# 2: Diffusion and Darcy's Law

• 2.0: Introduction to Diffusion and Darcy's Law
In this chapter, we will cover the numerous practical uses and applications of the diffusion equation, and break down how exactly to solve the equations, so that they are far more approachable. The chapter will also cover Darcy's law which helps us model how flow moves in a porous medium. Understanding diffusion will give you greater insight into how geologic processes function, such as dike emplacement, the cooling of the lithosphere, and erosion of fault scarps.
• 2.1: The Diffusion Equation
There are many, many applications and uses of the diffusion equation in geosciences, from diffusion of an element within a solid at the lattice-scale, to diffusion of heat at a local to regional scale, to diffusion of topography, and diffusion of a chemical species in the crust.
• 2.2: Geological Applications of the Diffusion Equation
Diffusivity, in general, describes the spreading out of some quantity (e.g. temperature) over space in some unit of time. Other diffusion processes will have other diffusivities, but they all will have the same unit.
• 2.3: Lithospheric Thickness Jupyter Notebook
An interactive example of how to calculate and plot the thickness of the lithosphere over time and distance from a spreading center. See how the spreading rate changes the lithospheric thickness.
• 2.4: Erosion Profile Jupyter Notebook
An interactive example of how to calculate and plot the fault scarp erosion application of diffusion. See how the topography of a fault scarp changes over time and with different diffusion coefficients.
• 2.5: Darcy's Law - Flow in a Porous Medium
Darcy's law is crucial to understanding many branches of geology, especially hydrogeology. Before we look at the law and what it can tell us, let's look at how it was developed. Darcy's law is named after Henry Darcy, a 19th century French engineer who developed an underground pressurized pipe system to deliver water around the city of Dijon. The system, which also provided water to the famous Dijon fountains, revolutionized city water and sewage systems and was driven purely by gravity.
• 2.6: Summary

Thumbnail: Annual Mean Temperature of the Earth. (CC BY-SA 3.0 Unported; Dragons flight via Wikipedia).