Chapter 14: External Diffusion Effects on Heteregeneous Reactions

Example: Relative Rates of Diffusional Transport

What are the relative rates of transport of a through a stagnant gas and equal molar counter diffusion for the same concentration boundary conditions. Recall the relative concentration profiles were

$Graph showing mole fraction yA versus dimensionless distance z over δ. A solid curved line labeled 'Stagnant film' decreases from yAb to yAs. A dashed straight line labeled 'Dilute concentration or EMCD' connects the same points linearly. The x-axis is labeled z/δ, ranging from 0 to 1.0.$

EMCD

$ W_{Az} = \frac{c D_{AB}}{\delta} \left( y_{Ab} - y_{As} \right) $

$Diagram showing vertical mass transfer with a downward arrow labeled WAZ between two horizontal lines. At z=0, the mole fraction yAb is indicated, and at z=δ, the mole fraction yAs is indicated.$

Stagnant film

$ W_{Az} = \frac{c D_{AB}}{\delta} \ln\left( \frac{1 - y_{As}}{1 - y_{Ab}} \right) $

Ratio of transport rates

$ R = \frac{W_{Azs}}{W_{AzEMCD}} = \frac{\ln\left( \frac{1 - y_{As}}{1 - y_{Ab}} \right)}{y_{Ab} - y_{As}} $

Let y_As = 0 @ surface (e.g., infinite reaction)

$ R = \frac{\ln\left( \frac{1}{1 - y_{Ab}} \right)}{y_{Ab}} $

We now will compare the relative rates as a function of the mole fraction, y_Ab, of the diffusing species, A, at the upper boundary z = 0.

y _Ao

0.999

0.99

0.90

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

6.91

4.65

2.56

2.01

1.72

1.53

1.39

1.28

1.19

1.12

1.65

Graph showing R versus yAo. A curve decreases from R=5 at yAo=1.0 toward R=1 at yAo=0. A dashed horizontal line is drawn at R=1. The y-axis is labeled R and yAb, and the x-axis is labeled yAo.

y_Ao

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