Rainwater-Friend theory

For the exact evaluation of the two-monomer contribution Bf the Rainwater-Friend theory includes results from the kinetic theory of dense gases (see, for example, Cohen 1969), which means that direct kinetic as well as collisional transfer effects are considered. In order to calculate reliable values for B Rainwater (1984) extended earlier results of Snider Curtiss (1958), Hoffman Curtiss (1965) and Bennett Curtiss (1969) so that the dynamics of the two particles for a more realistic potential (here the Lennard-Jones (12-6) potential) were included. At the same time, the effects of bound states have been excluded from the evaluation of the complicated set of integrals that defines the two-monomer contribution (see Rainwater 1984). 

Table 5.1. Reduced second transport virial coefficients and chemical reaction contribution according to the Rainwater-Friend theory for monatomic fluids. Reduced internal contribution for polyatomic gases according to MET-I.

Fig. 5.3. The reduced second viscosity virial coefficient as a function of reduced temperature. Curves 1 - Rainwater-Friend theory (S = 1.04 and 9 = 1.25) 2 - Rainwater-Friend theory (5 = 1.02 and 6> = 1.15) 3 - MET-I.

This procedure based on the Rainwater-Friend theory is valid only for reduced temperatures T > 0.7 (T = 175 K for ethane). This lower limit will not be exceeded by the viscosity representation of ethane in the vapor phase, since the range of validity of its zero-density contribution has a lower limit of T = 2(X) K. Nevertheless, experimental data in the liquid phase are available at much lower temperatures extending to T = 100 K. In order to use a single overall viscosity correlation it must be ensured that the initial-density contribution extrapolates satisfactorily to low temperatures. For this purpose, for temperatures below T = 0.7, the second viscosity virial coefficient has been estimated by use of the modified Enskog theory (see Chapter 5), which relates B,f to the second and third pressure virial coefficients. Although this method enables Brj to be evaluated, it is cumbersome for practical applications. Therefore, the calculated B, values using both methods have been fitted to the functional form... 

The Rainwater-Friend theory that has proved so successful in the representation of the initial-density dependence of the viscosity of pure gases has not been extended to mixtures. It is therefore necessary to make use of the Thome-Enskog equations... 

In general, there are two methods that can be applied in order to describe Bx(T) (x = T], X) The most up-to-date theory, proposed by Friend Rainwater (1984 Rainwater Friend 1987), models the moderately dense gas as a mixture of monomers and dimers which interact according to the Lennard-Jones (12-6) potential. Besides the fact that this potential is only a rough approximation of the real physical situation, this model has the disadvantage that it has not yet been extended to describe the internal contribution to the initial density dependence of thermal conductivity. 

The initial density dependence of the thermal conductivity of a polyatomic gas is given by expression (5.7). Neither the Rainwater-Friend model nor the modified Enskog theory accounts for the contribution of internal degrees of freedom, but it is assumed that this can be modeled as a purely diffusive process following an idea originally introduced by Mason Monchick (1962) for dilute gases... 

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