Analytical investigation of a falling plume caused by bioconvection of oxytactic bacteria in a fluid saturated porous medium

Lie Group Solution for Free Convective Flow of a Nanofluid Past a Chemically Reacting Horizontal Plate in a Porous Media

“…Here is the similarity variable and , , are dependent variables. Note that the similarity transformations in (31) are consistent with the well-known similarity transformations reported in the paper of Cheng and Chang [21] for = 0 in their paper. Thus, the dimensionless velocity components , V can be expressed as…”

“…For example, the symmetrical properties of the turbulent boundary-layer flows and other turbulent flows are investigated by using the Lie group techniques by Avramenko et al [30]. Kuznetsov et al [31] investigated a falling bioconvection plume in a deep chamber filled with a fluid saturated porous medium theoretically. Jalil et al [32] studied mixed convective flow with mass transfer using Lie group analysis.…”

Phenomenological model of bacterial aerotaxis with a negative feedback

“…such that dx * /dβ > 0. Combining (16) and 17we derive an equation forξ and then from (15) get an equation for B(x * ):…”

“…The solvability of the model was examined by Lorz [11], Duan et al [12], and Di Francesco et al [13]. Becker et al [14] and Kuznetsov [15,16] generalized the KS model and studied the bioconvection of oxytactic cells in a fluid saturated porous medium. Kuznetsov also investigated models for the thermo-bioconvection of oxytactic cells in a fluid layer [17][18][19] and in a fluid saturated porous layer [15,16] and carried out the stability analysis of their steady-state solutions.…”

“…Becker et al [14] and Kuznetsov [15,16] generalized the KS model and studied the bioconvection of oxytactic cells in a fluid saturated porous medium. Kuznetsov also investigated models for the thermo-bioconvection of oxytactic cells in a fluid layer [17][18][19] and in a fluid saturated porous layer [15,16] and carried out the stability analysis of their steady-state solutions. In all models of bioconvection and thermo-bioconvection, the oxytactic bacteria drift velocity, as in the KS model, is proportional to the gradient of oxygen concentration while the gravitational force is approximated by the buoyancy term.…”