On a moving liquid film and its instability on textured surfaces.

Recently, two regimes of viscous friction on textured surfaces were proposed in the context of penetration of liquid film into the texture (EPL 79, 56005 (2007)): the Poiseuille and Stokes regimes. With this idea on viscous friction, we theoretically discuss instabilities on a liquid film on textured surfaces when the film is forced to move with external forces. When a film recedes due to a pressure drop, we find scaling laws for instabilities to be checked in future experiments. When a circular film expands due to centrifugal force we find that the expanding film is stable against rim fluctuations (within the linear stability analysis) with its radius determined by a simple equation. Our discussion sheds light on the curvature of the front of the moving liquid film on textured surfaces and how the film thickness is kept fixed to the texture height on textured surfaces, aspects which have not been discussed in previous studies.