Page 400 - Modelling in Transport Phenomena A Conceptual Approach

380 CHAPTER 9. STEADY MTCROSCOPIC BALANCES WITH GEN.

0

I
0 0.2 0.4 0.6 0.8
4

Figure 9.15 Variation of 9 as a function of < with A being a parameter.

9.4.1.1 Macroscopic equation

Integration of the microscopic level equations over the volume of the system gives
the equations at the macroscopic level. Integration of Eq. (9.47) over the volume
of the system gives

-
Carrying out the integrations yields
L
dCA
=
(-DAB TIz=.>, nR2kl CAdZ (9.419)
1
Rate of moles of species A Rate of depletion of species A
entering into the liquid by homogeneous ehem. rxn.
Note that Eq. (9.419) is the macroscopic inventory rate equation for species A by
considering the liquid in the tank as a system. Substitution of Eq. (9.417) into
Eq. (9.419) gives the molar rate of depletion of species A, 7i~, as

(9.420)