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Nonlinear dynamics of capillary bridges: theory

Published online by Cambridge University Press:  26 April 2006

Tay-Yuan Chen  and
John Tsamopoulos
Tay-Yuan Chen
Affiliation:
Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA
John Tsamopoulos
Affiliation:
Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA
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Abstract

Finite-amplitude, forced and free oscillations of capillary bridges are studied. They are characterized by a resonant frequency and a damping rate which, in turn, depend on fluid properties, dimensions of the bridge, gravitational force relative to surface tension and amplitude of the external disturbance. The Navier–Stokes equations are solved numerically using the Galerkin/finite-element methodology for discretization in space and implicit finite differences with adaptive time stepping for discretization in time. It is found that the resonant frequency decreases and the damping rate increases almost linearly with the oscillation amplitude. Their relative changes from their corresponding values at infinitesimal amplitude depend on fluid properties and dimensions of the bridge. Moreover, careful measurement of the resonant frequency and damping rate in a well-controlled experiment may provide quite accurate values for properties of the liquid over a wide range of modified Reynolds numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 255 , October 1993 , pp. 373 - 409
Copyright
© 1993 Cambridge University Press

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