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TECHNICAL PAPERS

Thin-Film Flow at Moderate Reynolds Number

[+] Author and Article Information
Kenneth J. Ruschak, Steven J. Weinstein

Manufacturing Research and Engineering Organization, Eastman Kodak Company, Rochester, NY 14752-3701

J. Fluids Eng 122(4), 774-778 (Jul 05, 2000) (5 pages) doi:10.1115/1.1319499 History: Received December 20, 1999; Revised July 05, 2000
Copyright © 2000 by ASME
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References

Fulford,  G. D., 1964, “The Flow of Liquids in Thin Films,” Adv. Chem. Eng., 5, pp. 151–210.
Cerro,  R. L., and Whitaker,  S., 1971, “Entrance Region Flows With a Free Surface: the Falling Liquid Film,” Chem. Eng. Sci., 26, pp. 785–798.
Anderson, H. I., 1987, “The Momentum Integral Approach to Laminar Thin-Film Flow,” Proc. ASME Symposium on Thin Films, Vol. 48, pp. 7–13.
Wilkes,  J. O., and Nedderman,  R. M., 1962, “The Measurement of Velocities in Thin Films of Liquid,” Chem. Eng. Sci., 17, pp. 177–187.
Landau,  L., and Levich,  B., 1942, “Dragging of a Liquid by a Moving Plate,” Acta Physicochim. URSS, 17, pp. 42–54.
Ruschak,  K. J., 1976, “Limiting Flow in a Pre-Metered Coating Device,” Chem. Eng. Sci., 31, pp. 1057–1060.
Watson,  E. J., 1964, “The Radial Spread of a Liquid Jet Over a Horizontal Plane,” J. Fluid Mech., 20, pp. 481–499.
Cerro,  R. L., and Scriven,  L. E., 1980, “Rapid Free Surface Flows. An Integral Approach,” Ind. Eng. Chem. Fundam., 19, pp. 40–50.
Schlichting, H., 1979, Boundary-Layer Theory, 7th edition, McGraw-Hill, New York, pp. 157–158.
Haugen,  R., 1968, “Laminar Flow Along a Vertical Wall,” ASME J. Appl. Mech., 34, pp. 631–633.
Yang,  T. M. T., and Yarbrough,  D. W., 1973, ASME J. Appl. Mech., 40, pp. 290–292.
Bruley,  D. F., 1965, “Predicting Vertical Film Flow Characteristics in the Entrance Region,” A.I.Ch.E. Journal,11, No. 5, 945–950.
Ruschak,  K. J., and Weinstein,  S. J., 1999, “Viscous Thin-Film Flow Over a Round-Crested Weir,” ASME J. Fluids Eng., 121, pp. 673–677.
Anderson,  H. I., 1984, “On Integral Method Predictions of Laminar Film Flow,” Chem. Eng. Sci., 39, No. 6, pp. 1005–1010.
Ruschak,  K. J., 1980, “A Method for Incorporating Free Boundaries With Surface Tension in Finite Element Fluid-Flow Simulators,” Int. J. Numer. Methods Eng., 15, pp. 639–648.
Hassan,  N. A., 1967, “Laminar Flow Along a Vertical Wall,” ASME J. Appl. Mech., 34, pp. 535–537.
Rosenhead,  L., 1940, “The Steady Two-Dimensional Radial Flow of Viscous Fluid Between Two Inclined Plane Walls,” Proc. R. Soc. London, 175, pp. 436–467.
Ruschak, K. J., 1974, “The Fluid Mechanics of Coating Flows,” Ph.D. thesis, University of Minnesota.

Figures

Grahic Jump Location
Film profiles for flow over a quarter-round weir for Re=300, δ=0.00616, and ω00=0.01. The envelope of the boundary layer is additionally shown for the case of the Prandtl film equation.
Grahic Jump Location
Film profiles for flow over a quarter-round weir for Re=50 and δ=0.0282. The horizontal solid boundary was added for the solution of the Navier-Stokes equation.
Grahic Jump Location
Film profiles for flow over a half-round weir for Re=50 and δ=0.0286
Grahic Jump Location
Film profiles for developing flow on a vertical wall for Re=175
Grahic Jump Location
Film profiles near the origin for developing flow on a vertical wall for Re=175
Grahic Jump Location
Velocity profiles at X=0.001 for developing flow on a vertical wall for Re=175
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Film profiles for developing flow on a vertical wall for Re=175 for initial-to-final film-thickness ratios of 2.63, 1.6, and 1.0
Grahic Jump Location
Film profiles for decelerating flow on a horizontal plate for Re=300 and ζ0=0.4. Profiles computed with and without gravity are shown for the Prandtl film equation.

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