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The development of nonlinear waves on the surface of a horizontally rotating thin liquid film

Published online by Cambridge University Press:  21 April 2006

D. J. Needham  and
J. H. Merkin
D. J. Needham
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
J. H. Merkin
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds LS2 9JT, UK
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Abstract

We consider the axisymmetric thin liquid film formed on a horizontally spinning disk. The asymptotic structure of the steady film is obtained, after which a theory is developed to describe the evolution of localized disturbances imposed upon the steady film. It is shown that this can lead to the propagation of large gradients in the film. Moreover, it is found that under certain conditions the steady film can become unstable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 184 , November 1987 , pp. 357 - 379
Copyright
© 1987 Cambridge University Press

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References

Batchelor, G. K. 1974 An Introduction to Fluid Dynamics. Cambridge University Press.
Benjamin, T. B. 1957 J. Fluid Mech. 2, 554.
Benney, D. J. 1966 J. Math. Phys. 45, 150.
Binnie, A. M. 1957 J. Fluid Mech. 2, 551.
Crighton, D. G. & Scott, J. F. 1979 Phil. Trans. R. Soc. A 292, 101.
Dukler, A. E. & Bergelin, O. P. 1952 Chem. Engng Prog. 48, 557.
Friedman, S. J. & Miller, C. O. 1941 Ind. Engng Chem. 33, 885.
Gjevik, B. 1970 Phys. Fluids 13, 1918.
Gjevik, B. 1971 Acta Poly. Scandinavia Mech. engng 61.
Grimley, S. S. 1945 Trans. Instn Chem. Engrs 23, 228.
Kapitza, P. L. & Kapitza, S. P. 1949 Zh. Eksp. Teor. Fiz. 16, 105.
Kelmanson, M. A. & Ingham, D. B. 1984 Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems. Springer.
Kirkbride, C. G. 1934 Ind. Engng Chem. 26, 425.
Smith, P. 1967 J. Engng Maths 1, 273.
Smith, P. 1969 J. Engng Maths 3, 181.
Smith, P. 1972 J. Engng Maths 6, 15.
Tailby, S. P. & Portalski, S. 1962 Trans. Instn Chem. Engrs 40, 114.
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic.
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley Interscience.