Pattern formation of frictional fingers in a gravitational potential

This work concerns experiments and simulations of slow drainage in a deformable quasi 2D porous media Hele Shaw. We introduce gravity as a parameter in the experiments where air displaces a liquid- granular mixture during drainage of a Hele-Shaw cell, by imposing shallow tilt angles. The receding interface accumulates a front of granular material, and an instability caused by a competition between surface tension and frictional forces results in an emerging pattern of frictional fingers, canals of air separated by branches of compacted grains, as also observed in horizontal systems. Aligned finger structures, with a characteristic width, emerge during the slow drainage. A transition from vertical to horizontal alignment of the finger structures is observed as the tilting angle and the granular density are varied. An analytical model is presented, demonstrating that the alignment properties are the result of the competition between fluctuating granular stresses and the hydrostatic pressure. The dynamics is reproduced in simulations. We also show how the system may explain patterns observed in nature, created during the early stages of a dike formation.