A mathematical model for the study of gliding motion of bacteria on a layer of non-Newtonian slime

This paper is concerned with a mathematical hydrodynamical model of motility involving an undulating cell surface. The cell surface transmits stresses through a layer of exuded slime to the substratum. The slime is considered as a Johnson-Segalman fluid. A perturbation approach is used to find the analytic solution. Analytical expressions for the stream function, velocity, pressure gradient and pressure rise over a wavelength as well as the corresponding computational results are presented. The propulsive and lift forces and the power required for gliding propulsion have also been determined. The presented mechanism is found to generate a force for the propulsion of glider at a realistic speed and requires an output of power that is much less than the organism's metabolic rate of energy production. It is observed that unlike the Newtonian case of slime, the lift force is generated due to the Weissenberg number for non-Newtonian slime, represented by the model of Johnson-Segalman fluid. It is also found that power required for translation in Johnson-Segalman fluid is reduced.