Thin film flow over slippery substrates

We present a theoretical and experimental study of the free-surface flow of viscous fluids over a slippery, structured substrate. Much like classical hydrophobic surfaces, the substrate consists of a periodic sequence of two-dimensional, fluid-filled cavities. The shear stress exerted by the overlying viscous fluid drives a return flow within each cavity. This induces slip at the interface between the two fluids, which can be characterised in terms of a slip length proportional to the ratio of the viscosities of the two fluids. A series of experiments of a thin film of viscous fluid over a structured, fluid-saturated substrate confirms that the slip length is proportional to the viscosity ratio.