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Equilibrium shapes and stability of captive annular menisci

Published online by Cambridge University Press:  21 April 2006

J. A. Tsamopoulos ,
A. J. Poslinski  and
M. E. Ryan
J. A. Tsamopoulos
Affiliation:
Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA
A. J. Poslinski
Affiliation:
Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA
M. E. Ryan
Affiliation:
Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA
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Abstract

Equilibrium shapes and stability of annular fluid menisci held together by surface tension are analysed by applying asymptotic and computer-aided techniques from bifurcation theory. The shapes and locations of the menisci are governed by the Young–Laplace equation. These shapes are grouped together into families of like symmetry that branch from the basic family of annular shapes at specific values of the aspect ratio, α. Multiple equilibrium shapes exist over certain values of α. The inner, outer or both the inner and outer interfaces may possess either a cylindrical or sinusoidal equilibrium shape. Changes in applied pressure, fluid volume, or gravitational Bond number break families of the same symmetry which now develop limit points. Numerical calculations rely on a finite-element representation of the interfaces and the results compare very well with asymptotic analysis which is valid for small deformations. The results are important for the blow moulding process and are invaluable in understanding its dynamics. These dynamics are expected to be considerably different from the dynamics of a liquid jet first analysed by Rayleigh.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 197 , December 1988 , pp. 523 - 549
Copyright
© 1988 Cambridge University Press

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