Towards the zero-surface-tension limit in granular fingering instability

The finger-like branching pattern that occurs when a less viscous fluid displaces a more viscous one confined between two parallel plates has been widely studied as a classical example of a mathematically tractable hydrodynamic instability1,2,3. Fingering in such Hele–Shaw geometries has been generated not only with newtonian fluids4,5,6 but also with various non-newtonian fluids7,8,9 including fine granular material displaced by gas, liquid or larger grains10,11,12,13,14,15. Here, we study a granular Hele–Shaw system to explore the zero-surface-tension property of granular ‘fluids’16. We demonstrate that the grain–gas interface exhibits fractal structure and sharp cusps, which are associated with the hitherto-unrealizable singular hydrodynamics predicted in the zero-surface-tension limit of normal fluid fingering2,17,18,19,20,21,22,23. Above the yield stress, the scaling for the finger width is distinct from that for ordinary fluids, reflecting unique granular properties such as friction-induced dissipation as opposed to viscous damping24,25,26,27. Despite such differences, the dimension of the global fractal structure and the shape of the singular cusps on the interface agree with the theories based on simple laplacian growth of conventional fluid fingering in the zero-surface-tension limit2,17,18,19,20,21,22,23.