Model of Competitive Ion Transfer in an Electro-Baromembrane System with Track-Etched Membrane

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Abstract
The extraction of valuable components from brackish waters, such as lithium ions, is of considerable practical interest. A promising approach is the separation of solutes by their physical properties, such as charge and diffusion coefficient. We propose a simple one-dimensional model of ion transport in an electro-baromembrane system with a track-etched membrane, which makes it possible to calculate the flux densities of the separated components across the membrane as functions of the applied voltage and pressure drop. The model takes into account the parameters of the membrane (pore radius, length, and volume fraction in the membrane), hydrodynamic, and other external conditions of the separation process (thickness of diffusion layers, composition of the feeding and receiving solutions). The calculation results are given for a mixed solution containing three sorts of ions (two cations, K+ and Li+, and one anion, Cl−) with different diffusion coefficients, but the same absolute value of the charge. The electric field and the pressure drop are superimposed in such a way that the electromigration and convective transport of ions in the pore are directed oppositely. Since the mobility of competing cations is different, only lithium chloride or only potassium chloride is removed from the mixture at certain values of the potential drop and pressure.

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