Concentration polarization phenomenon during the nanofiltration of multi-ionic solutions: influence of the filtrated solution and operating conditions.

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.