Abstract

An invading meniscus between two fluids in a Hele-Shaw cell may bulldoze loose granular material into local compaction fronts. The flow becomes ‘frictionally unstable’, and as a result the invading fluid becomes shaped into fingers that plough the granular material to the side. In this talk we will see how the competition between friction and capillarity leads to a natural emergent length scale, the finger width. Then, by increasing viscosity or injection rate, we gradually amplify the role of viscous forces in the pattern formation. We know from classic fluid-fluid displacement that injection of a low viscosity fluid into a high viscosity fluid produces viscous fingering. The reverse scenario (high viscosity invading fluid) produces compact, viscously stabilised flow – just an expanding disc in a radial Hele-Shal cell. But what happens if we inject a high viscosity fluid into a bed of grains submerged in a low viscosity fluid? We inject water/glycerol into hydrophobic grains “submerged” in air. The bulldozing frictional instability generates fingers through which a viscous liquid flows. The viscous pressure gradient depends on injection rate and fluid viscosity, and we shall see how increasing either produces increased viscous stabilisation of the frictional fingering pattern, taking us through a transition from a single active finger, to multiple fingers, and finally to a fully compact “spoke” pattern.