Generalised Jeffery's equations for rapidly spinning particles. Part 2: Helicoidal objects with chirality

TL;DR

This paper extends Jeffery's equations to describe the motion of rapidly spinning, chiral, complex-shaped particles in shear flow, incorporating effects of chirality and asymmetry for better modeling of active, rigid objects.

Contribution

It derives generalized Jeffery's equations for helicoidal chiral particles using a multiscale framework, accounting for rapid rotation and complex shapes.

Findings

Derived effective equations of motion for chiral spinning objects.

Quantified the impact of rotation on the hydrodynamic shape.

Expanded Jeffery's theory to include chirality and asymmetries.

Abstract

In this two-part study, we investigate the motion of rigid, active objects in shear Stokes flow, focusing on bodies that induce rapid rotation as part of their activity. In Part 2, we derive and analyse governing equations for rapidly spinning complex-shaped particles - general helicoidal objects with chirality. Using the multiscale framework we develop in Part 1 (arXiv:2301.11311), we systematically derive emergent equations of motion for the angular and translational dynamics of these chiral spinning objects. We show that the emergent dynamics due to rapid rotation can be described by effective generalised Jeffery's equations, which differ from the classic versions via the inclusion of additional terms that account for chirality and other asymmetries. Furthermore, we use our analytic results to characterise and quantify the explicit effect of rotation on the effective hydrodynamic shape of the chiral objects, significantly expanding the scope of Jeffery's seminal study.