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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>) 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.

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# Infinite Integration of Fick's Second Law

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