纳滤膜对电解质溶液分离特性的理论研究(II): 混合电解质溶液

假定纳滤膜具有狭缝状孔, 使用纯水透过系数、膜孔径及膜表面电势来表征纳滤膜的分离特征, 用流体力学半径和无限稀释扩散系数表征了离子特性. 采用扩展Nernst-Planck方程、Donnan平衡模型和Poisson-Boltzmann理论描述了混合电解质溶液中离子在膜孔内的传递现象, 计算了三种商用纳滤膜(ESNA1-LF, ESNA1和LES90)对同阴离子、同阳离子和含四种离子的混合电解质体系中离子的截留率, 并与实验数据进行了比较. 计算结果表明, 电解质溶液中离子在纳滤膜孔内传递的主要机理是离子的扩散和电迁移, 纳滤膜对混合电解质溶液中离子的分离效果主要由空间位阻和静电效应决定. 该模型在低浓度时对含一价离子的混合电解质溶液通过纳滤膜的截留率计算结果比较准确, 但对高浓度或含高价离子的混合电解质溶液则偏差较大.

Theoretical Investigation on the Separation Characteristics of Electrolyte Solutions with the Nanofiltration Membranes (II): Mixed Electrolyte Solutions

The separation of mixed-electrolyte solutions with nanofiltration membranes was investigated by the combination of the extended Nernst-Planck equation, Donnan equilibrium model and the Poisson-Boltzmann equation. The nanofiltration membrane pores were modeled as slitlike pores characterized by the fixed pore size, pure water permeability and surface electrical potential. The ions in mixed-electrolyte solutions were represented as charged hard-spheres with the hydrodynamic diameters and diffusion coeffi- cients at infinite dilution. The membrane parameters for three commercial nanofiltration membranes (ESNA1-LF, ESNA1 and LES90) were determined from the experimental ion fluxes and rejections of the electrolyte solutions through the corresponding membranes. The theoretical predictions show that diffusion and electro-migration are the main mechanisms of ion transport, and the steric and electrostatic effects are dominant for the ion rejections in nanofiltration (NF) membranes. From comparisons of the predicted ion rejections with the experiment data, it is suggested that the theory should give satisfactory results at low concentration for the mixed-electrolyte solutions containing monovalent ions, while deviations were found at a high concentration or for divalent ions.