Page 333 - Modelling in Transport Phenomena A Conceptual Approach

8.5. MASS TRANSPORT WITH COWCTION 313

Substitution of Eq. (8.533) into Eq. (8.532) gives the molar flux of species A as

(8.534)
Since the total molar concentration, c, is not constant, it is necessary to express
c in terms of mole fractions. Assuming ideal solution behavior, i.e., the partial
molar volume is equal to the molar volume of the pure substance, the total molar
concentration is expressed in the form

(8.535)

Substitution of XB = 1 - XA yields
1
c= I (8.536)
VB + (VA - VB)zA
Combining Eqs. (8.534) and (8.536) and rearrangement gives

(8.537)
~ Jo

Integration of Eq. (8.5-37) results in

(8.538)

8.5.2.2 Analysis based on the volume average velocity

The use of Eq. (8.53) gives the total molar flux of species A as

.- (8.539)
From Eq. (C) in Table 8.12, the volume average velocity is expressed as
+
v, = ~ANA, ~BNB,
-
= VANA, = VANA, (8.540)
Using Eq. (8.5-40) in Eq. (8.5-39) yields

(8.541)