arXiv subjects

Craig R. Holloway

Publications and source records attributed to Craig R. Holloway.

2 recordsLinked to original sources

arXiv2017

Linear Rayleigh-Bénard stability of a transversely-isotropic fluid

Suspended fibres significantly alter fluid rheology, as exhibited in for example solutions of DNA, RNA and synthetic biological nanofibres. It is of interest to determine how this altered rheology affects flow stability. Motivated by the fact thermal gradients may occur in biomolecular analytic devices, and recent stability results, we examine the problem of Rayleigh-Bénard convection of the transversely-isotropic fluid of Ericksen. A transversely-isotropic fluid treats these suspensions as a continuum with an evolving preferred direction, through a modified stress tensor incorporating four viscosity-like parameters. We consider the linear stability of a stationary, passive, transversely-isotropic fluid contained between two parallel boundaries, with the lower boundary at a higher temperature than the upper. To determine the marginal stability curves the Chebyshev collocation method is applied, and we consider a range of initially uniform preferred directions, from horizontal to vertical, and three orders of magnitude in the viscosity-like anisotropic parameters. Determining the critical wave and Rayleigh numbers we find that transversely-isotropic effects delay the onset of instability; this effect is felt most strongly through the incorporation of the anisotropic shear viscosity, although the anisotropic extensional viscosity also contributes. Our analysis confirms the importance of anisotropic rheology in the setting of convection.

physics.flu-dyn↗

arXiv2017

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

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.

physics.bio-ph↗