Hydrodynamics of Active Polar Systems in a (Visco)Elastic Background

TL;DR

This paper develops comprehensive macroscopic equations to describe the complex dynamics of active polar systems embedded in viscoelastic or elastic media, capturing their coupled relaxation, sound spectrum, and effects of chirality.

Contribution

It introduces a detailed theoretical framework for active polar systems in elastic backgrounds, including coupling effects, relaxation dynamics, and chirality considerations.

Findings

Derived equations describe coupled polar order and elasticity dynamics.

Identified a unique excitation mode due to elasticity-polar order coupling.

Analyzed effects of chirality on the system's behavior.

Abstract

We derive the full set of macroscopic equations necessary to describe the dynamics of systems with active polar order in a viscoelastic or elastic background. The active polar order is manifested by a second velocity, whose non-zero modulus is the polar order parameter and whose direction is the polar preferred direction. Viscoelasticity is described by a relaxing strain field allowing for a straightforward change from transient to permanent elasticity. Relative rotations of the elastic structure with respect to the polar direction are taken into account. The intricate coupling between active polar order and (transient) elasticity leads to a combined relaxation of the polar order parameter and the strains. The rather involved sound spectrum contains a specific excitation due to a reversible coupling between elasticity and polar order. Effects of chirality are also considered.