Page 324 - Modelling in Transport Phenomena A Conceptual Approach

304 CHAPTER 8. STEADY MICROSCOPIC BALANCES WITHOUT GEN.

in which the molar average velocity is given by

(8.5-14)

which indicates non-zero convective flux. The use of Eq. (8.514) in Eq. (8.5-13)
results in
(8.5-15)

Substitution of (8.515) into Eq. (8.510) and rearrangement gives

(8.5-16)

(8.5-17)

Since jt~ is constant, Eq. (8.517) holds for 0 5 z 5 L.
Note that XA,, i.e., the value of XA at z = 0, is the mole fraction of species
A in the gas mixture that is in equilibrium with the pure liquid A at the existing
temperature and pressure. The use of Dalton’s and Raoult’s laws at the gas-liquid
interface indicates that
P;;”t
XA, = - (8.5- 18)
P
where P is the total pressure.

Example 8.14 One way of measuring the difiion weficients of vapors is to
place a small amount of liquid in a vertical capillary, generally known as the Stefan
diffusion tube, and to blow a gas stream of known composition across the top as
shown in Figure 8.33. Show how one can estimate the digusion coefficient by
observing the decrease in the liquiid-gas interface as a fisnction of time.
T 7

Liquid A u 1

Figure 8.33 The Stefan diffusion tube.