Labyrinth patterns in confined granular-fluid systems

A random, labyrinthine pattern emerges during slow drainage of a granular-fluid system in two-dimensional confinement. Compacted grains are pushed ahead of the fluid-air interface, which becomes unstable due to a competition between capillary forces and the frictional stress mobilized by grain-grain contact networks. We reproduce the pattern formation process in numerical simulations and present an analytical treatment that predicts the characteristic length scale of the labyrinth structure. The pattern length scale decreases with increasing volume fraction of grains in the system and increases with the system thickness.