Active Nematic Multipoles: Flow Responses and the Dynamics of Defects and Colloids

TL;DR

This paper develops a comprehensive framework for describing flow responses in active nematics using multipole expansions, enabling better understanding and design of defect and colloid dynamics in active materials.

Contribution

It introduces a multipole-based description of active nematic distortions, explicitly deriving flow responses up to quadrupole order and linking them to defect and colloid dynamics.

Findings

Flow responses are explicitly derived for multipoles up to quadrupole order.

The geometry-dependence of defect loop dynamics is characterized.

Insights into designing colloids for propulsion and rotation in active nematics.

Abstract

We introduce a general description of localised distortions in active nematics using the framework of active nematic multipoles. We give the Stokesian flows for arbitrary multipoles in terms of differentiation of a fundamental flow response and describe them explicitly up to quadrupole order. We also present the response in terms of the net active force and torque associated to the multipole. This allows the identification of the dipolar and quadrupolar distortions that generate self-propulsion and self-rotation respectively and serves as a guide for the design of arbitrary flow responses. Our results can be applied to both defect loops in three-dimensional active nematics and to systems with colloidal inclusions. They reveal the geometry-dependence of the self-dynamics of defect loops and provide insights into how colloids might be designed to achieve propulsive or rotational dynamics, and more generally for the extraction of work from active nematics. Finally, we extend our analysis also to two dimensions and to systems with chiral active stresses.