Author： Bringuier E
Publisher： IOP Publishing
ISSN： 0143-0807
Source： European Journal of Physics, Vol.32, Iss.4, 2011-07, pp. : 975-992
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Abstract
This paper is an elementary introduction to particle diffusion in a medium where the coefficient of diffusion varies with position. The introduction is aimed at third-year university courses. We start from a simple model of particles hopping on a discrete lattice, in one or more dimensions, and then take the continuous-space limit so as to obtain the differential equation of diffusion. The discrete-step model is next adapted to investigate diffusion by continuous-length steps; the coefficient of diffusion is related to the mean free path. In both the discrete- and continuous-step models, the diffusion law has the Fokker–Planck (instead of Fick) pattern if the jumps are not biased and occur equally likely in all directions. Lastly, three experimental examples of diffusion in inhomogeneous media are examined; the observed law can be of a Fokker–Planck, Fick or hybrid type.
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