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The nonlinear capillary instability of a liquid jet. Part 1. Theory

Published online by Cambridge University Press:  19 April 2006

K. C. Chaudhary  and
L. G. Redekopp
K. C. Chaudhary
Affiliation:
International Business Machines Corporation, General Products Division, San Jose, California
L. G. Redekopp
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, California
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Abstract

Nonlinear capillary instability of an axisymmetric infinite liquid column is investigated with an initial velocity disturbance consisting of a fundamental and one harmonic component. A third-order solution is developed using the method of strained co-ordinates. For the fundamental disturbance alone, the solution shows that a cut-off zone of wavenumbers (k) exists such that the surface waves grow exponentially below the cut-off zone, linearly in the middle of the zone (near k = 1), and an oscillatory solution exists for wavenumbers above the boundary of the zone. For an input including both the fundamental and a harmonic, all wave components grow exponentially when the fundamental is below the cut-off zone. Using a Galilean transformation, the solution is applied to a progressive jet issuing from a nozzle. The jet breaks into drops interspersed with smaller (satellite) drops for k < 0·65; no satellites exist for k > 0·65. It is shown theoretically that the formation of satellites can be controlled by forcing the jet with a suitable harmonic added to the fundamental.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 96 , Issue 2 , 29 January 1980 , pp. 257 - 274
Copyright
© 1980 Cambridge University Press

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References

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