Page 402 - Modelling in Transport Phenomena A Conceptual Approach

382 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

The use of Eq. (5.3-26) gives the rate of depletion of species A per unit volume as

?J?A=-kCA (9.425)
Substitution of Eqs. (9.421) and (9.425) into Eq. (9.424) gives

(9.426)

in which the diffusion coefficient is considered constant. The boundary conditions
associated with Eq. (9.426) are

dCA
at r=O -=O (9.427)
dr
at r= R CA=CA~ (9.428)
The physical significance and the order of magnitude of the terms in Eq. (9.426)
are given in Table 9.3.

Table 9.3 The physical significance and the order of magnitude of the terms in
Eq. (9.426).
Term Physical Significance Order of Magnitude
T~ dr (T2 9) Rate of diffusion DAB -j-g
--
DAB d
CAR
k CA Rate of reaction k CAR

Therefore, the ratio of the rate of reaction to the rate of diffusion is given by

k R2
-
Rate of reaction - k CAR =- (9.429)
Rate of diffusion DAB CA~/R~ VAB
and the Thiele modulus, A, is defined by

(9.430)

Introduction of the dimensionless quantities

e=- CA (9.431)
CAR
(9.432)