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Type: Journal article
Title: Influences of transversely isotropic rheology and translational diffusion on the stability of active suspensions
Author: Holloway, C.
Cupples, G.
Smith, D.
Green, J.
Clarke, R.
Dyson, R.
Citation: Royal Society Open Science, 2018; 5(8):1-18
Publisher: Royal Society
Issue Date: 2018
ISSN: 2054-5703
Statement of
C. R. Holloway, G. Cupples, D. J. Smith, J. E. F. Green, R. J. Clarke and R. J. Dyson
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.
Keywords: Transversely isotropic; stability; active suspensions; fibre-laden
Rights: © 2018 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License, which permits unrestricted use, provided the original author and source are credited.
RMID: 0030096034
DOI: 10.1098/rsos.180456
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Appears in Collections:Mathematical Sciences publications

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