The structure of the double layer on the boundary between solid and liquid phases is described by various models, of which the Stern–Gouy–Chapman model is still commonly accepted. Generally, the solid phase is charged, which also causes the distribution of the electric charge in the adjacent diffuse layer in the liquid phase. We propose a new mathematical model of electromigration considering the high deviation from electroneutrality in the diffuse layer of the double layer when the liquid phase is composed of solution of weak multivalent electrolytes of any valence and of any complexity. The mathematical model joins together the Poisson equation, the continuity equation for electric charge, the mass continuity equations, and the modified G‐function. The model is able to calculate the volume charge density, electric potential, and concentration profiles of all ionic forms of all electrolytes in the diffuse part of the double layer, which consequently enables to calculate conductivity, pH, and deviation from electroneutrality. The model can easily be implemented into the numerical simulation software such as Comsol. Its outcome is demonstrated by the numerical simulation of the double layer composed of a charged silica surface and an adjacent liquid solution composed of weak multivalent electrolytes. The validity of the model is not limited only to the diffuse part of the double layer but is valid for electromigration of electrolytes in general.

中文翻译：

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允许偏离电中性的电迁移数学模型

固液相边界上的双层结构有多种模型描述，其中 Stern-Gouy-Chapman 模型仍被普遍接受。一般固相带电，这也造成液相中相邻扩散层的电荷分布。我们提出了一种新的电迁移数学模型，考虑到当液相由任何价态和任何复杂度的弱多价电解质溶液组成时，双层扩散层中电中性的高度偏差。该数学模型将泊松方程、电荷连续性方程、质量连续性方程和修正的 G 函数连接在一起。该模型能够计算体积电荷密度、电势、以及双层扩散部分中所有电解质的所有离子形式的浓度分布，从而能够计算电导率、pH 和电中性偏差。该模型可以很容易地应用到 Comsol 等数值模拟软件中。通过对由带电二氧化硅表面和由弱多价电解质组成的相邻液体溶液组成的双层的数值模拟证明了其结果。该模型的有效性不仅限于双电层的扩散部分，而且通常适用于电解质的电迁移。该模型可以很容易地应用到 Comsol 等数值模拟软件中。通过对由带电二氧化硅表面和由弱多价电解质组成的相邻液体溶液组成的双层的数值模拟证明了其结果。该模型的有效性不仅限于双电层的扩散部分，而且通常适用于电解质的电迁移。该模型可以很容易地应用到 Comsol 等数值模拟软件中。通过对由带电二氧化硅表面和由弱多价电解质组成的相邻液体溶液组成的双层的数值模拟证明了其结果。该模型的有效性不仅限于双电层的扩散部分，而且通常适用于电解质的电迁移。