Numerical investigation of bioconvection of gravitactic microorganisms in an isotropic porous medium

A new continuum model is formulated 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 gravity. The aim of this paper is to analyze collective behavior and pattern formation in populations of swimming microorganisms. The existence and stability of a two-dimensional plume in a tall, narrow chamber with stress-free sidewalls is investigated. Governing equations include Darcy law as well as microorganism conservation equation. A conservative finite-difference scheme is used to solve these equations numerically.