Page 116 - Separation process principles 2

3.2 Diffusion Coefficients 81

Differentiating (2) with respect to time, For both hydrogen and helium, diffusivities increase rapidly
with increasing temperature. At ambient temperature the
diffusivities are three orders of magnitude lower than in liq-
uids. At elevated temperatures the diffusivities approach
Combining (1) and (3):
those observed in liquids. Solubilities vary only slowly with
temperature. Hydrogen is orders of magnitude less soluble
in glass than helium. For hydrogen, the diffusivity is some-
Integrating and solving for t,
what lower than in metals. Diffusivities for oxygen are also
included in Table 3.11 from studies by Williams [17] and
Sucov [18]. At lOOO"C, the two values differ widely be-
Assuming the ideal-gas law, cause, as discussed by Kingery, Bowen, and Uhlmann [19],
(200/14.7)[(3.14 x 103)/6)] in the former case, transport occurs by molecular diffusion;
n~~ = = 0.1515 mol
82.05(300 + 273) while in the latter case, transport is by slower network diffu-
sion as oxygen jumps from one position in the silicate net-
The mean-spherical shell area for mass transfer, A, is
work to another. The activation energy for the latter is much
3.14
=
A = -[(10)~ + (10.635)~~ 336 cm 2 larger than for the former (71,000 cal/mol versus 27,000
2
cal/mol). The choice of glass can be very critical in high-
The time for the pressure to drop to 100 psia is
vacuum operations because of the wide range of diffusivity.
Ceramics
Diffusion rates of light gases and elements in crystalline
ceramics are very important because diffusion must precede
Silica and Glass
chemical reactions and causes changes in the microstructure.
Another area of great interest is the diffusion of light gases Therefore, diffusion in ceramics has been the subject of
through various forms of silica, whose two elements, Si and numerous studies, many of which are summarized in
0, make up about 60% of the earth's crust. Solid silica can Figure 3.4, taken from Kingery et al. [19], where diffusivity
exist in three principal crystalline forms (quartz, tridymite, is plotted as a function of the inverse of temperature in the
and cristobalite) and in various stable amorphous forms, high-temperature range. In this form, the slopes of the
including vitreous silica (a noncrystalline silicate glass or curves are proportional to the activation energy for diffu-
fused quartz). Table 3.11 includes diffusivities, D, and solu- sion, E, where
bilities as Henry's law constants, H, at 1 atm for helium and
hydrogen in fused quartz as calculated from correlations of
experimental data by Swets, Lee, and Frank [15] and Lee
[16], respectively. The product of the diffusivity and the sol- An insert at the middle-right region of Figure 3.4 relates the
ubility is called the permeability, PM. Thus, slopes of the curves to activation energy. The diffusivity
curves cover a ninefold range from to 10-l5 cm2/s,
with the largest values corresponding to the diffusion of
Unlike metals, where hydrogen usually diffuses as the
potassium in P-A1203 and one of the smallest values for car-
atom, hydrogen apparently diffuses as a molecule in glass.
bon in graphite. In general, the lower the diffusivity, the
higher is the activation energy. As discussed in detail by
Kingery et al. [19], diffusion in crystalline oxides depends
Table 3.11 Diffusivities and Solubilities of Gases in Amorphous
not only on temperature but also on whether the oxide is stoi-
Silica at 1 atm
chiometric or not (e.g., FeO and Feo,9s0) and on impurities.
Gas Temp, C Diffusivity, cm2/s Solubility mol/cm3-atm Diffusion through vacant sites of nonstoichiometric oxides
is often classified as metal-deficient or oxygen-deficient.
Impurities can hinder diffusion by filling vacant lattice or
interstitial sites.

Polymers
6.49 x
Thin, dense, nonporous polymer membranes are widely
9.26 x
used to separate gas and liquid mixtures. As discussed in
6.25 x
detail in Chapter 14, diffusion of gas and liquid species
(molecular)
through polymers is highly dependent on the type of poly-
9.43 10-l5
mer, whether it be crystalline or amorphous and, if the latter,
(network)
glassy or rubbery. Commercial crystalline polymers are