Revisiting the 1954 suspension experiments of R. A. Bagnold
Revisiting the 1954 suspension experiments of R. A. Bagnold
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DOI：
10.1017/s0022112001006577
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发表时间：
2002-02-10
影响因子：
3.7
通讯作者：
Brennen, CE
中科院分区：
文献类型：
--
作者：
Hunt, ML;Zenit, R;Brennen, CE
1954年R. A.巴格诺尔德发表了他对液-固悬浮液的流变学性质的开创性发现。尽管这项工作在过去的50年里被广泛引用，但还没有对实验进行批判性的评论。本研究的目的是检查工作，并提出一个替代的原因，实验结果。同心圆筒流变仪设计用于同时测量大范围固体浓度、流体粘度和剪切速率下的剪切力和法向力。正如Bagnold所提出的，分析和实验表明，在“宏观粘性”状态下，剪切力和法向力与剪切速率呈线性关系;在“颗粒惯性”状态下，随着颗粒间相互作用的增加，应力取决于剪切速率的平方，而与流体粘度无关。然而，这些结果似乎是由实验设备的设计决定的。在Bagnold的实验中，流变仪的高度（h）与旋转外圆筒和固定内圆筒之间的间距（t）（h/t = 4.6）相比相对较短。由于顶部和底部端板与外圆柱体一起旋转，因此气流包含两个轴对称的反向旋转单元，其中气流沿着端板向外移动，并通过环形空间的中心区域向内移动。在更高的雷诺数，这些细胞显着贡献的测量扭矩，证明了通过比较Bagnold的纯流体测量与研究层流到湍流过渡，早于1954年的研究。通过考虑沿端壁的扭矩沿着，可以通过将液体-固体混合物建模为具有取决于固体浓度的校正粘度的牛顿流体来估计Bagnold的剪切应力测量。法向应力测量值的分析存在问题，因为未报告且无法获得总测量值。
In 1954 R. A. Bagnold published his seminal findings on the theological properties of a liquid-solid suspension. Although this work has been cited extensively over the last fifty years, there has not been a critical review of the experiments. The purpose of this study is to examine the work and to suggest an alternative reason for the experimental findings. The concentric cylinder rheometer was designed to measure simultaneously the shear and normal forces for a wide range of solid concentrations, fluid viscosities and shear rates. As presented by Bagnold, the analysis and experiments demonstrated that the shear and normal forces depended linearly on the shear rate in the 'macro-viscous regime; as the grain-to-grain interactions increased in the 'grain-inertia' regime, the stresses depended on the square of the shear rate and were independent of the fluid viscosity. These results, however, appear to be dictated by the design of the experimental facility. In Bagnold's experiments, the height (h) of the rheometer was relatively short compared to the spacing (t) between the rotating outer and stationary inner cylinder (h/t = 4.6). Since the top and bottom end plates rotated with the outer cylinder, the flow contained two axisymmetric counter-rotating cells in which flow moved outward along the end plates and inward through the central region of the annulus. At higher Reynolds numbers, these cells contributed significantly to the measured torque, as demonstrated by comparing Bagnold's pure-fluid measurements with studies on laminar-to-turbulent transitions that pre-date the 1954 study. By accounting for the torque along the end walls, Bagnold's shear stress measurements can be estimated by modelling the liquid-solid mixture as a Newtonian fluid with a corrected viscosity that depends on the solids concentration. An analysis of the normal stress measurements was problematic because the gross measurements were not reported and could not be obtained.