The motion of a microgranule, impermeable for anions, suspended in an electrolyte, under electrophoresis of the first and second kind is investigated in the paper. Mathematical model of such a movement is described by the system of Nernst-Planck-Poisson-Stokes equations in spherical coordinates with boundary conditions on the granule's surface and in the infinitely distant area. Besides, the system's behavior is described by four dimensionless parameters. In order to solve this problem, a stream function is introduced. The algorithm of the solution is based on eigenfunction expansion (those are Gegenbauer and Legendre polynomials) and Fourier transform on the corresponding functions. The algorithm uses a second-order central finite-difference scheme over a nonuniform grid and a semi-implicit third-order Runge-Kutta method. Our numerical simulation has shown a good correspondence with experimental data, particularly for the velocity dependence on the strength of the electric field and for determination of characteristic zones of the problem. It should be noted that the calculations take into account the influence of both the double electric layer and electroconvection. Determination of the conditions (i.e. the values of parameters) when the regime loses stability is our main result; the instability results in electrokinetic vortex formation both behind and in front of the microgranule.

Рассмотрен случай электрофореза в сильном электрическом поле, не подчиняющийся классической теории электрокинетических явлений. Построена математическая модель соответствующего явления на основе системы уравнений Нернста-Планка-Пуассона-Стокса, описаны параметры системы и проведены численные эксперименты. В результате получено распределение тока по поверхности гранулы. Обнаружено, что ток меняет своё значение примерно в одном и том же месте поверхности гранулы. Именно в этом месте проявляется механизма Духина — образование вихрей позади гранулы.