A law concerning the movement of mass by the process of diffusion. The law states that a species diffuses in the direction of decreasing concentration:
where J is the diffusion flux defined as the amount of substance per unit area per unit time, D is the diffusion coefficient or diffusivity, C is the concentration, and x is the position. The negative sign shows that the flux is driven in the direction of increasing position. The diffusion coefficient is proportional to the square of the velocity of the diffusing particles, which depends on the temperature, viscosity of the fluid, and the size of the particles, according to the Stokes–Einstein equation. The SI units for the diffusion coefficients are m2 s−1. The law was proposed in 1855 by Adolf Fick (1829–1901) and is analogous to the relationships discovered around the same time by other eminent scientists, such as Darcy’s law for fluid flow, Ohm’s law for the transport of charge, and Fourier’s law for heat transfer. Diffusion processes that do not follow Fick’s laws are known as non-Fickian.