Bioconvective linear stability of a forward light scattering microbial suspension under both oblique collimated and diffuse illumination

The bioconvective fluid motions (instabilities) within a forward light scattering microbial (algal) suspension under both oblique collimated and diffuse illumination are studied. The conditions leading to the onset of bioconvective fluid motions (instabilities) in the suspension are determined numerically via linear stability theory. The critical pattern wavelength reduces (or escalates) in size across the bottom half (or top half) of the suspension domain as the forward light scattering intensifies when the other governing parameters, such as diffuse illumination and lower value (or higher value) of light incidence angle, are kept fixed. In addition, the non-stationary (e.g., oscillatory/overstable) behavior of the bioconvection solution at instability converts into stationary behavior across the suspension domain as the forward light scattering escalates when the other governing parameters are kept fixed. Also, the mode 1 (or mode 2) type bioconvective solution switches into mode 2 (or mode 1) type with reduction mostly in pattern size as diffuse illumination enhances (or cell swimming speed rises) when the other governing parameters are kept fixed. In addition, the bifurcation analysis on the non-stationary bioconvective fluid motions (instabilities) in the microbial suspension predicts that the phase speed and also the corresponding orbit size of (appropriate) disturbances increase at the increment of forward light scattering coefficient. In addition, the competition between bioconvective stabilities (via diffuse illumination) and instabilities (via higher values in both forward light scattering coefficient and off-normal light incidence angle) reinforces the biomixing mechanism (via emergence of non-stationary behaviors) in the microbial suspension, which may resolve several bottleneck challenges in biofuel production technology.