Model problems on the separation of charge-carrying components into two streams using a membrane in a cell of a dialysis apparatus are considered. For a brighter detection of the separation effect, the components are taken such that they differ markedly from each other in the mass of ions and diffusion coefficients. The convective-diffusion process of transition of ions through membranes with different physical features that create resistance to the transition is considered. As a result of the solution, the potential and component distributions were obtained in the cell volume of the dialysis apparatus as a function of time. It was shown that a quasi-equilibrium state is established relatively quickly in the capillary and the membrane, which determines the ratio of the flow rates of the components in the cell channels.