12 ac=DAc also finds its similar counterpart applications in soil mechanics, at
ID: 701485 • Letter: 1
Question
12 ac=DAc also finds its similar counterpart applications in soil mechanics, at consolidation PDE: Cu well. For example, both diffusion coefficient D and Coefficient of Consolidation share the same unit of m/s. Discuss your understanding of the connections based on the overall mathematics knowledge learned so far and through your independent research study of their connections and how they may help you better understand the different ax2 = du and probably heat transfer differential equations as az2 at fields' connections through the fundamentals of PDE mathematics?Explanation / Answer
Ficks 2nd law governing equation is mathematically similar to governing equation of consolidation. From the mathematical similarity, the analytical solution for ficks 2nd law transformed to analytical solution of consolidation can be used for analyzing diffusion of aqueous miscible solutes in saturated porous media.
Based on this analogy, one-dimensional analytical 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 and the concepts of degree of diffusion and average degree of diffusion can be calculated.
Analytical solutions are presented for a variety of initial and boundary conditions. Application of the methodology can be 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.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.