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44 CHAPTER 2. TRANSPORT PHENOMENA IN GAS MIXTURES
Let (ε 1 , σ 1 ) and (ε 2 , σ 2 ) be the values of the constants for species A 1 and A 2 .
The values of the constants for mixed potentials between both species are 11
ε 12 = √ ε 1 ε 2 ,
σ 12 = 1 2 (σ 1 + σ 2 ) .
(2.21)
Table 1.1 in chapter 1 gives the values of ε and σ for certain number of gases. If such
values where not available any of the following formulas can be used for approximate
values [7]:
ε/k = 0.77T c , σ = 0.710(V c /N) 1 3 ,
ε/k = 1.15T b , σ = 0.984(V b /N) 1 3 ,
(2.22)
ε/k = 1.92T m , σ = 1.031(V m /N) 1 3 ,
ε/k = 0.292T B , σ = 1.030(V z /N) 1 3 .
Here V is the molar volume. Subscripts c, m, b, B and z denote the critical, melting,
boiling, Boyle’s 12 and absolute zero points.
Table 2.2, taken from Ref. [2], gives the diffusion coefficients for some binary
mixtures. Theoretical values correspond to a Lennard-Jones interaction potential.
Constants for the potential have been obtained through Eq. (2.21). It is seen that
agreement between theoretical and experimental values is, generally, excellent.
Except for rigid spheres where Ω (1,1)∗
12 is constant, this function decreases when
T is increased. Hence, according to formula (2.15) [D 12 ] 1
increases with T slightly
faster than T 3/2 . Fig. 2.3 represents as an example the coefficient [D 12 ] 1
versus T in
a mixture of N 2 and CO 2 for rigid spheres and for an interaction potential of Lennard-
Jones. In combustion problems, where temperature can change in a ratio of ten to one
from one point to another, the influence of temperature on the values of the transport
coefficients is very important. Formula (2.15) shows, as well, that diffusion coefficient
is inversely proportional to the mixture’s pressure and is independent from the mass
fractions of the species in first approximation. In order to obtain the influence of mass
fractions one must resort to higher approximations.
11 See Ref. [2], pp. 589 and following
12 Boyle’s temperature T B is the temperature at which curve pV vs. p has a horizontal tangent for p = 0.