Page 308 - Modelling in Transport Phenomena A Conceptual Approach

288 CHAPTER 8. STEADY MICROSCOPIC BALANCES WITHOUT GEN.

a) Determine the initial molar flow rate of species A between the vessels.
b) What would be the initial molar flow rate of species A if the conical duct were
replaced with a circular tube of 8mm diameter?

______
-20 cm
TANK 1 TANK2

90% A 25% A
10% B 75% B

-2

Figure 8.27 Diffusion through a conical duct.

Solution

Since the total pressure remains constant, the total number of moles in the conical
duct does not change. This implies that equimolar counterdiffwion takes place
within the conical duct and the molar average velocity is zero. Equation (B) in
Table 8.8 gives the molar flow rate of species A as

c DAB (SA, - 2~~ )
hA =
I”’ i$j

The variation of the diameter as a function of position is represented by

D(z) = 0.006 + 0.02 z

so that the area is
A(z) = E (0.006 + 0.02 z)~
4
Substitution of Eq. (3) into Eq. (1) and integmtion gives

The total molar concentmtion is

- 101.325 x lo3
-
(8.314 x 103)(25 + 273) = 0.041 kmol/ m3 (5)