Three-dimensional diffusion in inhomogeneous media

✍ Scribed by N.G. van Kampen

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 113 KB
• Volume: 23
• Category: Article
• ISSN: 0749-6036
• DOI: 10.1006/spmi.1997.0523

✦ Synopsis

The problem of diffusion in a medium with non-uniform temperature was first considered by Landauer, and subsequently discussed by a number of authors. The conclusion is that there is no universal diffusion equation; rather its precise form depends on the details of the underlying mechanism. Some examples were worked out for one-dimensional systems, but here we are concerned with more dimensions. In that case it may happen that the stationary distribution of the particle density involves a non-vanishing diffusion flow. The equations are established and solved for a simple toy system. Consideration is given to the subsequently more interesting case of dust particles diffusing in a quiescent atmosphere whose temperature varies irregularly in space. The resulting correction to the barometric formula is computed by means of perturbation theory.