The effect of deposition and declogging on the critical permeability in bioconvection in a porous medium

Summary.

 The goal of this research is to investigate the effect of deposition and declogging of motile microorganisms in a fluid saturated porous medium on the development of bioconvention. If permeability of the porous medium is infinitely large (this correspond to the clear fluid case) an infinite suspension of gyrotactic microorganisms with uniform number density of the suspended cells is unstable (Pedley et al. [1]). On the other hand, if permeability is very small, the system behaves as a solid body and therefore must be stable. This means that there is a critical permeability value that corresponds to marginal stability. This paper presents a model of bioconvection of gyrotactic motile microorganisms in a fluid saturated porous medium. The model takes into account the capturing of motile microorganisms by the porous matrix which results in their deposition on the matrix as well as their possible declogging. The focus of this research is the determination of how the rates of cell deposition and declogging affect the critical value of permeability.