Patterns and flow in frictional fluid dynamics.

Pattern-forming processes in simple fluids and suspensions have been studied extensively, and the basic displacement structures, similar to viscous fingers and fractals in capillary dominated flows, have been identified. However, the fundamental displacement morphologies in frictional fluids and granular mixtures have not been mapped out. Here we consider Coulomb friction and compressibility in the fluid dynamics, and discover surprising responses including highly intermittent flow and a transition to quasi-continuous dynamics. Moreover, by varying the injection rate over several orders of magnitude, we characterize new dynamic modes ranging from stick-slip bubbles at low rate to destabilized viscous fingers at high rate. We classify the fluid dynamics into frictional and viscous regimes, and present a unified description of emerging morphologies in granular mixtures in the form of extended phase diagrams.

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.