Notice of Retraction: The upscaling from microscopic PNP multi-ion transport model to macroscopic PNP multi-ion transport model

Abstract

Clay microscopic structure, particle surface electric field and the interaction between ions in clay pore fluid have an important influence upon ion transport, but how to consider the influence of above factors on ion transport has been a difficult problem not solved. Establish microscopic Poisson-Nernst-Planck (hereinafter referred to as PNP) multi-ion transport model in the clay based on electrochemical theory, and obtain macroscopic PNP multi-ion transport model using volume Averaging. Combining the steady diffusion test of NaCl saline solution in the clay, this paper constructs clay microscopic particle model adopting randomly growing quartet structure generation set, introduces in detail the principles and steps of the upscaling from microscopic model to macroscopic model, and successfully upgrades microscopic model (nanometer level) to macroscopic model (centimeter and meter level) by numerical analysis. The macroscopic transport parameters are obtained from microscopic model upscaling and the boundary conditions are determined according to the solution results of macroscopic model, that is, microscopic-macroscopic conjoint analysis method is adopted to solve the problem of stepping over between different scales. And issues such as anion exclusion and cation adsorption difficult to be explained by the classical diffusion law have been discussed.