Physical derivation of the multicomponent diffusion equation

This change in momentum of species i is manifest in changes in both the random velocity and the order velocity of the molecules. The rate of change of the ordered momentum is pY-Dy /Dt, where the substantial derivative with respect to time is 

Since (neglecting the off-diagonal elements of the pressure tensor ) the partial 

Under the assumption that the translational temperatures of all species, are the same, equations (D-9), (D-20), and (D-22) show that Dalton s law of partial pressures is valid, that is, 

The product in equation (11) may be related to the binary diffusion coefficients by considering the limiting case of a constant-pressure process in a two-component system with no body forces, for which equation (11) reduces to 

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