Powders or cohesive granular materials are widely handled in industries. However, our understanding of the rheology of these materials is limited. Here, we provide a comprehensive analysis of the rheology of a cohesive granular medium, sheared in a normal-stress-imposed plane shear cell over a wide range of shear rate, employing numerical simulations. At high imposed shear rates, the flow is homogeneous, and the rheology is well described by the existing scaling laws, involving the inertial number and the “effective” cohesion number [S. Mandal et al., Insights into the Rheology of Cohesive Granular Media, Proc. Natl. Acad. Sci. U.S.A. 117, 8366 (2020)]. However, at low imposed shear rates, the flow is inhomogeneous, exhibiting the coexistence of flowing and nonflowing regions in the material, popularly known as shear banding. We thoroughly analyze the crucial features of this shear-banded flow regime and discuss striking similarities between the shear banding for granular media and other complex fluids. We reveal that the occurrence of shear banding is related to the existence of a nonmonotonic intrinsic rheological curve and that increasing adhesion increases the nonmonotonicity and the tendency toward shear localization. A simple theoretical model based on a nonlocal rheological model coupled with a nonmonotonic flow curve is proposed and is shown to successfully reproduce all the key features of the shear banding observed in the numerical simulations. The results have important implications for the handling of powders in industries.

中文翻译：

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粘性颗粒介质的流变学：剪切带，滞后和非局部效应

粉末或粘性粒状材料在工业中得到了广泛处理。但是，我们对这些材料的流变学的理解是有限的。在这里，我们使用数值模拟，对在较大剪切速率范围内施加正应力的平面剪切单元中剪切的粘性颗粒介质的流变性进行了全面分析。在高剪切速率下，流动是均匀的，并且流变学可以通过现有的比例定律很好地描述，涉及惯性数和“有效”内聚数[S。曼达尔（Mandal）等人。，洞察粘性颗粒状介质的流变学，Proc。Natl。学院 科学 美国 117，8366（2020）]。但是，在施加低剪切速率时，流动是不均匀的，表现出材料中流动区域和非流动区域的共存，通常称为剪切带。我们彻底分析了这种剪切带流动状态的关键特征，并讨论了颗粒状介质和其他复杂流体的剪切带之间的惊人相似之处。我们揭示剪切带的发生与非单调固有流变曲线的存在有关，并且增加的粘附力增加了非单调性和剪切局部化的趋势。提出了一个基于非局部流变模型和非单调流动曲线的简单理论模型，该模型可成功再现数值模拟中观察到的剪切带的所有关键特征。