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to collapse of our simulation data. In fact, as we can see in Figure 3-18, the scaling for current for the ion removal data predicted by the simulation is exactly the same scaling that is predicted by the boundary layer model, meaning that it predicts a square root dependence on flow rate and an extra factor of z ̄. In essence, this means that the simulation is still missing some vital physics to be able to properly capture the scalings observed in experiment. Some possible culprits could be the simplistic formulation of electro-osmotic flow in the model or the fact that eddy dispersion was neglected in the model. In contrast to the inability to predict the scale for ion removal, Figure 3-19 shows that scaling an estimate of the electro-osmotic flow based on the Helmholtz- Smoluchowski formula by the applied flow rate yields the correct scaling for water recovery, as the simulation data in this figure does collapse onto a single curve rea- sonably well. Lastly, both the simulation and the boundary layer theory assume a current effi- ciency of 100% for all conditions, which is also not what was observed in experiment. 3.5 Conclusions In conclusion, this work develops and examines two theoretical models for the shock electrodialysis prototype. Both models are able to give some physical insight into the problem, such as predicting the order of magnitude of the currents necessary to achieve desalination. However, even though the simulation is an improvement over prior models, especially with regards to predicting changes in water recovery, both models still fail to capture basic scalings observed in experiment. Nevertheless, these models will serve as a useful basis for making informed decisions about choosing the right materials in experiment, such as choosing a porous medium with an appropriate surface charge. Improvements to the simulation model can be made by more rigorously treating electro-osmotic flow, by including eddy dispersion, or by accounting for the transport of hydrogen and hydroxide ions. The first two improvements would likely be useful in 96PDF Image | Shock Electrodialysis for Water Purification and Electrostatic Correlations
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