Towards the zero-surface-tension limit in granular fingering instability
Towards the zero-surface-tension limit in granular fingering instability
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DOI：
10.1038/nphys834
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发表时间：
2008-03-01
期刊：
影响因子：
19.6
通讯作者：
Nagel, Sidney R.
中科院分区：
文献类型：
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作者：
Cheng, Xiang;Xu, Lei;Nagel, Sidney R.
当粘性较小的流体取代限制在两个平行板之间的粘性较大的流体时，会出现指状分支模式，作为数学上可处理的流体动力学不稳定性的经典示例 (1-3) 已得到广泛研究。这种 Hele-Shaw 几何形状中的指状现象不仅由牛顿流体 (4-6) 产生，而且还由各种非牛顿流体 (7-9) 产生，包括被气体、液体或较大颗粒 (10-15) 取代的细颗粒材料。在这里，我们研究了粒状 Hele-Shaw 系统，以探索粒状“流体”的零表面张力特性 (16)。我们证明，颗粒-气体界面表现出分形结构和尖锐的尖点，这与在正常流体指法的零表面张力极限中预测的迄今为止无法实现的奇异流体动力学有关(2,17-23)。在屈服应力之上，指宽的缩放与普通流体的缩放不同，反映了独特的颗粒特性，例如与粘性阻尼相反的摩擦引起的耗散(24-27)。尽管存在这些差异，整体分形结构的维数和界面上奇异尖点的形状与基于零表面张力极限下常规流体指进的简单拉普拉斯生长的理论一致(2,17-23)。
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(1-3). Fingering in such Hele-Shaw geometries has been generated not only with newtonian fluids(4-6) but also with various non-newtonian fluids(7-9) including fine granular material displaced by gas, liquid or larger grains(10-15). 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 fingering(2,17-23). 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 damping(24-27). 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-surfacetension limit(2,17-23).