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The effect of applied pressure on the shape of a two-dimensional liquid curtain falling under the influence of gravity

Published online by Cambridge University Press:  26 April 2006

Douglas S. Finnicum ,
Steven J. Weinstein  and
Kenneth J. Ruschak
Douglas S. Finnicum
Affiliation:
Emulsion Coating Technologies, Eastman Kodak Company, Rochester, NY 14652-3701, USA
Steven J. Weinstein
Affiliation:
Emulsion Coating Technologies, Eastman Kodak Company, Rochester, NY 14652-3701, USA
Kenneth J. Ruschak
Affiliation:
Emulsion Coating Technologies, Eastman Kodak Company, Rochester, NY 14652-3701, USA
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Abstract

The shape of a two-dimensional liquid curtain issuing from a slot and falling under the influence of gravity is predicted theoretically and verified experimentally for cases where a pressure is applied to the curtain. A set of approximate equations is derived which governs the location of the curtain for a liquid having surface tension σ, density ρ, volumetric flow per unit width Q, and local free-fall velocity V. These equations possess a singularity at the point where the local Weber number, We = ρQV/2σ, is equal to 1. Despite the fact that previous work on the stability of two-dimensional curtains shows that curtains having locations where We < 1 are unstable to small disturbances, our experiments show that these curtains can exist over a wide range of flow conditions. Thus, it is necessary to consider how the singularity is resolved when a pressure is applied.

It is found that the singularity can be eliminated from the governing equations if the curtain assumes a definite direction as it leaves the slot. By contrast, if the curtain leaves the slot such that We > 1, there is no such restriction, and experimentally it is found that the curtain leaves parallel to the slot walls. The theoretical predictions of the curtain shapes are in agreement with those measured experimentally for all Weber numbers investigated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 255 , October 1993 , pp. 647 - 665
Copyright
© 1993 Cambridge University Press

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References

Baird, M. H. I. & Davidson, J. F. 1962 Annular jets–I. Fluid dynamics. Chem. Engng Sci.. 17, 467–472.Google Scholar
Boussinesq, J. 1869a Theorie des experiences de Savart sur la forme que prend une veine liquide apres s’etre heurtee contre un plan circulaire. C. R. Acad. Sci., Paris. 69, 45–48.Google Scholar
Boussinesq, J. 1869b Theorie des experiences de Savart sur la forme que prend une veine liquide apres s’etre heurtee contre un plan circulaire. C. R. Acad. Sci. Paris. 69, 128–131.Google Scholar
Brown, D. R. 1961 A study of the behaviour of a thin sheet of a moving liquid. J. Fluid Mech.. 10, 297–305.Google Scholar
Clarke, N. S. 1969 Two-dimensional flow under gravity in a jet of viscous liquid. J. Fluid Mech.. 31, 481–500.Google Scholar
Dumbleton, J. H. 1969 Effect of gravity on the shape of water bells. J. Appl. Phys.. 40, 3950–3954.Google Scholar
Georgiou, G. C., Papanastasiou, T. C. & Wilkes, J. O. 1988 Laminar Newtonian jets at high Reynolds number and high surface tension. AIChE J.. 34, 1559–1562.Google Scholar
Hoffman, M. A., Takahashi, R. K. & Monson, R. D. 1980 Annular liquid jet experiments. Trans. ASME I: J. Fluids Engng 102, 344–349.Google Scholar
Hopwood, F. L. 1952 Water bells. Proc. Phys. Soc. Lond.. B 65, 2–5.Google Scholar
Lance, G. N. & Perry, R. L. 1953 Water bells. Proc. Phys. Soc. Lond.. B 66, 1067–1072.Google Scholar
Lin, S. P. 1981 Stability of a viscous liquid curtain. J. Fluid Mech. 104, 111–118.Google Scholar
Lin, S. P. & Roberts, G. 1981 Waves in a viscous liquid curtain. J. Fluid Mech. 112, 443–458.Google Scholar
Padday, J. F. 1957 A direct reading electrically operated balance for static and dynamic surface-tension measurement. Proc. Intl Congr. of Surface Activity (ed.J. H. Schulman), vol. 1, pp. 1–6. Academic.
Ramos, J. I. 1988 Liquid curtains–I. Fluid mechanics. Chem. Engng Sci.. 43, 3171–3184.Google Scholar
Rosen, M. J. 1989 Surfactants and Interfacial Phenomena. John Wiley & Sons.
Ruschak, K. J. 1980 A method for incorporating free boundaries with surface tension in finite-element fluid-flow simulators. Intl. J. Numer. Meth. Engng. 15, 639–648.Google Scholar
Taylor, G. I. 1959 The dynamics of thin sheets of fluid – III. Disintegration of fluid sheets. Proc. R. Soc. Lond.. A 253, 18–21.Google Scholar
Tillet, J. P. K. 1968 On the laminar flow of a free jet of liquid at high Reynolds numbers. J. Fluid Mech.. 32, 273–292.Google Scholar