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.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference4 articles.
1. Donnelly, R. J. & Glaberson, W. 1966 Experiment on capillary instability of a liquid jet.Proc. Roy. Soc A290,547–56.
2. Emmons, H. W. , Chang, C. T. & Watson, B. C. 1960 Taylor instability of finite surface waves J. Fluid Mech. 7,177–93.
3. 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.
4. Rayleigh, LORD. 1945 The Theory of Sound , vol. II (2nd ed.).New York:Dover.
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