The Poisson-Nernst-Planck (PNP) theory is one of the most widely used analytical methods to describe electrokinetic phenomena for electrolytes. The model, however, considers isolated charges and thus is valid only for dilute ion concentrations. The key importance of concentrated electrolytes in applications has led to the development of a large family of generalized PNP models. However, the wide family of generalized PNP models fails to capture key phenomena recently observed in experiments and simulations, such as self-assembly, multiple-time relaxation, and under-screening in concentrated electrolytes.

In this talk, we derive a thermodynamically consistent mean-field model for concentrated solutions that goes beyond the PNP framework. The result is a modeling framework that is valid over the whole range of concentrations - from dilute electrolyte solutions to highly concentrated solution, such as ionic liquids. The model describes self-assembly, multiple-time relaxation, and under-screening, and reveals a novel mechanism of under-screening. Furthermore, the model predicts distinct transport properties which are not governed by Einstein-Stokes relations, but are rather effected by inter-diffusion and emergence of nano-structure.

Joint work with Doron Elad and Arik Yochelis.