Fick's Second Law of Diffusion

From the law of conservation of matter, the change of solute concentration with time must be the same as the local decrease of the diffusion flux, in the absence of a source or a sink, that is

Substituting from Fick's 1^st law we get

When the concentration of the solute is low, the diffusivity at a given temperature can be considered as a constant and we get

Units of D (Diffusion Coefficient) are cm²/sec those of C (x, t) atoms/cm³