynamics with theoretical expectations.

Abstract

We present a numerical method that consistently implements thermal fluctuations and hydrodynamic interactions to the motion of Brownian particles dispersed in incompressible host fluids. In this method, the thermal fluctuations are introduced as random forces acting on the Brownian particles. The hydrodynamic interactions are introduced by directly resolving the fluid motions with the particle motion as a boundary condition to be satisfied. The validity of the method has been examined carefully by comparing the present numerical results with the fluctuation-dissipation theorem whose analytical form is known for dispersions of a single spherical particle. Simulations are then performed for more complicated systems, such as a dispersion composed of many spherical particles and a single polymeric chain in a solvent.