The fractal nature of a diffusion front and the relation to percolation

Bernard Sapoval (1) , Michel Rosso (1) , Jean-François Gouyet (1)

1 LPMC - Laboratoire de physique de la matière condensée

Using a two dimensional simulation, a diffusion front is shown to have a fractal geometry in a range increasing with the diffusion length. The number of particles on the front, and the width measuring its spread, follow power laws as a function of the diffusion length. The associated exponents and the fractal dimension can be expressed as simple functions of the critical exponents of the two dimensional percolation problem.

Mots clés: Brownian motion; diffusion in solids; fractals; diffusion front spread; diffusion front; percolation; two dimensional simulation; fractal geometry; diffusion length; power laws; fractal dimension; critical exponents; two dimensional percolation problem

Domaines: Articles anciens

Bernard Sapoval, Michel Rosso, Jean-François Gouyet. The fractal nature of a diffusion front and the relation to percolation. Journal de Physique Lettres, 1985, 46 (4), pp.149-156. ⟨10.1051/jphyslet:01985004604014900⟩. ⟨jpa-00232493⟩