摘要翻译：
自Saffman和Taylor时代以来，当一个粘性较小的流体取代一个粘性较大的流体时出现的指状分支模式作为一个数学上可处理的流体动力不稳定性的经典例子得到了广泛的研究。在这种Hele-Shaw几何中，指进不仅在牛顿流体中产生，而且在各种非牛顿流体中也产生，包括被气体、液体或大颗粒置换的细颗粒物质。本文研究了一个颗粒Hele-Shaw系统，以探索干燥颗粒材料中没有内聚力是否能为研究在零表面张力极限下预测的迄今无法实现的奇异流体力学提供一个理想的场所。我们证明了颗粒-气体界面确实表现出分形结构和与有限时间奇点相关的尖锐尖点。在屈服应力以上，手指宽度的尺度与普通流体的尺度不同，反映了独特的颗粒特性，如摩擦诱导的耗散，而不是粘性阻尼。尽管存在这些差异，但整体分形结构的维数和界面上奇异尖点的形状与基于传统流体指进的简单拉普拉斯增长的理论在零表面张力极限下是一致的。我们的研究不仅对两相密粒流的动力学和颗粒形态的形成提供了新的见解，而且对零表面张力极限下的流体动力学也提供了新的见解。
---
英文标题：
《Toward the zero surface tension limit: The granular fingering
  instability》
---
作者：
Xiang Cheng, Lei Xu, Aaron Patterson, Heinrich M. Jaeger, Sidney R.
  Nagel
---
最新提交年份：
2007
---
分类信息：

一级分类：Physics        物理学
二级分类：Soft Condensed Matter        软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
--
一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--

---
英文摘要：
  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.
---
PDF链接：
https://arxiv.org/pdf/712.2019