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Depth-averaged relations for granular-liquid uniform flows over mobile bed in a wide range of slope values

机译：宽斜率范围内流动床上颗粒-液体均匀流动的深度平均关系

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The behavior of liquid-granular flows, driven by gravity, is experimentally analyzed. Two types of free-surface uniform flow can take place, having different boundary conditions at the bottom. The first one runs over a fixed surface behaving as a solid (non-deformable) impermeable wall; the second one runs over a mobile-bed at rest, formed by the same loose grains and liquid of the flowing mixture. In the paper we will mark the differences between the two, but focus on the latter one. The experiments span over, and characterize, the possible flow regimes. In mobile-bed uniform flows it has been found that the Froude number reduces as the slope increases. Accordingly, there is an increment of the solid-concentration. These results are meaning that as slope increases a progressive dominance and thickening of frictional layers over colli-sional ones is taking place through the flow depth. Same behaviours have been observed by changing the type of grains in the flowing mixture. These findings contrast with the case of flows over a solid wall, where different trends are observed. Application of force balances by means of Coulomb law provides interesting confirmation of what observed and allows to take into account the surface-tension effects, which come into play when the particles on top are going to desaturate. Experimental data have also been employed to assess the applicability of kinetic theories to wet granular flows. Energy and momentum balances, under the hypothesis of no contribution in the liquid phase (except for the added mass concept) to shear stress and to the energy processes, are applied throughout the flow depth of the solid phase. Although depth-averaged quantities come out to have a trend similar to the experimental one, deficiencies in the theoretical approach, mainly due to its inability to represent frictional contacts, are clearly detected. Same conclusions may be drawn by applying the quite simple Bagnold theory. Altogether, a more appropriate theory able to deal with both collisional and frictional mechanisms, including the transition between, is demanded.
机译：实验分析了重力作用下的液体-颗粒流的行为。可以发生两种类型的自由表面均匀流动，在底部具有不同的边界条件。第一个穿过固定的表面，该表面表现为坚固的（不可变形的）不可渗透的墙；第二个在静止的流动床上方运行，流动床由流动混合物中相同的疏松颗粒和液体组成。在本文中，我们将标记两者之间的区别，但重点是后者。实验跨越并表征了可能的流动状态。在流动床均匀流中，已经发现弗洛德数随斜率的增加而减小。因此，固体浓度增加。这些结果意味着，随着斜率的增加，逐渐占据主导地位，并且在整个流动深度上，摩擦层的厚度都超过了碰撞层。通过改变流动混合物中的晶粒类型，可以观察到相同的行为。这些发现与实心壁上流动的情况形成对比，在实心壁上观察到不同的趋势。通过库仑定律应用力平衡可以有趣地证实所观察到的结果，并可以考虑表面张力效应，当顶部的粒子要去饱和时，表面张力效应就起作用了。实验数据也已用于评估动力学理论对湿颗粒流的适用性。在液相（除了增加的质量概念之外）对剪切应力和能量过程无贡献的假设下，能量和动量平衡适用于整个固相的流动深度。尽管深度平均数量的趋势与实验趋势相似，但主要由于其无法表示摩擦接触而在理论上存在缺陷，这已被清楚地发现。通过应用非常简单的Bagnold理论可以得出相同的结论。总之，需要一种能够处理碰撞和摩擦机制（包括两者之间的过渡）的更合适的理论。

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