Free-surface stability of a damped thin-film flow

Abstract

An idealized model is presented, describing the flow of a thin film through a dilute porous layer of immobile obstacles. Damping due to the obstacles extends the linear stability of the flow, where the depth-integrated flowrates retrieved at each order of the film expansion are expressed in terms of hyperbolic functions. Threedimensional numerical simulations reveal a transition from steepening waves to stationary travelling waves for increasing values of the damping parameter.