The transport of ions in an electrolyte solution creates the electrical double layer (EDL) which is formed at the charged surface. Such a structure having nanometer-scale thickness is essentially like a capacitor and plays an important role in many physical and electrochemical fields, such as semiconductors, electro-kinetic fluids and colloidal systems. 

In order to investigate the behavior of the EDL structure, we treat a charge conserving Poisson-Boltzmann (CCPB) equation as the basis for a framework of the ion transport in electrolyte solutions and study its boundary layer solutions. The CCPB equation is a Poisson-Boltzmann type equation with nonlocal nonlinear coefficients derived from the steady-state Poisson-Nernst-Planck (PNP) equation under the conservation of ion concentrations. 

In this second lecture, we will introduce (i) Boundary layer solutions of 1-dimensional CCPB equation in two situations under global electroneutrality and non-electroneutrality and (ii) Open problems: the boundary curvature effect on high-dimensional boundary layer solutions.