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Frequency and damping of non-axisymmetric surface oscillations of a viscous cylindrical liquid bridge

Published online by Cambridge University Press:  29 June 2011

RANGACHARI KIDAMBI
RANGACHARI KIDAMBI*
Affiliation:
Computational and Theoretical Fluid Dynamics Division, National Aerospace Laboratories, Bangalore 560017, India
*
†Email address for correspondence: [email protected]
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Abstract

We present a semi-analytic solution for the non-axisymmetric oscillations of a viscous cylindrical free-standing liquid bridge formed between two coaxial discs of radius R. Even though a streamfunction does not exist, a Helmholtz decomposition is used to obtain an analytic representation of the velocity field. An eigenvalue problem is formulated by projecting the free-surface boundary conditions onto a suitable space of test functions. This is then solved iteratively along with the dispersion relation obtained from the satisfaction of endwall boundary conditions. Extensive comparison with previous theoretical and numerical results, for a range of Reynolds number and bridge slenderness ratio, shows very good agreement in most cases. The present solution generalises that of Tsamopoulos, Chen & Borkar (J. Fluid Mech., vol. 235, 1992, p. 579), which employed a streamfunction formulation and was for the axisymmetric case.

JFM classification

Interfacial Flows (free surface): Liquid bridges Waves/Free-surface Flows: Capillary waves Mathematical Foundations: Computational methods
Type
Papers
Information
Journal of Fluid Mechanics , Volume 681 , 25 August 2011 , pp. 597 - 621
Copyright
Copyright © Cambridge University Press 2011

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