Second transport virial coefficient

Recent advances in the theoretical description of the initial density dependence of the transport properties justify a separate treatment. If moderately dense gases are considered, only the linearized equations (5.1) are needed that is, the virial form of the density expansion can be truncated after the term linear in density. This means that the deviation from the dilute-gas behavior can be represented by the second transport virial coefficients Bx or alternatively by the initial-density coefficients which are... 

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.

The expressions for the transport coefficients given by Enskog theory (equations (5.2)-(5.4)) lead to the following results for the second transport virial coefficients... 

The first density correction for viscosity and for the translational part of the thermal conductivity is best predicted by the Rainwater-Friend model, for which values for the reduced second transport virial coefficients are given in Table 5.1. For computer codes the tabulated values can be approximated using the correlation... 

Hoffman, D. K. Curtiss, C. F. (1965). Kinetic theory of dense gases. V. Evaluation of the second transport virial coefficients. Phys. Fluids, 8,890-895. 

The viscosity, themial conductivity and diffusion coefficient of a monatomic gas at low pressure depend only on the pair potential but through a more involved sequence of integrations than the second virial coefficient. The transport properties can be expressed in temis of collision integrals defined [111] by... 

Miscellaneous Generalized Correlations. Generalized charts and corresponding states equations have been pubhshed for many other properties in addition to those presented. Most produce accurate results over a wide range of conditions. Some of these properties include (/) transport properties (64,91) (2) second virial coefficients (80,92) (J) third virial coefficients (72) (4) Hquid mixture activity coefficients (93) (5) Henry s constant (94) and 6) diffusivity (95). 

A key question about the use of any molecular theory or computer simulation is whether the intermolecular potential model is sufficiently accurate for the particular application of interest. For such simple fluids as argon or methane, we have accurate pair potentials with which we can calculate a wide variety of physical properties with good accuracy. For more complex polyatomic molecules, two approaches exist. The first is a full ab initio molecular orbital calculation based on a solution to the Schrddinger equation, and the second is the semiempirical method, in which a combination of approximate quantum mechanical results and experimental data (second virial coefficients, scattering, transport coefficients, solid properties, etc.) is used to arrive at an approximate and simple expression. 

It is more usual with closed-shell atoms to consider potential models such as the exchange-Coulomb and Hartree-Fock dispersion potentials and to determine the parameters from dilute gas properties such as the second virial coefficient and the transport properties, viscosity and thermal conductivity, together with... 

Fig. 10. A plot of the reduced second virial coefficient B (T ) = vs T, where T = k T/e. The quantities a and e are the length and energy scaling factors determined using the hypothesis that the law of corresponding states is valid. [From J. Kestin and E. A. Mason, in Transport Phenomena (J.

The determination of accurate intermolecular potentials has been a key focus in the understanding of collision and half-collision dynamics, but has been exceedingly difficult to obtain in quantitative detail for even the simplest molecular systems. Traditional methods of obtaining empirical intermolecular potential information have been from analysis of nonideal gas behavior, second virial coefficients, viscosity data and other transport phenomena. However, these data sample highly averaged collisional interactions over relative orientations, velocities, impact parameters, initial and final state energies, etc. As a result intermolecular potential information from such methods is limited to estimates of the molecular size and stickiness, i.e., essentially the depth and position of the energy minimum for an isotropic well. 

To calculate a trajectory requires knowledge of the intermolecular potential, which is not readily measured. To circumvent this difficulty a guess is made as to the form of the potential which is then used to compute the transport coefficients, the second virial coefficient, and a few other properties dependent upon two-particle interaction only. Good agreement between theory and experiment provides a posteriori justification for the assumed potential. A simple model potential was suggested by Lennard-Jones. It is... 

Theoretical expressions for the reduced viscosity and thermal conductivity second virial coefficients are presented in Section 5.3. An important contribution arises from the effect of the formation of dimers, even though the concentration of dimers is still small. For the evaluation of these transport property virial coefficients it was assumed that both the interaction potential between two monomers and between a monomer and a dimer is of the Lennard-Jones (12-6) form but with different potential parameters. The ratios of these parameters, which are characterized by the constants 8 and 6 defined in Section 5.3, are determined from a large selection of experimental data. According to Stogryn Hirschfelder (1959), the mole fraction of dimers in argon is 0.2% at 0.1 MPa and 200 K, while this fraction reduces to 0.04% when the temperature rises to 600 K. 

To obtain numerical values for the parameters c and macroscopic property, typically vapor phase volumetric behavior, as expressed through the second virial coefficient and transport properties, such as viscosity and diffiisivity. Values for several compounds are given by Reid et al. 

The Lennard-Jones potential represents an approximation, even for simple molecules. As a result, different sets of parameter values are obtained from second virial coefficient data and from transport properties data and the discrepancy increases, for the aforementioned reasons, as the deviation from the simple molecule concept becomes larger (Hirsch-felder et al, 1954). 

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