Continuum approach to wide shear zones in quasistatic granular matter

被引:38
作者
Depken, M
van Saarloos, W
van Hecke, M
机构
[1] Leiden Univ, Inst Lorentz Theoret Phys, NL-2300 RA Leiden, Netherlands
[2] Leiden Univ, Kamerlingh Onnes Lab, NL-2300 RA Leiden, Netherlands
来源
PHYSICAL REVIEW E | 2006年 / 73卷 / 03期
关键词
D O I
10.1103/PhysRevE.73.031302
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
Slow and dense granular flows often exhibit narrow shear bands, making them ill suited for a continuum description. However, smooth granular flows have been shown to occur in specific geometries such as linear shear in the absence of gravity, slow inclined plane flows and, recently, flows in split-bottom Couette geometries. The wide shear regions in these systems should be amenable to a continuum description, and the theoretical challenge lies in finding constitutive relations between the internal stresses and the flow field. We propose a set of testable constitutive assumptions, including rate independence, and investigate the additional restrictions on the constitutive relations imposed by the flow geometries. The wide shear layers in the highly symmetric linear shear and inclined plane flows are consistent with the simple constitutive assumption that, in analogy with solid friction, the effective-friction coefficient (ratio between shear and normal stresses) is a constant. However, this standard picture of granular flows is shown to be inconsistent with flows in the less symmetric split-bottom geometry-here the effective friction coefficient must vary throughout the shear zone, or else the shear zone localizes. We suggest that a subtle dependence of the effective-friction coefficient on the orientation of the sliding layers with respect to the bulk force is crucial for the understanding of slow granular flows.
引用
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页码:1 / 10
页数:10
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