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experiment. Hence, in this work, we will also develop a more advanced 2-D model that is based on the model in Dydek et al [24]. This model will not assume a simple plug flow, but it will incorporate a simple description of electro-osmotic flow in order to capture the flow that occurs from anode to cathode in our problem. Furthermore, this model is also more general, since it does not assume a binary electrolyte with ions having the same diffusion coefficients. The geometry of the system mimics our experimental geometry in order to be able to compare results as well as possible. We find that at high and low currents, we get relatively good agreement between model and simulation; however that there is some disagreement at moderate currents. The possible reasons for this disagreement are explored. 3.2 Mathematical Model for Simulation The shock electrodialysis cell consists of two flat ion-exchange membranes with a charged porous medium between them through which the electrolyte will flow. The flow within the porous medium is assumed to be fully developed and is assumed to behave according to a combination of Darcy’s law and linear electro-osmosis. Ion transport is governed by the Nernst-Planck equations, which predict concentration polarization. The charged surfaces are treated in a continuum fashion by smearing out the surface charge throughout the volume of the pore and hence only including a constant background charge (ρs) in the equations, via a modified electroneutrality condition, as done by Dydek et al [24]. Furthermore, we also neglect charge regulation (i.e. ∂ρs = 0) and assume a uniform porous medium with constant charge and mi- ∂t crostructure (i.e. ρs, εp = constants). However, unlike Dydek et al [24], we here will include electrokinetic phenomena, such as electro-osmotic flow and streaming cur- rent, with the aim of being able to explain the change in water recovery with current. Furthermore, this model will not assume a symmetric binary electrolyte and hence will be much more general. We will however assume that we have only one simple electrolyte and will ignore hydrogen and hydroxide ions. The relevant parameters, their symbols, and their values and scales are listed in Table 3.1. 77PDF Image | Shock Electrodialysis for Water Purification and Electrostatic Correlations
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