Brief Discussion on Species Diffusion

To derive the species-continuity equations that follow, it is important to establish some relationships between mass fluxes and species concentration fields. At this point the needed relationships are simply stated in summary form. The details are discussed later in chapters on thermochemical and transport properties. 

Working with multicomponent mixtures requires quantifying the amounts of various chemical constituents that comprise the mixture. In the conservation equations a mass fraction will be the most appropriate measure, since mass is a conserved quantity. By definition, the mass fraction is 

Chemical behaviors, such as chemical reactions, are usually best quantified on a molar basis. That is, a certain number of moles of one species reacts with a certain number of moles of another to produce a certain amount of product species. Here a mole fraction, not a mass fraction, is the most appropriate measure of the mixture composition. The mole fraction is the number of moles of species k in a volume divided by the total moles in the volume. For a perfect gas, the mole fraction is related to mass fraction as 

The molar concentration [X ] is the measure of chemical composition that is most natural for the description of chemical reaction. For a perfect gas it is given as 

The partial pressure of a species in an ideal-gas mixture is equivalent to the mole fraction. Thus 

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