Fickian

Fickian diffusion refers to transport that follows Fick's laws of diffusion, typically characterized by a diffusion coefficient D that is constant with respect to concentration and time. The term is named after Adolf Eugen Fick, who formulated the laws in 1855.

Fick's first law states that the diffusive flux J is proportional to the negative gradient of the concentration: J = -D ∇C. Fick's second law describes how concentration changes in time: ∂C/∂t = D ∇^2 C. These equations describe diffusion under ideal conditions, assuming isotropic media, no sources or sinks, and a constant diffusion coefficient.

In practice, many systems only approximate Fickian diffusion. For example, diffusion in polymers can be non-Fickian when D depends on concentration or when the matrix relaxes during transport, leading to anomalous diffusion or Case II diffusion. Non-Fickian behavior can also arise in complex porous materials, crowded environments, or when coupling with chemical reactions or mechanical processes occurs.

Fickian diffusion is a common starting point for modeling mass transport in membranes, coatings, and drug-release systems. It provides a mathematically tractable framework for predicting how substances spread due to concentration gradients, even though real materials often exhibit deviations that require more complex descriptions.