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Electrohydrodynamic stability of a slightly viscous jet

Published online by Cambridge University Press:  26 April 2006

A. J. Mestel
A. J. Mestel
Affiliation:
Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2BZ, UK
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Abstract

Many electro-spraying devices raise to a high electric potential a pendant drop of weakly conducting fluid, which may adopt a conical shape from whose apex a thin, charged jet is emitted. Such a jet eventually breaks up into fine droplets, but often displays surprising longevity. This paper examines the stability of an incompressible cylindrical jet carrying surface charge in a tangential electric field, allowing for the finite rate of charge relaxation. The viscosity is assumed to be small so that the shear resulting from the tangential surface stress can be large, even for relatively small fields. This shear can suppress surface tension instabilities, but if too large, it excites electrical ones. For imperfect conductors, surface charge is redistributed by the rapid fluid reaction to variations in tangential stress as well as by conduction. Phase differences between the effects due to the tangential field and the surface charge lead to charge ‘over-relaxation’ instabilities, but the maximum growth rate can still be lower than in the absence of electric effects.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 274 , 10 September 1994 , pp. 93 - 113
Copyright
© 1994 Cambridge University Press

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References

Bailey, A. G. 1988 Electrostatic Spraying of Liquids J. Wiley.
Bassett, A. B. 1894 Waves and jets in a viscous liquid. Am. J. Maths 16, 93–110.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Cloupeau, M. & Prunet-Foch, B. 1989 Electrostatic spraying of liquids in cone-jet mode. J. Electrostat 22, 135–159.Google Scholar
Drazin, P. & Reid, W. 1981 Hydrodynamic Stability. Cambridge University Press.
Drozin, V. G. 1955 The electrical dispersion of liquids as aerosols. J. Colloid Sci. 10, 158–164.Google Scholar
Fernández de la Mora, J., & Loscertales, I. G. 1993 The current emitted by highly conducting Taylor cones. J. Fluid Mech. 260, 155–184.Google Scholar
Fernández de la Mora, J., Navascues, J. J., Fernandez, F. & Rosell-Llompart, J. 1990 Generation of submicron monodisperse aerosols in electrosprays. J. Aerosol Sci. 21 (special issue), S673–S676.Google Scholar
Hayati, I., Bailey, A. I. & Tadros, Th. F. 1987 Investigations into the mechanisms of electrohydrodynamic spraying of liquids, parts I and II. J. Colloid Interface Sci. 117, 205–221, 222–230.Google Scholar
Henrici, P. 1974 Applied and Computational Complex Analysis, vol. 1. J. Wiley.
Heubner, A. L. 1969 Disintegration of charged liquid jets. J. Fluid Mech. 38, 679–688.Google Scholar
Hines, R. L. 1966 Electrostatic atomization and spray painting. J. Appl. Phys. 37, 2730–2736.Google Scholar
Jones, A. R. & Thong, K. C. 1971 The production of charged monodisperse fuel droplets by electrostatic dispersion. J. Phys. D: Appl. Phys. 4, 1159.Google Scholar
Leib, S. J. & Goldstein, M. E. 1986 The generation of capillary instabilities on a liquid jet. J. Fluid Mech. 168, 479–500.Google Scholar
Melcher, J. R. & Schwarz, W. J. 1968 Interfacial relaxation overstability in a tangential electric field. Phys. Fluids 11, 2604–2616.Google Scholar
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: A review of the role of interfacial shear stresses. Ann. Rev. Fluid Mech. 1, 111–146.Google Scholar
Mestel, A. J. 1994 The electrohydrodynamic cone-jet at high Reynolds number. J. Aerosol Sci. (special issue) (to appear).Google Scholar
Michelson, D. 1990 Electrostatic Atomization. A. Hilger.
Nayyar, N. K. & Murty, G. S. 1960 The stability of a dielectric liquid jet in the presence of a longitudinal electric field. Proc. Phys. Soc. Lond. 75, 369–373.Google Scholar
Pekeris, C. L. 1948 Stability of the laminar flow through a straight pipe of circular cross-section to infinitesimal disturbances which are symmetric about the axis of the pipe. Proc. Natl. Acad. Sci. Wash. 34, 285–295.Google Scholar
Rayleigh, Lord, 1879 On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13 (also Scientific Papers, vol. 1, pp. 361–371, Cambridge University Press, 1899).Google Scholar
Saville, D. A. 1970 Electrohydrodynamic stability: Fluid cylinders in longitudinal electric fields. Phys. Fluids 13, 2987–2994.Google Scholar
Saville, D. A. 1971a Electrohydrodynamic stability: Effects of charge relaxation at the interface of a liquid jet. J. Fluid Mech. 48, 815–827.Google Scholar
Saville, D. A. 1971b Stability of electrically charged viscous cylinders. Phys. Fluids 14, 1095–1099.Google Scholar
Sherwood, J. D. 1988 Breakup of fluid droplets in electric and magnetic fields. J. Fluid Mech. 188, 133–146.Google Scholar
Smith, D. P. H. 1986 The electrohydrodynamic atomization of liquids. IEEE Trans. Ind. Applic. 22, 527–535.Google Scholar
Taylor, G. I. 1964 Disintegration of water drops in an electric field. Proc. R. Soc. A 280, 383–397.Google Scholar
Taylor, G. I. 1969 Electrically driven jets. Proc. R. Soc. A 313, 453–475.Google Scholar
Zeleny, J. 1915 On the conditions of instability of liquid drops, with applications to the electrical discharge from liquid points. Proc. Camb. Phil. Soc. 18, 71–93.Google Scholar
Zeleny, J. 1917 Instability of electrified liquid surfaces. Phys. Rev. 10, 1–6.Google Scholar