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Non-linear capillary instability of a liquid jet

Published online by Cambridge University Press:  28 March 2006

Man-Chuen Yuen
Man-Chuen Yuen
Affiliation:
Gas Dynamics Laboratory, Northwestern University, Evanston, Illinois
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Abstract

A third-order theory has been developed to study capillary instability of a liquid jet. The result shows that the asymmetrical development of an initially sinusoidal wave is a non-linear effect with generation of higher harmonics as well as feedback into the fundamental. The growth of the surface wave is found to depend explicitly on the dimensionless initial amplitude of the disturbance and the dimensionless wave-number k of the wave. For the same initial disturbance, the wave is found to have a maximum growth rate at k = 0·7 in agreement with the linearized theory. For the same wave-number, the growth is proportional to the initial amplitude of the disturbance. The cut-off wave-number and the fundamental frequency (or growth rate for the unstable case) of the wave for a given k are found to be different from the linearized theory. Furthermore, at the cut-off wave-number, the present theory shows the disturbance experiences a growth which is proportional to t2. The excellent agreement between Donnelly & Glaberson's experiment and Rayleigh's linearized theory is found to be due to their method of measurement.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 33 , Issue 1 , 12 July 1968 , pp. 151 - 163
Copyright
© 1968 Cambridge University Press

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References

Crane, L., Birch, S. & Mccormack, P. D. 1964 The effect of mechanical vibration on the break-up of a cylindrical water jet in air Br. J. appl. Phys. 15, 743.Google Scholar
Donnelly, R. J. & Glaberson, W. 1966 Experiment on capillary instability of a liquid jet. Proc. Roy. Soc A 290, 547–56.Google Scholar
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