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cause of the propensity of both Cl2(g) and HCl(g) to dehydrate the membrane, meaning that continuous delivery of H2O molecules to the membrane is essential. With two-phase flow, however, it is imperative that the mass transport is handled properly. If the aqueous phase sets up a diffusion barrier that is too large, the cell can become “flooded” and perfor- mance is drastically reduced. This is a problem that the low temperature hydrogen-oxygen fuel cell community has made considerable effort to overcome (18). In order to understand mass transport through the HCl(aq) thin film bubble wall, we need to know the film thickness, ε [cm], which is predictable from fluid dynamics (17,19- 22). Cl2 from inside the bubble must diffuse across this HCl(aq) thin film to the electrode surface to react according to Equation 4b. As the reaction goes forward, the thin film be- comes enriched in Cl-. If the current density is sufficiently high that considerable depletion of the reactant and accumulation of the product occurs, then mass transport would limit the cell performance. We assume that at the bubble/film boundary the concentration of Cl2 in solution is pinned at Csat., which is the equilibrium concentration of Cl2(aq) dissolved in HCl(aq) for the actual pressure of Cl2(g). This assumption is justified because the flux of Cl2 toward the electrode surface is significantly smaller than the impingement rate of Cl2 gas onto the thin film surface (alternatively, one can justify this by realizing that, since the film itself is quite thin, its surface area to volume ratio is large, meaning that Cl2(g) will be able to quickly equilibrate with the liquid film). The diffusive flux, J [ mol ], is given by cm2 ·s J = −DdC ≈ −D∆C, [19] dx ∆x where in the second expression we have made the quasi-stationary, linear concentration gradient approximation across the thin HCl(aq) film. D is the diffusion coefficient in cm2 . s For diffusion of Cl2 in HCl(aq), we label the diffusion coefficient DCl2. ∆x is equal to ε, the film thickness, and ∆C is the concentration difference across the thin film, namely Cs (i) − C in mol . For each mole of Cl that diffuses to the electrode surface to react, O sat. cm3 2 2F coulombs of electrons pass through the external circuit for chlorine reduction. Thus, the flux is expressed as a current density according to i = 2F J · 1000, where the factor of 1,000 is necessary for conversion from A to mA. Equation 19 can be solved for COs (i): COs(i)=Csat.−ε i. [20] 2FDCl2 1000 The film thickness ε [cm] is approximated by the following equation (16): ε ≈ wCa23 , [21] where w is the width of the capillary channel and the capillary number Ca is a dimension- less number given by Ca= μVb . [22] σsurf 14PDF Image | Regenerative Hydrogen Chlorine Fuel Cell for Grid-Scale
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