In this Letter, we discuss how flow inhomogeneity affects the self-diffusion behavior in granular flows. Whereas self-diffusion scalings have been well characterized in the past for homogeneous shearing, the effect of shear localization and nonlocality of the flow has not been studied. We, therefore, present measurements of self-diffusion coefficients in discrete numerical simulations of steady, inhomogeneous, and collisional shearing flows of nearly identical, frictional, and inelastic spheres. We focus on a wide range of dense solid volume fractions, that correspond to geophysical and industrial shearing flows that are dominated by collisional interactions. We compare the measured values first with a scaling based on shear rate and, then, on a scaling based on the granular temperature. We find that the latter does much better than the former in collapsing the data. The results lay the foundations of diffusion models for inhomogeneous shearing flows, which should be useful in treating problems of mixing and segregation.

中文翻译：

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不均匀颗粒剪切流中的自扩散

在这封信中，我们讨论了流动不均匀性如何影响颗粒流动中的自扩散行为。虽然自扩散尺度在过去已经很好地表征了均匀剪切，但尚未研究剪切局部化和流动的非局部性的影响。因此，我们在几乎相同、摩擦和非弹性球体的稳定、非均匀和碰撞剪切流的离散数值模拟中展示了自扩散系数的测量值。我们专注于范围广泛的致密固体体积分数，它们对应于以碰撞相互作用为主的地球物理和工业剪切流。我们首先将测量值与基于剪切速率的比例进行比较，然后再将测量值与基于颗粒温度的比例进行比较。我们发现后者在折叠数据方面做得比前者好得多。该结果为非均匀剪切流的扩散模型奠定了基础，这对于处理混合和分离问题应该是有用的。