Bifurcation resulting in self-focusing of the electric field near the poles of a conducting microgranule

The experimentally found phenomenon of self-focusing of an electric field and the concentration of ions near the poles of an ion-selective granule in an electrolyte solution under the action of an external electric field is theoretically justified. An asymptotic solution of the problem is obtained, and it is shown that the solution found loses stability at high field strengths and, after the corresponding bifurcation, passes into a new solution in which there is a sharp local amplification of the electric field and the ion concentration.