A hybrid numerical study of bacteria gliding on a shear rate-dependent slime

Various phylogenetic categorized groups of rod-shaped bacteria exhibit the gliding mechanism over solid surfaces without any aid of flagella. It is postulated that such gliding bacteria push themselves by means of generating waves in their own surface and leave an adhesive trail of slime. In the subsequent analysis, two different non-Newtonian fluid models i.e., Bingham model and Carreau model are used to describe the complex rheology of the slime. We assumed that the solid substrate present beneath the bacterium is inclined at a certain angle to the horizontal. We derive equations governing the flow for each fluid model under long wavelength assumption. In order to calculate the bacterial gliding speed and slime flow rate we employ finite difference method combined with Broyden root finding algorithm. The obtained speed and energy dissipation are plotted for various inclination angles and rheological parameters. Moreover, by using the realistic (calculated) pairs of the glider’s speed and flow rate, the flow patterns are shown graphically and discussed in detail. The present work is an extension to our previous study Ali et al. (2016) in which a reduced constitutive equation of Carreau model was solved by perturbative approach to obtain the gliding speed on a straight substrate valid for small values of rheological parameters. The most significant outcome of the present numerical work is that the speed of gliding bacteria can be controlled by adjusting the slime rheology and inclination angle.