Onset of gravitactic bioconvection in a square anisotropic porous medium with arbitrary orientation of the principal axes

摘要

This paper examines the onset of negative gravitactic bioconvection in a porous square cavity. The porous medium is assumed to be anisotropic in permeability with its principal axes arbitrarily oriented with respect to the gravity vector, and contains a concentration of microorganisms which are assumed to be swimming upward against gravity (negative gravitaxis). The critical Rayleigh number Ra_c at marginal stability is calculated as a function of the microorganism swimming speed V_c, of the anisotropy ratio R, and of the orientation angle θ.