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A general free surface rule for Stokes flow of fluid films over obstacles

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Summary

A general rule is derived for the free surface profile of a gravity–driven fluid film on an inclined wall as it flows over a local irregularity, or obstacle, in the present case a trench. Starting from an exact analytical solution of Stokes' equations, based on complex function theory, it is proved that the integral of the free surface profile, from its planer asymptotic equilibrium level, vanishes. This general analytical result, which is valid for arbitrary wall irregularities where the spatial extension is small compared to an intrinsic length, is not only an interesting feature in itself but also provides a useful check of the accuracy of numerical schemes that are used to solve such problems.

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Authors and Affiliations

  1. Department of Applied Mechanics and Fluid Dynamics, University of Bayreuth, D-95440, Bayreuth, Germany

    M. Scholle & N. Aksel

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  1. M. Scholle
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  2. N. Aksel
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Correspondence to M. Scholle.

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Scholle, M., Aksel, N. A general free surface rule for Stokes flow of fluid films over obstacles. Acta Mechanica 191, 155–159 (2007). https://doi.org/10.1007/s00707-006-0429-1

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  • DOI: https://doi.org/10.1007/s00707-006-0429-1

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