Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T16:29:27.201Z Has data issue: false hasContentIssue false
  • English
  • Français

Breakup of fluid droplets in electric and magnetic fields

Published online by Cambridge University Press:  21 April 2006

J. D. Sherwood
J. D. Sherwood
Affiliation:
Schlumberger Cambridge Research, P.O. Box 153, Cambridge CB3 0HG, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A drop of fluid, initially held spherical by surface tension, will deform when an electric or magnetic field is applied. The deformation will depend on the electric/magnetic properties (permittivity/permeability and conductivity) of the drop and of the surrounding fluid. The full time-dependent low-Reynolds-number problem for the drop deformation is studied by means of a numerical boundary-integral technique. Fluids with arbitrary electrical properties are considered, but the viscosities of the drop and of the surrounding fluid are assumed to be equal.

Two modes of breakup have been observed experimentally: (i) tip-streaming from drops with pointed ends, and (ii) division of the drop into two blobs connected by a thin thread. Pointed ends are predicted by the numerical scheme when the permittivity of the drop is high compared with that of the surrounding fluid. Division into blobs is predicted when the conductivity of the drop is higher than that of the surrounding fluid. Some experiments have been reported in which the drop deformation exhibits hysteresis. This behaviour has not in general been reproduced in the numerical simulations, suggesting that the viscosity ratio of the two fluids can play an important role.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 188 , March 1988 , pp. 133 - 146
Copyright
© 1988 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

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions. Dover.
Allan, R. S. & Mason, S. G. 1962 Particle behaviour in shear and electric fields: I Deformation and burst of fluid drops. Proc. R. Soc. Lond. A 267, 45.Google Scholar
Arkhipenko, V. I., Barkov, Y. D. & Bashtovoi, V. G. 1978 Shape of a drop of magnetized fluid in a homogeneous magnetic field. Magnetohydrodyn. 14, 373.Google Scholar
Bacri, J. C. & Salin, D. 1982 Instability of ferrofluid magnetic drops under magnetic field. J. Phys. Lett. 43, L649.Google Scholar
Bacri, J. C. & Salin, D. 1983 Dynamics of the shape transition of a magnetic ferrofluid drop. J. Phys. Lett. 44, L415.Google Scholar
Bacri, J. C., Salin, D. & Massart, R. 1982 Shape of the deformation of ferrofluid droplets in a magnetic field. J. Phys. Lett. 43, L179.Google Scholar
Borzabadi, E. & Bailey, A. G. 1978 The profiles of axially symmetric electrified pendent drops. J. Electrostatics 5, 369.Google Scholar
Brazier-Smith, P. R. 1971 Stability and shape of isolated and pairs of water drops in an electric field. Phys. Fluids 14, 1.Google Scholar
Brazier-Smith, P. R., Jennings, S. G. & Latham, J. 1971 An investigation of the behaviour of drops and drop-pairs subjected to strong electrical forces. Proc. R. Soc. Lond. A 325, 363.Google Scholar
Cowley, M. D. & Rosensweig, R. E. 1967 The interfacial stability of a ferromagnetic fluid. J. Fluid Mech. 30, 671.Google Scholar
Drozdova, V. I., Skrobotova, T. V. & Chekanov, V. V. 1979 Experimental study of the hydrostatics characterizing the interphase boundary in a ferrofluid. Magnetohydrodyn. 15, 12.Google Scholar
Garton, C. G. & Krasucki, Z. 1964 Bubble in insulating liquids: stability in an electric field. Proc. R. Soc. Lond. A280, 211.Google Scholar
Kozhenkov, V. I. & Fuks, N. A. 1976 Electrohydrodynamic atomisation of liquids. Russ. Chem. Rev. 45, 1179Google Scholar
Ladyzenskaya, O. A. 1969 The Mathematical theory of Viscous Incompressible Flow, 2nd edn. Gordon & Breach.
Mackay, W. A. 1931 Some investigations on the deformation and breaking of water drops in strong electric fields. Proc. R. Soc. Lond. 133, 565.Google Scholar
Melcher, J. R. 1963 Field-coupled Surface Waves. MIT Press.
Melcher, J. R. 1981 Continuum Electromechanics. MIT Press.
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: a review of the role of interfacial shear stress. Ann. Rev. Fluid Mech. 1, 111.Google Scholar
Miksis, M. J. 1981 Shape of a drop in an electric field. Phys. Fluids 24, 1967.Google Scholar
O'Konski, C. T. & Thacher, H. C. 1953 The distortion of aerosol droplets by an electric field. J. Phys. Chem. 57, 955.Google Scholar
Rallison, J. M. 1981 A numerical study of the deformation and burst of a viscous drop in general shear flows. J. Fluid Mech. 109, 465.Google Scholar
Rallison, J. M. & Acrivos, A. 1978 A numerical study of the deformation and burst of a viscous drop in an extensional flow. J. Fluid Mech. 89, 191.Google Scholar
Stratton, J. A. 1958 Electromagnetic Theory. McGraw-Hill.
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A 146, 501.Google Scholar
Taylor, G. I. 1964 Disintegration of water drops in an electric field. Proc. R. Soc. Lond. A 280, 383.Google Scholar
Taylor, G. I. 1966 The circulation produced in a drop by an electric field. Proc. R. Soc. Lond. A 291, 159.Google Scholar
Taylor, G. I. & McEwan, A. D. 1965 The stability of a horizontal fluid interface in a vertical electric field. J. Fluid Mech. 22, 1.Google Scholar
Torza, S., Cox, R. G. & Mason, S. G. 1971 Electrohydrodynamic deformation and bursts of liquid drops. Phil. Trans. R. Soc. Lond. A 269, 295.Google Scholar
Vonnegut, B. & Neubauer, R. L. 1952 Production of monodisperse liquid particles by electrical atomization. J. Colloid. Sci. 7, 616.Google Scholar
Wilson, C. T. R. & Taylor, G. I. 1925 The bursting of soap bubbles in a uniform electric field. Proc. Camb. Phil. Soc. 22, 728Google Scholar
Youngren, G. K. & Acrivos, A. 1975 Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech. 69, 377, and Corrigenda, J. Fluid Mech. 69, (1975) 813.Google Scholar