The formation of a thin liquid film onto a moving substrate is a commonly encountered industrial process, and one that is encountered in lubrication, oil extraction processes, and coating flows. The formation of such a film is analyzed via the analytical Stokes flow solution for the flow in a wedge bounded on one side by a free surface and on the other by a moving surface. The full solution is obtained by numerically integrating a set of ordinary differential equations from far downstream, in the region of the final film thickness. The results show excellent agreement with the results obtained by the Bretherton equation, the Ruschak equation, the Coyne and Elrod model, and a two-dimensional free surface finite element simulation of the problem.
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April 2009
Research Papers
Free Surface Model Derived From the Analytical Solution of Stokes Flow in a Wedge
R. W. Hewson
R. W. Hewson
School of Mechanical Engineering,
e-mail: r.w.hewson@leeds.ac.uk
University of Leeds
, Woodhouse Lane, Leeds, LS2 9JT UK
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R. W. Hewson
School of Mechanical Engineering,
University of Leeds
, Woodhouse Lane, Leeds, LS2 9JT UKe-mail: r.w.hewson@leeds.ac.uk
J. Fluids Eng. Apr 2009, 131(4): 041205 (5 pages)
Published Online: March 11, 2009
Article history
Received:
July 24, 2008
Revised:
January 15, 2009
Published:
March 11, 2009
Citation
Hewson, R. W. (March 11, 2009). "Free Surface Model Derived From the Analytical Solution of Stokes Flow in a Wedge." ASME. J. Fluids Eng. April 2009; 131(4): 041205. https://doi.org/10.1115/1.3089540
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