Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T00:29:48.120Z Has data issue: false hasContentIssue false
  • English
  • Français

The break-up of axisymmetric liquid sheets

Published online by Cambridge University Press:  29 March 2006

J. C. P. Huang
J. C. P. Huang
Affiliation:
Department of Mechanical Engineering, Washington State University, Pullman, Washington 99163 Present address: Engineering Research Department, Minnesota Mining and Manufacturing Company, St Paul, Minnesota 55112.
Get access Rights & Permissions [Opens in a new window]

Abstract

The break-up mechanism of axisymmetric liquid sheets formed by the impingement of two co-axial jets has been examined. Three break-up regimes in the Weber number range from 100 to 3 × 104 are reported. In the first break-up regime, droplets are formed through successive mergings of liquid beads along the nearly circular periphery of the sheet. The formation of beads is caused by Rayleigh instability. In the transition regime, Taylor's cardioid wave pattern prevails in the first half of this regime, while the sheet begins to flap in the second half.

In the second break-up regime, antisymmetric waves on the sheet grow radially. A semi-empirical equation has been deduced to predict the break-up radius of the sheet. The motion of an axisymmetric vibrating membrane with radially decreasing thickness has been studied to include Helmholtz instability as an analogue of the wave motion of the expanding circular sheet. A distorted progressive wave equation has been solved by the WKBJ method to indicate the effect of cylindrical geometry. The calculated wave speed agrees fairly well with experimental data at low Weber numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 43 , Issue 2 , 28 August 1970 , pp. 305 - 319
Copyright
© 1970 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

Bond, W. N. 1935 Proc. Phys. Soc. 47, 54.
Dombrowski, N. & Hooper, P. C. 1962 Chem. Engng Sci. 17, 29.
Dombrowski, N. & Hooper, P. C. 1964 J. Fluid Mech. 18, 39.
Dombrowski, N. & Johns, W. R. 1963 Chem. Engng Sci. 18, 20.
Fraser, R. P., Eisenklam, P., Dombrowski, N. & Hasson, D. 1962 A.I.Ch.E.J. 8, 67.
Goldin, M., Yerushalmi, J., Pfeffer, R. & Shinnar, R. 1969 J. Fluid Mech. 38, 68.
Grant, R. P. & Middleman, S. 1966 A.I.Ch.E.J. 12, 66.
Huang, J. C. P. 1967 Research Division, College of Engineering, Washington State University, Bulletin 306.
Lienhard, J. H. & Newton, T. A. 1966 Z. angew Math. Phys. 17, 34.
Lienhard, J. H. & Wong, P. T. Y. 1963 J. Heat Transfer, 86, 220.
Mathews, J. & Walker, R. L. 1964 Mathematical Methods of Physics. New York: Benjamin.
Miles, J. W. 1957 J. Fluid Mech. 3, 18.
Ostrach, S. & Koestel, A. 1965 A.I.Ch.E.J. 11, 29.
Savart, F. 1833 Ann. Chem. Phys. 59, 55, 113.
Squire, H. B. 1953 Br. J. Appl. Phys. 4, 16.
Taylor, G. I. 1959 Proc. Roy. Soc. A 253, 289, 296, 313.
Taylor, G. I. 1960 Proc. Roy. Soc. A 259, 1.
Weber, C. 1931 Z. angew Math. Mech. 2, 13.