ELECTROSTATIC INTERACTION BETWEEN 2 WATER-IN-OIL EMULSION DROPLETS IN AN ELECTRIC-FIELD

The electrostatic interaction of two charged water-in-oil emulsion droplets at arbitrary separation in an applied uniform electric field is investigated theoretically. The problem is greatly simplified by assuming the droplets to be perfectly conducting spheres. After the potential distribution in the continuous-oil medium is expressed in terms of bipolar coordinates, the interaction energy of the two spheres is obtained in two steps. First, the energy of two uncharged spheres in the presence of the applied field is found by adapting a simple formula for the energy of an electric dipole in a uniform electric field. Then, the additional energy due to charges on the droplets is determined by means of a standard charging process. The force exerted by one sphere on the other is calculated from the gradient of the interaction energy. Valid for any nonzero separation, the result is shown to be equivalent to a previously published solution. © 1992.