Bio-thermal convection induced by two different species of microorganisms

This paper develops a theory of bio-thermal convection in a suspension that contains two species of microorganisms exhibiting different taxes, gyrotactic and oxytactic microorganisms. The developed theory is applied to investigating the onset of bio-thermal convection in such a suspension occupying a horizontal layer of finite depth. A linear stability analysis is utilized to derive the equations for the amplitudes of disturbances. The obtained eigenvalue problem is solved by the Galerkin method. The case of non-oscillatory instability in a layer with a rigid lower boundary and a stress-free upper boundary is investigated. The resulting eigenvalue equation relates three Rayleigh numbers, the traditional Rayleigh number (Ra) and two bioconvection Rayleigh numbers, one for gyrotactic (Rbg) and one for oxytactic (Rbo) microorganisms. The neutral stability boundary is presented in the form of a diagram showing that boundary in the (Ra, Rag) plane for different values of Rao.