Application of Multiple Scales Method to the Problem About Characteristics of the Ionic Layer Near The Surface of Lithium Niobate Crystal in a Benzoic Acid Melt

The authors present an analytical solution of equations describing the diffusion transfer and recombination of positive lithium ions and negative benzoate ions in benzoic acid after their injection from the surface of a protonated lithium niobate substrate. In the course of the solving one-dimensional stationary problem, the profiles of ions concentrations and electric potential distribution have obtained, corresponding to different values of governing parameters. The benzoate ions form thin boundary layer, while the ions of lithium completely fill considered region and have relatively uniform distribution. The comparison of analytical solution with numerical results permits to estimate the degree of the influence of electric field on the final distributions, which is formed due to the difference of ions concentrations. The expression, which determines the thickness of boundary layer, is obtained by the multiple scales method.