Investigation of the Effect of Cell Deposition and Declogging on Bioconvection in Porous Media

Abstract

The mechanisms of deposition and declogging are considered while formulating a new continuum model for bioconvection in a dilute suspension of swimming, gravitactic microorganisms in a porous medium. “Bioconvection” is the name given to pattern-forming convective motions set up in suspensions of swimming microorganisms. “Gravitaxis” means that microorganisms tend to swim against the gravitational force. The aim of this paper is to analyze the collective behavior and pattern formation in populations of swimming microorganisms. The decrease of permeability due to cell adsorption by the porous medium is considered and the influence this permeability decrease has on the development of bioconvection is studied. The existence and stability of a two-dimensional plume in a rectangular chamber with stress-free sidewalls is investigated. Governing equations include the Darcy law as well as the microorganism conservation equation. A conservative finite-difference scheme is utilized to solve these equations numerically. The analysis of the proposed model reveals that major factors that affect the development of bioconvection are the initial permeability of the porous medium and the rate of cell deposition. For small permeability, the resistance to the fluid flow is too large, and bioconvection does not develop. If the rate of cell deposition is too large, the number of suspended cells quickly becomes too small because of the capturing of cells by the porous medium. For this reason the critical density difference in the top fluid layer cannot be reached, and bioconvection does not develop.