Diffusion

· Fick's second law describes the transient situation in which the concentration at a point in the material is changing with time:
(Rate of Concentration Change) = (dc/dt) = D(T)(d²c/dx²)
· The concentration gradient is position dependent and the flux into a small region of the sample differs from the flux out of this region as shown.

From: Newey & Weaver,
"Materials Principles and Practice," Butterworths (1990)

· The net atom increase in the small region in time Δt is: (J₁ - J₂) A Δt, and so the rate of increase in the concentration is: (Δc/Δt) = ((J₁ - J₂)/ Δx) with J given by Fick's first law. A concentration independent D(T) gives the form of the second law shown above.