Infinite Integration of Fick's Second Lawby DiffUser2349 Tags: diffusion, fick, integration, second law 

#1
Jul1413, 01:57 PM

P: 2

Hi everyone!
Recently, I've been trying to understand how the error function pertains to solving for concentration in a nonsteady 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/lecture4.pdf>) 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. 


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