Influences of transversely-isotropic rheology and translational diffusion on the stability of active suspensions

TL;DR

This paper extends Ericksen's transversely-isotropic fluid model to include active motility and analyzes how anisotropic rheology and translational diffusion influence the stability of suspensions of elongated active particles.

Contribution

It introduces a modified Ericksen model incorporating self-motility and analyzes the effects of anisotropic rheology and diffusion on suspension stability.

Findings

Anisotropic rheology increases instability of small perturbations.

Translational diffusion stabilizes certain wave-directions and wave-numbers.

Both effects significantly influence active suspension behavior.

Abstract

Suspensions of self-motile, elongated particles are a topic of significant current interest, exemplifying a form of `active matter'. Examples include self-propelling bacteria, algae and sperm, and artificial swimmers. Ericksen's model of a transversely-isotropic fluid [J. L. Ericksen, Colloid Polym. Sci. 173(2):117-122 (1960)] treats suspensions of non-motile particles as a continuum with an evolving preferred direction; this model describes fibrous materials as diverse as extracellular matrix, textile tufts and plant cell walls. Director-dependent effects are incorporated through a modified stress tensor with four viscosity-like parameters. By making fundamental connections with recent models for active suspensions, we propose a modification to Ericksen's model, mainly the inclusion of self motility; this can be considered the simplest description of an oriented suspension including transversely-isotropic effects. Motivated by the fact that transversely-isotropic fluids exhibit modified flow stability, we conduct a linear stability analysis of two distinct cases, aligned and isotropic suspensions of elongated active particles. Novel aspects include the anisotropic rheology and translational diffusion. In general anisotropic effects increase the instability of small perturbations, whilst translational diffusion stabilises a range of wave-directions and, in some cases, a finite range of wave-numbers, thus emphasising that both anisotropy and translational diffusion can have important effects in these systems.