Binary Diffusion Coefficients for Gases

​
A
O
2
B
CO
2
T (K)
296
p (atm)
1

AB
​(T,P) Contour Plot
Binary diffusion coefficients

AB
at low to moderate pressures (such that the ideal gas behavior is valid) can be predicted with reasonable accuracy (to within about 5% of experimental data) from the kinetic theory of gases using results from the Chapman–Enskog theory based on the Lennard–Jones (6-12) potential[1].
In this Demonstration, you can select a pair of molecules from the pull-down menus and then use the sliders to select a temperature and pressure for the process. The binary diffusion coefficient for the selected gas pair is shown in a

AB
contour plot. You can also view the binary mixture parameters and the molecular parameters for the selected binary mixture.

Details

A brief outline of the formulas used in the calculations is given below. The calculations are based on the Lennard–Jones (6-12) potential:
φ
AB
=4
ϵ
AB

12
σ
AB
r
-
6
σ
AB
r

.
In the above expression,
σ
AB
is called the collision diameter (a measure of the diameter of the molecule), and
ϵ
AB
is the maximum energy of attraction between a pair of molecules. The resulting working equation from Chapman–Enskog kinetic theory for estimating the product of the mixture molar density with binary diffusion coefficient
c

AB
is
c

AB
=2.2646
-5
10
T
1
M
A
+
1
M
B
1
2
σ
AB
Ω
D,AB
,
where
c(mol/
3
cm
)
is the molar density of the binary mixture,
M
i
(g/mol) is the molecular weight of species
i
, and
σ
AB
(Å)
is the binary collision diameter, which is estimated from collision diameter parameters
σ
i
(Å)
using the following mixing rule:
σ
AB
=
1
2
(
σ
A
+
σ
B
)
.
The quantity
Ω
D,AB
is called the collision integral for diffusion and is a function of the reduced temperature
T
R
, defined as
T
R
=
κ
B
T/
ϵ
AB
.
In this expression,
κ
B
is the Boltzmann constant and
ϵ
AB
is the characteristic energy appearing in the Lennard–Jones potential for the binary pair estimated using the mixing rule
ϵ
AB
=
ϵ
A
ϵ
B
,
where the units of
T
are kelvins. For ideal gases, we can estimate
c
as
p/RT
. The resulting binary diffusivity is then given by

AB
=0.0018583
3
T
1
M
A
+
1
M
B
1
p
2
σ
AB
Ω
D,AB
,
where
p
is in atm. In these calculations, a correlation for
Ω
D,AB
as a function of the reduced temperature
T
R
is computed from data (table E.2 in[1]). The molecular parameters for the individual species are taken from table E.1 in[1].

References

[1] R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd ed., New York: John Wiley & Sons, 2002.

Permanent Citation

Brian G. Higgins, Housam Binous
​
​"Binary Diffusion Coefficients for Gases"​
​http://demonstrations.wolfram.com/BinaryDiffusionCoefficientsForGases/​
​Wolfram Demonstrations Project​
​Published: February 21, 2013