# Infinite Integration of Fick's Second Law

1. Jul 14, 2013

### DiffUser2349

Hi everyone!

Recently, I've been trying to understand how the error function pertains to solving for concentration in a non-steady state case (with a constant diffusivity D), but I've been having some trouble with the initial assumptions. The source I am currently using (Crank's The Mathematics of Diffusion) claims that, for a the case of a plane source,

C = A/sqrt(t) * exp(-(x^2)/4Dt)

Where C is the concentration (with respect to position and time), x is the position (assuming one dimension only), t is the time, and A is an arbitrary constant, which is a solution for Fick's Second Law (dC/dt = D (d2C/dx2)). Crank (as well another source I've been using <http://www.eng.utah.edu/~lzang/images/lecture-4.pdf>) [Broken] claim that this is solvable by integrating Fick's Second Law, but whether I am making a mistake or otherwise not understanding the concept, I can't seem to get this result to work. Could someone help me with this, either by providing the math, or a source which has this derivation? Thanks again.

Edit: I put this post in General Physics, feeling it would be a bit more suitable. Now, I can't seem to delete this thread. How would I go about it? If I cannot by myself, can the moderators? Thanks.

Last edited by a moderator: May 6, 2017