Cross-flow Nanofiltration Of Polymeric Membrane:Theoretical Analysis And Fem Simulation

The lack of water resources and the water pollution have become a worldwide problem. Compared with traditional separation technology, Membrane separation technology has drawn universal attention because of its outstanding advantages of no-phase transformation, no secondary pollution and high separation efficiency. As the important function of separation membrane, the nanofiltration membrane is a type of pressure-driven charged membrane and has drawn worldwide attention, with several advantages such as high flux, low operation pressure, high retention of multivalent anion salts. 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. Due to the charged groups on the membrane, the separation of the inorganic salts is governed by not only controlled by the chemical potential, but also electric potential. In another hand, during the process of membrane separation, concentration polarization lead to the decline in membrane flow flux and separation efficiency, which severely restricts the wide application of membrane technology. Therefore it is of great importance to carry out the research on in-depth understanding of the rejection mechanism and promote the wider application of nanofiltration. It remains as a challenge in the field of nanofiltration to develop a practical model for the retention of ions that describes the fundamental physical phenomena of nanofiltration process.At first, the Donnan Steric Pore Model (DSPM) is described in this paper. The extended Nernst-Planck equation is adopted to describe ionic migration in the membrane caused by diffusion, convection and electric field, and the differential equation of ionic concentration gradient along the membrane pore axis is obtained. Membrane volumetric charge density is obtained by the Gouy-Chapman theory. Combining the electroneutral conditions inside the membrane and in the bulk solution, Donnan equilibrium model and steric effects, the boundary conditions of both the inlet and outlet of the membrane pores are solved. It is carried out to investigate a variety of influencing factors on the nanofiltration membrane electrical properties, such as operating conditions and test conditions by finite element method. The transport and rejection mechanism of the membrane have also been investigated from structure parameters and separation performance to understand the rejection mechanism better. The results are compared with experimental results from the literature to verify the reliability of the mathematical model and calculation method. As permeation flux increased,the gradient of ion concentration in the membrane increased that lead to the retention declines. As the ion concentration increasing, the convection-diffusion-migration transport reinforces in nanofiltration that lead to the retention declines. For high valence ion such as MgSO4, Donnan effect enhances that lead to the retention escalate. And the influence of the concentration for the rejection rate is small. The pore size of CA30(one of the of the cellulse acetate membrane) is large. Therefore, the separation performance of CA30is bad under the low permeation flux. The pore size of AFC40(one of the of the polyamide membrane) is small1and the membrane thickness of AFC40is thick. Therefore, the separation performance of AFC40is good under the low permeation flux. When the permeation flux reach3×10-5m/s, the separation performance of AFC40is stable. NTR7450(one of the sulfonated polyether sulfone membrane) has excellent water-soluble and surface activity and increasing the volumetric charge density. The separation performance of NTR7450is good under the high permeation flux.As the supplement of DSPM, CP-DSPM which involved a concentration polarization layer, DSPM&DE which concerned dielectric exclusion, and PPTM which considered the above two factors are reviewed. In addition, the numerically simulated results of ion rejections under conditions of different water fluxes by means of the above-mentioned four models are compared. The coupled model of CP provides considerable insight of the importance of the introduction of concentration polarization layer, and the DE effect plays a heavy role in the patitioning of the multivalent counter-ions. 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 with finite element method by coupling with mass-transfer in the membrane, ion concentration and velocity profile in solution. Nanofiltration membrane is a pressure driven membrane separation process. The water flux increases with the increasing of the pressure that lead to ion rejection and concentration polarization increases. Wall diffusion increases with the increasing of cross-flow rate, so increasing cross-flow rate will reduce the effect of nanofiltration membrane polarization and fouling. 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. It is found that the modified PPTM is able to precisely predict ion concentration and velocity profile in solution. The results obtained by optimized model are useful for nanofiltration design and operation.