Electrical Quadruple Layer under the AC Electric Field

In this paper we show that solutions of the nonlinear Nernst-Planck equation possesses the quadruple-layer structure near the interface when the electrolyte receives a high frequency forcing such as a high-frequency alternating current. Very near to the interface wall, the well-known, classical Stern layer exists. Near to the Stern layer we have the secondly thin layer (to be called inner layer in this paper) where the ion concentrations behave under the same frequency as the external forcing. However, in this layer, the positive and negative ion concentrations develop with the time phase 180-degree different from each other. Next to this second layer, we have the third layer (called middle layer) in which two ion concentrations change with the time period double the forcing, and both concentrations behave in the same time phase. In the outermost layer, i.e. the forth layer, (called outer layer) the ion concentrations show the same-phase development as the third one but decaying very slowly in time. Our assertion is mostly based on the 1-D numerical simulation for the Nernst-Planck equation under a high frequency AC field assuming that the quadruple layer is very thin compared with the length scale representative of the bulk region.