Gliding motion of bacterium in a non-Newtonian slime

Gliding bacteria are a taxonomically heterogeneous group of rod-shaped prokaryotes that adhere to and translocate on certain substrata by mechanism(s) that are unknown. Organelles of motility, such as flagella, have not been observed on these bacteria. Furthermore, their rigidified cell walls preclude amoeboid type locomotion. The present investigation analyzes a motility model that involves an undulating cell surface which transmits stresses through a layer of exuded slime to the substratum. The non-Newtonian nature of the slime is taken into account by considering a specific fluid of the differential type, namely an incompressible homogenous fluid of grade three. The non-linear differential equation resulting from the balance of momentum and mass is solved analytically and numerically.