Irreducible Representations Of Oscillatory And Swirling Flows In Active Soft Matter

TL;DR

This paper develops a comprehensive mathematical framework to describe complex oscillatory and swirling flows in active soft matter, revealing the importance of higher-order tensor contributions and angular momentum considerations.

Contribution

It introduces a general flow expansion using irreducible Cartesian tensors, including third-rank tensors, to accurately model active flows around microorganisms.

Findings

Explicit expressions for irreducible stress components

Higher-order tensors are essential for flow accuracy

Active stresses can violate angular momentum conservation

Abstract

Recent experiments imaging fluid flow around swimming microorganisms have revealed complex time-dependent velocity fields that differ qualitatively from the stresslet flow commonly employed in theoretical descriptions of active matter. Here we obtain the most general flow around a finite sized active particle by expanding the surface stress in irreducible Cartesian tensors. This expansion, whose first term is the stresslet, must include, respectively, third-rank polar and axial tensors to minimally capture crucial features of the active oscillatory flow around translating Chlamydomonas and the active swirling flow around rotating Volvox. The representation provides explicit expressions for the irreducible symmetric, antisymmetric and isotropic parts of the continuum active stress. Antisymmetric active stresses do not conserve orbital angular momentum and our work thus shows that spin angular momentum is necessary to restore angular momentum conservation in continuum hydrodynamic descriptions of active soft matter.