Page 666 - Bird R.B. Transport phenomena

646 Chapter 20 Concentration Distributions with More Than One Independent Variable

100,000

10,000
Taylor's
solution in
Eq. 20.5-15
1000

Q S
ll 13
Ей 100

Taylor solution :
with Aris 1 ;
modification ;
10 = Equations
I (48) and (50) \ in Eq. 20.5-15 \
: of Ref. 6

diffusion
0.01 0.1 1.0 10 100
Dimensionless time
® AB t/R 2
Fig. 20.5-2. Sketch showing the limits of the Taylor (Eq. 20.3-15)
and Aris (Eq. 20.5-19) expressions for the axial dispersion
coefficient. This figure is patterned after one in Ref. 6.

is an important extension of Eq. 20.5-15. From this result, we see that molecular diffusion
enhances the axial dispersion when the Peclet number Pe = R(v )/^ AB is less than V48
z
and inhibits axial dispersion at larger Peclet numbers, where Taylor's mode of transport
predominates.
The ranges of validity of the Taylor and Aris dispersion formulas have been studied
6
7
thoroughly by finite difference calculations and by orthogonal collocation. Figure 20.5-
2 shows the useful ranges of Eq. 20.5-15 and 19. The latter formula has been widely used
8
for measurements of binary diffusivities, and an extension of it has been used to mea-
sure ternary diffusivities in liquids.
Several further investigations on convective dispersion will be mentioned here.
Coiled tubes give reduced longitudal dispersion, as shown by the experiments of Koutsky
and Adler 9 and analyzed for laminar flow by Nunge, Lin, and Gill. This effect is impor-
10
tant in chemical reactor design and in diffusivity measurements, where coiling is often
necessary to get enough tube length into a compact apparatus.
Extra-column dispersion, caused by the pump and connecting tubing of chromato-
graphic systems, was investigated by Shankar and Lenhoff 11 with detailed predic-

V. Ananthakrishnan, W. N. Gill, and A. J. Barduhn, AlChE Journal 11,1063-1072 (1965).
6
7
J. C. Wang and W. E. Stewart, AIChE Journal, 29,493-497 (1983).
Ph. W. M. Rutten, Diffusion in Liquids, Delft University Press, Delft, The Netherlands (1992).
8
J. A. Koutsky and R. J. Adler, Can. J. Chem. Eng., 42, 239-246 (1964).
4
10
R. J. Nunge, T. S. Lin, and W. N. Gill, /. Fluid Mech., 51,363-382 (1972).
11
A. Shankar and A. M. Lenhoff, /. Chromatography, 556, 235-248 (1991).