Abstract
The main purpose of this paper is to perform a 2D stability analysis of bioconvection in a suspension of motile gyrotactic microorganisms in a fluid saturated porous medium and to obtain an analytical expression for the critical permeability of the porous medium. Recent numerical investigation by Kuznetsov and Jiang [1] suggests that permeability is a very important parameter for bioconvection in porous media. Their numerical results indicate that for small permeability bioconvection is stable (the microorganisms swim in the upward direction), while for large permeability it is unstable (variations of density are enhanced and macroscopic fluid circulation is induced). In the present investigation, a simple but elegant criterion of stability of the bioconvection is obtained. This criterion gives the critical permeability of the porous medium through the cell eccentricity, average swimming velocity, fluid viscosity, and other relevant parameters.
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