Untitled - Aerobib - Universidad Politécnica de Madrid

46 CHAPTER 2. TRANSPORT PHENOMENA IN GAS MIXTURES
4.0
3.5
3.0
2.5
[D 12
] 1
2.0
1.5
1.0
Rigid spheres
Lennard−Jones potential
0.5
0.0
0 200 400 600 800 1000 1200 1400 1600 1800 2000
T(K)
Figure 2.3: Coefficient [D 12] 1
as a function of temperature in a mixture of N 2 and CO 2, for
rigid spheres and for an interaction potential of Lennard-Jones.
Hence, the influence of mass fractions on the value of D 12 is always small and
can, generally, be neglected by adopting for it the value given by the first approximation.
Frequently, the value given by elementary diffusion theory is approximate
enough. According to it,
D 12 ∼ T 3/2
p . (2.24)
Or else, an empirical formula of the form
D 12 ∼ T n
p , (2.25)
where n is an exponent ranging from 1.5 to 2 whose value is determined empirically.
With respect to thermal diffusion ratio k T , even in the first approximation it is
a complicated function of the molar masses, mass fractions of the species and of the
temperature of the mixture. It is also very much influenced by the laws of molecular
interaction. The expression of the first approximation of k T can be obtained from
Ref. [2], p. 541, where tables for the calculation of their values are also included as
well as a comparison between theoretical and experimental values for many binary
mixtures. It appears that the agreement is not so good for k T as for the other transport
coefficients. When comparing the successive approximations to the value of k T , it is
also verified that in first approximation the error is larger here than for other transport