Chapter 14: External Diffusion Effects on Heteregeneous Reactions

Equal Molar Counter Diffusion (EMCD)

(W_A= -W_B)

Dilute Solutions (B_A=0)

$ \text{Mole Balance} $: $ \frac{dW_Az}{dz} = 0 $

$Diagram showing mass transfer of component A from z = 0 to z = δ with flux W_AZ. Concentrations and mole fractions are C_A0, y_A0 at z = 0 and C_Aδ, y_Aδ at z = δ.$

$ W_A = K_1 = -D_{AB} \frac{dC_A}{dz} $

$ C_A = -\frac{K_1 z}{D_{AB}} + K_2 $

at $ z = 0, \quad C_A = C_{A0} $

$ K_2 = C_{A0} $

at $ z = \delta, \quad C_A = C_{AS} $

$ C_{AS} = \frac{K_1 \delta}{D_{AB}} + C_{A0} $

$ K_1 = (C_{AS} - C_{A0}) \frac{D_{AB}}{\delta} $

$ C_A = (C_{AS} - C_{A0}) \frac{z}{\delta} + C_{A0} $

$ \frac{C_{A0} - C_A}{C_{A0} - C_{AS}} = \frac{z}{\delta} $

$ \frac{y_{A0} - y_A}{y_{A0} - y_{AS}} = \frac{z}{\delta} $

$ W_{Az} = -D_{AB} \frac{dC_A}{dz} = -D_{AB} [C_{AS} - C_{A0}] \frac{1}{\delta} $

Graph showing concentration CA versus position Z. CA decreases linearly from CA0 at z=0 to CAS at z=δ. The x-axis is labeled Z, and the y-axis is labeled CA. A dashed horizontal line marks CAS.

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