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Steady symmetric low-Reynolds-number flow past a film-coated cylinder. (English) Zbl 1322.76009

Summary: In this study, we examine a steady two-dimensional slow flow past a rigid cylinder coated with a thin layer of immiscible fluid. The Reynolds number for the external bulk flow is assumed small and flow within the film is driven by the action of the bulk fluid’s tangential viscous stress acting at the interface. Using double asymptotic expansions based on the bulk fluid’s Reynolds number and the aspect ratio of the film thickness to the cylinder’s radius, we derive the leading- and first-order equations governing the steady-state film dynamics, and obtain analytical solutions, in terms of the film thickness, for the bulk flow. We solve the governing film equations, finding that solutions feature a drained region. We briefly discuss the influence of the Capillary number and fluid viscosities, and conclude by showing how the presence of the film affects the drag on the film-coated cylinder.

MSC:

76A20 Thin fluid films
76D07 Stokes and related (Oseen, etc.) flows
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
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