Fick's law describes the diffusion of substances, such as sugar in tea, proportional to concentration gradients.In 1855, German physician and physiologist Adolf Fick sought a way to describe how substances penetrate living membranes. He noticed that the particle flux is always directed against the concentration gradient — toward where there are fewer particles. Fick wrote this as an equation similar to Fourier's law of heat conduction: the amount of substance passing through a unit area per unit time is proportional to the difference in its concentration. The proportionality coefficient — the diffusion coefficient — depends on the properties of the medium and the particles themselves. Today, Fick's law is the foundation of all mass transfer engineering, from semiconductor manufacturing to dialysis.
Adolf Fick formulated his law in 1855, drawing an analogy between diffusion and heat conduction, which had been mathematically described earlier by Joseph Fourier. Fick experimentally verified his equations on the diffusion of salts in water. Later, Albert Einstein (1905) linked the diffusion coefficient to particle mobility and temperature, and Jean Baptiste Perrin used Fick's law to determine Avogadro's number from the motion of Brownian particles. In the 1940s, the law was generalized for multicomponent systems by Lars Onsager.
The law applies wherever there is spontaneous mass transfer: from respiration and cell nutrition to creating homogeneous alloys and semiconductor structures. Its limits of applicability are isotropic media without convection and chemical reactions; at high concentrations or in non-ideal solutions, the diffusion coefficient ceases to be constant, and the law requires modification.
Calculating the rate of oxygen delivery from blood to tissues and designing water purification systems.
The diffusion coefficient of glucose in water is about 10,000 times smaller than that of oxygen in air — that's why sugar in a cup of tea dissolves so slowly, even when stirred.
| J | variable | Diffusive flux (amount per unit area per unit time) — diffusive flux mole per square metre per second |
| c | variable | Concentration of the diffusing species — concentration mole per cubic metre |
| x | variable | Spatial coordinate along the diffusion direction — position metre |
| D | constant | Material-specific proportionality constant relating flux to concentration gradient — diffusion coefficient = varies square metre per second |
| ∂/∂x | operator | Partial derivative with respect to position — partial derivative |
