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

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