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Technical Briefs

An Accurate Low Dimension Model for the Waves on Thin Layer Fluid Flowing Down an Inclined Plane

[+] Author and Article Information
H. Ait Abderrahmane, G. H. Vatistas

 Concordia University, 1515 St. Catherine West, EV-S3.460, Montreal, QC, H3G 2W1, Canada

J. Appl. Mech 76(6), 064501 (Jul 21, 2009) (5 pages) doi:10.1115/1.3114968 History: Received August 08, 2006; Revised January 30, 2009; Published July 21, 2009

This technical brief deals with the surface instability mode of a liquid film flowing down an inclined plane. A four-equation model that describes the development of the film depth, the flow rate, the free-surface velocity, and the wall shear stress is proposed. The obtained results were found to be in very good agreement with experimental and theoretical results of Liu (1993, “Measurements of the Primary Instability of Film Flow,” J. Fluid Mech., 250, pp. 69–101) and Brevdo (1999, “Linear Pulse Structure and Signalling in Film Flow on an Inclined Plane,” J. Fluid Mech., 396, pp. 37–71).

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of the problem

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Figure 2

Cutoff frequency θ=4.6, ν=5.02×10−6 m2 s−1, ρ=1130 kg m−3, and σ=69×10−3 N m−1; experimental data from Ref. 12

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Figure 3

Phase velocity cr/kr as function of wave number kr: θ=4.6, ν=5.02×10−6 m2 s−1, ρ=1130 kg m−3, and σ=69×10−3 N m−1

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Figure 4

Spatial growth rate −ki as function of wave number kr: θ=4.6, ν=5.02×10−6 m2 s−1, ρ=1130 kg m−3, and σ=69×10−3 N m−1

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Figure 5

(a) Image of different branches when the growth rate is ci=0.02 and (b) close view on the curve (1) R=40

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Figure 6

(a) Image of different branches when the growth rate is ci=0 and (b) close view on the curve (1) R=40

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Figure 7

Pinching process in the complex wave number plane (ki,kr) for V=1.15, R=200, We=14.18:θ=4.6, ν=5.02×10−6 m2 s−1, ρ=1130 kg m−3, and σ=69×10−3 N m−1

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Figure 8

Pinching process in the complex wave number plane (ki,kr) for V=1.15, R=200, We=14.18:θ=4.6, ν=5.02×10−6 m2 s−1, ρ=1130 kg m−3, and σ=69×10−3 N m−1

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