Diffusion theory binary term derivation

In reactor modeling only the ordinary concentration diffusion term j° is generally considered. The rigorous kinetic theory model derivation for multi-component mixtures is outlined in chap 2. Meanwhile, the Tick s law for binary systems is used. 

The ordinary kinetics theory of neuter gas, the Boltzmann equation is considered with collision term for binary collisions and is despised the body s force F . This simplified Boltzmann equations is an integro - differential non lineal equation, and its solution is very complicated for solve practical problems of fluids. However, Boltzmann equation is used in two important aspects of dynamic fluids. First the fundamental mechanic fluids equation of point of view microscopic can be derivate of Boltzmann equation. By a first approximation could obtain the Navier-Stokes equations starting from Boltzmann equation. The second the Boltzmann equation can bring information about transport coefficient, like viscosity, diffusion and thermal conductivity coefficients (Pai, 1981 Maxwell, 1997). 

Rates of binary O2/N2 diffusion in CMS s were also reported by Chen et al. (1994). It was found that the cross-term diffusivities. Ay, are quite significant, hence the diffusion rates cannot be predicted by approximating the system as pure component diffusion. A simple kinetic theory is derived in Chapter 3 for predicting binary (or mixture) diffusion from pure-component diffusivities (Chen and Yang, 1992). The concentration dependence of the pure component diffusivities are needed for this prediction. Figure 5.26 compares the rates predicted by the kinetic model with experimental data. Also shown are results predicted from pure component diffusivities. It is clear that pure component diffusivities cannot be used for predicting rates for binary diffusion. A statistical theory by MacElroy et al. (1997) has also been used to predict binary diffusion in CMS s with satisfactory results. 

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