Nanofiltration of Multi-Ion Solutions: Quantitative Control of Concentration Polarization and Interpretation by Solution-Diffusion-Electro-Migration Model

Abstract

For effective use of advanced engineering models of nanofiltration quality of experimental input is crucial, especially in electrolyte mixtures where simultaneous rejections of various ions may be very different. In particular, this concerns the quantitative control of concentration polarization (CP). This work used a rotating disklike membrane test cell with equally accessible membrane surface, so the CP extent was the same over the membrane surface. This condition, which is not satisfied in the conventional membrane test cell, made possible correcting for CP easily even in multi-ion systems. Ion rejections were studied experimentally for several dominant salts (NaCl, MgCl2, Na2SO4 and MgSO4) and trace ions (Na+, NH4+, Cl− and NO3−) using NF270 membrane. The solution–diffusion–electro–migration model was used to obtain ion permeances from the experimental measurements. The model could well fit the experimental data except in the case of NH4+. The correlations between the ion permeances and type of dominant salt are discussed in the context of the established mechanisms of NF such as Donnan and dielectric exclusion. The obtained information contributes to the systematic transport characterization of NF membranes and may be ultimately useful for computational fluid dynamics simulations of the performance of the membranes in various applications.

The Adverse Effect of Concentration Polarization on Ion–Ion Selectivity in Nanofiltration

“…The different k values yielded similar real rejections for all of the monovalent cations, eliminating the “reversed” trend (Figure a). Although the conventional film theory equation (eq ) does not describe the transport in mixed-salt solutions, as it does not account for electromigration (i.e., migration of ions driven by the electric field imposed by the diffusion of other ions), − the elimination of the “reversed” trend suggests that CP plays a role in the trend of the observed rejections. As our calculated Reynold’s number in the flow channel was in the borderline between laminar and turbulent flow conditions, we also employed correlations for turbulent flow (eq S2, Table S2), which also yielded plots with reduced manifestation of the “reversed” rejection trend (Figure S3).…”

Comparative Analysis of Donnan Steric Partitioning Pore Model and Dielectric Exclusion Applied to the Fractionation of Aqueous Saline Solutions through Nanofiltration

“…The Donnan exclusion mechanism retains counter-ions, ensuring stoichiometric passage through the membrane. In concentrated or multi-ionic solutions, interactions between different ions may alter ion permeability [76,77].…”

Model-Based Optimization of Multi-Stage Nanofiltration Using the Solution-Diffusion–Electromigration Model

“…A detailed description of the derivation of the model as well as application examples can be found in the works of Yaroshchuk et al [19,20]. Recently, research groups have started to apply the SDEM [21,22], e.g., Labastida and Yaroshchuk [21] used the SDEM model to fit ion permeances to experimental data obtained by a rotating disk-like membrane in order to study the effect of concentration polarization. Recently, the model was extended by López et al [22], who also considered the formation of the MgSO 4 ion pairs resulting from an equilibrium dissociation reaction and determined a permeance for the ion pair species as well.…”