Abstract
A linear dispersion relation is derived for waves on the free surface of an infinitely deep viscous fluid covered by an elastic surfactant film. The solutions of the dispersion relation are studied over a wide range of variations of the fluid viscosity and the film elasticity. Dynamics of the Marangoni mode associated with the presence of the elastic film is considered in detail. Values of the film elasticity modulus corresponding to both wave motions in fluid and motions damped monotonically with time are found. The elasticity and viscosity parameters at which the nature of the fluid motion changes qualitatively are determined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R.V. Birikh, M.O. Denisova, and K.G. Kostarev, “The Development of Marangoni Convection Induced by Local Addition of a Surfactant,” Fluid Dynamics 46, No. 6, 890–900 (2011).
A.I. Mizev and A.I. Trofimenko, “Effect of an Insoluble Surfactant Film on the Stability of the Concentration-Driven Marangoni Flow,” Fluid Dynamics 49, No. 1, 26–36 (2014).
O.Yu. Dinariev and N.V. Evseev, “Modeling of Surface Phenomena in the Presence of Surface-Active Agents on the Basis of the Density-Functional Theory,” Fluid Dynamics 45, No. 1, 85–95 (2010).
M.G. Velarde, V.Ya. Shkadov, and V.P. Shkadova, “Influence of a Surfactant on the Instability of a Falling Liquid Film,” Fluid Dynamics 35, No. 4, 515–524 (2010).
E.N. Pelinovskii and T.G. Talipova, “Scale Effects in Simulating Internal Waves in a Tank Covered by Surfactant Films,” Izvestiya RAN, Fizika Atmosfery i Okeana 31, No. 5, 701–704 (1995).
V.G. Levich, Physico-Chemical Hydrodynamics (Fizmatgiz, Moscow, 1959) [in Russian].
R. Dorrestein, “General Linearized Theory of the Effect of Surface Films on Water Ripples,” Proc. Ned. Wet. Acad. Sci. B54, 260–272 (1951).
H. Lamb, Hydrodynamics (Dover, New York, 1932; OGIZ, Moscow-Leningrad, 1947).
J. Lucassen and M. van den Tempel, “Longitudinal Waves on Viscoelastic Surfaces,” J. Colloid and Interface Sci. 41, No. 3, 491–498 (1972).
J. Lucassen, “Longitudinal Capillary Waves,” Trans. Faraday Soc. 64, No. 8, Pt. 1. Theory, 2221–2239; Pt. 2. Experiments, 2230–2235 (1968).
S.A. Ermakov, Influence of Films on Dynamics of Gravity-Capillary Waves (IPF RAN, N. Novgorod, 2010) [in Russian].
P.P. Lombardini, F. Piazzese and R. Cini, “The Marangoni Wave in Ripples on an Air-Water Interface Covered by a Spreading Film,” II Nuovo Chimento 5C, No. 2, 256 (1982).
Yu.A. Buevich and L.M. Rabinovich (Eds.), Phase Interface Hydrodynamics (Mir, Moscow, 1984) [in Russian].
P.N. Antonyuk, “Dispersion Relation for a Plane Capillary-Gravity Wave on the Free Surface of Viscous Incompressible Fluid,” Dokl. Akad. Nauk SSSR, 286, No. 6, 1324–1328 (1986).
S.A. Ermakov, E.N. Pelinovskii, and T.G. Talipova, “Influence of Surfactant on Variation of Wind Wave Spectrum under the Action of Internal Waves,” Izvestiya Akad. Nauk SSSR, Fizika Atmosfery i Okeana 16, No. 10, 1068–1076 (1980).
J. Lucassen and R.S. Hansen, “Dam** of Waves on Monolayer-Covered Surfactants,” II. J. Colloid Interface Sci. 23, No. 3, 319–328 (1967).
A.A. Lazarev, K.V. Pokazeev, and N.K. Shelkovnikov, Physicochemical Inhomogeneity of the Ocean Surface and Surface Waves, Pts. 1 and 2 (Moscow University Press, Moscow, 1988) [in Russian].
S.A. Ermakov, “Resonance Dam** of Gravity-Capillary Waves on Water Covered by a Surfactant Film,” Izvestiya RAN, Fizika Atmosfery i Okeana 39, No. 5, 691–696 (2003).
A.A. Abramzon, Surfactants and Their Properties and Application (Khimiya, Leningrad, 1975) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © E.L. Averbukh, A.A. Kurkin, Yu.A. Stepanyants, T.G. Talipova, 2014, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2014, Vol. 49, No. 6, pp. 109–117.
Rights and permissions
About this article
Cite this article
Averbukh, E.L., Kurkin, A.A., Stepanyants, Y.A. et al. Dispersion properties of waves on the surface of a viscous fluid covered by an elastic film. Fluid Dyn 49, 796–803 (2014). https://doi.org/10.1134/S0015462814060118
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462814060118