Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Rd, Cambridge CB3 0WA, United Kingdom.
Phys Rev E. 2019 Jul;100(1-1):012902. doi: 10.1103/PhysRevE.100.012902.
In this study, we perform experiments that reveal the distribution of dynamic forces in the bulk of granular free-surface flows. We release photoelastic disks from an incline to create steady two-dimensional avalanches. These gravity-driven dry granular flows are in the slow to intermediate regime (I≤1), dense (φ≈0.8), and thin (h≈10d). The transition between solidlike (quasisteady) and fluidlike (inertial) regimes is observable for certain experimental settings. We measure constant density and quasilinear velocity profiles through particle tracking at several points down the chute, for two different basal topographies. The photoelastic technique allows the visualization and quantification of instantaneous forces transmitted between particles during individual collisions. From the measured forces we obtain coarse-grained profiles of all stress tensor components at various positions along the chute. The discreteness of the system leads to highly fluctuating individual force chains which form preferentially in the directions of the bulk external forces: in this case, gravity and shear. The behavior of the coarse-grained stress tensor within a dynamic granular flow is analogous to that of a continuous fluid flow, in that we observe a hydrostatic increase of the mean pressure with depth. Furthermore, we identify a preferential direction for the principal stress orientation, which depends on the local magnitudes of the frictional and gravitational forces. These results allow us to draw an analogy between discrete and continuous flow models.
在这项研究中，我们进行了实验，揭示了散粒体自由表面流体内动态力的分布。我们从斜坡上释放光弹圆盘，以产生稳定的二维崩塌。这些由重力驱动的干颗粒流处于缓慢到中等（I≤1）、密集（φ≈0.8）和薄（h≈10d）的状态。在某些实验条件下，可以观察到固态（准稳态）和流态（惯性）之间的转变。我们通过在滑槽的几个点上进行粒子跟踪，测量了两种不同基底地形的恒定密度和准线性速度分布。光弹技术允许在单个碰撞过程中可视化和量化颗粒之间传递的瞬时力。从测量的力中，我们在滑槽的不同位置获得了各个应力张量分量的粗粒化分布。系统的离散性导致了高度波动的单个力链，这些力链优先在散装外力的方向上形成：在这种情况下，是重力和剪切力。在动态颗粒流中，粗粒化应力张量的行为类似于连续流体流，因为我们观察到平均压力随深度呈静水压增加。此外，我们确定了主应力方向的优先方向，这取决于摩擦力和重力的局部大小。这些结果允许我们在离散和连续流动模型之间进行类比。
