Capillary damping of inviscid surface waves in a circular cylinder

Kidambi, R (2009) Capillary damping of inviscid surface waves in a circular cylinder. Journal of Fluid Mechanics, 627. pp. 323-340.

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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 x3C6; and the free surface elevation x3B7; are sought as complex eigenfunction expansions. The x3C6; eigenvalues are the classical ones whereas the x3B7; 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 x2013; 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 x3A9;, which has to be solved iteratively with the wetting condition. The variation of x3A9; with liquid depth h, Bond number Bo, capillary coefficient x3BB; and static contact angle x3B8;c0 is explored for the (1, 0), (2, 0), (0, 1), (3, 0) and (4, 0) modes. The damping vanishes for x3BB; = 0 (pinned-end edge condition) and x3BB;=x221E; (free-end edge condition) with a maximum in the interior while the frequency decreases with increasing x3BB;, 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, amp; 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.

Item Type: Article
Additional Information: Copyright for this article belongs to Cambridge University Press
Uncontrolled Keywords: Circular cylinder;Inviscid surface waves;Static meniscus
Subjects: ENGINEERING > Fluid Mechanics and Thermodynamics
AERONAUTICS > Aeronautics (General)
Depositing User: Ms. Alphones Mary
Date Deposited: 02 Mar 2010
Last Modified: 14 Aug 2015 05:21

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