Page 105 - Separation process principles 2

70 Chapter 3 Mass Transfer and Diffusion

N2 over the length of the tube, The factor (1 - xA) accounts for the bulk-flow effect. For a
mixture dilute in A, the bulk-flow effect is negligible or
small. In mixtures more concentrated in A, the bulk-flow
effect can be appreciable. For example, in an equimolar
mixture of A and B, (1 - xA) = 0.5 and the molar mass-
transfer flux of A is twice the ordinary molecular-diffusion
= 9.23 x molls in the positive z-direction
flux.
nH2 = 9.23 x moVs in the negative z-direction
For the stagnant conlponent, B, (3-13) becomes
(b) For equimolar counterdiffusion, the molar-average velocity of
the mixture, UM, is 0. Therefore, from (3-9), species velocities are
equal to species diffusion velocities. Thus,

Thus, the bulk-flow flux of B is equal but opposite to its
I
0.0287 diffusion flux.
-- in the positive z-direction
-
At quasi-steady-state conditions, that is, with no accumu-
xN2
lation, and with constant molar density, (3-27) becomes in 1
Similarly, integral form: I
0.0287
= -
in the negative z-direction
XH2
Thus, species velocities depend on species mole fractions, as I
which upon integration yields
follows: I
,
Z, cm XN1 -%I VN* , CII~/S VH~ cm/s
0 (end 1) 0.800 0.200 0.035 1 -0.1435
5 0.617 0.383 0.0465 -0.0749
Rearrangement to give the mole-fraction variation as a func-
10 0.433 0.567 0.0663 -0.0506
tion of z yields
15 (end 2) 0.250 0.750 0.1148 -0.0383
Note that species velocities vary across the length of the connect- XA = 1 - (1 - XA~) exp [NA2biZ1)] (3-32)
ing tube, but at any location, z, VM = 0. For example, at z = 10 cm,
from (3-8),
Thus, as shown in Figure 3.lb, the mole fractions are non-
linear in distance.
An alternative and more useful form of (3-31) can be
derived from the definition of the log mean. When z = 22,
(3-3 1) becomes
Unimolecular Diffusion

In unimolecular diffusion (UMD), mass transfer of compo-
nent A occurs through stagnant (nonmoving) component B.
Thus,
The log mean (LM) of (1 - xA) at the two ends of the stag-
NB = 0 (3 -24) nant layer is

and
N = NA (3-25)
Therefore, from (3- 12),

Combining (3-33) with (3-34) gives

which can be rearranged to a Fick's-law form,