An electrokinetic model of drop deformation in an electric field

An electrokinetic model is proposed to describe a slight drop deformation which is induced by a weak external electric field. The fluids forming the system are considered Newtonian incompressible dielectric liquids containing free electric charge carriers. According to the model, the charge carriers take part in migration, diffusion and convection transport and there is no solute adsorption at the interface. Thermodynamic quasi-equilibrium at the interface is assumed for the charge carriers in the contacting liquids. The interfacial thermodynamic equilibrium is described using a common distribution coefficient for all the carriers. The problem is simplified by assuming equal diffusion coefficients for the different charge carriers within the same liquid. An analytical expression is obtained for slight drop deformation which is proportional to the second power of the applied field strength magnitude. The expression derived represents the drop deformation as a function of the parameters employed in previous theories (O'Konski Thacher 1953; Allan Mason 1962; Taylor 1966) as well as two additional parameters. The additional parameters are the ratios of the drop radius to the Debye lengths of the outer and inner liquids, respectively. The expression obtained for the drop deformation is valid for arbitrary values of these parameters. According to the theory prediction, with an increase in the drop radius, the drop deformation monotonically changes from that obtained by O'Konski & Thacher (1953) and Allan & Mason (1962) for perfect dielectric liquids to that obtained by Taylor (1966) for leaky dielectric liquids. Two simplified versions of the general expression are suggested to describe particular cases of a conducting drop in a perfect dielectric liquid and of a perfect dielectric drop in a conducting liquid.