Research Papers: Fundamental Issues and Canonical Flows

Free Surface Model Derived From the Analytical Solution of Stokes Flow in a Wedge

[+] Author and Article Information
R. W. Hewson1

School of Mechanical Engineering, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT UKr.w.hewson@leeds.ac.uk


Corresponding author.

J. Fluids Eng 131(4), 041205 (Mar 11, 2009) (5 pages) doi:10.1115/1.3089540 History: Received July 24, 2008; Revised January 15, 2009; Published March 11, 2009

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.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Illustration of the fluid film forming process

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Figure 2

Definition of the local coordinate system (r,θ), the local tangent to the free surface θ=0, and the moving substrate θ=α

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Figure 3

Graphical representation of the addition of ψ1 and ψ2: note the free surface stagnation point predicted by the addition of the two stream functions ψ1 and ψ2

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Figure 4

COMSOL MULTIPHYSICS finite element implementation of the free surface problem

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Figure 5

Free surface meniscus shape, pressure distribution and constant radius at θ=90 deg, as obtained by the analytical model (Eqs. 10,11,12,13)

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Figure 6

Results of the model, compared with Bretherton equation, Ruschak equation, and Coyne and Elrod (CE) results; for (a) gap, hθ=0 (at θ=90 deg) and (b) scaled meniscus radius of curvature dθ/ds/(hθ=π−1)



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