Granular labyrinth structures in confined geometries
Henning Arendt Knudsen, Bj{ \ o} rnar Sandnes, Eirik Grude Flekk{\o}y, and Knut J{ \ o} rgen M\r{a}l{\o}y

Pattern forming processes are abundant in Nature. Here, we report on a particular pattern forming process. Upon withdrawal of fluid from a particle/fluid dispersion in a Hele-Shaw cell, the particles are shown to be left behind in intriguing maze-like patterns. The particles, initially being uniformly spread out in a disc, are slowly pulled inwards and together by capillary- and pressure forces. Invading air forms branching fingers, whereas the particles are compiled into comparably narrow branches. These branches are connected in a tree-like structure, taking the form of a maze. The characteristic length scale within the structure is found to decrease with the volume fraction of the particles and increase with the plate separation in the Hele-Shaw cell. We present a simulator designed to simulate this phenomenon, which reproduce qualitatively and quantitatively the experiments, as well as a theory that can predict the observed wavelengths.

© 2008 The American Physical Society.