Analyzing Diffusion by Analogy with Consolidation
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 131, Issue 11
Abstract
The analogy between Terzaghi’s governing equation for consolidation and Fick’s governing equation for diffusion (i.e., Fick’s second law) is used as the basis for analyzing diffusion of aqueous miscible solutes (e.g., contaminants) in saturated porous media. Based on this analogy, one-dimensional analytical (closed-form) solutions to the consolidation equation can be transformed into one-dimensional analytical solutions to Fick’s second law. The general methodology for transforming the analytical solutions in terms of solute concentration, solute mass flux, and cumulative solute mass is presented, and the concepts of degree of diffusion and average degree of diffusion are introduced. Analytical solutions are presented for a variety of initial and boundary conditions. Application of the methodology is illustrated through an example analysis for a problem involving matrix diffusion associated with pump-and-treat remediation. The example analysis illustrates the ability to analyze relatively complex problems involving diffusive solute transport based on the analogy between consolidation and diffusion.
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Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 131 • Issue 11 • November 2005
Pages: 1345 - 1359
Copyright
© 2005 ASCE.
History
Received: Jun 10, 2004
Accepted: May 10, 2005
Published online: Nov 1, 2005
Published in print: Nov 2005
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