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Theory of shock electrodialysis

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Theory of shock electrodialysis ( theory-shock-electrodialysis )

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overlimiting current is widely observed in electrochemical systems, and possible mechanisms include water splitting, electro-convective instability, surface conduction, and electroosmotic flow [11, 12]. In the shock ED prototype, because the macroporous material has surface charge and pore size of around 1 μm, surface conduction and electroosmotic flow should dominate overlimiting current, which enables a deionization shock wave that propagates from one membrane to the other [13, 5, 14, 15]. A contaminated stream fed to our shock ED device can therefore be split into fresh and waste products at the outlet. This process is continuous, scalable, and potentially free of membranes (for example by replacing the ion exchange membranes with nanoporous ceramics), making it promising for water treatment [16]. anolyte catholyte anode (+) + feed CEM brine splitter fresh CEM macroporous material (-) + - - deionization shock + - cathode (-) Figure 1: Schematic of the shock ED system comprising a negatively charged microporous frit between two cation exchange membranes (CEMs). Schlumpberger et al. built and tested the first shock ED device and achieved over 99% removal of Na+ and K+ from binary electrolytes with water recovery as high as 80% [8]. Very recently, the Bazant group also proved the selective ion removal from electrolyte mixtures by shock ED [17, 18, 19], which will be discussed in more detail in the second part of the series paper. Despite the significance of these recent experimental results, there remain open questions in the underlying theory that must be addressed by mathematical modeling. Dydek et al. were the first to describe the bi-ion shock ED system with plug crossflow using a simple homogenized model [13], which assumes thin electrical double layer (EDL) and may be invalid in the ion-depleted zone. Schlumpberger et al. then introduced linear electroosmotic flow to the system [20] and compared the model to experimental data [8]. This work captured to some extent the trends of desalination and water recovery observed experimentally, but it significantly overestimated desalination and underestimated the overlimiting conductance (which determines energy consumption). Possible reasons for this discrepancy include oversimplification of boundary conditions, the neglect of water ion transport, and the assumption of thin EDLs. The microscopic Poisson-Nernst-Plank-Stokes model, which is applicable for any EDL thickness and considers surface conduction, electroosmosis, and diffusioosmosis, has been used for ion depletion in a single microchannel [21, 22] and pore-networks [23, 24, 25] at overlimiting current. However, it has never been applied to the shock ED system with cross flow. Finally, there has also been no theoretical work demonstrating the selective removal of multivalent ions by shock ED, for which models more robust than the homogenized model may be required. In this paper, we present a comprehensive model for multiple-ion, planar shock ED systems, as shown in Fig.2. Salt ions as well as hydronium and hydroxide ions are all included in the system. Instead of the macroporous material, this system involves either a single charged channel or a stack of these channels. The system can therefore be described by a three-dimensional pore-scale Poisson-Nernst-Planck-Stokes model, which is applicable for any EDL thickness and can be integrated to produce the depth-averaged model under the assumption of thin channels. The depth-averaging strategy used in this paper is similar to the area-averaging in Ref. [22, 26]. The shock ED system in this work also considers the electrode streams and ion exchange membranes because the assumption of ideal membranes does not provide enough boundary 2

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