4 - Molecular Diffusion

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.