Gravity-driven thin-film flow on a flexible substrate

We study the flow of a thin liquid film along a flexible substrate. The flow is modelled using lubrication theory, assuming that gravity is the dominant driving force. The substrate is modelled as an elastic beam that deforms in two dimensions. Steady solutions are found using numerical and perturbation methods, and several different asymptotic regimes are identified. We obtain a complete characterization of how the length and stiffness of the beam and the imposed liquid flux determine the profile of the liquid film and the resulting beam deformation.