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Linear stability of a cylindrical falling film

Published online by Cambridge University Press:  21 April 2006

Francisco J. Solorio  and
Mihir Sen
Francisco J. Solorio
Affiliation:
Facultad de Ingeniería, Universidad Nacional Autónoma de México, 04510 México, DF, México
Mihir Sen
Affiliation:
Facultad de Ingeniería, Universidad Nacional Autónoma de México, 04510 México, DF, México Present address: Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA.
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Abstract

The problem of a cylindrical falling film, descending vertically outside an infinitely long cylinder is considered. The linear stability of the fully developed flow is studied, first with a perturbation technique for small wavenumbers, and then by direct numerical computation. The numerical results are in agreement with other published values for the cylindrical jet and flat plate limits. The study shows that the cylindrical falling film is unstable for all Reynolds numbers, Weber numbers and radius ratios. Stability and amplification curves are calculated for different values of the parameters. With increasing curvature of the film the range of unstable wavenumbers and the wavenumber of the most amplified wave increase. For low curvature the wavenumber of the most amplified wave decreases with Reynolds number or Weber number, while for high curvatures it increases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 183 , October 1987 , pp. 365 - 377
Copyright
© 1987 Cambridge University Press

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References

Atherton, R. W. & Homsy, G. M. 1976 On the derivation of evolution equations for interfacial waves. Chem. Engng Commun. 2, 57–77.Google Scholar
Binnie, A. M. 1957 Experiments on the onset of wave formation on a film of water flowing down a vertical plane. J. Fluid Mech. 2, 551–553.Google Scholar
Benjamin, T. B. 1957 Wave formation in a laminar flow down an inclined plane. J. Fluid Mech. 2, 554–574 (see also Corrigendum 1958, J. Fluid Mech. 3, 657).Google Scholar
de Bruin, G. J. 1974 Stability of a layer of liquid flowing down an inclined plane. J. Engng Maths 8, 259–270.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
Davey, A. 1973 A simple numerical method for solving Orr–Sommerfeld problems. Q. J. Mech. Appl. Maths 26, 401–411.Google Scholar
Goren, S. L. 1962 The instability of an annular thread of fluid. J. Fluid Mech. 12, 309–319.Google Scholar
Homsy, G. M. & Geyling, F. T. 1977 A note on instabilities in rapid coating of cylinders. AIChE J. 23, 587–590.Google Scholar
Kapitza, P. L. & Kapitza, S. P. 1949 Experimental study of undulatory flow conditions. Zh. Eksp. Teor. Fiz. 19 (see Collected Papers of P. L. Kapitza, 1964, pp. 690–709. Macmillan).Google Scholar
Krantz, W. B. & Goren, S. L. 1971 Stability of thin liquid films flowing down a plane. Ind. Engng Chem. Fundam. 10, 91–101.Google Scholar
Krantz, W. B. & Zollars, R. L. 1976 The linear hydrodynamic stability of film flow down a vertical cylinder. AIChE J. 22, 930–938.Google Scholar
Lin, S. P. & Liu, W. C. 1975 Instability of film coating of wires and tubes. AIChE J. 21, 775–782.Google Scholar
Pierson, F. W. & Whitaker, S. 1977 Some theoretical and experimental observations of the wave structure of falling liquid films. Ind. Engng Chem. Fundam. 16, 401–408.Google Scholar
Rayleigh, Lord 1879 On the capillary phenomenon of jets. Proc. R. Soc. Lond. 29, 71–97.Google Scholar
Rayleigh, Lord 1892 On the instability of a cylinder of viscous liquid under capillary forces. Phil. Mag. 34, 145–154.Google Scholar
Shlang, T. & Sivashinsky, G. I. 1982 Irregular flow of a liquid film down a vertical column. J. Phys. Paris 43, 459–466.Google Scholar
Weber, C. 1931 Zum Zerfall eines Flussigkeitsstrahles. Z. angew. Math. Mech. 11, 136–141.Google Scholar
Whitaker, S. 1964 Effect of surface active agents on the stability of falling liquid films. Ind. Engng Chem. Fundam. 3, 132–142.Google Scholar
Yih, C.-S. 1954 Stability of parallel laminar flow with a free surface. Proc. 2nd U.S. Natl Congr. Appl. Mech. ASME, pp. 623–628.
Yih, C.-S. 1963 Stability of liquid flow down an inclined plane. Phys. Fluids 6, 321–334.Google Scholar
Yih, C.-S. 1969 Fluid Mechanics. McGraw-Hill.