To establish a framework for the discussion of transport, we look at a general analytical treatment for a static fluid in a (
−) semi-infinite volume of a species of number density,
n, which at time
t =
0 begins diffusing into a (+) semi-infinite region. In this case, the general equation for the diffusion of density is

, which can be solved analytically depending on the boundary conditions (
Wylie, 1966).