Fick's law

Advanced

Diffusion flux is proportional to the concentration gradient.

Key relationJ = −D dn/dx

Diffusion flux is proportional to the concentration gradient: J = −D dn/dx. D for gases is ~10⁻⁵ m²/s, for liquids ~10⁻⁹.

Worked example

Oxygen diffusing into the blood in the lungs.

Common mistake

Flux runs down the gradient.

In more detail

Fick's law states that the diffusion flux is proportional to the concentration gradient, J = −D dC/dx, where D is the diffusion coefficient.

Drug delivery models use Fick's law to predict release rates.
Designing membranes and filters with controlled diffusion.
Biologists use Fick's law to model how oxygen diffuses from the lungs into the blood through thin membranes.

What does the minus sign mean?

Diffusion moves particles down the concentration gradient, from high to low.

What affects D?

Temperature, the medium and the size of the diffusing particles.

Why does diffusion flux depend on the gradient?

Particles move from high to low concentration, so a steeper gradient produces a larger net flow.