New Developments in Bioconvection in Porous Media: Bioconvection Plumes, Bio-Thermal Convection, and Effects of Vertical Vibration

This chapter reviews new developments in bioconvection in a fluid saturated porous medium caused by either gyrotactic or oxytactic microorganisms. Bioconvection arises as a result of an unstable density stratification caused by upswimming microorganisms. This unstable density stratification occurs when the microorganisms, heavier than water, accumulate in the upper regions of the fluid. This hydrodynamic instability may lead to the development of bioconvection plumes, which in case of oxytactic microorganisms transport cells and oxygen from the upper fluid region to the lower fluid regions. The presented modeling is limited to the situation when the average pore size is much larger than the size of a microorganism; therefore, local vorticity generated by flow through the pores does not affect the ability of microorganisms to reorient.

The chapter introduces bio-thermal convection, which, contrary to traditional bioconvection, has two destabilizing mechanisms that contribute to creating the unstable density stratification. The utilization of the Galerkin method to solve a linear stability problem leads to a correlation between the critical value of the bioconvection Rayleigh number and the traditional “thermal” Rayleigh number. The chapter also investigates the potential of utilizing the vertical vibration for controlling bioconvection. The linear stability analysis indicates that vertical vibration has a stabilizing effect on the suspension.