倾斜沙漏流与颗粒休止角研究∗

摘要

本文发现在测量误差内颗粒物质的下列三个临界角度相等：1)从直径为D的倾斜孔洞流出的Beverloo颗粒流的流量开始停止的临界倾角θc向大孔径极限线性外推θc∞≡θc (D→∞)的补角θs∞=180◦−θc∞；2)从靠近堆顶的点源向光滑底板缓慢下落颗粒形成的圆锥形堆的休止角θr；3)直接剪切矩形颗粒固体测得的库仑内摩擦角φ。该结果倾向支持倾斜孔洞和颗粒堆自由表面的固-液转变与颗粒固体内部的库仑屈服均来自材料的同一临界性质。由于三种情况样品的内部应力和变形等都是目前还远不能定量分析的复杂非均匀分布，我们仅从定性角度对此给出一些讨论。%Systematic experimental study on inclined orifice flow and the measurement of the angle of repose are carried out in this work. The inclined orifice flow is formed by glass beads in an inclined channel. The flow is discharged near the bottom of the channel under gravity. The flow rates are measured at various inclination angles of the channel and opening sizes of the orifice. We then record the inclination angle when the rate becomes zero. We compare this zero-rate inclination angle with the repose angle of glass-beads, and the internal friction angle is determined by the yield stress obtained from a direct shear experiment. It is interesting to find that the experimental values at these three measured critical angles are equal within the experimental errors: 1) the supplementary angle of the extrapolating inclined angle at which the flow rate becomes zero and the inclined hole of diameter approaches infinitely large value (i. e. D→∞),θs∞=180−θc∞, whereθc is the critical angle for the inclined hole of diameter D andθc∞≡θc(D→∞);2) the repose angleθr of a cone-shaped pile, which is formed when particles fall from the top point of the heap onto a smooth bottom plate; and 3) the internal friction angle φ that is measured by direct shear experiment. This result intends to support that the solid-liquid transitions occurring in the inclined orifice flow and free surface of granular heap, and the Coulomb yield occurring in the bulk of the granular solid all originate from the same critical property. Owing to the fact that the internal stresses and strains of samples in the three cases all have complicated and nonuniform distributions so that they cannot be analyzed quantitatively at present, Only some qualitative discussion on this issue is given in this paper.