Book contents
- An Introduction to Solute Transport in Heterogeneous Geologic Media
- An Introduction to Solute Transport in Heterogeneous Geologic Media
- Copyright page
- Contents
- Preface
- 1 Fundamental Concepts
- 2 Well-Mixed Models for Surface Water Quality Analysis
- 3 Well-Mixed Models for Subsurface Water Quality Analysis
- 4 Molecular Diffusion
- 5 Numerical Methods for Advection–Diffusion Equations
- 6 Shear Flow Dispersion
- 7 Solute Transport in Soil Columns
- 8 Parameter Estimation
- 9 Solute Transport in Field-Scale Aquifers
- 10 Field-Scale Solute Transport Experiments under Natural Gradient
- 11 Forced Gradient Field-Scale Tracer Experiments
- 12 High-Resolution Characterization (Tomographic Surveys)
- References
- Index
4 - Molecular Diffusion
Published online by Cambridge University Press: 02 February 2023
- An Introduction to Solute Transport in Heterogeneous Geologic Media
- An Introduction to Solute Transport in Heterogeneous Geologic Media
- Copyright page
- Contents
- Preface
- 1 Fundamental Concepts
- 2 Well-Mixed Models for Surface Water Quality Analysis
- 3 Well-Mixed Models for Subsurface Water Quality Analysis
- 4 Molecular Diffusion
- 5 Numerical Methods for Advection–Diffusion Equations
- 6 Shear Flow Dispersion
- 7 Solute Transport in Soil Columns
- 8 Parameter Estimation
- 9 Solute Transport in Field-Scale Aquifers
- 10 Field-Scale Solute Transport Experiments under Natural Gradient
- 11 Forced Gradient Field-Scale Tracer Experiments
- 12 High-Resolution Characterization (Tomographic Surveys)
- References
- Index
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 PressPrint publication year: 2023