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Three-dimensional large-amplitude drop oscillations: experiments and theoretical analysis

Published online by Cambridge University Press:  25 August 1999

HISAO AZUMA  and
SHOICHI YOSHIHARA
HISAO AZUMA
Affiliation:
National Aerospace Laboratory, 7-44-1 Jindaiji-higashimachi, Chofu, Tokyo Present address: Osaka Prefecture University, 1-1 Gakuen-Cho, Sakai, Osaka, Japan.
SHOICHI YOSHIHARA
Affiliation:
National Aerospace Laboratory, 7-44-1 Jindaiji-higashimachi, Chofu, Tokyo
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Abstract

Three-dimensional large-amplitude oscillations of a mercury drop were obtained by electrical excitation in low gravity using a drop tower. Multi-lobed (from three to six lobes) and polyhedral (including tetrahedral, hexahedral, octahedral and dodecahedral) oscillations were obtained as well as axisymmetric oscillation patterns. The relationship between the oscillation patterns and their frequencies was obtained, and it was found that polyhedral oscillations are due to the nonlinear interaction of waves.

A mathematical model of three-dimensional forced oscillations of a liquid drop is proposed and compared with experimental results. The equations of drop motion are derived by applying the variation principle to the Lagrangian of the drop motion, assuming moderate deformation. The model takes the form of a nonlinear Mathieu equation, which expresses the relationships between deformation amplitude and the driving force's magnitude and frequency.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 393 , 25 August 1999 , pp. 309 - 332
Copyright
© 1999 Cambridge University Press

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