Van der Bruggen B, Vandecasteele C
Department of Chemical Engineering, de Croylaan 46, Heverlee, Belgium.
Water Res. 2002 Mar;36(5):1360-8. doi: 10.1016/s0043-1354(01)00318-9.
In this paper, a model is developed for the retention of organic molecules with a given nanofiltration membrane at different pressures as a function of the molecular weight. The Spiegler-Kedem transport equations were used to derive the reflection coefficient, the maximal retention that would theoretically be obtained at infinite transmembrane pressure, from experimental retention values for a large set of molecules with the effective diameter of the molecule as a size parameter. Secondly, the pore size distribution of the membrane is derived from the experimental reflection coefficients. This allows to calculate the reflection coefficient for a molecule with a given effective diameter. Since this parameter is not readily available, a correlation between the effective diameter and the molecular weight has been established and introduced in the model equations. Subsequently, the contribution of diffusion in the transport of molecules through the membrane was evaluated by introducing a membrane diffusion parameter, which was determined experimentally for the membranes NF70, NTR 7450 and UTC-20. Finally, the pore size distribution, the diffusion parameter and the experimental water flux through the membrane were used to calculate the retention as a function of the molecular weight and pressure for the same three membranes. This allows to determine retention curves at different pressures, and to calculate the variation of the MWC with pressure.
在本文中，建立了一个模型，用于描述在不同压力下，给定纳滤膜对有机分子的截留率与分子量之间的函数关系。利用斯皮格勒-凯德姆传输方程，以分子的有效直径作为尺寸参数，从大量分子的实验截留值中推导出反射系数，即理论上在无限跨膜压力下可获得的最大截留率。其次，根据实验反射系数推导出膜的孔径分布。这使得能够计算具有给定有效直径的分子的反射系数。由于该参数不易获得，因此建立了有效直径与分子量之间的相关性，并将其引入模型方程中。随后，通过引入膜扩散参数来评估分子通过膜传输过程中扩散的贡献，该参数是针对NF70、NTR 7450和UTC - 20膜通过实验确定的。最后，利用孔径分布、扩散参数以及通过膜的实验水通量，计算了相同三种膜的截留率与分子量和压力的函数关系。这使得能够确定不同压力下的截留曲线，并计算截留分子量随压力的变化。
