Dielectric enhancement and electrophoresis due to an electrochemical double layer: A uniform approximation

We present here a method to calculate the response of a charged, insulating sphere immersed in an electrolytic solution in the presence of an externally applied electric field. Due to the charge on the sphere, it acquires a layer of counterions on the outside known as the electrochemical double layer. Since this double layer is complex, the response of the sphere to an externally applied electric field is complicated. In the past, ad hoc models have been proposed to circumvent the difficulty in the analysis of this problem. Recently, we presented a rigorous analysis of this problem using the technique of matched asymptotic expansions commonly used in boundary layer theory. Our previous solution was not valid for high zeta potential that corresponded to a highly charged sphere. In this paper, we present an analysis where this restriction is removed, and incorporate the effect of induced solvent osmotic flow. Our solutions is valid for larger value of the zeta potential compared to previous works. When the zeta potential is zero, corresponding to an uncharged sphere, we reproduce the classical result of an insulating sphere in a conducting medium. When the zeta potential is high, we reproduce a correction to the result of Fixman and O'Brien. With the response of one sphere known, we can use it to calculate the dielectric response of an ensemble of spheres, for example, in a colloidal suspension.