Stability of a thin viscoelastic film falling down an inclined plane

Abstract

We study the long-wave instability of a falling film of the Oldroyd-B fluid. The weighted residual method is adopted to model the film dynamics in both linear and nonlinear regimes. The mechanism of the viscoelastic effect on the instability is explored within the framework of the Whitham wave hierarchy theory. We further analyze the film evolution and the traveling waves by means of nonlinear simulations.