Modeling the dynamics of the electrical double layer in the non-stationary time process. Part 1. About the simple layer potential

We put the problem of modeling in the electrostatic approximation of the dynamics of the electrical double layer in electrokinetic processes in conditions of non-equilibrium state of the ions’ flow. It is the necessity of replacing of the Poisson-Boltzmann equation by the solution of the Neumann’s boundary problem for the Poisson equation in the general system of related equations which describe the electrokinetic process as a whole. In this work we considered the problem for a simple layer without account of bulk density of the charges. The required facts from potential theory are presented. The full solution of the problem will be presented in the next part of the work.