Ficka

Meet Ficka, molecules from a teabag spreading from where they are crowded to where they are sparse.

Molecules jiggle randomly. Where there are many, more of them happen to wander out than wander in, so on average there is a net flow from high concentration to low. Adolf Fick described this in 1855: the flux J, the amount passing through each square metre per second, is proportional to the concentration gradient. The minus sign means the flow runs down the gradient. The diffusion coefficient D sets how fast.

Because diffusion is a random walk, the distance spread grows only as the square root of time. Small molecules in water have D around 10⁻⁹ m²/s. Spreading 1 millimetre takes minutes, while spreading 1 centimetre by diffusion alone takes over a day. That is why stirring tea helps so much.

Diffusion moves oxygen from the lungs into blood, carries nutrients into cells and is used to add impurities when making silicon chips.

The law assumes a constant D and no flow. In real liquids convection usually dominates over centimetres.