Fick's first law

Fick's first law puts a simple number on a simple idea: the steeper the concentration difference, the faster molecules diffuse across a barrier. If one side of a membrane is very crowded with drug and the other side nearly empty, drug crosses quickly; as the two sides even out, the flow slows down. Flux (the amount crossing per unit area per unit time) is proportional to the concentration gradient.

Written out, flux equals the diffusion coefficient times the membrane area times the concentration difference, divided by the membrane thickness. In words: more area, a bigger concentration drop, and an easier-to-cross or thinner barrier all speed transport. The law assumes a steady state, where the gradient is not changing with time.

This single relationship underpins much of controlled and transdermal delivery. A skin patch is engineered to keep a near-constant drug concentration against the skin so that, by Fick's law, drug crosses at a steady rate for hours or days. The law also explains why keeping a high gradient (sink conditions) is essential in dissolution testing, and why a drug reservoir is sized to deplete slowly enough to maintain that gradient.