© 1989 by Oxford University Press
FLUID DYNAMICS AND STABILITY ANALYSIS OF A COMPOUND DROPLET IN AN ELECTRIC FIELD
(
1Department of Mechanical Engineering, The Johns Hopkins University Baltimore, Maryland 21218, USA
2Department of Mechanical Engineering, University of Southern California Los Angeles, California 90089–1453, USA
)
The presence of an electric field in a multiphase fluid system often generates charges at the interfaces and results in fluid motion due to the electrostatic forces. In this paper we study the effect of an electric field on a compound multiphase drop or bubble formed by a fluid sphere completely covered by another immiscible fluid drop in an infinite fluid. When surface tension is high enough the interfaces can be considered to be two eccentric spheres. In many situations of interest one desires dynamical equilibrium between the two spherical interfaces. This corresponds to no relative motion between them. Under a uniform electric field internal circulation builds up and in the case of an eccentric configuration the drag on both the inner and the outer sphere is non-zero in contrast to the case of a single sphere. Semianalytical solutions can be obtained for both the electric and the flow fields using the bipolar coordinate system. When the flow field generated by the electric field is superposed on that due to translation, it is found that an equilibrium configuration can be obtained by adjusting the electric field if the electrical parameters are suitable. The equilibrium is generally stable when the centre of the inner sphere is on the upstream side of the translatory velocity. The use of the electric field can give stable equilibrium configurations which are otherwise not possible in a purely buoyant force field. The study of the streamlines shows interesting double-vortex structures both in the shell and the inner sphere. Additional vortices are observed when the shear forces are in the same direction on both interfaces.