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2.0: Introduction to Diffusion and Darcy's Law

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  • Diffusion is a concept many students are first introduced to in physics or chemistry. However, once the partial differential equation aspect of solving the diffusion equation is introduced, diffusion can seem like an intimidating and abstract concept. 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. 

    Figure \(\PageIndex{1}\): Basic Gas Diffusion (Public Domain; Sbyrnes321, via Wikimedia)

    Simply put, diffusion is how a substance moves from a region of high concentration to a region of low concentration. This is likely already a concept you are familiar with from everyday life, such as when you spray air freshener in one area of a room and then can smell it throughout the entire room, or how helium balloons from a party drop after several days as the helium diffuses out of the balloon. 

    By the end of this chapter, you should be comfortable with heat flow in 1-D and 3-D, how we derive the diffusion equation, and how heat diffuses over various times and lengths. Additionally, you will gains skills in solving partial differential equations, specifically for various geologic processes, and learn how to use Darcy's law to model flow in a porous medium for both laminar and non laminar flows.