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

Abstract

Light gradient can allow many motile photosynthetic microorganisms to bias their motion towards moderate light (positive phototaxis) or away from intense light (negative phototaxis). The proposed work presents the penetrative phototactic bioconvection in a non-scattering algal suspension. The suspension is confined by a stress-free top boundary, and rigid bottom and periodic lateral boundaries. The resulting bioconvective patterns of the problem strongly resemble to that of a spatially extended domain in the same vicinity. The bioconvection solution appears in the form of a two-rolls pattern (or any even number of rolls) due to the periodic lateral boundaries.

Requirement of Volume of Dredging and Capacity Enhancement of Dredgers in India

“…Similar to previous continuum models [2][3][4][5][6][7][8][9][10][11]16,[21][22][23][24][26][27][28][29][30] , the suspension is composed of cells with a volume of v and density of ρ + δ ρ (ρ is water density and 0 < δ ρ ≪ ρ. The velocity and concentration of the cells in the suspension are denoted by U and n, respectively.…”

“…Now, there is a need to scaled the governing equations to make the governing equations dimensionless. Here, we use a set of characteristic scales for length, time, velocity, pressure, and concentration similar to the previous models [2][3][4][5][6][7][8][9][10][11]16,[21][22][23][24][26][27][28][29][30] . Therefore, the scaled governing equations are expressed as…”

“…Panda and Ghorai 26 proposed a model for isotropically scattering medium in two-dimension and found results that were different from those found by Ghorai and Hill 22 due to scattering effects. Panda and Singh 23 investigated phototactic bioconvection in two dimensions in which the suspension was confined between rigid side walls, observing a considerable stabilizing effect on the suspension. Panda et al 7 proposed a model to investigate the effect of diffuse flux in the presence of collimated flux.…”

Photofocusing of Microorganisms Swimming in a Flow With Shear

“…The bulk response of cells that align with light gradients (phototactic) has previously been modelled, notably by Vincent and Hill [17], and Williams and Bees [18], and examined in the context of bulk suspension motions such as bioconvection [6,7,12]. These models incorporate the effects of light absorption and scattering by other cells in the suspension, and predict cell-rich layers at finite depth where light levels are sufficiently high to meet the cells' needs, but not so high as to be damaging.…”

Light Control of Localized Photobioconvection

“…The ensuing global instability, characterised by steady vortical flows for all parameter values, can easily lead to the emergence of isolated bioconvective plumes whose spatio-temporal localisation is simply tuned by the external illumination. These properties contrast with the limited control afforded by standard bioconvection [41,[67][68][69][70], and enable rapid light-mediated control of the flow which can be used to regulate the transport properties of the suspension. The simple minimal model we use provides a surprisingly accurate quantitative description of the experimental system with no fitting parameters, but only when viewed in terms of the reduced time τ .…”