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Electrolyte Type / Concentration 1:1 / 1 mM 1:1 / 10 mM 1:1 / 100 mM 1:2 / 10 mM 2:1 / 10 mM Surface Charge (mC/m2) -10.42 -20.80 -38.39 -25.59 -36.90 Zeta Potential (mV) -90.23 -68.69 -46.52 -61.61 -48.08 Table 3.2: Surface Charge and Zeta Potential for the Shock Electrodialysis Prototype Outlet Conditions (Boundary 4) Boundary 4 is the outlet to the system. Here we only specify the outlet pressure (P ̃ = P1), which together with the inlet pressure condition determines the normal pressure drop across the system. Furthermore, since we are far removed from the region of applied current/potential, we can safely assume that there is no longer a normal electric field (∂φ ̃ = 0). Lastly, we assume an outflow boundary condition ∂ x ̃ for the anions, meaning we assume that the concentration no longer changes in the normal direction (∂c ̃− = 0). ∂ x ̃ 3.2.3 Surface Charge Model The surface charge of the silica frit was calculated using the following equations [9, 102]: kBT −σ σ ζ(σ) = e ln eΓ+σ +ln(10)(pK −pH) − C (3.22) z+eψ z−eψ σ(ζ)=sign(ζ) 2kBTc0εw s+exp −kBT +s−exp −kBT −s+−s− (3.23) Equation 3.23 is based on the Gouy-Chapman model and reduces to the Grahame equation for binary symmetric electrolytes. The values for surface charge and zeta potential used in the simulations are shown in table 3.2. 83PDF Image | Shock Electrodialysis for Water Purification and Electrostatic Correlations
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