Mass transfer during solute extraction from a droplet with internal circulation in the presence of a constant uniform electric field

Mass transfer, under the influence of an constant uniform electric field in a ternary system, comprised of a transformed solute, a liquid dielectric continuous phase, and a stationary dielectric droplet, was considered in this study. The solubilities of the solute in the dispersed and continuous phases have the same order of magnitude, and the resistance to mass transfer in both phases is taken into account. The applied electric field causes Taylor circulation around the droplet, while the droplet deformation under the influence of the electric field is neglected. The problem is solved in the approximations of a thin concentration boundary layer in the dispersed and continuous phases. The bulk of a droplet, beyond the diffusion boundary layer, is completely mixed and the concentration of solute is homogeneous and time-dependent in the bulk. The system of transient coupled equations of convective diffusion for solute transport in the dispersed and continuous phases with time-dependent boundary conditions is solved by combining a generalized similarity transformation method with Duhamel's theorem; the solution is obtained in the form of a Volterra integral equation of the second kind. Numerical calculations essentially show an enhancement of the rate of mass transfer for dispersed liquid-liquid systems, under the influence of an electric field.