Isotropic scattering with a rigid upper surface at the onset of phototactic bioconvection

Abstract

In this article, we investigate a phototactic bioconvection model that includes both absorption and isotropic scattering in the suspension with the top and bottom boundaries assumed to be rigid. To solve the steady-state boundary value problem, a shooting method is used. Through the use of this model, a linear stability analysis is examined. Newton–Raphson–Kantorovich method of fourth order is used to investigate the linear stability of the system. The critical wavenumber is zero for vanishing scattering albedo and becomes non-zero as scattering albedo is increased. The system is more stable for the rigid upper surface than the stress-free upper surface.