Abstract
The theory of creeping motion is used to study the relaxation of an infinite viscous fluid layer (membrane) of nonuniform thickness. The propagation of boundary perturbations in a semi-infinite layer under the action of surface-tension forces is also considered. The layer has at least one common boundary with a gas. It is found that relaxation processes of an infinite layer or the propagation of boundary perturbations inside a bounded layer are non-monotonic, and that wave-like surface perturbations always arise. Relaxation times are determined. Maximum distances are found over which separate regions of the layer can affect each other.
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H. Shlichting, Boundary Layer Theory [Russian translation], Izd-vo inostr. Lit., Moscow, 1956.
V. G. Levich, The Physicochemical Theory of Hydrodynamics [in Russian], Fizmatgiz, Moscow, 1959.
K. J. Mysels, K. Shinoda, and S. Frankel, Soap Films, Pergamon Press, London, 1959.
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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 73–77, January–February, 1970.
The author wishes to thank V. G. Levich for discussions.
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Voinov, O.V. Relaxation of a liquid layer under the action of capillary forces. J Appl Mech Tech Phys 11, 71–75 (1970). https://doi.org/10.1007/BF01102677
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DOI: https://doi.org/10.1007/BF01102677