Penetrative phototactic bioconvection in a two-dimensional non-scattering suspension

Abstract

Phototaxis is a directed swimming response dependent upon the light intensity sensed by microorganisms. Positive (negative) phototaxis denotes the motion directed towards (away from) the source of light. In this paper, we simulate numerically penetrative phototactic bioconvection in a non-scattering suspension of phototactic algae in the non-linear regime. The suspension is confined by a stress-free top boundary, and rigid bottom and lateral boundaries. The algae receive light from the source directly above it and thus they swim vertically upward by neglecting the effects of scattering. We use the phototaxis model proposed by Vincent and Hill [“Bioconvection in a suspension of phototactic algae,” J. Fluid Mech. 327, 343 (1996)] to investigate the onset of bioconvection in two dimensions using the stream function-vorticity formulation. The critical conditions from the onset of bioconvection are used to study the effects of different governing parameters on the structure and stability of the obtained solutions. The resulting bioconvective patterns differ qualitatively from those found by Ghorai and Hill [“Penetrative phototactic bioconvection,” Phys. Fluids 17, 074101 (2005)] at some particular swimming velocity of microorganisms due to rigid lateral walls. A significant stabilizing effect on suspension has been also observed due to lateral rigid walls for some governing parameters.