Modelling combined phototaxis and gyrotaxis in suspensions of swimming microorganisms
by
Rosie Williams
University of Glasgow
Coauthors: Martin Bees

Hydrodynamic instabilities associated with cell aggregations in suspensions of swimming, typically negatively buoyant, microorganisms can lead to the formation of intricate patterns, termed bioconvection. Phototaxis, a response to light, and gyrotaxis, defined as the balance between gravitational (due to bottom heavy cells) and viscous torques, bias the cell swimming direction, cause aggregations and influence the resulting instabilities. We construct a general model to predict stability of suspensions of photo-gyrotactic unicellular microorganisms, specifically looking for the wavenumber and growth rate of the first most unstable mode that grows from an equilibrium state. We extend recent models for purely gyrotactic cells, which couple the Navier-Stokes equation with a cell conservation equation and model cell swimming directions probabilistically using the Fokker-Planck equation. We include the effect of phototaxis in three separate ways. First we include the effect of light in the cell swimming speed, secondly we model the cells as though they change their center of mass offset depending on available light and thirdly we consider torque-like effects due to gradients in light. Equilibrium solutions are found for each model and then perturbed to assess stability for a range of realistic parameter values for the green alga Chlamydomonas nivalis. Results of the stability analysis are presented and the differences between each model are highlighted and their relative viability discussed.

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Date received: May 14, 2008