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 (rb_g) and one for oxytactic (rb_o) 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 ra_o.