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Electrohydrodynamic stability of a highly viscous jet

Published online by Cambridge University Press:  26 April 2006

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

When a pendant drop of weakly conducting fluid is raised to a high electric potential, it frequently adopts the shape of a Taylor cone from whose apex a thin, charged jet is emitted. Such a jet can display surprising longevity, but eventually breaks up into fine droplets, a fact utilized in electro-spraying devices. This paper examines the linear stability of an incompressible cylindrical jet carrying surface charge q in a tangential electric field E, for various values of the permittivity ratio λ and the finite rate of charge relaxation, τ. The viscosity is assumed to be large. It is shown that all axisymmetric temporal modes can be stabilized for suitable values of (q, E), but sinuous modes with logarithmically large wavelengths are unstable. If these very long waves are excluded, the jet can sometimes be completely stabilized. It is also shown that an uncharged jet with low permittivity is unstable to sinuous waves for large E, contrary to previous belief.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 312 , 10 April 1996 , pp. 311 - 326
Copyright
© 1996 Cambridge University Press

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References

Bassett, A. B. 1894 Waves and jets in a viscous liquid. Am. J. Maths 16, 93–110.Google Scholar
Cloupeau, M. & Prunet-Foch, B. 1989 Electrostatic spraying of liquids in cone-jet mode. J. Electrostatics 22, 135–159.Google Scholar
Drozin, V. G. 1955 The electrical dispersion of liquids as aerosols. J. Colloid Sci. 10, 158–164.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. 1987a Investigations into the mechanisms of electrohydrodynamic spraying of liquids, part I. J. Colloid Interface Sci. 117, 205–221.Google Scholar
Hayati, I., Bailey, A. I. & Tadros, Th.F. 1987b Investigations into the mechanisms of electrohydrodynamic spraying of liquids, part II. J. Colloid Interface Sci. 117, 222–230.Google Scholar
Huebner, A. L. 1969 Disintegration of charged liquid jets. J. Fluid Mech. 38, 679–688.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
Magarvey, R. H. & Outhouse, L. E. 1962 Note on the break-up of a charged liquid jet. J. Fluid Mech. 13, 151.Google Scholar
Melcher, J. R. & Schwarz, W. J. 1968 Interfacial relaxation overstability in a tangential electric field. Phys. Fluids 11(12), 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. 1994a The electrohydrodynamic cone-jet at high Reynolds number. J. Aerosol Sci. (special issue on electrosprays) 25(6), 1037–1047.Google Scholar
Mestel, A. J. 1994b Electrohydrodynamic stability of a slightly viscous jet. J. Fluid Mech. 274, 93–113.Google Scholar
Plateau, J. A. 1873 Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires, Vol II, p. 231.
Rayleigh, Lord 1879 On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13.Google Scholar
Rayleigh, Lord 1882 On the equilibrium of liquid conducting masses charged with electricity. Phil Mag. 14, 184.Google Scholar
Rayleigh, Lord 1892 On the instability of a cylinder of viscous liquid under capillary forces. Phil Mag. 34, 145–154.Google Scholar
Saville, D. A. 1970 Electrohydrodynamic stability: Fluid cylinders in longtitudinal 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
Taylor, G. I. 1964 Disintegration of water drops in an electric field. Proc. R. Soc. Lond. A 280, 383–97.Google Scholar
Taylor, G. I. 1969 Electrically driven jets. Proc. R. Soc. Lond. A 331, 453–475.Google Scholar
Tomotika, S. 1935 On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous liquid. Proc. R. Soc. Lond. A 150, 322–337.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