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Weakly nonlinear oscillations of nearly inviscid axisymmetric liquid bridges

Published online by Cambridge University Press:  26 April 2006

José A. NicoláS  and
José M. Vega
José A. NicoláS
Affiliation:
ETSI Aeronáuticos, Universidad Politécnica de Madrid, 28040-Madrid, Spain
José M. Vega
Affiliation:
ETSI Aeronáuticos, Universidad Politécnica de Madrid, 28040-Madrid, Spain
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Abstract

A weakly nonlinear analysis is presented of the small oscillations of nearly inviscid liquid bridges subjected to almost resonant axial vibrations of the disks. An amplitude equation is derived for the evolution of the complex amplitude of the oscillations that exhibits hysteresis and period doublings. We also analyse the steady streaming in the bulk forced by the oscillatory boundary layers near the disks; the boundary layer near the free surface produces no forcing terms. In particular some experimentally observed patterns are explained, and some new, non-observed ones are predicted. We conclude that the structure of this steady flow is not the appropriate one to counterbalance steady thermocapillary convection, but our results indicate how to get the desired counterbalancing effect.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 328 , 10 December 1996 , pp. 95 - 128
Copyright
© 1996 Cambridge University Press

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