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Rheology of dense granular flows in two dimensions: Comparison of fully two-dimensional flows to unidirectional shear flow

机译:二维致密颗粒流动的流变学:完全比较   二维流向单向剪切流

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摘要

This work utilizes soft-particle discrete element simulations to examine therheology of steady two-dimensional granular flows with reference to aunidirectional shear flow, which has been extensively employed for validatingthe local visco-plastic model of Jop et al. [Nature 441, 727--730 (2006)]. The$\mu$-$I$ scaling proposed by Jop et al. is found to be valid in bothtwo-dimensional and unidirectional flows, as observed in previous studies,however, each flow type results in a different curve. Here $\mu$, ratio of theshear stress magnitude to the pressure, is the friction coefficient and $I$ isthe dimensionless inertial number, which is proportional to the ratio of themagnitude of the rate of strain tensor, $\dot{\gamma}$, to the square root ofthe pressure. The friction coefficient is found not to scale in a simple waywith the flow classification parameter $\psi$, which characterizes the localflow type. All the data collapse to a single curve using the scaling proposedby Zhang and Kamrin [Phys. Rev. Lett. 118, 058001 (2017)], in which the scaledgranular fluidity ($f=1/(\mu T)$, where $T \propto u/\dot{\gamma}$ and $u$ isthe fluctuation velocity) is found to depend only on the solid fraction $\phi$.The data for variation of $\phi$ with inertial number $I$ collapse to a singlecurve for all the flows.
机译:这项工作利用软粒子离散元模拟,参照单向剪切流,研究了稳定的二维颗粒流的流变性,该流已被广泛用于验证Jop等人的局部粘塑性模型。 [Nature 441,727--730(2006)]。 Jop等人提出的scaling mu scaling缩放。如先前的研究中所观察到的,在二维和单向流动中都被认为是有效的。这里,剪切应力大小与压力之比$ \ mu $是摩擦系数,$ I $是无量纲惯性数,它与应变张量率的大小之比$ \ dot {\ gamma}成比例$,到压力的平方根。摩擦系数没有以简单的方式随流量分类参数$ \ psi $缩放,该参数表征了局部流量类型。使用Zhang和Kamrin提出的缩放比例,所有数据都折叠成一条曲线[Phys。牧师118,058001(2017)],其中找到了按比例缩放的颗粒流动性($ f = 1 /(\ mu T)$,其中$ T \ propto u / \ dot {\ gamma} $和$ u $是波动速度)仅依赖于固体分数$ \ phi $。具有惯性数$ I $的$ \ phi $变化量的数据对于所有流都折叠为单个曲线。

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