Effects of anisotropic scattering on the onset of phototactic bioconvection with diffuse and collimated irradiation

Abstract

The ability of many photosynthetic micro-organisms (algae) to detect a localized light source in their environment and move toward (away from) it is known as positive (negative) phototaxis. The phototactic algae absorb the incident light and scatter it isotropically or anisotropically thereafter across the suspension, which is illuminated by both diffuse and collimated irradiation. In this paper, we use the generic model of Panda et al. [“Effects of both diffuse and collimated incident radiation on phototactic bioconvection,” Phys. Fluids 28, 124104 (2016)] for phototaxis and investigate the effects of anisotropic (forward) scattering at the onset of phototactic bioconvection. In the motionless basic state, the up and down swimming caused by positive and negative phototaxis is balanced by diffusion due to randomness in the swimming behavior of algae. The forward scattering improves the underwater light distribution (radiation field) by propagating the light deeper into the algal suspension. At the equilibrium state, the bimodal (respectively, unimodal) base concentration profiles are shifted into the unimodal (respectively, bimodal) ones due to forward scattering for some fixed governing parameters when self-shading (absorption) is insignificant. As a result of forward scattering, for some parameter values, the most unstable solution shifts from mode 1 to mode 2 and a single oscillatory branch bifurcates from the stationary branch or disappears at bioconvective instability when self-shading (absorption) is significant. The dominant bioconvection pattern wavelength at instability is also qualitatively in good agreement with the experimental observations as the forward scattering coefficient is varied.