Chapman-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... 

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) ... 

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... 

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) ... 

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,...

Dw-nh3 s estimated as 0.212 x 10 " m /s from the Chapman-Enskog equation (see spreadsheet in appendix to Chapter 15V... 

Use the Chapman—Enskog equation for the binary diffiisivity at low density (Eqn (2.43)) ... 

The bulk diffusivity Dab is inversely proportional to total pressure and hence becomes significant as pressure increases but does not depend on the pore size. The temperature dependence of Dab is The Chapman-Enskog equation is suitable for accurate estimations of Dab at moderate temperatures and pressures [30]. Knudsen diffusivity D a is directly proportional to the pore radius, and the average molecular velocity as predicted by the kinetic theory of gases, and hence its temperature dependence is Its contribution to Dcomb increases as pore size decreases, but Die)A is independent of total pressure [30]. 

A. molecular diffusivity in gas phase Molecular diffusivity in gas phase may be estimated by the Chapman-Enskog equation. For a mixture of components 1 and 2,... 

This is the proof of the variational principle that Eq. 93 gives the solution of the Chapman-Enskog equation. The variational principle given in the form of Eq. 93 is much more convenient for practical purposes, because we need not consider restrictions other than simple ones such as the auxiliary conditions, Eqs. 70, 71, and 72. In the case of thermal conduction in a simple gas, Eq. 93 reduces to... 

The pure component low pressure viscosity is predicted from the Chapman-Enskog equation which includes the effect of intermolecular forces. The equation for the viscosity rj is ... 

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