Bio-thermal convection induced by two different species of microorganisms

摘要

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, Ra_g) plane for different values of Ra_o.