Diffusion of a Brownian ellipsoid in a force field

TL;DR

This paper derives and verifies the long-term effective motion equations for a Brownian ellipsoid under a constant force, accounting for rotation and translation effects through a multi-scale analysis.

Contribution

It introduces a systematic multi-scale method to derive effective long-term equations of motion for a Brownian ellipsoid in a force field, validated by numerical simulations.

Findings

Effective convective velocity and dispersion are characterized.

Theoretical results match numerical simulations.

Long-term behavior is governed by averaged effects of rotation and translation.

Abstract

We calculate the effective long-term convective velocity and dispersive motion of an ellipsoidal Brownian particle in three dimensions when it is subjected to a constant external force. This long-term motion results as a "net" average behavior from the particle rotation and translation on short time scales. Accordingly, we apply a systematic multi-scale technique to derive the effective equations of motion valid on long times. We verify our theoretical results by comparing them to numerical simulations.