Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-04T21:34:37.640Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Birkhoff, G., Macdougall, D. P., Pugh, E. M. & Taylor, G. I. 1948 Explosives with lined cavities. J. Appl. Phys. 19, 563–582.Google Scholar
Frankel, I. & Weihs, D. 1985 Stability of a capillary jet with linearly increasing axial velocity (with application to shaped charges). J. Fluid Mech. 155, 289–307.Google Scholar
Frankel, I. 1984 Flow and stability in liquid jets with longitudinal distribution of axial velocity. PhD thesis, Technion, Haifa.
Goldstein, S. 1932 Some two dimensional diffusion problems with circular symmetry. Proc. Lond. Math. Soc. 34, 51–88.Google Scholar
Gray, A., Mathews, G. B. & Macrobert, T. M. 1922 A Treatise on Bessel Functions and Their Applications to Physics, 2nd edn. Macmillan.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press. (Reprinted by Dover 1945.)
Mayseless, M., Erlich, Y., Falcovitz, Y., Rosenberg, G. & Weihs, D. 1984 Interaction of shaped charge jets with reactive armor. In Proc. 6th Intl Symp. on Ballistics, Orlando, Fl., pp. 7–15 to 7–20. American Defense Preparedness Association.
Mikami, T., Cox, R. G. & Mason, S. G. 1975 Breakup of extending liquid threads. Intl J. Multiphase Flow 2, 113–138.Google Scholar
Prosperetti, A. 1976 Viscous effects on small amplitude surface waves. Phys. Fluids 19, 195–203.Google Scholar
Prosperetti, A. 1980 Free oscillations of drops and bubbles, the initial value problem. J. Fluid Mech. 100, 333–347.Google Scholar
Rosenhead, L. 1963 Laminar Boundary Layers. Oxford University Press.
Tomotika, S. 1936 Breaking up of a drop of viscous liquid immersed in another viscous fluid which is extending at a uniform rate. Proc. R. Soc. Lond. A 153, 302–318.Google Scholar