We employ a recently proposed model [Murisic et al., "Dynamics of particle settling and resuspension in viscous liquids," J. Fluid. Mech. 717, 203-231 (2013)] to study a finite-volume, particle-laden thin film flowing under gravity on an incline. For negatively buoyant particles with concentration above a critical value and buoyant particles, the particles accumulate at the front of the flow forming a particle-rich ridge, whose similarity solution is of the rarefaction-singular shock type. We investigate the structure in detail and find that the particle/fluid front advances linearly to the leading order with time to the one-third power as predicted by the Huppert solution [H. E. Huppert, " Flow and instability of a viscous current down a slope," Nature 300, 427-419 (1982)] for clear fluid (i.e., in the absence of particles). We also explore a deviation from this law when the particle concentration is high. Several experiments are carried out with both buoyant and negatively buoyant particles whose results qualitatively agree with the theoretics. (C) 2015 AIP Publishing LLC.
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机译：我们采用了最近提出的模型[Murisic等，“在粘性液体中颗粒沉降和再悬浮的动力学”，J。Fluid。机甲717，203-231（2013）]以研究有限体积的，载有颗粒的薄膜，该薄膜在重力作用下倾斜。对于浓度高于临界值的负浮力粒子和浮力粒子，这些粒子积聚在流的前端，形成一个富粒子的脊，其相似性解决方案是稀疏奇异冲击型。我们对结构进行了详细研究，发现粒子/流体前沿随时间线性上升至提前阶，随时间变化达到了Huppert解[H. P. H. E.Huppert，“粘性电流沿斜坡的流动和不稳定性，” Nature 300，427-419（1982）]，用于澄清流体（即，在没有颗粒的情况下）。当颗粒浓度高时，我们也探索了与该定律的偏差。对浮力和负浮力粒子都进行了一些实验，其结果在质量上与理论相符。 （C）2015 AIP Publishing LLC。
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