Bioconvection is a recently-developed problem of fluid mechanics. The term bioconvection refers to the flow induced by the collective motion of a large number of motile microorganisms. This flow is characterized by regular fluid circulation patterns. The interactions between the motile microorganisms and the surrounding fluid depend strongly on their physiological activities, in contrast to the case of inanimate mass transfer. The basic mechanism of bioconvection is similar to that of the well-known natural convection in the sense that both are due to the buoyancy force resulting from a density gradient which, in the case of bioconvection, occurs when a large number of microorganisms (which are slightly heavier than water) accumulate in a certain region of the fluid medium, while in the case of natural convection a density gradient is due to a temperature gradient. A model of bioconvection has been developed by Childress, Levandowsky and Spiegel for gravitactic microorganisms, based on the Navier-Stokes equation for the fluid flow and the diffusion-convection equation for the concentration of the motile microorganisms. They first derived the equilibrium state resulting from the upward swimming and the downward diffusion of the motile organisms in a quiescent fluid. They then determined analytically the critical Rayleigh number for the onset of convection as well as the preferred wavenumber and growth rates. The first part of this study is focused on the stability criteria of bioconvection caused by gravitactic microorganisms in a fluid-saturated porous medium as shown in Fig. 1. In the second part of this study, we will consider the combined effects of density stratifications due to both the upswimming of microorganisms and the thermal solicitations. This problem of thermo-bioconvection occurs in a number of geophysical applications, such as the investigation of the dynamics of some species of thermophiles (heat loving microorganisms) living in hot springs.
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