Individual constituent balance equations are often used to derive expressions for species specific segregation velocities in flows of dense granular mixtures. We propose a semi-empirical expression for the interspecies momentum exchange in density bidisperse granular flows as an extension of ideas from kinetic theory and compare it to a previous viscous drag approach that is analogous to particles settling in a fluid. The proposed model expands the range of the granular kinetic theory from short-duration binary collisions to the multiple enduring contacts characteristic of dense shear flows and incorporates the effects of particle friction, concentration ratio, and local flow conditions. The segregation velocities derived from the momentum balance equation using both interspecies drag models match the downward and upward segregation velocities of heavy and light particles obtained from DEM simulations through the flowing layer depth for different density ratios and constituent concentrations in confined shear flows. Predictions of the kinetic theory inspired approach are additionally compared to results from free surface heap flow simulations, and, again, a close match is observed.

中文翻译：

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密度-双分散颗粒流的分离模型

通常使用单个成分平衡方程式来导出致密颗粒混合物流中特定于物种的分离速度的表达式。我们提出了密度双分散颗粒流中种间动量交换的半经验表达式，作为动力学理论思想的扩展，并将其与以前的类似于颗粒在流体中沉降的粘性阻力方法进行了比较。所提出的模型将颗粒动力学理论的范围从短时二进制碰撞扩展到致密剪切流的多重持久接触特性，并纳入了颗粒摩擦，集中比和局部流动条件的影响。使用两个种间阻力模型从动量平衡方程推导的偏析速度，与DEM模拟通过流动层深度对DEM模拟获得的重，轻粒子的向下和向上的偏析速度相匹配，适用于密闭剪切流中不同的密度比和组分浓度。另外，将动力学理论启发方法的预测与自由表面堆流模拟的结果进行了比较，并且再次观察到了紧密匹配。