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Langmuir Article flow rate (Q) is controlled by a syringe pump. Two sets of experiments are conducted with initial concentrations of 100 and 10 mM, holding the applied voltage constant at Vapp = 1.5 V, well into the OLC regime (Figure 3). The current remains steady for hours, indicating stable continuous operation during deionization. (See the Supporting Information on chronoam- perometry.) At low flow rates, we find that the salt concentration can be reduced by 4 orders of magnitude to 15 μM (Figure 7c). Essentially all of the CuSO4 ions are removed, down to the level of the water ions (pH ≈5.5) and below the U.S. regulatory limit for copper in drinking water (<0.02 mM).53 As in Figure 1d, the region of deionization (>0.5 mm) near the outlet extends across more than half of the frit thickness (1.0 mm) and is maintained in the outgoing flow. This establishes the existence of a stable deionization shock propagating against the flow (in the moving frame of reference)24,25 over a macroscopic distance in the porous medium.27 Such extreme deionization propagating so far into the frit cannot be explained by theories of ED based on convection−diffusion in neutral electrolytes.9 This observation suggests the possibility of harnessing deionization shocks in porous media for water purification. Although our apparatus has not been optimized for this purpose, it serves to illustrate the principles of shock electrodialysis. The basic idea is to drive over-limiting current through a porous medium and extract deionized water between the membrane and the shock with a pressure-driven cross-flow. In a scalable system for continuous operation (discussed below), additional outlets must also collect brine from the frit (deflected by the shock) and reaction products from electrode streams (such as hydrogen and oxygen from water splitting, as in standard ED). Here, we have just one, small freshwater outlet and negligible brine accumulation at the anode, but this suffices to demonstrate the general trade-off between flow rate and deionization29 (Figure 7c): For a given geometry and current, the flow rate must be small enough to allow the shock to propagate across the outlet in order to deionize the outgoing stream fully. As the flow rate is increased, the shock retracts toward the membrane and crosses the outlet, thereby causing the salty fluid from the diffusion layer to be mixed with the deionized fluid behind the shock. Flow-Rate Dependence. At fixed voltage, the deionization factor f = c0/cout (ratio of inlet to outlet salt concentrations) is controlledbythePećletnumber,Pe=Ud/D=Q/dD,whereU is the mean outlet velocity. In our apparatus (Figure 3e), asymmetric flow leads to complicated concentration profiles (Figure 7a), but we can use similar solutions for simple uniform flows to understand the scaling of f for Pe ≫ 1 (Figure 7c). For the SC mechanism, the shock has a self-similar nested boundary layer structure consisting of an outer convection−diffusion layer (or diffusive wave54) and an inner depleted region whose overall thickness (distance from the membrane) scales as Pe−γ, where γ = 1 for uniform normal flow through the membrane29 and γ = 1/2 for uniform cross-flow along the membrane (Mani and Bazant, to be submitted for publication). Integrating the self-similar concentration profile over a fixed-diameter outlet then implies the scaling c ⎛D⎞γ f= 0 ∼Pe−γ∼⎜ ⎟ cout ⎝Q⎠ (12) with 1/2 ≤ γ ≤ 1 for the SC mechanism with pressure-driven flow. For the EOF mechanism in a microchannel without net 16174 flow,12 the depleted region has nearly uniform mean concentration scaling as cd/c0 ∼ (I/Ilim)v, where ν ∼ 0.3 to 0.4. Although the theory needs to be extended for porous media and pressure-driven net flow, this result with I/Ilim ∼ Peγ (for the convection−diffusion layer) and f ∼ cd̃ −1 (if the depleted region spans the outlet) suggests that exponent γ in eq 12 may be replaced by the smaller value γν for the EOF. Both sets of experiments show the expected trend of the deionization factor with the flow rate (Figure 7c). The conductivity of the inlet and outlet solutions is measured by impedance and calibrated against solutions of known salt concentration. (See the Supporting Information.) At the lowest flow rate, on the order of 0.1 μL/min, we obtain f > 10 starting fromc0 =0.1Mandf≈102 startingfromc0 =10mM.Ateach flow rate, the solution with the lower initial ion concentration (10 mM) consistently yields a greater percentage reduction of conductivity (or concentration) than that of the higher initial ion concentration (100 mM). The larger deionization factor results from the larger dimensionless current (I/Ilim) and more extended deionization region (or shock) at lower salt concentrations, consistent with the theory.12 This trend is also a consequence of mass balance, f ∼ I/(Qc0), as in standard ED. Energy Efficiency. The energy cost per volume of deionized water in the experiments of Figure 7c is plotted in Figure 7d versus the outlet concentration cout. Comparing the energy cost with (dashed line) and without (solid line) the electrode and reservoir series resistances shows that less than half of the total energy cost is spent driving the copper reactions. As in standard ED, such electrode resistances can be made negligible compared to a larger total voltage in a scalable, multilayer system (Figure 9). As indicated by the green arrows, the button cell can desalinate brackish water (0.1 M) to produce potable water (<10 mM) at a cost of ≈10 kWh/m3 and then deionize close to 0.01 mM in a second step at roughly the same cost. The net energy cost of ≈20 kWh/m3 is well above the thermodynamic limit of ≈0.15 kWh/m3, but this is mainly a consequence of the experimental geometry, which was not designed for this purpose. To boost the efficiency in a practical shock ED system, the cross-flow must cover as much of the active area (drawing current) as possible. Because our device has a point outlet from the frit at only one azimuthal angle rather than a gap spanning its circumference, fluid is extracted from only a very small area, ≈πd2/2, which is roughly 1/50 of the total cell area πR2. As a result, the total power use is nearly independent of the flow rate, and the energy/volume = power/(flow rate) should scale as Pe1− ≈ f1/γ from eq 12, which is consistent with the data in Figure 7d. With uniform cross-flow covering the entire active area as in Figure 9, the energy cost could, in principle, be reduced by the same factor to ≈1 kWh/m3. This suggests that shock ED has the potential to be competitive with other approaches on efficiency while having some other possible advantages in separations discussed below. Electrolyte Dependence. Until this point, our copper electrolytic cell has provided a convenient model system to establish the basic principles of shock ED, but the method is much more general and can be applied to arbitrary electrolytic solutions. As in standard ED, the electrodes can be chosen to drive any desired brine-producing reactions, such as water electrolysis, while the current is carried across a stack of many membranes by the input solution (see below). In our device, we have only one separation layer and copper electrodes, but we dx.doi.org/10.1021/la4040547 | Langmuir 2013, 29, 16167−16177PDF Image | Overlimiting Current and Shock Electrodialysis in Porous Media
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