The file Diffusion.xls contains various sheets with solutions for various boundary conditions for diffusion only (no advection or sorption):

• infinite column: Solution for a diffusion problem with the following boundary conditions: C(x)=0 at t=0 and x>0, C(X=0)=1 for t>0 and dc/dt=0 for x=∞. In words: an infinite column is contaminated at x=0 starting at t=0 with a constant concentration.
• semi-infinite column (1): Solution of the diffusion equation in a semi-infinite (i.e. there is a wall at x=0) uncontaminated (i.e. C(x)=0 at t=0 und L>x>0) column. The contamination with c0=1 starts at x=L and t=0 and continues for t>0.
• semi-infinite column (2): This solution does not provide the concentration as a function of time and distance but the total amount of compound that has diffused in or out of the defined column with length L under the given boundary conditions: at t=0 the concentration within the column (0<x<L) equals 1. On the one side of the column there is an impenetrable wall, on the other side the column is open (semi-infinite). On the open side of the column a constant concentration of C=0 is maintained at t>0.
• spherical diffusion: diffusion into or out of a sphere differs from the one in a column because the intersectional area through which diffusion can take place various with x in the case of a sphere while it stays constant in case of a column. The solution presented here provides the total amount of compound that has diffused in or out of a sphere with the defined radius r under the given boundary conditions.

Problem: often one can find that the total amount of compound that has diffused in or out of the defined plane is described by first-order kinetics. Is this correct? Generate data with Diffusion.xls, sheet semi-infinite column (2) and fit them to an exponential function in time.