An exact solution for directional cell movement over Jeffrey slime layer with surface roughness effects

The role of marine microbes in the aquatic ecosystem is dynamic. The current work explores the fluid mechanics of gliding organisms near a porous boundary. Surface roughness effects are utilized on the lower substrate. The ooze layer between the two-dimensional sheet (micro-swimmers) and the rough substrate is considered a non-Newtonian Jeffrey fluid. The laminar flow of incompressible slime is generated by organism movement. Darcy's law is applied to capture the porous effects. This law is compatible with our study since the laminar flow of slime is driven via bacterial movement. The lubrication assumption is utilized on Navier-Stokes equations. The closed-form solution of a reduced differential equation is calculated. The unknowns present in the boundary conditions are refined by the root-finding algorithm. Finally, the organism speed, flow rate, energy losses, and streamlines are visually represented. These obtained results are elaborated, and key points are mentioned at the end.