Fluid-inertia torques from particle-shape symmetry

TL;DR

This paper uses symmetry analysis and perturbation theory to determine hydrodynamic torque forms on particles with various symmetries at low Reynolds numbers, extending understanding beyond simple shapes.

Contribution

It introduces a method to derive torque models for complex particle shapes based on symmetry considerations, advancing beyond empirical models for simple geometries.

Findings

Symmetry constrains the form of hydrodynamic torque.

Explicit calculations verify the symmetry-based predictions.

Results apply to particles with different point-group symmetries.

Abstract

Numerical simulation of particle motion in fluids at low particle Reynolds numbers is often based on empirical force and torque models obtained by fitting force and torque from ab-initio computations for simple particle shapes such as spheres, spheroids, or cylindrical disks and fibres. To do the same for more complex particles shapes, one needs to first know how particle shape constrains the dependence of force and torque on flow velocity, its gradient, and on particle orientation. Here we use symmetry analysis and perturbation theory to determine the form of the hydrodynamic torque on a particle settling in a quiescent fluid at low but non-zero particle Reynolds numbers, for particle shapes with different point-group symmetries. The symmetry conclusions are verified by comparing with explicit calculations for nearly spherical particles.