Institut UTINAM (UMR CNRS 6213), Université de Franche-Comté, 16 route de Gray, 25030 Besançon cedex, France.
Water Res. 2013 May 1;47(7):2260-72. doi: 10.1016/j.watres.2013.01.044. Epub 2013 Feb 8.
One of the major difficulties for the prediction of separation performances in the case of multi-ionic mixtures nanofiltration lies in the description of the concentration polarization phenomenon. Usual models available in literature do not take account of the polarization phenomenon or only describe it cursorily. Very few studies dedicated to the understanding and the specific description of the concentration polarization phenomenon are available in literature and a 2-D multi-ionic model describing the layer heterogeneity along the membrane length has never been proposed yet. The model used in the present work, called Pore and Polarization Transport Model (PPTM), allows an accurate description of the concentration polarization layer occurring during the filtration of multi-ionic solutions by taking account of the radial electromigrative transport in the layer, the turbulence, as well as the axial heterogeneity. In this context, the present paper aims at proposing a numerical investigation of the influence of operating conditions on the behavior of the polarization layer occurring at the membrane vicinity. The input parameters governing the transport through the membrane have been assessed in a previous study in the same experimental conditions so that only the polarization layer is investigated here. The proposed model which was previously validated on experimental observed rejection curves is then used to understand how operating conditions, such as applied pressure, feed flow-rate, or divalent ion proportion, govern the polarization phenomenon. For this purpose, concentration and thickness axial profiles along the membrane length and radial profiles within the polarization layer are investigated for various conditions. Finally, the impact of the type of divalent ion and the number of ions is also studied on various mixtures.
多离子混合物纳滤分离性能预测的主要困难之一在于对浓差极化现象的描述。文献中常用的模型没有考虑到极化现象，或者只是粗略地描述了它。文献中很少有专门用于理解和具体描述浓差极化现象的研究，也从未提出过描述膜长度方向上的层异质性的二维多离子模型。本工作中使用的模型称为孔和极化传输模型（PPTM），通过考虑层内的径向电迁移输运、湍流以及轴向异质性，能够准确描述多离子溶液过滤过程中发生的浓差极化层。在这种情况下，本文旨在提出一种数值研究，以探讨操作条件对膜附近极化层行为的影响。在相同的实验条件下，在之前的研究中评估了控制膜透过性的输入参数，因此这里只研究极化层。所提出的模型之前已经在实验观察到的截留曲线的基础上进行了验证，然后用于理解操作条件（如施加压力、进料流速或二价离子比例）如何控制极化现象。为此，针对各种条件，研究了沿膜长度的浓度和厚度轴向分布以及极化层内的径向分布。最后，还研究了各种混合物中二价离子的类型和数量对极化现象的影响。
