Linear stability of thermal-bioconvection in a suspension of gyrotactic micro-organisms

Abstract

By utilizing a randomly swimming model, a linear stability analysis is applied to investigate the stability of bioconvection in a horizontal suspension layer of motile gyrotactic micro-organisms with heated from below. The micro-organisms under consideration are orientated by a balance between a gravitational torque, due to them being bottom heavy, and viscous torque arising from local fluid velocity gradients. The obtained eigenvalue problem containing thermal Rayleigh number and bioconvection Rayleigh number is solved numerically using one-term Galerkin method. The case of non-oscillatory instability is analyzed, the relationship among thermal Rayleigh number, bioconvection Rayleigh number, Lewis number, critical wavenumber and the shape of microorganisms are discussed. We point out that the heating from below makes the layer more unstable. When increasing the value of thermal Rayleigh number to 1750, the suspension becomes unstable itself, which imply that bioconvection Rayleigh number has nothing to do with the stability of this system. We also find that Lewis number has no effect on critical value of thermal Rayleigh number, but has a great influence on critical bioconvection Rayleigh number. The increasing cell eccentricity enlarges the critical value of bioconvection Rayleigh number, which means that the suspension is more stable.