Page 332 - Modelling in Transport Phenomena A Conceptual Approach

312 CHAPTER 8. STEADY MICROSCOPIC BALANCES WITHOUT GEN.

+-L+

Figure 8.36 Diffusion of liquid d through a stagnant liquid film 8.

Over a differential volume of thickness Az, the conservation statement for
species d, Eq. (8.41), is written as

NAz 1% A - NA. I.z+A,z A = 0 (8.529)
Dividing Eq. (8.529) by A AZ and letting AZ -+ 0 gives

(8.530)

or,
-- dNAz - 0 I;$ NA, = constant (8.531)
dz
To proceed further, it is necessary to express the total molar flux of species d, Le.,
NA,, either by Eq. (8.52) or by &. (8.53).

8.5.2.1 Analysis based on the molar average velocity

From Eq. (8.52), the total molar flux of species A is given as

(8.532)

It is important to note in this problem that the total molar concentration, c, is not
constant but dependent on the mole fractions of species A and B. Since species B
is stagnant, the expression for the molar average velocity becomes

(8.5-33)