Shape of a frictional fluid finger

Abstract

Frictional fluid dynamics describes the displacement patterns that arise when a confined mixture of liquid and grains are displaced by an immiscible fluid under pressures that are too small to cause drainage into single pores. The flow, which is governed by solid friction and capillary forces, thus bulldozes the grains into compaction fronts which give rise to propagating fingers that eventually interact to create a range of patterns, including labyrinthine ones. We derive an analytic description that successfully reproduces the experimental results for the shape of a single finger as well as the compaction front profile. The theory thus depends on only one fitting parameter.