Untitled - Aerobib - Universidad Politécnica de Madrid

52 CHAPTER 2. TRANSPORT PHENOMENA IN GAS MIXTURES
Values Ω (2,2)∗ as function of T ∗ for the Lennard-Jones potential have been
taken into Table 2.1. It is seen that for many gases this potential represents experimental
results better than others. 24
For numerical computations it is more convenient to express Eq. (2.44) as
√
MT
10 7 [µ] 1
= 266.93
σ 2 Ω (2,2)∗ (T ∗ ) , (2.47)
where all quantities are measured in the same units than in Eq. (2.17) and [µ] 1
is
expressed in gr cm −1 s −1 .
The preceding formulae show that the viscosity coefficient of a gas is independent
from pressure and increases with temperature slightly over √ T . Fig. 2.6 gives
the law of variation with temperature of viscosity coefficients for several gases. For
additional information, see Refs. [2], [8], [9], [11] and [16], where complementary
bibliography is listed.
7000
6000
O 2
N 2
5000
10 7 µ (g cm −1 s −1 )
4000
3000
2000
CO 2
CH 4
H 2
1000
0
0 200 400 600 800 1000 1200 1400 1600
T(K)
Figure 2.6: Viscosity coefficient as function of temperature, for several gases.
Often, for practical applications an empirical formula of the form
µ ∼ T n (2.48)
is used, where n is an exponent ranging from 0.5 to 1.
With respect to bulk viscosity coefficient µ ′ it is zero for dilute monatomic
gases. For polyatomic and dense gases µ ′ is generally different from zero, yet small.
24 See Ref. [2], pp. 589 and following.