Multicomponent diffusion equation

The balance over the ith species (equation IV. 5) consists of contributions from diffusion, convection, and loss or production of the species in ng gas-phase reactions. The diffusion flux combines ordinary (concentration) and thermal diffusions according to the multicomponent diffusion equation (IV. 6) for an isobaric, ideal gas. Variations in the pressure induced by fluid mechanical forces are negligible in most CVD reactors therefore, pressure diffusion effects need not be considered. Forced diffusion of ions in an electrical field is important in plasma-enhanced CVD, as discussed by Hess and Graves (Chapter 8). 

Despite these differences both solutions of the multicomponent diffusion equations will give identical results if... 

In the literature the net momentum flux transferred from molecules of type s to molecules of type r has either been expressed in terms of the average diffusion velocity for the different species in the mixture [77] or the average species velocity is used [96]. Both approaches lead to the same relation for the diffusion force and thus the Maxwell-Stefan multicomponent diffusion equations. In this book we derive an approximate formula for the diffusion force in terms of the average velocities of the species in the mixture. The diffusive fluxes are introduced at a later stage by use of the combined flux definitions. 

It may be shown that this equation is equivalent to the phenomenological equations derived from irreversible thermodynamics, as weU as the multicomponent diffusion equations derived from the Stefan-Maxwell equations, which were first used to describe diffusion in multicomponent gases. 

The foundation of concentrated solution theory is the Stefan-Maxwell multicomponent diffusion equation [16,17],... 

Solution The chemical reaction produces a ternary mixture of ethane, ethylene, and hydrogen. Such a mixture may require consideration of the multicomponent diffusion equations in Chapter 7. However, if conversion is low, the diffusion coefficient... 

Nonetheless, some concentrated systems are best described using multicomponent diffusion equations. Examples of these systems, which commonly involve unusual chemical interactions, are listed in Table 7.0-1. They are best described using the equations derived in Section 7.1. These equations can be rationalized using the theory of irreversible thermodynamics, a synopsis of which is given Section 7.2. In most cases, the solution to multi-component diffusion problems is automatically available if the binary solution is available the reasons for this are given in Section 7.3. Some values of ternary diffusion coefficients are given in Section 7.4 as an indication of the magnitude of the effects involved. Finally, tracer diffusion is detailed as an example of ternary diffusion in Section 7.5. 

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