Toward the zero surface tension limit: The granular fingering instability

Details Toward the zero surface tension limit: The granular fingering instability Toward the zero surface tension limit: The granular fingering instability

2007-12-12

arxiv.org/abs/0712.2019v1

Physics

Condensed Matter

Soft Condensed Matter

18 pages, 3 pages. accepted by Nature Physics

Scientific paper

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 instability since the time of Saffman and Taylor. Fingering in such Hele-Shaw geometries have been generated not only with Newtonian fluids but also with various non-Newtonian fluids including fine granular material displaced by gas, liquid, or large grains. Here we study a granular Hele-Shaw system to explore whether the absence of cohesive forces in dry granular material can produce an ideal venue for studying the hitherto-unrealizable singular hydrodynamics predicted in the zero-surface-tension limit. We demonstrate that the grain-gas interface does indeed exhibit fractal structure and sharp cusps associated with finite-time singularities. 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 damping. 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 limit. Our study provides new insights not only on the dynamics of two-phase dense granular flows and granular pattern formation, but also on the fluid dynamics in the zero-surface-tension limit.

Affiliated with

Also associated with

No associations

Rating

Toward the zero surface tension limit: The granular fingering instability does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Toward the zero surface tension limit: The granular fingering instability, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Toward the zero surface tension limit: The granular fingering instability will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-662233