Effects of both diffuse and collimated incident radiation on phototactic bioconvection

Abstract

Phototaxis denotes swimming towards (positive) or away (negative) from light. The suspension containing phototactic algae is illuminated by both the diffuse and collimated solar radiation. The algae absorb the incident light and scatter it. We use the phototaxis model of Ghorai et al. [“Bioconvection in a suspension of isotropically scattering phototactic algae,” Phys. Fluids 22, 071901 (2010)] and investigate the onset of bioconvection with particular emphasis on the effects of diffuse irradiation. The basic equilibrium state of the bioconvective governing system is defined by assuming that the bulk velocity of the fluid to be zero and the up and down swimming, caused by the positive and negative phototaxis, is balanced with the diffusion. For some values of the parameters, the bimodal steady-state profile transits to a unimodal equilibrium state as the diffuse irradiation is increased. For a small scattering albedo, at the onset of bioconvective instability, this model differs significantly from the up-swimming model of Vincent and Hill [“Bioconvection in a suspension of phototactic algae,” J. Fluid Mech. 327, 343 (1996)], even for small wavelengths. Furthermore, the solutions show a transition of the most unstable mode from the stationary to oscillatory state, and then back to the stationary state again, as the governing parameters are varied. A significant stabilizing effect on suspension has also been observed due to the effects of diffuse irradiation. The effect of the diffuse irradiation on a dominant bioconvection pattern wavelength at instability is also qualitatively in good agreement with the bioconvection experiments.

Photo-bioconvection: towards light control of flows in active suspensions

“…The latter corresponds to oscillating flow and concentration fields that occur when upswimming due to phototaxis is dominant over convective downwelling. Panda et al [68] extended Ghorai and Hill’s work to show that these instabilities are opposed by the presence of rigid side walls, which enhance stability for some parameter regimes.…”

Effects of both diffuse and collimated incident radiation on phototactic bioconvection

“…However, these studies did not include the effects of diffuse irradiation. Panda et al 39 investigated the effects of diffuse irradiation on an isotropic scattering algal suspension and the diffuse irradiation had significant stabilizing effect as reported by them. Also, the transition of bimodal vertical concentration profiles at base state to unimodal ones were observed due to diffuse irradiation.…”

“…The effect of scattering appears to be twofold: it decreases G at a point by deflecting light away from the incidence trajectory whereas, it increases G at that point due to contributions to intensity by scattering from the elemental volume of algal suspension. The phototaxis model proposed by Panda et al 39 is used here. In their model, the governing system for bioconvection consists of the Navier-Stokes equations for an incompressible fluid coupled with a conservation equation for algae and the radiative transfer equation (hereafter referred to as RTE) to govern transport of oblique light.…”

“…13,[15][16][17] Thus it is necessary to include oblique collimated irradiation in addition to diffuse irradiation in realistic and reliable models of phototaxis to describe the swimming behavior of algae accurately. 8,14,18,36 Panda et al 39 calculated the radiation field by neglecting the oblique collimated irradiation in their phototaxis model. In contrast to Panda et al, 39 here the finite-depth algal suspension is illuminated uniformly by both diffuse and oblique collimated irradiation…”

“…8,14,18,36 Panda et al 39 calculated the radiation field by neglecting the oblique collimated irradiation in their phototaxis model. In contrast to Panda et al, 39 here the finite-depth algal suspension is illuminated uniformly by both diffuse and oblique collimated irradiation…”