Enskog equation

Binary Mixtures—Low Pressure—Polar Components The Brokaw correlation was based on the Chapman-Enskog equation, but 0 g and were evaluated with a modified Stockmayer potential for polar molecules. Hence, slightly different symbols are used. That potential model reduces to the Lennard-Jones 6-12 potential for interactions between nonpolar molecules. As a result, the method should yield accurate predictions for polar as well as nonpolar gas mixtures. Brokaw presented data for 9 relatively polar pairs along with the prediction. The agreement was good an average absolute error of 6.4 percent, considering the complexity of some of... 

When the mean free path is small compared with pore diameter, the dominating experience of molecules is that of collision with other molecules in the gas phase. In that respect, the situation is much the same as that which exists in the bulk gas. The appropriate diffusion coefficient Dm may be obtained from published experimental values, or calculated from a theoretical expression. For molecular diffusion in a binary gas, the Chapman and Enskog equation may be used, as discussed by Bird, Stewart and Lightfoot(32). This takes the form ... 

The binary diffusion coefficient, D k, can be either experimentally measured or calculated using the Chapman—Enskog equation. The dependence of the diffusion coefficient on temperature and pressure is generally given by ... 

The Chapman-Enskog equation (see Chapman and Cowling, 1970) is semi-empirical because it uses equation (3.11) and adjusts it for errors in the observations of diffusivity in gases. It also includes a parameter, S2, to account for the elasticity of molecular collisions ... 

Wilke and Lee (1955) found that the Chapman-Enskog equation could not estimate the diffusivity of lower molecular weight compounds, as well as those with a higher molecular weight. They therefore adjusted the constant, p, as follows ... 

The Chapman-Enskog equation missed the measurement by 19% and the Wilke-Lee adjustment by 12%. Both of these are greater than the 8% mentioned previously, but water is a highly polar molecule. 

If not available experimentally, the binary diffusion coefficient, Ay, may also be calculated using elementary kinetic theory (Chapman-Enskog equation proposed by Cussler [61]). A first order approximation for DtJ is given by Yakabe et al., as follows [57] ... 

From a detailed analysis of molecular motion in dilute gases a much better prediction of diffusion coefficients results with the Chapman-Enskog equation. This equation, which describes a mixture of two solutes A and B (binary gas system) is ... 

Use the Chapman-Enskog equation for the binary diffusivity at low density (Eq. 2.72) ... 

This extended Boltzmann equation is called the Enskog equation. 

This operator formulation is similar to the one used in the Enskog equation (2.550). However, the simplifying assumption that the collisions are elastic is not yet introduced making the relation more general (i.e., at this stage g2i is not necessarily equal to g2i). 

Substituting these values in the Chapman-Enskog equation (11-11) gives the bulk diffusivity,... 

Solution a) According-to the procedure of Example 11-1 (the Chapman-Enskog equation), the bulk diffusivity in the isobutane-helium system at 750 mm Hg pressure and 25°C is... 

A similar expansion can be carried out for the inelastic Boltzmann-Enskog equation (Garzo et al, 2007 Jenkins Richman, 1985) to find an approximation for Tp that will be valid when TcoI is much smaller than all other characteristic times of the system. 

The kinetic theory of dilute gases accounts for collisions between spherical molecules in the presence of an intermolecular potential. Ordinary molecular diffusion coefficients depend linearly on the average kinetic speed of the molecules and the mean free path of the gas. The mean free path is a measure of the average distance traveled by gas molecules between collisions. When the pore diameter is much larger than the mean free path, collisions with other gas molecules are most probable and ordinary molecular diffusion provides the dominant resistance to mass transfer. Within this context, ordinary molecular diffusion coefficients for binary gas mixtures are predicted, with units of cm /s, via the Chapman-Enskog equation (see Bird et al., 2002, p. 526) ... 

To predict the deposition rate for a given reactor geometry, the flow equations must be solved to provide information about 8, while more precise values for can be either obtained experimentally, or estimated from correlations such as the Chapman-Enskog equation (Bird et al., 1996). 

Binary gaseous diffusion coefficients are important parameters in the design of reactors for two-phase reactions that involve a gas and a liquid or a solid (either as catalyst or reactant). The recommended equation for low pressures is a modified form of the theoretical Chapman-Enskog equation, but a more readily usable equation is the following modification (Fuller et al., 1966) of the original equation proposed by Gilliland (1934) ... 

This method solves the Enskog equation for a dense gas statistically while keeping the gas transport properties in good agreement with... 

Montanero JM, Santos A (1996) Monte Carlo simulation method for the Enskog equation. Phys Rev E 54 438 144... 

The binary diffusivities are calculated from the Chapman-Enskog equation (7.7-9) are given below ... 

Table 15-2. Lennard-Jones potential parameters and values of the collision integral for ideal Fickian gas diffusivity calculation with Chapman-Enskog equation (15-221 (Cussler. 2009 Hirshfelder et aL,...

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