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Capillary instability of an annular liquid jet

Published online by Cambridge University Press:  21 April 2006

J. Meyer  and
D. Weihs
J. Meyer
Affiliation:
Department of Aeronautical Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel
D. Weihs
Affiliation:
Department of Aeronautical Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel
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Abstract

An analytical investigation of the stability of a viscous, annular liquid jet moving in an inviscid medium is presented. This problem is a generalization of the well-known cases of a round cylindrical jet (obtained here when the ratio of internal to external radii tends to zero) and the flat thin liquid sheet (when the ratio above tends to unity). A critical ‘penetration’ thickness T is defined. When the annulus thickness is greater than T, the annular jet behaves like a full liquid jet; the only unstable perturbations are axisymmetric, and their growth rate is independent of thickness. When the annulus thickness is less than T, the jet behaves like a two-dimensional liquid sheet; the most unstable perturbations are antisymmetric and their growth rate increases as the jet thickness decreases. Therefore, an annular liquid jet with a sufficiently small ring thickness will disintegrate into spherical shells much faster than a full liquid jet disintegrates into drops, in accordance with existing experimental data. Non-dimensional expressions for the penetration thickness are given for both viscous and inviscid jets.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 179 , June 1987 , pp. 531 - 545
Copyright
© 1987 Cambridge University Press

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