Theory of shock electrodialysis

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Theory of shock electrodialysis ( theory-shock-electrodialysis )

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1 0.8 0.6 0.4 0.2 0 01234 cathode-side, DAfull anode-side, DAfull cathode-side, DAp anode-side, DAp Figure 4: The current efficiency η through each of the membranes for the base case shown in Fig.3. Base case Q = 38 L/min Q = 152 L/min 1 mM NaCl 100 mM NaCl 10 mM KCl 01 5 10 15 20 25 30 Model [20] DAp/Hp Hfull DAfull Exp. [8] Figure 5: The conductance scaled by the theoretical surface conductance (κ ̃ = κ/κsc) at overlimiting current from different models and experimental data [8]. the theoretical surface conductance. With the adding of hydronium transport (note that DH+ ≈ 7DNa+ ), the DAp model and Hp model both increases κ ̃ to about 1.5. With the electroosmotic vortices, the Hfull and DAfull model predict even higher conductance. Between these two, the DAfull model gives higher conductance because of the overall more negative zeta potential. F We now consider the fresh concentration c ̃k and water recovery ω of the fresh stream for the base case, as shown in Fig.6(a). For the models in this paper, cF = cFNa. For the model of [20], cF = cF− (the authors use the anion concentration in the frit to represent the outlet salt concentration, since they do not have unsupported electrolyte in inlet and outlet zones for simplicity). As we can see, the model of [20] predicts almost perfect desalination at I ̃ ≈ 1. With hydronium transport included, the DAp and Hp model both ̃ show less ion removal at the same I, and the curve reaches a plateau since the membrane is not ideal and the deionization shock passes the splitter. The fresh concentration decreases most slowly with current for the DAfull and Hfull model, which should be the result of a thin deionization zone near the outlet zone induced by electroosmotic vortices. In addition, the DAfull and Hfull models predict greater water recovery than the model from [20], while DAp and Hp models cannot predict an increase in water recovery with current. The small differences between DAp and Hp as well as DAfull and Hfull indicate that the homogenized model works well for shock ED with a binary electrolyte. 3.2.2. Comparison with experiments In this part, we use the DAfull model to calculate additional cases with different working conditions relative to the base case, and we compare the overlimiting conductance, fresh concentration, and water recovery with experimental results [8]. The new working conditions are as follows: change the feed flow rate Q to 38 or 152 μL/min, change the concentration of NaCl to 1 or 100 mM (the corresponding surface charge densities are σ = −10.4, −38.4mC/m2), or change NaCl to KCl. 12

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