Abstract
A model is developed for the unsteady laminar flow of athin fluid film over a substrate with roughness of the same order as the film height. The limits of large and small surface resistance and small surface-roughness are investigated and it is shown that at leading order the classical parabolic form for the velocity profile is retrieved in all cases. Empirical expressions for the depth-averaged velocity and the ratio of the average to maximum velocities are investigated and shown to agree with the present theory under certain conditions. The method is verified by comparison with experiments for steady uni-directional flow over a surface of known roughness.
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