On the flow of a thin liquid film over a rotating disk

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Abstract
The depletion of thin liquid films due to the combined effect of centrifugation, surface roughness, and air shear has recently been studied. While surface roughness of a rotating solid disk can be represented by deterministic curves, it has been argued that spatial random processes provide a more realistic description. Chiefly because of surface roughness, there is an asymptotic limit of retention of a thin film flowing on the rotating disk. The aim of this article is twofold. First, the effect of disjoining pressure on the retention of a thin film is investigated. It is found that incorporating disjoining pressure term has small but still appreciable effect on the asymptotic limits of lubricant retention. For a partially wetting lubricant, the two components of the disjoining pressure function tend to have opposite influence on the lubricant retention; one enhances the retention, while the other diminishes it. Second, the robustness of stochastic description of surface roughness is examined. For a given mean and variance, it is noted that different probability distributions of the surface fluctuations lead, in the absence of air shear, to significantly different asymptotic limits of thin-film retention. If air shear is incorporated, this sensitivity is substantially attenuated.

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