Thin film flow with an undulating surface: The inertial effects

Free surface flows driven by boundary undulations are observed in many biological phenomena, including the feeding and locomotion of water snails. The undulating boundaries deform the air-liquid interface and generate a net fluid flux inside the thin film. We experimentally observe that the fluid flux varies non-monotonically with the increasing wave speed in the low Reynolds number, while the non-monotonicity is eliminated in the finite Reynolds number regime. To rationalize these observations, we develop a two-dimensional thin-film mathematical model to explore the physical mechanism of free surface flows driven by periodic undulations. The model combines the effects of inertia, viscosity, gravity, and surface tension in a tractable way. In this talk, we will present the new model results along with the experimental findings and focus on how inertia influences the flow system.