Diffusion Reaction Interaction for a Pair of Spheres - ETD ...

the dimensionless center-to-center separation distance is
and the Thiele modulus is
d = d / a , (5.9)
1
1
int
1
a k D
φ . (5.10)
T =
When the modulus is large the rate is limited by the internal diffusion process and
a small φ T implies that internal reaction is the rate limiting step (Levenspiel,
1999). The ratio of external to internal diffusion rate is
int
int
ε = D D . (5.11)
Since the reaction is volume distributed within the sink, the probability P, that a
molecule created at the surface of sphere 2 will diffuse to the surface of sphere 1
and be consumed inside sphere 1, is defined as the volume integral
P
int
a1
π 2π
2 −1
2
( 4πa 2 σ 2 ) kintcintr1
sinθ1
dφ1dθ1dr1
∫∫∫
= . (5.12)
00
0
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