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solution and/or the electrolyte to move to the iron Solut10n 1n order to achieve equilibrium. The relative mobilities of water and electrolyte determine the extent to which each moves (i.e., one can expect a higher water diffusion coeffic1ent, which 1mplies that the net result is greater water transport to the chromium ion solution). Slmilar results have been observed in s11ver-hydrogen batteries (ref. 8). Slmilar calculations, where the water moves to the iron solution (a more unusual situation), are shown 1n table 14. It is interest1ng to note that different combinations of transference numbers determine the direct10n of osmotic pressure gradient. 01fferences in hydrogen ion concentrat10ns at the end of charge or discharge are also calculated, and the pos1tive values 1ndicate the tendency for electrolyte to diffuse to the iron Solut10ns and water to diffuse to the chromium Solut10ns. The approx1mation used in calculat1ng the values in tables 13 and 14 assumes constant transference numbers, and effects such as current effi- ciency, pressure d1fferences, and concentration gradients are considered independently. A more realist1c calculation uses a Nernst-Planck formal1sm modified to include convect10n: acH+) (af) J+ =(CH+) (v) - (OH+) (-ax- + (CH+) ax ( ) ( aCC1-) (ac) (3) J_ =(CC1-) v - (OC1-) ax - (CC1-) ax v = d ( RTwX ~_ lE.) h axax where v 1S the volume flow, db 1S the hydrodynamic permeabil1ty, wX is the membrane charge dens1ty. CH+ 1S the concentration of hydrogen lon, Cel- is the concentration of chlor1de ion, 0H+ is the hydrogen 10n diffus10n coefficient, DC1- is the chloride ion dlffusion coefficlent, af/ax is the potential gradient, and ap/ax is the pressure gradient. Integrated forms of these coupled differential equat10ns derived by Schlog (ref. 9) assume the form J _ vwX DH+ + DC1- +- 4 0Cl- (1 + r) (1 + s) 0+0- ) vwX H+ C1 (1_r) (1_s J=--4D tf+ (4) v = ~o (~_ WH) where 0 is the membrane thickness, 6f is the potential difference, and Do is the hydrodynam1c dlffuSlon coefficient. 18PDF Image | NASA Redox Storage System Development Project 1980
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