464
Chapter 10
j _________
4^ ; / 3
(10.45)
The ratio between the observed volumetric reaction rate and that obtained in the absence of any
mass transfer resistance is also called an effectiveness factor. This particular effectiveness factor is
now an
internal effectiveness
factor,
rjeg,
to distinguish it from the previously defined film
effectiveness factor,
rjf
* i K . )
(10.46)
For a spherical geometry, Eq. 10.44 may be transformed into the dimensionless form given by Eq.
(10.47)
1
d (
2 dSA\
R 2
pq ffs A = sAf f
'
qA
X 1 dX \
d x )
DAeifsAs
q ffsA = s As)
(10.47)
by introducing
X =
(10.48)
The dimensionless
Thiele modulus,
is defined by
o> =
r p<
j'a(s a = saJ
^ d ) A^ s A^qA{sA = sAs)
(10.49)
For a first order reaction, i.e.
-q A = k,sA,
the Thiele modulus is given by
(10.50)
It can be shown (see e.g. Fogler, 1999) that the internal effectiveness factor for a first order reaction
in a sphere is given by:
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