Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other non-Newtonian fluids

Abstract

Consider the evolution of a thin layer of non-Newtonian fluid. I model the case of a nonlinear viscosity that depends only upon the shear-rate; power law fluids are an important example, but the analysis is for general nonlinear dependence upon the shear-rate. The modelling allows for large changes in film thickness provided the changes occur over a large enough lateral length scale. The modelling is based on two macroscopic modes by fudging the spectrum: here fiddle the surface boundary condition for tangential stress so that, as well as a mode representing conservation of fluid, the lateral shear flow u ∝ y is a neutral critical mode. Thus the resultant model describes the dynamics of gravity currents of non-Newtonian fluids when their flow is not very slow. For an introduction I first report on an analogous case of nonlinear diffusive dissipation.