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Capillary damping of inviscid surface waves in a circular cylinder

Published online by Cambridge University Press:  25 May 2009

R. KIDAMBI
R. KIDAMBI*
Affiliation:
Computational & Theoretical Fluid Dynamics Division, National Aerospace Laboratories, Bangalore 560017, India
*
†Email address for correspondence: kidambi@ctfd.cmmacs.ernet.in
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Abstract

We consider the effect of a wetting condition at the moving contact line on the frequency and damping of surface waves on an inviscid liquid in a circular cylinder. The velocity potential φ and the free surface elevation η are sought as complex eigenfunction expansions. The φ eigenvalues are the classical ones whereas the η eigenvalues are unknown and have to be computed so as to satisfy the wetting condition on the contact line and the other free surface conditions – these turn out to be complex in general. A projection of the latter conditions on to an appropriate basis leads to an eigenvalue problem, for the complex frequency Ω, which has to be solved iteratively with the wetting condition. The variation of Ω with liquid depth h, Bond number Bo, capillary coefficient λ and static contact angle θc0 is explored for the (1, 0),(2, 0),(0, 1),(3, 0) and (4, 0) modes. The damping vanishes for λ = 0 (pinned-end edge condition) and λ = ∞ (free-end edge condition) with a maximum in the interior while the frequency decreases with increasing λ, approaching limiting values at the endpoints. A comparison with the analytic results of Miles (J. Fluid Mech., vol. 222, 1991, p. 197) for the no-meniscus case and the experimental results of Cocciaro, Faetti, & Festa (J. Fluid Mech., vol. 246, 1993, p. 43), where a meniscus is present, is good. The study provides a simple procedure for calculating the inviscid capillary damping associated with the moving contact line in a circular cylinder of finite depth with meniscus effects also being considered.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 627 , 25 May 2009 , pp. 323 - 340
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Ablett, R. 1923 An investigation of the angle of contact between paraffin wax and water. Phil. Mag. 46, 244–256.CrossRefGoogle Scholar
Benjamin, T. B. & Scott, J. C. 1979 Gravity-capillary waves with edge constraints. J. Fluid Mech. 92, 241–267.Google Scholar
Case, K. M. & Parkinson, W. C. 1957 Damping of surface waves in an incompressible liquid. J. Fluid Mech. 2, 172–184.CrossRefGoogle Scholar
Cocciaro, B., Faetti, S. & Festa, C. 1993 Experimental investigation of capillarity effects on surface gravity waves: non-wetting boundary conditions. J. Fluid Mech. 246, 43–66.CrossRefGoogle Scholar
Graham-Eagle, J. 1983 A new method for calculating eigenvalues with applications to gravity-capillary waves with edge constraints. Math. Proc. Camb. Phil. Soc. 94, 553–564.Google Scholar
Henderson, D. M. & Miles, J. W. 1994 Surface-wave damping in a circular cylinder with a fixed contact line. J. Fluid Mech. 275, 285–299.CrossRefGoogle Scholar
Hocking, L. M. 1987 The damping of capillary-gravity waves at a rigid boundary. J. Fluid Mech. 179, 253–266.CrossRefGoogle Scholar
Howell, D. R., Buhrow, B., Heath, T., McKenna, C., Hwang, W. & Schatz, M. F. 2000 Measurements of surface-wave damping in a container. Phys. Fluids 12 (2), 322–326.CrossRefGoogle Scholar
Jiang, L., Perlin, M. & Schultz, W. W. 2004 Contact-line dynamics and damping for oscillating free surface flows. Phys. Fluids 16 (3), 748–758.CrossRefGoogle Scholar
Johnson, R. S. 1997 A Modern Introduction to the Mathematical Theory of Water Waves. Cambridge University Press.Google Scholar
Keulegan, G. H. 1959 Energy dissipation in standing waves in rectangular basins. J. Fluid Mech. 6, 33–50.CrossRefGoogle Scholar
Kidambi, R. 2009 Meniscus effects on the frequency and damping of capillary-gravity waves in a brimful circular cylinder. Wave Motion 46, 144–154, doi:10.1016/j.wavemoti.2008.10.001.CrossRefGoogle Scholar
Lamb, H. 1895 Hydrodynamics, 2nd ed. Cambridge University Press.CrossRefGoogle Scholar
Martel, C., Nicolás, J. A. & Vega, J. M. 1998 Surface-wave damping in a brimful circular cylinder. J. Fluid Mech. 360, 213–228.Google Scholar
Miles, J. W. 1967 Surface-wave damping in closed basins. Proc. R. Soc. Lond. A 297, 459–475.Google Scholar
Miles, J. W. 1990 Capillary-viscous forcing of surface waves. J. Fluid Mech. 219, 635–646.CrossRefGoogle Scholar
Miles, J. W. 1991 The capillary boundary layer for standing waves. J. Fluid Mech. 222, 197–205.CrossRefGoogle Scholar
Nicolás, J. A. 2002 The viscous damping of capillary-gravity waves in a brimful circular cylinder. Phys. Fluids 14, 1910–1919.Google Scholar
Nicolás, J. A. 2005 Effects of static contact angles on inviscid capillary-gravity waves. Phys. Fluids 17, 022101.CrossRefGoogle Scholar
Shankar, P. N. 2007 Frequencies of gravity-capillary waves on highly curved interfaces with edge constraints. Fluid Dyn. Res. 39, 457–474.CrossRefGoogle Scholar
Van Dorn, W. G. 1966 Boundary dissipation of oscillatory waves. J. Fluid Mech. 24, 769–779.CrossRefGoogle Scholar