Page 560 - Bird R.B. Transport phenomena

540 Chapter 17 Diffusivity and the Mechanisms of Mass Transport

17A.6. Diffusivity and Schmidt number for chlorine-air mixtures.
(a) Predict ЯЬ for chlorine-air mixtures at 75°F and 1 atm. Treat air as a single substance
АВ
with Lennard-Jones parameters as given in Appendix E. Use the Chapman-Enskog theory re-
sults in §17.3.
(b) Repeat (a) using Eq. 17.2-1.
(c) Use the results of (a) and of Problem 1A.5 to estimate Schmidt numbers for chlorine-air
mixtures at 297K and 1 atm for the following mole fractions of chlorine: 0, 0.25, 0.50, 0.75, and
1.00.
2
2
Answers: (a) 0.121 cm /s; (b) 0.124 cm /s; (c) Sc = 1.27, 0.832,0.602,0.463,0.372
17A.7. The Schmidt number for self-diffusion at high density.
(a) Use Eqs. 1.3-lb and 17.2-2 to predict the self-diffusion Schmidt number Sc = ц/рЧЬ * at
АЛ
the critical point for a system with M ~ M *.
A A
(b) Use the above result, along with Fig. 1.3-1 and Fig. 17.2-1, to predict Sc = jx/p4b * at the
AA
following states:
Phase Gas Gas Gas Liquid Gas Gas
T, 0.7 1.0 5.0 0.7 1.0 2.0
0.0 0.0 0.0 saturation 1.0 1.0
Vr

17A.8. Correction of high-density diffusivity for temperature. The measured value 3 of c%b AB for a
mixture of 80 mole% CH and 20 mole% C H at 313K and 136 atm is 6.0 X 10" 6 g-mol/cm • s
4 2 6
(see Example 17.2-3). Predict сЯЬ for the same mixture at 136 atm at 351K, using Fig. 17.2-1.
АВ
6
Answer: 6.3 X 10" g-mole/cm • s
Observed: 3 6.33 X 10~ g-mol/cm • s
6
17A.9. Prediction of critical сЯЬ values. Figure 17.2-1 gives the low-pressure limit (c£b AA*) r = 1.01
АВ
at T r = 1 and p r -> 0. At this limit, Eq. 17.2-13 gives
) c = 2.2646 X 10- 5 IT CA - L + - U — - 1 (17A.9-1)
(
\ \м м */ oiv ut *
А А JrAA
Here the argument кТ /е * of П^, * is reported 4 as = 1.225 for Ar, Kr, and Xe. We use the
АА
сА
AA
value 1/0.77 from Eq. 1.4-lla as a representative average over many fluids.
(a) Combine Eq. 17A.9-1 with the relations
* . = 2.ЩТ /р У /3 е >/к = 0.77T cA (17A.9-2,3)
сА
АА
AA
сА
and Table E.2 to obtain Eq. 17.2-2 for (d& *) c
AA
(b) Show that the approximations
(TAB = Vo^o-g e = Ve A£ B (17A.9-4,5)
AB
for Lennard-Jones parameters for the A-B interaction give
IT T V /6 F
2
a AB = .441-p-^-l — = 0.77VT cAT cB (17A.9-6,7)
when Eqs. 17A.9-2, 3 (with A* replaced by B) are inserted. Combine these expressions with
Eq. 17A.9-1 (with A* replaced by В and T cA by VT T ) to obtain Eq. 17.2-3 for (сЯЬ \. The
cA
АВ
cB
corresponding replacement of p c and T in Fig. 17.2-1 by \Zp p B an< ^ ^T T cB amounts to re-
C
cA
c
cA
garding the A-B collisions as dominant over collisions of like molecules in determining the
value of сЯЬ .
АВ
3
V. J. Berry and R. С Koeller, AIChE Journal, 6, 274-280 (1960).
4
J. J. van Loef and E. G. D. Cohen, Physica A, 156, 522-533 (1989).