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imentally in a somewhat different geometry using seawater. They essentially used a branching channel in which a nanojunction was fabricated into one of the branches. The presence of this nanojunction would form a depletion zone in this branch and therefore cause the ions in the salt water to go into the other branch, leaving the water in this branch deionized. One problem that Kim et al face with their device is that the design parameters, such as the position of the nanojunction, have to be very carfully optimized in order to avoid having ions go into the desalted stream and also to avoid having the depletion region extent too far into the brine channel and there- fore sending desalted water into the brine channel. Furthermore, it is not obvious how this system could be scaled up. 1.3.3 Concentration Shock Dynamics in Porous Media Shocks propagating from a microchannel-nanochannel interface are definitely of sci- entific interest; however, they are of very limited application. Hence, it is important to look at the shock phenomenon on a macroscopic scale. Mani and Bazant [67] inves- tigated the formation of shocks in microstructures that are capped by a nanoporous membrane. The physics in this system are very similar to that in a microchannel- nanochannel system. The shock is initially triggered by the nanoporous membrane. As the ensuing depleted region spreads into the microstructure away from the mem- brane, the bulk conductivity in the depleted region is reduced. The ensuing amplifi- cation of the electric field drives the co-ions away into the bulk in front of the shock and drives the counterions into the double layers in order to carry the current around the depleted region. The system can be represented by the following PDEs: ∂cb + ⃗u · ∇cb = D ̄[∇2cb − z ̄∇ · (ρ∇φ ̃)] (1.12) ∂t e 0 = ∇ · ⃗j (1.13) In this model, any nonlinear response would be due to the surface charge. Hence, in this model, the shock would be entirely due to conduction at the surface. In the 37PDF Image | Shock Electrodialysis for Water Purification and Electrostatic Correlations
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