# 2.3 Fluxes That Comprise Total Diffusion Flux

Graham’s (1833) experiments clearly demonstrate that the components of a binary gas at uniform pressure in a porous medium diffuse at different rates in general. Consequently, the sum of the total diffusive fluxes of the individual components, , is not zero. Rather, this sum contributes to the motion of the fluid as a whole—a feature of diffusion in porous solids that is not observable in systems free of solid obstructions. We refer to this net diffusive flux as the non-equimolar flux (Cunningham and Williams, 1980) and write Equation 5.

 (5)

Similar to the viscous flux, the non-equimolar flux imparts motion to the individual species in the mixture by advection (i.e., xi ND, i = A, B), but is distinguished from advection via a viscous flux by the fact it arises solely as a result of diffusion. The sum of advection by the non-equimolar flux and by the viscous flux is the total advection by the phase motion.

The increment of motion for component i that is in addition to advection via the phase motion is the equimolar diffusion flux Ji defined by Equation 6.

 , (6)

Because equimolar diffusion makes no net contribution to motion of the phase, we have Equation 7.

 (7)

Equation 7 expresses a condition that holds under all circumstances treated in this book.

It is common to rearrange Equation 6 so that the mole flux is expressed as the sum of the equimolar and advection fluxes as in Equation 8a for constituent A. We may then express the flux of component A by any one of Equations 8a through 8d. The subscripts can be interchanged to obtain the equivalent expressions for component B.

 (8a)
 (8b)
 (8c)
 (8d)

The reader is encouraged to become thoroughly familiar with these definitional equations and the various forms they may take. For example, if there is no viscous flux then , and Equation 8d becomes Equation 9.

 (9)

Rearranging and solving for JA gives Equation 10.

 (10)

This is in the form of a Stefan-Maxwell equation for a binary gas that we soon will have occasion to use in our calculations.