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化学学报
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化学学报 ›› 2013, Vol. 71 ›› Issue (11): 1511-1515.DOI: 10.6023/A13070790 上一篇    下一篇

研究论文

高分子膜错流纳滤的多场耦合有限元分析

王钊a, 贾玉玺a, 徐一涵a, 石彤非b, 安立佳b   

  1. a 山东大学材料液固结构演变与加工教育部重点实验室 济南 250061;
    b 中国科学院长春应用化学研究所高分子物理与化学国家重点实验室 长春 130022
  • 投稿日期:2013-07-26 发布日期:2013-09-17
  • 通讯作者: 贾玉玺 E-mail:jia_yuxi@sdu.edu.cn
  • 基金资助:

    项目受国家973计划(No. 2012CB821500)和山东省自然科学杰出青年基金(No. JQ201016)资助.

Finite Element Analysis on Multi-field Coupling of Cross-flow Nanofiltration of Polymeric Membrane

Wang Zhaoa, Jia Yuxia, Xu Yihana, Shi Tongfeib, An Lijiab   

  1. a Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061;
    b State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022
  • Received:2013-07-26 Published:2013-09-17
  • Supported by:

    Project supported by the National Key Basic Research Program of China (No. 2012CB821500) and the Natural Science Foundation of Shandong Province for Distinguished Young Scholars (No. JQ201016).

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纳滤膜的应用日益广泛, 但其传质机理和优化设计的研究还有待深入. 本文首先描述了表征高分子膜纳滤的道南-位阻孔模型(Donnan Steric Pore Model, DSPM), 进而描述了在DSPM模型基础上发展起来的表征错流纳滤的孔-极化输运模型(Pores and Polarization Transport Model, PPTM). 针对在PPTM模型中用经验模型描述膜上方溶液速度场的不足, 用Navier-Stokes方程和连续性方程来描述溶液在膜上方自由空间内的流动, 并用有限元方法模拟膜上方的溶液错流速度场, 从而实现了膜内传质的DSPM模型、膜上方离子浓度场、膜上方自由空间流场的多场耦合有限元分析. 通过与实验结果以及传统PPTM结果的对比可以发现, 该修正方法能反映膜上方自由空间中的溶液速度场和离子浓度场的变化趋势并且在数值上也更为逼近实验值. 改进后的模型将为高分子膜错流纳滤过程的优化设计提供更可靠的理论依据.

关键词: 纳滤膜, 浓差极化, 输运模型, 速度场, 有限元模拟

The application of nanofiltration in industrial fields is increasing rapidly in recent years, especially in drinking water treatment. Nevertheless, the mechanism of mass transport through these membranes has not yet been fully understood. And the optimal design of nanofiltration processes still faces challenges. At first, the Donnan Steric Pore Model (DSPM) is described in this paper, which is constructed on the basis of the extended Nernst-Planck equation for the prediction of the nanofiltration process of polymeric membrane. Then the DSPM model is used to characterize three kinds of membranes (AFC40, CA30 and NTR7450) for the nanofiltration of 50 mol/m3 NaCl solution and NTR7450 membrane for the nanofiltration of NaCl and MgSO4 solution with different concentrations. The simulated results and their comparison with experimental results show that the DSPM model can effectively predict the membrane performance. And then a description of the Pores and Polarization Transport Model (PPTM) is presented, which is developed on the basis of the DSPM model, in order for characterizing cross-flow nanofiltration. The PPTM model combines the convection-diffusion-migration transport in the nanopores with the transport through the concentration polarization layer. To improve the PPTM model in the aspect of using an empirical model to describe the velocity field of solution above the membrane, the velocity profile in solution is solved by Navier-Stokes equation and continuity equation in this paper. The cross-flow nanofiltration of polymeric membrane is simulated using the finite element method, by coupling mass transfer in the membrane with ion concentration and velocity profile in solution above the membrane. By the comparison with experimental results and traditional PPTM results, it can be found that the modified method can reflect the change tendencies of ion concentration and velocity profile in solution, and their values are more in line with the values of experiments. The improved model can provide more reliable theoretical basis for the optimal design of cross-flow nanofiltration processes of polymeric membrane.

Key words: nanofiltration membrane, concentration polarization, transport model, velocity profile, finite element simulation