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Capillary-wave scattering from an infinitesimal barrier and dissipation at dynamic contact lines

Published online by Cambridge University Press:  19 February 2013

Likun Zhang  and
David B. Thiessen
Likun Zhang
Affiliation:
Department of Physics and Astronomy, Washington State University, Pullman, WA 99164-2814, USA
David B. Thiessen*
Affiliation:
Department of Physics and Astronomy, Washington State University, Pullman, WA 99164-2814, USA
*
†Email address for correspondence: thiessen@wsu.edu
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Abstract

The interaction of pure capillary waves with boundaries that constrain the contact line are of interest for problems involving liquids contained by minimal solid contact for applications in low gravity and at small scales in normal gravity. Time-harmonic capillary waves on a liquid cylinder axially incident on and scattered by an infinitesimal concentric barrier are considered theoretically in the inviscid limit. The barrier is taken to be infinitesimally small in the sense that its immersed depth is of the order of the amplitude of contact-line motion. Edge conditions on the barrier that are investigated include a pinned contact line and a moving contact line by an effective-slip model, assuming that contact-line velocity is proportional to the deviation of the contact angle from equilibrium multiplied by a slip coefficient. The incident waves are taken to be those with wavelengths short enough to be stable on the liquid cylinder. Scattering and dissipation by the contact line are determined as a function of wavenumber and slip coefficient. Zero transmission is approached in the long-wave limit. The short-wave limit agrees with established results for the scattering of planar gravity–capillary waves on a deep liquid by a surface-piercing vertical barrier in the limit of zero barrier depth and zero gravity. We find that contact-line dissipation at the barrier is a maximum for incident waves whose phase speed is of the order of the slip coefficient, which is interpreted as an effect of impedance matching. Transmission past an infinitesimal barrier is found to be low over all parameter space, illustrating the importance of contact-line constraints.

JFM classification

Waves/Free-surface Flows: Capillary waves Interfacial Flows (free surface): Contact lines Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 719 , 25 March 2013 , pp. 295 - 313
Copyright
©2013 Cambridge University Press

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Footnotes

‡

Present address: Department of Physics and Center for Nonlinear Dynamics, University of Texas at Austin, Austin, TX 78712, USA.

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