Interaction of gliding motion of bacteria with rheological properties of the slime

Bacteria which do not have organelles of motility, such as flagella, adopt gliding as a mode of locomotion. In gliding motility bacterium moves under its own power by secreting a layer of slime on the substrate. The exact mechanism by which a glider achieves motility is yet in controversy but there are evidences which support the wave-like undulation on the surface of the organism, as a possible mechanism of motility. Based on this observation, a model of undulating sheet over a layer of slime is examined as a possible model of the gliding motion of a bacterium. Three different non-Newtonian constitutive equations namely, finite extendable nonlinear elastic-peterline (FENE-P), Simplified Phan-Thien-Tanner (SPTT) and Rabinowitsch equations are used to capture the rheological properties of the slime. It is found that the governing equation describing the fluid mechanics of the model under lubrication approximation is same for all the considered three constitutive equations. In fact, it involves a single non-Newtonian parameter which assumes different values for each of the considered constitutive relations. This differential equation is solved using both perturbation and semi-analytic procedure. The perturbation solution is exploited to get an estimate of the speed of the glider for different values of the non-Newtonian parameter. The solution obtained via semi-analytic procedure is used to investigate the important features of the flow field in the layer of the slime beneath the glider when the glider is held fixed. The expression of forces generated by the organism and power required for propulsion are also derived based on the perturbation analysis.