Linear stability analysis for the thermotactic microorganisms in porous media

Abstract

Thermotaxis or motion in the field of temperature gradient is a very common phenomenon and can be found in many events in nature, from biological ones to the migration of colloidal particles. In this paper, we suggest a deterministic model to describe the collective behavior of a microorganism population with a general form of stimuli gradient-based taxis in porous media. This population has the mass density slightly heavier than the water density and forms a suspension. The suspended cells are actively in motion with a thermotaxis behavior (temperature gradient follower). Based on an Eulerian framework, the model comprises basically the Darcy equation for the fluid motion in porous media, equation of cell conservation for the microorganism population and equation of conservation for the considered stimuli. To take into account the density effects, the Boussinesq’s approximation will be used. Linear stability analysis shows that there are interesting effects of temperature on the bioconvection pattern of the thermotactic microorganisms.