%0 Report
%9 Technical Report
%A Roberts, A. J.
%D 2007
%F usqep3:2010
%I University of Southern Queensland
%K thin film flow
%T Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other non-Newtonian fluids  
%U http://eprints.usq.edu.au/2010/
%X 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.