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

Xiang Cheng, Lei Xu, Aaron Patterson, Heinrich M. Jaeger, Sidney R. Nagel

Research output: Contribution to journalArticlepeer-review

79 Scopus citations

Abstract

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. Fingering in such Hele-Shaw geometries has been generated not only with newtonian fluids but also with various non-newtonian fluids including fine granular material displaced by gas, liquid or larger grains. Here, we study a granular Hele-Shaw system to explore the zero-surface-tension property of granular fluids. 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 fingering. 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 2,17-23 .

Original languageEnglish (US)
Pages (from-to)234-237
Number of pages4
JournalNature Physics
Volume4
Issue number3
DOIs
StatePublished - Mar 2008
Externally publishedYes

Bibliographical note

Funding Information:
We thank E. Bettelheim, E. Corwin, S. Y. Lee, J. Royer, P. Wiegmann and L. N. Zou for fruitful discussions. This work was supported by the MRSEC program of the NSF under No. DMR-0213745 and by the W. M. Keck Foundation. Correspondence and requests for materials should be addressed to X.C.

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