Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T15:08:13.531Z Has data issue: false hasContentIssue false
  • English
  • Français

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

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

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

Chaudhary, K. C. 1977 Ph.D. thesis, University of Southern California.
Donnelly, R. J. & Glaberson, W. 1966 Proc. Roy. Soc. A 290, 547.
Goedde, E. F. & Yuen, M. C. 1970 J. Fluid Mech. 40, 495.
Lafrance, P. 1975 Phys. Fluids 18, 428.
Nayfeh, A. H. 1970 Phys. Fluids 13, 841.
Rayleigh, Lord 1945 The Theory of Sound. 2nd edn., vol. II, cha. xx. Dover.
Rutland, D. F. & Jameson, G. J. 1971 J. Fluid Mech 46, 267.
Yuen, M. C. 1968 J. Fluid Mech. 33 151.