This book: Flux Equations for Gas Diffusion in Porous Media concerns a topic that few groundwater scientists and engineers encounter in their education and day-to-day experience, and it fills that gap by addressing fundamental processes important to many aspects of groundwater science. Diffusion is most commonly associated with Fick’s “law”. Applications of Fick’s law in groundwater quality are analogous to use of Darcy’s “law” for groundwater flow but, in the context of subsurface processes, diffusion has more complexities than flow. Groundwater flow is founded on Darcy’s equation for the relationship between flow and the hydraulic gradient and it serves us well in nearly all cases of practical relevance. However, Darcy’s “law” is not universal as are the fundamental laws of physics and fluid mechanics because it is only valid for a limited range of flow conditions in porous media. Awareness of the fundamentals underlying relationships known as “laws” is essential for avoidance of confusion and errors in the solution of practical problems.

Independent of Henry Darcy’s work in 1856-France, which showed that hydraulic gradient drove the flow of water in saturated porous sand, Adolf Fick’s work in 1855-Germany demonstrated that concentration gradient drove the diffusive movement of chemical molecules and ions in liquids. This became known as Fick’s law and is a law of fundamental importance for chemical engineering, much as Darcy’s law is for groundwater science. Fick’s law applies to movement of dissolved constituents in water and in water saturated porous media and serves as a building block for the development of the equations that describe diffusive movement of gaseous constituents in partially saturated porous media (i.e., the vadose zone). In groundwater geochemistry and subsurface contamination, Fick’s equation is as important and, in many situations, is more important than Darcy’s equation.

This book is an introduction to the fundamental processes governing the movement of gases in the vadose zone. These processes are key to understanding important topics such as the fate of petroleum products that leak into the subsurface and how harmful vapors from toxic chemicals move through the vadose zone to cause deterioration of indoor air. Moreover, this book examines how the movement of gases in the vadose zone came to be correctly understood in the context of both Fick’s law of diffusion and Graham’s law of gas diffusion. Although the behavior of gases in porous media has been the subject of scientific scrutiny and engineering applications for more than a century, it was not until the middle part of the twentieth century that clarity of understanding emerged in the fields of physical chemistry and chemical engineering, yet confusion persists about how the fundamental processes apply to problems concerning subsurface contamination. This book is an examination of the intellectual journey from confusion to clarity, which began nearly two centuries ago with the work of Thomas Graham in 1833. This journey is akin to a scientific detective story.

David McWhorter is an emeritus professor of Colorado State University who, early in his career, authored a textbook on groundwater hydraulics. His career then focused on research into the fundamental processes of movement and fate of oily liquids and solutes in the subsurface and the application of his finding to groundwater contamination problems.

John Cherry, Groundwater Project Leader
Guelph, Ontario, Canada, May 2021



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