Fluctuating force-coupling method for simulations of colloidal suspensions

TL;DR

This paper introduces a fluctuating force-coupling method (FCM) that efficiently simulates colloidal suspensions with Brownian motion, ensuring accurate dynamics and suspension properties at large scales.

Contribution

The paper develops a fast fluctuating FCM framework that accurately models Brownian motion in colloidal suspensions, satisfying the fluctuation-dissipation theorem even with higher-order multipoles.

Findings

The fluctuating FCM reproduces correct particle velocities and angular velocities.

Numerical experiments confirm the analytical results and effectiveness of the method.

Brownian drift can be effectively resolved with proper time integration and conjugate gradient methods.

Abstract

The resolution of Brownian motion in simulations of micro-particle suspensions can be crucial to reproducing the correct dynamics of individual particles, as well as providing an accurate characterisation of suspension properties. Including these effects in simulations, however, can be computationally intensive due to the configuration dependent random displacements that would need to be determined at every time step. In this paper, we introduce the fluctuating force-coupling method (FCM) to overcome this difficulty, providing a fast approach to simulate colloidal suspensions at large-scale. We show explicitly that by forcing the surrounding fluid with a fluctuating stress and employing the FCM framework to obtain the motion of the particles, one obtains the random particle velocities and angular velocities that satisfy the fluctuation-dissipation theorem. This result holds even when higher-order multipoles, such as stresslets, are included in the FCM approximation. Through several numerical experiments, we confirm our analytical results and demonstrate the effectiveness of fluctuating FCM, showing also how Brownian drift can be resolved by employing the appropriate time integration scheme and conjugate gradient method.