Discussion and recommendations to estimate the lowpressure viscosity of gas mixtures

As is obvious from the estimation methods discussed in this section, the viscosity of a gas mixture can be a complex function of composition. This is evident from Fig. 9-4. There may be a maximum in mixture viscosity in some cases, e.g., system 3, ammonia-hydrogen. No cases of a viscosity minimum have, however, been reported. Behavior similar to that of the ammonia-hydrogen case occurs most often in polar-nonpolar mixtures in which the pure component viscosities are not greatly different [101, 172], Maxima are more pronounced as the molecular weight ratio differs from unity.

Of the five estimation methods described in this section, three (Herning and Zipperer, Wilke, and Reichenberg) use the kinetic theory approach and yield interpolative equations between the pure component viscosities. Reichenberg's method is most consistently accurate, but it is the most complex. To use Reichenberg's procedure, one needs, in addition to temperature and composition, the viscosity, critical temperature, critical pressure, molecular weight, and dipole moment of each constituent. Wilke's and Herning and Zipperer's methods require only the pure component viscosities and molecular weights; these latter two yield reasonably accurate predictions of the mixture viscosity.

Arguing that it is rare to have available the pure gas viscosities at the temperature of interest, both Lucas and Chung et al. provide estimation methods to cover the entire range of composition. At the end points where only pure components exist, their methods reduce to those described earlier in Sec. 9-3. Although the errors from these two methods are, on the average, slightly higher than those of the interpolative techniques, they are usually less than ± 5 percent as seen from Table 9-4. Such errors could be reduced even further if pure component viscosity data were available and were employed in a simple linear correction scheme.

Many other estimation methods for determining i)m have been proposed [25, 26, 33, 54, 75, 90, 97, 118, 119, 174, 191, 192, 207, 225], but they were judged either less accurate or less general than those discussed in this section.

It is recommended that Reichenberg's method [Eq. (9-5.8)] be used to calculate i}m if pure component viscosity values are available. Otherwise, either the Lucas method [Eq. (9-4.15)] or the Chung et al. method [Eq. (9-5.24)] can be employed if critical properties are available for all components.

A compilation of references dealing with gas mixture viscosities (low and high pressure) has been prepared by Sutton [193].

9-6 Effect of Pressure on the Viscosity of Pure Gases

The viscosity of a gas is a strong function of pressure near the critical point and at reduced temperatures of about 1 to 2 at high pressures. The complexity of the T-P-tj phase diagram is seen in Figs. 9-5 and 9-6 [188]. In Fig. 9-5, the viscosity of carbon dioxide is graphed as a function of temperature with various isobars shown; for C02, Tc = 304.1 K and Pc - 73.8 bar. If the viscosity were plotted as a function of pressure with isotherms, one would have a phase diagram as illustrated in Fig. 9-6 for nitrogen (Tc = 77.4 K, Pc = 33.9 bar). Lucas [136, 137] has generalized the viscosity phase diagrams (for nonpolar gases) as shown in Fig. 9-7. In this case the ordinate is and the temperatures and pressures are reduced values. £ is the inverse reduced viscosity defined earlier in Eq. (9-4.14).

In Fig. 9-7, the lower limit of the Pr curves would be indicative of the dilute gas state, as described in Sec. 9-4. In such a state, tj increases with temperature. At high reduced pressures, we see there is a wide range of temperatures where 77 decreases with temperature. In this region the viscosity behavior more closely simulates a liquid state, and, as will be shown in Sec. 9-10, an increase in temperature results in a decrease in viscosity.

Viscosity Stephan And Lucas

200 300 400 500 600 700 800 900 Temperature, K

Figure 9-5 Viscosity of carbon dioxide. (From Stephan and Lucas, Ref. 188.)

200 300 400 500 600 700 800 900 Temperature, K

Figure 9-5 Viscosity of carbon dioxide. (From Stephan and Lucas, Ref. 188.)

Finally, at very high reduced temperatures, there again results a condition in which pressure has little effect and viscosities increase with temperature.

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  • shishay
    How do you calculate viscosity of mixtures of gases,?
    8 years ago
  • caramella
    Is the viscosity of gas function of pressure or temperature?
    7 years ago

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