Buoyancy-driven exchange flow in a vertical duct is studied theoretically for a light pure fluid and a heavy fluid. The latter is a suspension composed of a Newtonian fluid and two populations of negatively buoyant particles of the same size but different densities (bidensity). In a previous study (Mirzaeian & Alba, J. Fluid Mech. , vol. 847, 2018, pp. 134–160), the authors developed a lubrication model for monodensity suspension of particles of uniform size. The main observation of the monodensity study was the discovery of particle-enriched zones near heavy and light fluid fronts due to the relative motion of particles and the fluid. Distinct from the previous work, here, mismatched densities instigate a relative motion of lighter and heavier particles in addition to the movement of fluids. Other than the previously observed enrichment case, the bidensity case gives rise to a novel flow regime where there is enrichment of heavy particles but depletion of light particles near the interface. The transition to this regime is governed by a balance between the densities of heavy and light particles as well as those of light and carrying fluids for a given choice of initial volume fractions of particles. Such density balance is characterized by two dimensionless parameters comprising light and heavy particle-to-carrying-fluid density ratios. The transition mechanism is studied through additional simulations, revealing that the former increases with initial volume fraction of particles of either type, while the latter contrarily decreases. The effect of other parameters on the flow are discussed within the context of the paper.

中文翻译：

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垂直管道中的双密度颗粒交换流

对轻质纯流体和重质流体在垂直管道中浮力驱动的交换流进行了理论研究。后者是一种由牛顿流体和两组大小相同但密度不同（双密度）的负浮力颗粒组成的悬浮液。在之前的一项研究 (Mirzaeian & Alba, J. Fluid Mech., vol. 847, 2018, pp. 134–160) 中，作者开发了一种用于均匀尺寸颗粒的单密度悬浮液的润滑模型。单密度研究的主要观察结果是由于粒子和流体的相对运动，在重流体和轻流体前沿附近发现了粒子富集区。与之前的工作不同，这里的不匹配的密度除了流体的运动外，还会引发较轻和较重的粒子的相对运动。除了之前观察到的浓缩案例，双密度情况产生了一种新的流动状态，其中重粒子富集但轻粒子在界面附近耗尽。对于给定的粒子初始体积分数的选择，向该状态的过渡取决于重粒子和轻粒子的密度以及轻和携带流体的密度之间的平衡。这种密度平衡的特征在于两个无量纲参数，包括轻和重粒子与载流流体的密度比。通过额外的模拟研究了过渡机制，表明前者随着任一类型粒子的初始体积分数增加而增加，而后者则相反地减少。其他参数对流动的影响在本文的上下文中进行了讨论。