Angular dynamics of small crystals in viscous flow

TL;DR

This paper investigates the angular behavior of small, discrete-symmetry crystals in viscous flow, extending Jeffery's theory to new particle shapes with specific symmetry properties.

Contribution

It computes the angular dynamics of crystals with discrete rotation and mirror symmetries, identifying cases that follow or deviate from Jeffery's theory.

Findings

Some crystals with discrete symmetries obey Jeffery's theory.

Other crystals exhibit more complex angular dynamics.

The study broadens understanding of particle behavior in viscous flows.

Abstract

The angular dynamics of a very small ellipsoidal particle in a viscous flow decouples from its translational dynamics, and the particle angular velocity is given by Jeffery's theory. It is known that cuboid particles share these properties. In the literature a special case is most frequently discussed, namely that of axisymmetric particles with a continuous rotation symmetry. Here we compute the angular dynamics of crystals that possess a discrete rotation symmetry and certain mirror symmetries, but that do not have a continuous rotation symmetry. We give examples of such particles that nevertheless obey Jeffery's theory. But there are other examples where the angular dynamics is determined by a more general equation of motion.