Fick's laws of diffusion

Molecular diffusion from a microscopic and macroscopic point of view. Initially, there are solute molecules on the left side of a barrier (purple line) and none on the right. The barrier is removed, and the solute diffuses to fill the whole container. **Top**: A single molecule moves around randomly. **Middle**: With more molecules, there is a clear trend where the solute fills the container more and more uniformly. **Bottom**: With an enormous number of solute molecules, randomness becomes undetectable: The solute appears to move smoothly and systematically from high-concentration areas to low-concentration areas. This smooth flow is described by Fick's laws.

Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, $D$ . Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation.

Fick's first law: Movement of particles from high to low concentration (diffusive flux) is directly proportional to the particle's concentration gradient.^[1]

Fick's second law: Prediction of change in concentration gradient with time due to diffusion.

A diffusion process that obeys Fick's laws is called normal or Fickian diffusion; otherwise, it is called anomalous diffusion or non-Fickian diffusion.

^ Vallero, Daniel A. (2024). "Physical transport of air pollutants". Air Pollution Calculations. pp. 163–190. doi:10.1016/B978-0-443-13987-1.00017-X. ISBN 978-0-443-13987-1.

[1] Vallero, Daniel A. (2024). "Physical transport of air pollutants". Air Pollution Calculations. pp. 163–190. doi:10.1016/B978-0-443-13987-1.00017-X. ISBN 978-0-443-13987-1.

[1]