Bacterial gliding fluid dynamics on a layer of non-Newtonian slime: Perturbation and numerical study. (21st May 2016) - Ali, N.; Asghar, Z.; Anwar Bég, O.; Sajid, M.
Abstract: Gliding bacteria are an assorted group of rod-shaped prokaryotes that adhere to and glide on certain layers of ooze slime attached to a substratum. Due to the absence of organelles of motility, such as flagella, the gliding motion is caused by the waves moving down the outer surface of these rod-shaped cells. In the present study we employ an undulating surface model to investigate the motility of bacteria on a layer of non-Newtonian slime. The rheological behavior of the slime is characterized by an appropriate constitutive equation, namely the Carreau model. Employing the balances of mass and momentum conservation, the hydrodynamic undulating surface model is transformed into a fourth-order nonlinear differential equation in terms of a stream function under the long wavelength assumption. A perturbation approach is adopted to obtain closed form expressions for stream function, pressure rise per wavelength, forces generated by the organism and power required for propulsion. A numerical technique based on an implicit finite difference scheme is also employed to investigate various features of the model for large values of the rheological parameters of the slime. Verification of the numerical solutions is achieved with a variational finite element method (FEM). The computations demonstrate that the speed of the glider decreases as the rheology of the slime changes from shear-thinning (pseudo-plastic) to shear-thickening (dilatant). Moreover, the viscoelastic nature of the slime tends to increase the swimming speed for the shear-thinning case. The fluid flow in the pumping (generated where the organism is not free to move but instead generates a net fluid flow beneath it) is also investigated in detail. The study is relevant to marine anti-bacterial fouling and medical hygiene biophysics. Highlights: We investigate the motility of bacteria on a layer of non-Newtonian slime, particularly taken as Carreau fluid. To obtain closed form expressions for pressure rise per wavelength, forces generated by the organism and power required for propulsion, perturbation approach is used. For large values of We, FDM is used. The results obtained via FDM are further verified by FEM. For shear-thinning of slime, the glider׳s speed increases with increasing We . However, a converse trend is noted for an organism gliding on shear-thickening slime. Also the glider׳s speed is an increasing function of the amplitude of the undulating wave. The flow exhibits boundary layer characteristics with strong shear-thinning properties.