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In this paper, we consider a depleted stationary diffusion layer adjacent to the ion-exchange membrane. The main goal is to study the structure of the diffusion layer over time. A one-dimensional non-stationary mathematical model of the transport of a binary electrolyte in a diffusion layer in a potentiostatic mode is investigated using the Nernst-Planck and Poisson equations. For the first time, it is shown that the left boundary of the space charge region is established quickly, approaching a certain straight line xc =const asymptotically. Using this fact, a new asymptotic solution is constructed. The original feature of the proposed asymptotic method is that it is based not only on asymptotic simplifications in the equations, but also on replacing the exact description of the structure of the diffusion layer with an approximate one.

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