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Here μ is the viscosity in mPa · s, Vb is the bubble velocity in ms , and σsurf is the surface tension of HCl(aq) against Cl2 in mN . In our system, we have considerable flexibility in m choosing a value for ε, given that w and Vb are parameters not constrained by any other part of the system and are amenable to engineering design. We bound values of ε by considering the relevant extremes of these parameters. We may expect Vb to vary reasonably from 0.001 to 0.1 ms . Over the temperature and con- centration range presented in work done by Laliberte ́, the viscosity μ varies from 0.6 to 2.4 mPa · s (23, 24). σsurf is assumed to vary similarly to the surface tension of water against air, 62-76 mN over 0-80 ◦C(6). With these extremes, Ca varies from a minimum m of 7.89 × 10−6 to a maximum of 0.00387. A typical channel width for a fuel cell is one millimeter. We allow the channel width to vary from 0.5 to 3 mm, in which case Equation 21 yields a range on ε of 0.2 to 74 μm. The diffusion coefficient of Cl2 in HCl(aq) is fit to the data of Tang and Sandall (25), resulting in DCl2 = 0.0392exp where kB is Boltzmann’s constant, 8.617 x 10−5 eV , the activation energy, -0.204, is in eV, K and the prefactor is in cm2 . We assume DCl is independent of acid concentration. s2 We take the dependence of the saturated chlorine concentration, C [ mol ], from the sat . cm3 work of Hine and Inuta (26). The solubility follows Henry’s law (based on the rapid impingement argument made previously), with a temperature and concentration dependent −0.204 kB(T +273.15) , [23] coefficient. Csat. =HpCl2 · 1 , [24] 1000MCl2 where H is Henry’s law coefficient in g , and the latter factor yields our working units of L·atm mol for C , with M being the molecular weight of Cl of 70.9 g . The concentration cm3 sat. Cl2 2 and temperature dependence are empirically fit by H =α′MHClM+β logα′ = −1.21×10−2T −1.603 β = 2.14 × 102T −1.21 mol where α′ is in grams-chlorine per liter/grams-HCl per liter · atm, and β is in grams-chlorine per liter/atm. We model the chloride mass transport in a similar way to the chlorine transport, with a few key differences. As Cl2 is reduced at the electrode, Cl- is produced and the local concentration, CRs (i), increases. Protons also enter through the electrode at the same flux as the chloride is generated. As the concentrations increase at the electrode surface, the concentration gradient generates a diffusive flux of Cl- and H+ away from the electrode. We model the concentration of HCl(aq) as pinned at the bubble-thin film interface due to exchange of HCl(g) in the bubble with HCl(aq) in the thin film. The bulk solution molarity 15 [25] [26] [27]PDF Image | Regenerative Hydrogen Chlorine Fuel Cell for Grid-Scale
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