Page 104 - Separation process principles 2

3.1 Steady-State, Ordinary Molecular Diffusion 69

Figure 3.1 Concentration profiles for limiting
cases of ordinary molecular diffusion in binary
mixtures across a stagnant film: (a) equimolar
21 z2 Zl z2
Distance, z Distance, z counterdiffusion (EMD); (b) unimolecular
(a) (b) diffusion (UMD).

where in (3-12) and (3-13), ni is the molar flow rate in moles Thus, in the steady state, the mole fractions are linear in dis-
per unit time, A is the mass-transfer area, the first terms on the tance, as shown in Figure 3.la. Furthermore, because c is
right-hand sides are the fluxes resulting from bulk flow, and constant through the film, where
the second terms on the right-hand sides are the ordinary mol-
ecular diffusion fluxes. Two limiting cases are important:
1. Equimolar counterdiffusion (EMD) by differentiation,
2. Unimolecular diffusion (UMD)

Thus,
Equimolar Counterdiffusion
In equimolar counterdiffusion (EMD), the molar fluxes of A
and B in (3-12) and (3-13) are equal but opposite in direc- From (3-3a), (3-3b), (3-15), and (3-22),
tion; thus,

Thus, from (3-12) and (3-13), the diffusion fluxes are also Therefore, DAB = DBA.
equal but opposite in direction: This equality of diffusion coefficients is always true in a
binary system of constant molar density.

This idealization is closely approached in distillation. From
(3-12) and (3-13), we see that in the absence of fluxes other EXAMPLE 3.1
than molecular diffusion, Two bulbs are connected by a straight tube, 0.001 m in diameter
and 0.15 m in length. Initially the bulb at end 1 contains N2 and the
bulb at end 2 contains H2. The pressure and temperature are main-
tained constant at 25OC and 1 atrn. At a certain time after allowing
diffusion to occur between the two bulbs, the nitrogen content of
and
the gas at end 1 of the tube is 80 mol% and at end 2 is 25 mol%. If
the binary diffusion coefficient is 0.784 cm2/s, determine:
(a) The rates and directions of mass transfer of hydrogen and
nitrogen in moVs
If the total concentration, pressure, and temperature are
(b) The species velocities relative to stationary coordinates,
constant and the mole fractions are maintained constant (but
in cmls
different) at two sides of a stagnant film between zl and 22,
then (3-16) and (3-17) can be integrated from zl to any z
between zl and 22 to give SOLUTION

(a) Because the gas system is closed and at constant pressure and
temperature, mass transfer in the connecting tube is equimolar
counterdiffusion by molecular diffusion.
and The area for mass transfer through the tube, in cm2, is A =
3.14(0.1)~/4 = 7.85 x cm2. The total gas concentration (molar
density) is c = & = & = 4.09 x moVcm3. Take the
reference plane at end 1 of the connecting tube. Applying (3-18) to