The deformation of a liquid drop by an electric field

  • N. Dodgson
  • C. Sozou
Original Papers


The shape and stability of an incompressible dielectric drop which is stressed by a uniform external electric field are re-examined by considering small perturbations from a prolate spheroid. Compared with the shapes predicted by other approximations it is found that, for a given field strength, the drops should be a little longer and consequently a little flatter at the equator in order to satisfy the equilibrium conditions. It is also shown that beyond a certain drop deformation the L. P. E. (Legendre polynomial expansion) method fails because the equilibrium conditions at the surface of the drop are not satisfied.


Equilibrium Condition Field Strength Mathematical Method Small Perturbation Prolate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Lord Rayleigh,On the capillary phenomena of jets. Proc. Roy. Soc.29, 71 (1879).Google Scholar
  2. [2]
    C. G. Garton and Z. Krasucki,Bubbles in insulating liquids: stability in an electric field. Proc. Roy. Soc. A280, 211 (1964).Google Scholar
  3. [3]
    S. B. Sample, B. Raghupathy and C. D. Hendricks,Quiescent distortion and resonant oscillations of a liquid drop in an electric field. Int. J. Engng. Sci.8, 97 (1970).Google Scholar
  4. [4]
    G. Taylor,Disintegration of water drops in an electric field. Proc. Roy. Soc. A280, 383 (1964).Google Scholar
  5. [5]
    C. A. Morrison, R. P. Leavitt and D. E. Wortman,The extended Rayleigh theory of the oscillation of liquid droplets. J. Fluid Mech.104, 295 (1981).Google Scholar
  6. [6]
    P. R. Brazier-Smith,On the limitations of spherical harmonics for the solution of Laplace's equation. J. Comp. Physics54, 524 (1984).Google Scholar
  7. [7]
    J. D. Jackson, Classical Electrodynamics. Wiley, New York 1975.Google Scholar
  8. [8]
    C. E. Rosenkilde,A dielectric fluid drop in an electric field. Proc. Roy. Soc. A312, 473 (1969).Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1987

Authors and Affiliations

  • N. Dodgson
    • 1
  • C. Sozou
    • 1
  1. 1.Dept. of Applied and Computational MathematicsUniversity of SheffieldSheffieldEngland

Personalised recommendations