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4 - Molecular Diffusion

Published online by Cambridge University Press:  02 February 2023

Tian-Chyi Jim Yeh
Affiliation:
University of Arizona
Yanhui Dong
Affiliation:
Chinese Academy of Sciences, Beijing
Shujun Ye
Affiliation:
Nanjing University, China
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Summary

Chapter 4 introduces the molecular diffusion concept and Fick’s Law to explain the mixing phenomena at a small-scale CV in the distributed models rather than the large CV of the well-mixed model. For this purpose, it begins with describing diffusion phenomena, then formulating Fick’s law and developing the diffusion equation. Subsequently, examining the random velocity of Brownian particles and their pure random walk, we articulate the probabilistic nature of the molecular diffusion process and the reason why Fick’s Law is an ensemble mean law. Next, analytical solutions to the diffusion equation for various types of inputs are introduced. The advection-dispersion equation (ADE) formulation then follows, which couples the effect of fluid motion at fluid continuum scale and random motion of fluid molecules at the molecular scale to quantify solute migration. Likewise, we present analytical solutions to the ADE for several input forms and discuss snapshots and breakthroughs for different input forms.

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Publisher: Cambridge University Press
Print publication year: 2023

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  • Molecular Diffusion
  • Tian-Chyi Jim Yeh, University of Arizona, Yanhui Dong, Chinese Academy of Sciences, Beijing, Shujun Ye, Nanjing University, China
  • Book: An Introduction to Solute Transport in Heterogeneous Geologic Media
  • Online publication: 02 February 2023
  • Chapter DOI: https://doi.org/10.1017/9781009049511.005
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  • Molecular Diffusion
  • Tian-Chyi Jim Yeh, University of Arizona, Yanhui Dong, Chinese Academy of Sciences, Beijing, Shujun Ye, Nanjing University, China
  • Book: An Introduction to Solute Transport in Heterogeneous Geologic Media
  • Online publication: 02 February 2023
  • Chapter DOI: https://doi.org/10.1017/9781009049511.005
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Molecular Diffusion
  • Tian-Chyi Jim Yeh, University of Arizona, Yanhui Dong, Chinese Academy of Sciences, Beijing, Shujun Ye, Nanjing University, China
  • Book: An Introduction to Solute Transport in Heterogeneous Geologic Media
  • Online publication: 02 February 2023
  • Chapter DOI: https://doi.org/10.1017/9781009049511.005
Available formats
×