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

Author:

Holloway C. R.1ORCID,Cupples G.1ORCID,Smith D. J.12ORCID,Green J. E. F.3ORCID,Clarke R. J.4ORCID,Dyson R. J.1ORCID

Affiliation:

1. School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK

2. Institute for Metabolism and Systems Research, University of Birmingham, Birmingham B15 2TT, UK

3. School of Mathematical Sciences, University of Adelaide, Adelaide, Australia

4. Department of Engineering Science, University of Auckland, Auckland, New Zealand

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 (Ericksen 1960 Colloid Polym. Sci. 173 , 117–122 ( doi:10.1007/bf01502416 )) 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, while translational diffusion stabilizes a range of wave-directions and, in some cases, a finite range of wavenumbers, thus emphasizing that both anisotropy and translational diffusion can have important effects in these systems.

Funder

Biotechnology and Biological Sciences Research Council

Australian Research Council

Engineering and Physical Sciences Research Council

Publisher

The Royal Society

Subject

Multidisciplinary

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