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Influence of viscosity on the capillary instability of a stretching jet

Published online by Cambridge University Press:  21 April 2006

I. Frankel  and
D. Weihs
I. Frankel
Affiliation:
Dept. of Aeronautical Engineering, Technion, Haifa 32000, Israel
D. Weihs
Affiliation:
Dept. of Aeronautical Engineering, Technion, Haifa 32000, Israel
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Abstract

The hydrodynamic stability of a rapidly elongating, viscous liquid jet such as obtained in shaped charges is presented. The flow field depends on three characteristic timescales associated with the growth of perturbations (due essentially to the effect of the surface tension), the elongation of the jet, and the inward diffusion of vorticity from the free surface, respectively. The latter process introduces a time lag resulting in the current values of the free-surface perturbation and its time derivative being a function of their past history. Solutions of the integro-differential equation for the evolution of disturbances exhibit a novel dual role played by the viscosity: besides the traditional damping effect it is associated with a destabilizing mechanism in the elongating jet. The wavelength of maximum instability is also a function of time elapsed since the jet formation, longer wavelengths becoming dominant at later stages. Understanding of these instability processes can help in both promoting and delaying instability as required by specific applications.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 185 , December 1987 , pp. 361 - 383
Copyright
© 1987 Cambridge University Press

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