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Sloshing in a Hele-Shaw cell: experiments and theory

Published online by Cambridge University Press:  13 October 2017

Francesco Viola ,
François Gallaire Open the ORCID record for François Gallaire [Opens in a new window]  and
Benjamin Dollet Open the ORCID record for Benjamin Dollet [Opens in a new window]
Francesco Viola
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
François Gallaire
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Benjamin Dollet
Affiliation:
Institut de Physique de Rennes, UMR 6251 CNRS and Université Rennes 1, Campus Beaulieu, Bâtiment 11A, 35042 Rennes CEDEX, France
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Abstract

The response of the free liquid surface in a Hele-Shaw cell subjected to a horizontal oscillation is investigated. We study the low-oscillation-amplitude regime and we show, by varying the fluid viscosity, $\unicode[STIX]{x1D708}$, and the forcing frequency, $\unicode[STIX]{x1D714}$, that the ratio between the Stokes viscous length, $\sqrt{2\unicode[STIX]{x1D708}/\unicode[STIX]{x1D714}}$, and the cell thickness greatly affects the amplitude and phase lag of the gravity waves. In particular, the sloshing system undergoes an underdamped/overdamped transition for sufficiently large viscosities. A consistent theoretical model, based on a modification of Darcy’s law to include unsteadiness, is then introduced to rationalize the experimental observations. Contrary to traditional sloshing wave theory, the viscous flow dissipation comes at leading order in the analysis, rather than as a higher-order asymptotic correction to the inviscid sloshing dynamics. The analytical expression for the resonance curves agrees well with experimental results without tunable parameters.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 831 , 25 November 2017 , R1
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Copyright
© 2017 Cambridge University Press 

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