14.5 I Boundany Conditions and Discontinuou.s Concentrations at Intedaces 96r Flow of species A in gas mixture B _-> Diffurion of A from I ^,,, "A,' catatytic surface Ithe Frcunn 14.7 One-dimensional Catalytic surface for the production diffusion or consumption with heterogeneous of species A catalysis. where D* is the binary diffusion coefficient for A in B and B may be a multicomponent mixture. Assuming C and D* to be constant, Equation 14.64 may be solved subjecf to the conditions that xo(L): xo, and : N{,,(o) f, (r4.6s) -cDts*|.:,: This expression follows from Equation 14.63 and the substitution of Fick's law, Equation 14.42. For a catalytic surface, the surface reaction rotte N'[generally depends on the surface concentration CA(O). For a reaction that results fi,rst-order in species consumption at the surface, the reaction rate is of the form N';: (14.66) -kic^(o) where ki(m/s) is the reaction rate constant. Accordingly, the surface boundary condition, Equation 14.65, reduces to (r4.67) -o**1"_o: -ri-roto) Solving Equation 14.64 subject to the above conditions, it is readily verified that the con- centration distribution is linear and of the form ra(x)_ l+(xk'UDn) (14.68) x^L I + (LkilD^B) At the catalytic surface this result reduces to xe(0) : (r4.6e) xe,,t | + (LH1/D^B)
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