THE STABILITY AND NONLINEAR FLOW DEVELOPMENTS OF A VISCOELASTIC DRAINING FILM WITH SHEAR THINNING

The surface-wave instability of a draining viscoelastic film is studie d. The Oldroyd four-constant model is used to incorporate elastic and shear-thinning effects into the previous analysis for a Newtonian flui d. A long-wave evolution equation is derived, and used in the subseque nt linear-stability analysis, dynamical system approach, and nonlinear spectral computation. Nonlinear developments of the instability are d iscussed, including the damping effect of shear thinning, not explaine d by a linear theory.