Fick's law is a mathematical description of

diffusion.

**J** = -D**∇**n (Fick's first law)

where **J** is the flux of a particular particle species across a surface, in boldface to indicate a vector quantity;

*D* is the diffusion coefficient, a function of the medium of diffusion and its temperature;

**∇** is the gradient operator; and

*n* is the number of particles per unit volume. In chemistry this is often replaced with concentration, *C.*

Though this equation is generally known as "Fick's law," there are actually two Fick's laws, the previously stated one being the first. The second can be derived by requiring conservation of mass:

*∂n/∂t = -***∇J**

which leads to:

*∂n/∂t = D ∇*^{2}n (Fick's second law)

The time derivative of the concentration is proportional to the rate of change of its gradient.

The linear model of diffusion provided by Fick's law doesn't work in situations where the diffusing particles are charged ions, electrons, etc., but is usually sufficient otherwise.