Developing flow on a vertical wall

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Abstract
Developing laminar flow in a liquid film issuing from a full slot and descending along a vertical wall is analysed for the limiting cases of low flow rate and high surface tension. Neither limiting case is approached uniformly and the singular perturbation method with matched asymptotic expansions is employed. The location of a free boundary, the curved meniscus, is unknown a priori, and the limiting meniscus profiles are obtained. An interesting viscous boundary layer is found at low flow rates.