# 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., *x*_{i} *N*^{D}*, **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 *J*_{i} 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 *J*_{A} 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.