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Summary: Acoustic excitation of superharmonic capillary waves on a meniscus
in a planar microgeometry
Jie Xu and Daniel Attinger
Laboratory for Microscale Transport Phenomena, Department of Mechanical Engineering,
Columbia University, New York, New York 10027, USA
Received 22 January 2007; accepted 6 September 2007; published online 18 October 2007
The effects of ultrasound on the dynamics of an air-water meniscus in a planar microgeometry are
investigated experimentally. The sonicated meniscus exhibits harmonic traveling waves or standing
waves, the latter corresponding to a higher ultrasound level. Standing capillary waves with
subharmonic and superharmonic frequencies are also observed, and are explained in the framework
of parametric resonance theory, using the Mathieu equation. © 2007 American Institute of Physics.
DOI: 10.1063/1.2790968
Instabilities at a liquid-gas interface appear in a wide
range of physical systems, from large ocean waves to micro-
scopic oscillations of a cavitating bubble.1,2
For a linear and
conservative system the response is harmonic; i.e., with the
same frequency as the excitation frequency.3
However, in
1831, Faraday observed4
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