Self-consistent problem of induced polarization of electrokinetic origin

In the first part of the paper, with some constraints, we find the analytical solution of the self-consistent problem of induced polarization (IP) for an electrokinetically polarized sphere. The stationary (on long time intervals) solution of the self-consistent problem is a set of the potential fields that are interconnected with each other: the exciting electric field, the extraneous hydrodynamical field (electroosmotic flow of a viscous incompressible fluid), and the resulting electromagnetic IP field. The extraneous field is the field of the osmotic flow of a charged liquid and the field of the charges that emerge due to the membrane effect in the narrowed segments of the pore channels. The calculations show that the IP fields derived by solving the self-consistent problem and by the Seigel-Komarov phenomenological approach are different. In the second part of the paper, by generalization of the obtained analytical solution, we formulate the self-consistent IP problem for isotropic σ-η media of arbitrary shape, which are bounded by a smooth surface. The problem can be solved by the numerical methods.