Aumaitre S, Puls C, McElwaine J N, Gollub J P
Physics Department, Haverford College, Haverford, Pennsylvania 19041, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jun;75(6 Pt 1):061307. doi: 10.1103/PhysRevE.75.061307. Epub 2007 Jun 27.
The onset and dynamics of flow in shallow horizontally oscillating granular layers are studied as a function of the depth of the layer and imposed acceleration. Measurements of the flow velocity made from the top and side are presented in the frame of reference of the container. As is also found for avalanches of inclined layers, the thresholds for starting and stopping of flow are slightly different. The variation with depth of the starting acceleration Gamma{start} for the oscillating layer is similar to the corresponding variation of the tangent of the starting angle tan(theta{start}) for avalanches in the same container at low frequencies, but deviates as the frequency is increased. However, the threshold behavior depends significantly on the measurement protocol. Just above Gamma{start} , the motion decays with time as the material reorganizes over a minute or so, causing the apparent threshold to increase. Furthermore, the rms velocity as a function of acceleration rises more sharply above the starting threshold if the first minute or so of excitation is discarded. Once excited, the rheology of the material is found to vary in time during the cycle in surprising ways. If the maximum inertial force (proportional to the container acceleration amplitude) is slightly higher than that required to produce flow, the flow velocity grows as soon as the inertial force exceeds zero in each cycle, but jamming occurs long before the inertial force returns to zero. At higher Gamma , the motion is fluidlike over the entire cycle. However, the fraction of the cycle during which the layer is mobile is typically far higher than what one would predict from static considerations or the behavior of the inclined layer. Finally, we consider the flow profiles as a function of both the transverse distance across the cell at the free surface and also as a function of the vertical coordinate in the boundary layer near the sidewall. These profiles have time-dependent shapes and are therefore significantly different from profiles previously measured for avalanche flows.
研究了浅水平振荡颗粒层中流动的起始和动力学，作为层深度和外加加速度的函数。在容器的参考系中给出了从顶部和侧面测量的流速。正如在倾斜层雪崩中也发现的那样，流动开始和停止的阈值略有不同。振荡层起始加速度Γ{起始}随深度的变化类似于同一容器中低频雪崩起始角正切tan(θ{起始})的相应变化，但随着频率增加而偏离。然而，阈值行为显著取决于测量协议。就在Γ{起始}之上，随着材料在大约一分钟内重新组织，运动随时间衰减，导致表观阈值增加。此外，如果丢弃激发的前一分钟左右，均方根速度作为加速度的函数在起始阈值之上上升得更急剧。一旦被激发，发现材料的流变学在循环过程中随时间以惊人的方式变化。如果最大惯性力（与容器加速度幅值成正比）略高于产生流动所需的力，那么在每个循环中，一旦惯性力超过零，流速就会增加，但在惯性力回到零之前很久就会发生堵塞。在较高的Γ下，运动在整个循环中呈流体状。然而，层处于流动状态的循环部分通常远高于从静态考虑或倾斜层行为所预测的。最后，我们考虑了流动剖面，它是自由表面处细胞横向距离以及侧壁附近边界层中垂直坐标的函数。这些剖面具有随时间变化的形状，因此与先前测量的雪崩流剖面有显著不同。
