The Maxwell-Stefan Equations for Multicomponent Systems

For mixtures containing even more species, n say, we just continue to add similar terms for each additional species. The generalization of Eq. 2.1.11 is 

Equations 2.1.15 are not yet in the form that is most useful to us we eliminate the velocities using the definition of the molar fluxes to get 

These are the Maxy ell-Stefan diffusion equations for multicomponent systems. These equations are named after the Scottish physicist James Clerk Maxwell and the Austrian scientist Josef Stefan who were primarily responsible for their development (Maxwell, 1866, 1952 Stefan, 1871). These equations appeared, in more or less the complete form of Eq. 2.1.15, in an early edition of the Encyclopedia Britannica (incomplete forms had been published earlier) in a general article on diffusion by Maxwell (see Maxwell, 1952). In addition to his major contributions to electrodynamics and kinetic theory. Maxwell wrote several articles for the encyclopedia. Stefan s 1871 paper is a particularly perceptive one and anticipated several of the multicomponent interaction effects to be discussed later in this book. 

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