Evolution of disturbances on shallow layers of non-Newtonian fluids

We study the stability of shallow layers of non-Newtonian fluids considered in the frame of the two-parametric power-law model of Ostward-de Waele, ta king into account the surface tension effect, which gives rise to decreasin g domains of unstable wave modes. For the weak nonlinearities two equations , valid in the limits of small and large Ostwald-de Waele numbers, are deri ved. They are analytically studied and the evolution of some finite disturb ance is served numerically by making use of the upwind explicit finite-diff erence scheme. (C) 2000 Elsevier Science B.V. All rights reserved.