On solution of non-linear differential equation arising in gliding motion of bacteria

Abstract

A two-dimensional undulating surface model for the motility of bacteria gliding on a layer of non-Newtonian slime is constructed. The slime considered is that of the Johnson–Segalman fluid type. The hydrodynamical model assumes the existence of a transverse surface wave propagating in the axial direction. The solution of the non-linear partial differential equation resulting from the balance of momentum and mass is found analytically.