Low Reynolds Number Film Flow Down a Three-Dimensional Bumpy Surface

[+] Author and Article Information
C. Y. Wang

Departments of Mathematics and Mechanical Engineering, Michigan State University, East Lansing, MI 48824cywang@mth.msu.edu

J. Fluids Eng 127(6), 1122-1127 (May 06, 2005) (6 pages) doi:10.1115/1.2060730 History: Received November 08, 2004; Revised May 06, 2005

The slow film flow down a doubly periodic bumpy surface is studied for the first time. Perturbations on the primary variables and the complex boundary conditions lead to a system of successive equations. The secondary flow and the free surface shape depend on the wavelength of the bumps and a surface tension-inclination parameter. There exists an optimum aspect ratio of the protuberances for maximal flow rate.

Copyright © 2005 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

(a) The three-dimensional bumpy surface; (b) A cross section of the film

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Figure 2

Amplitude of the free surface (α=β)

Grahic Jump Location
Figure 3

Phase lag of the free surface (α=β)

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Figure 4

Typical secondary flow velocity vectors (α=β=π, D=5). The square domain is 0⩽z⩽1 and −0.5⩽y⩽0.5; (a) x=0; (b) x=0.375; (c) x=0.625; (d) x=1.

Grahic Jump Location
Figure 5

The decrease in flow rate χ. Dashed curve is the locus of the optimum aspect ratio.




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