Meniscus effects on the frequency and damping of capillary-gravity waves in a brimful circular cylinder

Kidambi, Rangachari (2007) Meniscus effects on the frequency and damping of capillary-gravity waves in a brimful circular cylinder. Technical Report. National Aerospace Laboratories, Bangalore, India.

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    Abstract

    We study the effects of a meniscus on the oscillations of a viscous liquid filling a right circular cylindrical container by using the natural viscous complex eigenfunctions of the problem. The free surface of the liquid is assumed to have a pinned contact line. By projecting the governing equations onto an appropriate basis, a nonlinear eigenvalue problem for the complex frequencies is obtained. This is then solved to13; obtain the modal frequencies as a function of the contact angle $\theta_c$, the Reynolds and Bond numbers Re and Bo and the liquid depth h. At shallow depths, the13; effect of the meniscus is, in general, to increase the modal frequency and decrease the damping rate with increasing $\theta_c$. At large depths and for higher modes, the13; damping rate monotonically decreases with increasing $\theta_c$ while the frequency attains13; a maximum in the neighbourhood of $90^0$. However, there are parameter values for13; which the meniscus results in anomalous behaviours in the damping rate. Extensive13; comparison with experimental and computational results for the $\theta_c = 90^0$ case is13; very good; comparison with the one available experimental result for $\theta_c = 62^0$ is also13; very good. Extensive results for a variety of contact angles have been tabulated for13; Reynolds and Bond numbers for which experimental results exist in the flat interface13; case, for comparison with future experimental results that may be obtained with13; curved menisci.

    Item Type: Proj.Doc/Technical Report (Technical Report)
    Uncontrolled Keywords: Frequency;Damping;Meniscus effects;Pinned contact line
    Subjects: ENGINEERING > Fluid Mechanics and Thermodynamics
    Division/Department: Computational and Theoretical Fluid Dynamics Division
    Depositing User: Dr. Rangachari Kidambi
    Date Deposited: 16 Jan 2009
    Last Modified: 17 Jun 2010 10:37
    URI: http://nal-ir.nal.res.in/id/eprint/4654

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