2 Definition of Fluxes

Key to the understanding and analysis of diffusion is the careful consideration of the various fluxes involved in the transport processes. In general, the flux of some entity is the quantity of that entity that passes through a unit area per unit time, the unit area being oriented normal to the direction of the flux. Because we are working with porous media, the area referred to here is the bulk or total area. The bulk area is generally comprised of portions occupied by solids, liquids, and gas. Flux defined in this way is a macroscopic quantity in the same sense that specific discharge of groundwater is a macroscopic quantity.

Flux can be in reference to many different entities (e.g., electrical current, energy, heat, water, and other entities that are commonly transported). We will have occasion to use fluxes that reference volume, mass, moles and momentum, but we have selected moles of gas as our reference quantity for calculating flux and concentration in the central developments of this book. Developments entirely parallel to those in this book can be made using mass flux and mass concentration. Flux is, in general, a multi-component vector. In the interest of simplicity, we limit our treatment to transport along one coordinate, so the flux can be considered a scalar that may be positive or negative, depending upon direction.

The mole flux (moles per unit bulk area per unit time) of an individual component, say species i, of a mixture is given the symbol Ni. The mole flux of the mixture as a whole is denoted by N and is the sum of the component mole fluxes N = Σi Ni, i = A, B. Therefore, N is the flux of gas as a whole (i.e., the phase motion). Recall the discussion of the second experiment relating to Figure 1b in which we observed that diffusion engenders bulk gas flow that is not driven by a pressure gradient. For this reason, we purposely do not equate phase motion with the viscous flow calculated by Darcy’s law. Gas flow calculated by Darcy’s law is only one contributor to flow of the phase, a concept that will likely be foreign and seem incredible to those encountering it for the first time.


Flux Equations for Gas Diffusion in Porous Media Copyright © 2021 by David B. McWhorter. All Rights Reserved.