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Capillary instability of an annular liquid jet

Published online by Cambridge University Press:  21 April 2006

J. Meyer  and
D. Weihs
J. Meyer
Affiliation:
Department of Aeronautical Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel
D. Weihs
Affiliation:
Department of Aeronautical Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel
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Abstract

An analytical investigation of the stability of a viscous, annular liquid jet moving in an inviscid medium is presented. This problem is a generalization of the well-known cases of a round cylindrical jet (obtained here when the ratio of internal to external radii tends to zero) and the flat thin liquid sheet (when the ratio above tends to unity). A critical ‘penetration’ thickness T is defined. When the annulus thickness is greater than T, the annular jet behaves like a full liquid jet; the only unstable perturbations are axisymmetric, and their growth rate is independent of thickness. When the annulus thickness is less than T, the jet behaves like a two-dimensional liquid sheet; the most unstable perturbations are antisymmetric and their growth rate increases as the jet thickness decreases. Therefore, an annular liquid jet with a sufficiently small ring thickness will disintegrate into spherical shells much faster than a full liquid jet disintegrates into drops, in accordance with existing experimental data. Non-dimensional expressions for the penetration thickness are given for both viscous and inviscid jets.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 179 , June 1987 , pp. 531 - 545
Copyright
© 1987 Cambridge University Press

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References

Baird, M. H. I. & Davidson, J. F. 1962 Annular jets. I. Fluid dynamics. Chem. Engng Sci. 17, 467–472.Google Scholar
Binnie, A. M. & Squire, H. B. 1941 Liquid jets of annular cross section. Engineer 171, 236–238.Google Scholar
Bogy, D. B. 1979 Drop formation in a circular liquid jet. Ann. Rev. Fluid Mech. 11, 207–228.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability, pp. 537–542. Clarendon.
Dombrowski, N. & Johns, W. R. 1963 The aerodynamic instability and disintegration of viscous liquid sheets. Chem. Engng Sci. 18, 203–214.Google Scholar
Gardner, G. C. & Lloyd, T. 1984 Annular buoyant jets. Intl J. Multiphase Flow 10, 635–641.Google Scholar
Hagerty, W. W. & Shea, J. F. 1955 A study of the stability of plane fluid sheets. Trans. ASME E: J. Appl. Mech. 22, 509–514Google Scholar
Keller, J. B., Rubinow, S. I. & Tu, Y. 1973 Spatial instability of a jet. Phys. Fluids 16, 2052–2955.Google Scholar
Kendall, J. M. 1981 Hydrodynamic performance of an annular liquid jet. In Proc. 2nd Intl Coll. on Drops and Bubbles, Monterey, Ca, JPL Publication 82–7, pp. 79–87.
Lance, G. N. & Perry, R. L. 1953 Water bells. Proc. Phys. Soc. B66, 1067–1072.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics, pp. 372–377, 626–650. Prentice-Hall.
Meyer, J. 1983 Investigation of the instability of an annular hollow jet. M.Sc. thesis, Technion-Israel Institute of Technology, 102 pp.
Rayleigh, Lord 1894 Theory of Sound, vol. 11, 2nd edn, pp. 351–365. Dover.
Sanz, A. & Meseguer, J. H. 1985 One-dimensional linear analysis of the compound jet. J. Fluid Mech. 159, 55–68.Google Scholar
Squire, H. B. 1953 Investigation of the instability of a moving liquid film. Brit. J. Appl. Phys. 4, 167–169.Google Scholar
Sterling, A. M. & Sleicher, C. A. 1975 The instability of capillary jets. J. Fluid Mech. 68, 477–495.Google Scholar
Tuck, E. O. 1982 Annular water jets. IMA J. Appl. Maths 29, 45–58.Google Scholar
Walker, G. & East, R. A. 1984 Shock tube studies of a water sheet inertial energy absorber to reduce blast overpressure. In Proc. Symp. Shock and Blast Wave Phenomena, Cranfield, UK. Paper C–2, 16 pp.
Weber, K. 1931 Zum zerfall eines flussigkeitsstrahles. Z. angew. Math. Mech. 11, 136–154.Google Scholar
Weihs, D. 1978 Stability of thin, radially moving liquid sheets. J. Fluid Mech. 87, 289–298.Google Scholar