Recently, a wide variety of Poisson-Boltzmann (PB) type equations have been established to approach the phenomena of ion transport in various electrolyte solutions. Due to the finite sized effect on the electric double layer at the surface, Andelman et al. consider a modified Poisson-Boltzmann (MPB) equation for electrolyte solutions with two types of ions having the same size (ref. PRL 1997). The MPB equation is a good model for describing the effect of ions' radii on the behavior of the electric double layer. However, in the case when different size ion species occupy electrolyte solutions, the MPB equation seems unavailable. 

The main purpose of this talk is to introduce a new PB equation with finite size effects, called the PB_ns equation. To briefly study this model, we are going to focus on the case of one cation and one anion species and formally derive a limiting form of the PB_ns equation which is more general than the MPB equation. In particular, when the size of all ions are the same, we show that solutions of the PB_ns equation and the MPB equation have the same asymptotic behavior in the limit of zero Debye length.

The talk is based on a joint work with Tai-Chia Lin (NTU) and Chun Liu (PSU).