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Universality in edge-source diffusion dynamics

N. A. Mortensen·F. Okkels·H. Bruus
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Abstract

We show that in edge-source diffusion dynamics the integrated concentration N(t) has a universal dependence with a characteristic time-scale tau=(A/P)^2 pi/(4D), where D is the diffusion constant while A and P are the cross-sectional area and perimeter of the domain, respectively. For the short-time dynamics we find a universal square-root asymptotic dependence N(t)=N0 sqrt(t/tau) while in the long-time dynamics N(t) saturates exponentially at N0. The exponential saturation is a general feature while the associated coefficients are weakly geometry dependent.

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N. A. Mortensen, F. Okkels, H. Bruus. 2005-12-22. Universality in edge-source diffusion dynamics. https://doi.org/10.1103/physreve.73.012101

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