A mathematical modeling of light-induced bioconvection in an isotropic porous medium

The study of bioconvection within porous medium saturated with a suspension of phototactic microorganisms is a research area of substantial importance, with wide-ranging implications in scientific and engineering disciplines. Understanding bioconvection in such systems is crucial for optimizing light distribution and reduces reliance on mechanical mixing. Hence, we examine the light-induced bioconvection in a suspension of phototactic microorganisms in an isotropic porous medium illuminated by collimated irradiation from above. The main objective of this study is to investigate the effects of key parameters such as the Darcy number, critical light intensity, and cell swimming speed on the initiation of bioconvection. The findings via linear stability analysis reveal that an increase in these parameters stimulates bioconvection, which leads to enhanced nutrient distribution within the medium. Additionally, the study reveals that the bioconvective solution transits from stationary and oscillatory types and vice-versa as the Darcy number increases. These results may help to optimize biofuel production and enhance industrial filtration processes.