Phototaxis-driven bioconvection in a rotating isotropic porous medium saturated with an algal suspension

Abstract Understanding how rotation influences phototaxis-driven bioconvection in porous medium is essential for optimizing systems in algal bioengineering, wastewater treatment, and microbial transport modeling. Motivated by these applications, this study investigates the effects of rotation on the onset of phototactic bioconvection in an isotropic porous medium saturated with an algal suspension under collimated solar flux. A linear stability analysis is performed, and the resulting eigenvalue problem is solved using a fourth-order accurate finite-difference scheme which iterates using Newton-Raphson-Kantorovich technique. The results indicate that increasing the Taylor number raises the critical Rayleigh number, thereby stabilizing the system, whereas increasing the Darcy number lowers the critical Rayleigh number, promoting instability. Additionally, the pattern wavelength decreases with increasing Taylor number and increases with rising Darcy number. Furthermore, the study shows that the most unstable mode transitions between stationary and oscillatory states as the Taylor number (Darcy number) varies. Moreover, oscillatory solutions emerge when the basic state develops at approximately three-quarters of the suspension height. The most important observation of this study is that, at oscillatory bioconvective instabilities, an increase in the Taylor number (Darcy number) leads to an increase (decrease) in the phase speed of disturbances and results in larger (smaller) orbit sizes in the phase portraits of the perturbed fluid velocity. These findings reveal how rotation and permeability jointly control flow instabilities in porous algal systems and offer actionable insights for enhancing mixing, nutrient transport, and flow regulation in biotechnological and environmental applications.