Thermal-bioconvection instability in a suspension of phototactic microorganisms heated from below

Abstract

In this study, we investigate the linear stability of a suspension of motile algae under the combined influence of phototaxis and temperature gradients. The suspension, heated from below and illuminated from above with vertical collimated irradiation, sheds light on the intricate interplay between biological responses and thermal dynamics. The Navier–Stokes equation, thermal energy equation, and cell conservation equation are considered for the mathematical model. In suspension, the upper surface is taken as stress-free, while the lower surface is taken as rigid. The resulting eigenvalue problem, including the bioconvection Rayleigh and thermal Rayleigh numbers, is resolved numerically. Changes in the critical total intensity and Lewis number do not impact the critical threshold of the thermal Rayleigh number; however, they notably influence the critical bioconvection Rayleigh number. The critical total intensity and Lewis number destabilize the suspension. It is observed that heating from below enhances the instability of the layer. At higher temperatures, Rayleigh–Bénard convection dominates bioconvection, resulting in a single convection cell. Neutral curves of linear stability reveal transitions between stationary and oscillatory solutions. The results, validated against established methods, highlight the system’s response to parameters and phenomena such as Hopf bifurcations and limit cycles.