Mean field models for interacting ellipsoidal particles

TL;DR

This paper develops a hierarchy of mean field models for large systems of interacting ellipsoids in fluid, from microscopic Langevin-based models to macroscopic equations, with numerical comparisons validating the approximations.

Contribution

It introduces a comprehensive hierarchy of mean field models for ellipsoidal particles in fluid, bridging microscopic and macroscopic descriptions with validation.

Findings

Numerical comparisons support the validity of the mean field approximations.

The models effectively capture the interactions and fluid influence on ellipsoids.

The hierarchy provides a scalable framework for simulating large particle systems.

Abstract

We consider a mean field hierarchy of models for large systems of interacting ellipsoids suspended in an incompressible fluid. The models range from microscopic to macroscopic mean field models. The microscopic model is based on three ingredients. Starting from a Langevin type model for rigid body interactions, we use a Jefferys type term to model the influence of the fluid on the ellipsoids and a simplified interaction potential between the ellipsoids to model the interaction between the ellipsoids. A mean field equation and corresponding equations for the marginals of the distribution function are derived and a numerical comparison between the different levels of the model hierarchy is given. The results clearly justify the suitability of the proposed approximations for the example cases under consideration.