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7 convert the velocity into a flow rate by assuming that current flows only in the transverse 8 direction in our system (i.e. directly from anode to cathode), which is a crude approximation 9 of the true boundary layer structure of the shock, but might capture the correct scalings. 10 This means that we can simply multiply by the cross-sectional area A to obtain the flow rate QEOF = εζAj = εζI (2) μσ μσ 11 Since we know the magnitude of the zeta potential, we can use this formula to estimate 12 electroosmotic flow. The best way to see the effect of electroosmotic flow in our system is 13 to compare the theoretical water recovery to the obtained data. Water recovery is defined 14 as Rw = Qd/Q, where Qd is the flow rate of fresh water and Q is the total flow rate. As 15 we see in the data, Qd changes as a function of current. Assuming that the bulk EO flow 16 is not completely hindered by pressure-driven back flow, we estimate the fresh water outlet 17 flow rate as Qd = αQ + QEOF , where α is the water recovery at zero current, which depends 18 directly on the placement of the splitter and hence is a known parameter. We can then 19 obtain a new formula for water recovery: Rw = Qd = αQ + QEOF = α + εζI (3) Q Q μσQ 20 The second term is the rescaling of current that was used in figure 3(d) in the paper and 21 this formula (with a prefactor in front of the second term to allow fitting) was used to fit 22 the water recovery data. 23 Method Details 24 Before assembly, the membranes were cut into roughly 2.5×1.5 cm rectangles and then 25 treated chemically to remove any impurities and to activate them. They were first soaked in 26 3% (v/v) hydrogen peroxide at 80◦C for an hour, rinsed with deionized (DI) water, and then S2PDF Image | Continuous Water Deionization by Shock Electrodialysis
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