Effect of rigid top surface on the onset of phototactic bioconvection

TL;DR

This study models how a rigid top surface influences the onset of phototactic bioconvection in algae suspensions illuminated by diffuse and collimated light, revealing effects on stability and steady states.

Contribution

It introduces a model analyzing the impact of a rigid top surface on bioconvection patterns under combined light conditions, including stability analysis.

Findings

Rigid top surface increases suspension stability.

Diffuse irradiation affects steady state transitions.

Bimodal to unimodal transition depends on light intensity.

Abstract

Phototaxis is the movement of microorganisms towards or away from light. In presence of dim (intense) light, microorganisms move towards (away from) the light sources, which is known as positive (negative) phototaxis. In this study, we present a model in which isotropic scattering algae suspension is illuminated by both diffuse and collimated irradiation, and the top surface is assumed to be rigid. Bimodal steady states result from the scattering Effect (for almost purely scattering suspension), which transits into a unimodal steady state as diffuse light intensity increases. The linear stability of the same suspension is also examined using the linear perturbation theory, which predicts the solutions' stable and oscillatory nature for specific parameter values. Here, we also observe that suspension becomes more stable in a rigid top surface and diffuse irradiation.