Viscosity collision integral

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... 

Case of General Central Force Law.—The evaluation of the collision integrals for tire viscosity, Eq. (1-89), was simplified for... 

Our previous study (J 6) of self diffusion in compressed supercritical water compared the experimental results to the predictions of the dilute polar gas model of Monchick and Mason (39). The model, using a Stockmayer potential for the evaluation of the collision integrals and a temperature dependent hard sphere diameters, gave a good description of the temperature and pressure dependence of the diffusion. Unfortunately, a similar detailed analysis of the self diffusion of supercritical toluene is prevented by the lack of density data at supercritical conditions. Viscosities of toluene from 320°C to 470°C at constant volumes corresponding to densities from p/pQ - 0.5 to 1.8 have been reported ( 4 ). However, without PVT data, we cannot calculate the corresponding values of the pressure. 

With these parameters, we calculate the values of Tk/e and the collision integrals, and use them in the following equation (Eq. 2.20) for estimating the viscosity ... 

Gas transport properties are required to apply the theory given in Sections 3.3 and 3.4. Viscosities of pure nonpolar gases at low pressures are predicted from the Chapman-Enskog kinetic theory with a Lennard-Jones 12-6 potential. The collision integrals for viscosity and thermal conductivity with this potential are computed from the accurate curve-fits given by Neufeld et al. (1972). 

As a result of the secular growth of the /-body collision integrals with time, we are compelled to conclude that, although the cluster expansion method can be used successfully to derive the Boltzmann equation from the liouville equation and to obtain corrections to the Boltzmann equation, there are serious difficulties in trying to represent these corrections as a power series in the density. An example of the difficulties that appear if one attempts to apply the generalized Boltzmann equation as it stands now to a problem of some interest is provided by the calculation of the density expansion of the coefficient of shear viscosity. By constructing normal solutions to the generalized Boltzmann equation, one finds that the viscosity 17 has the expansion of the form mentioned in Eq. (224),... 

If correlations of a spherical monatomic gas are considered, the dilute-gas effective collision cross sections or collision integrals, evaluated for a specific intermolecular potential, can be substimted directly for calculation of the dilute-gas term. From this point of view, it may not be appropriate to fit dilute-gas thermal conductivity and viscosity... 

The first-order Chapman-Enskog solution of the Boltzmann equation for the viscosity and thermal conductivity of monatomic species are given by the expressions in terms of effective collision cross sections outlined in Chapter 4. However, in order to be consistent with the original papers, here the equivalent expressions in terms of collision integrals are adopted. 

The prediction of the viscosity and thermal conductivity coefficients of the mixtures on purely theoretical grounds is not possible at present, as the interaction viscosity, thermal conductivity, A.md> and the ratios of collision integrals, and cannot be theoretically evaluated in the absence of reliable pair potentials for the monomer-dimer interactions. Similarly, the pure dimer viscosity, n>> and thermal conductivity, A-d, cannot be determined either experimentally or theoretically, without resort to an accurate pair potential for the dimer-dimer interaction. 

However, a data assessment procedure based on the above model is devisable, which is endowed with a fairly sound theoretical basis. Testing the compliance of the data and the mutual consistency of viscosity and thermal conductivity to the outlined nKxlel needs the establishment of a practical procedure. Namely, the collision integrals, or rather their ratios, involving the dimer species will have to be calculated by fitting the model expressions to the experimental data. For this purpose, some further simplifications of the model were necessary ... 

Collision density caused by turbulent motion and expressed in the framework of a discrete numerical scheme ( ) Collision density due to laminar shear Collision integral for viscosity in kinetic theory (—) Eddy-bubble collision rate ( )... 

Wilke (DIPPR) - This is the Wilke mixture viscosity method (Poling, Prausnitz, and O Connell, 2001) using DIPPR pure component values (Daubert et al., 1992) with no collision integrals required... 

In terms of the collision integrals, the viscosity rji of a pure component is given to first approximation by... 

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