When a species is distributed nonuniformly, random microscopic motion can produce a net diffusive flux from regions of high concentration toward regions of low concentration.

For one-dimensional diffusion in a simple isotropic medium, Fick's first law is

$$J=-D\frac{dC}{dx},$$

where $J$ is the amount crossing unit area per unit time, $C$ is a concentration measure and $D$ is the diffusivity. The minus sign says that the flux points down the concentration gradient.

The particular units of $J$ follow the chosen concentration. If $C$ is mass per volume, then $J$ is mass per area per time.

For a planar layer of thickness $L$ with constant $D$ and fixed boundary concentrations $C_1$ and $C_2$, steady state gives a linear concentration profile, so

$$J=-D\frac{C_2-C_1}{L}.$$

Example

Suppose $D=2\times10^{-11},\mathrm{m^2/s}$, $L=1,\mathrm{mm}$, and mass concentration falls by $0.30,\mathrm{kg/m^3}$ across the layer. The flux magnitude is

$$|J|=\frac{(2\times10^{-11})(0.30)}{10^{-3}}=6\times10^{-9},\mathrm{kg/(m^2,s)}.$$

Fick's first law is a constitutive relation: it connects flux to a local gradient. The microscopic mechanism that determines $D$ can be atomic jumps in a crystal, molecular motion in a fluid or another transport process. The law does not by itself describe how concentration changes with time; that requires combining flux with conservation.