In a rapidly moving multiphase mass flow, drag and virtual mass forces are important interfacial forces. However, in many existing literatures, virtual mass force has often been ignored or employed empirically. In this contribution, we construct analytical, full and explicit expressions for the virtual mass coefficients in the true three-phase typical debris flow consisting of coarse-solid, fine-solid and fluid. Similar to virtual mass coefficients, three different linear functions are introduced to connect the volume fractions and velocities of three distinct bulks of phases with other three entrapped fields, namely fine-solid entrapped in coarse-solid, and fluid entrapped in coarse-solid and fine-solid. This results in the emergence of three fundamentally different virtual mass forces expressed as analytical functions of phase-fractions, phase-densities, and the capacity of the solid-type material to hold the fluid-type materials in the mixture. Emergence of the virtual mass force coefficients induced enhanced viscosities, phase fractions, drags, viscous stresses and gravity forces of the coarse-solid and fine-solid indicate the further importance of the newly constructed multiphase mass flow model. For different local distributions of the viscous fluid and the fine particle concentrations, the model can be applied to the different flow regimes of the mixture from dilute to dense so as to cover the whole spectrum of the mixture rheology for each phase limit. In our generic model, entrapment coefficients, viscous rheology and drag coefficients can be used according to the nature of the materials involved and the flow situation. The reductions to existing two-phase mass flow models further indicate that the developed model is more generalized than the existing two-phase models. The reduced virtual mass coefficients for two-phases are still more generalized than the existing two-phase models. The simulation results using the new virtual mass coefficient with two different values of the entrapment coefficients reveal dynamically different flow-obstacle-interactions resulting in more phase-separation for the lower value of the entrapment coefficient.

在快速移动的多相质量流中，阻力和虚拟质量力是重要的界面力。但是，在许多现有文献中，虚拟质量力经常被忽略或凭经验使用。在此贡献中，我们构造了由粗固体，细固体和流体组成的真实三相典型泥石流中虚拟质量系数的解析，完整和显式表达式。与虚拟质量系数相似，引入了三个不同的线性函数，以将三个不同的相块的体积分数和速度与其他三个截留场联系起来，即细固体截留在粗固体中，流体截留在粗固体和细中-固体。结果导致出现了三种根本不同的虚拟质量力，它们表示为相分数的解析函数，相密度，以及固态材料将流体型材料固定在混合物中的能力。虚拟质量力系数的出现引起了粗固体和细固体的粘度，相分数，阻力，黏性应力和重力的增强，表明了新构建的多相质量流模型的重要性。对于粘性流体和细颗粒浓度的不同局部分布，可以将模型应用于从稀到浓的混合物的不同流动方式，从而涵盖每个相限的混合物流变学的整个范围。在我们的通用模型中，可以根据所涉及物料的性质和流动情况来使用截留系数，粘性流变学和阻力系数。现有两相质量流模型的减少进一步表明，所开发的模型比现有两相质量模型更具通用性。相较于现有的两相模型，用于两相的减小的虚拟质量系数仍然更加通用。使用具有两个不同截留系数值的新虚拟质量系数进行的仿真结果揭示了动态不同的流-障碍相互作用，从而为较低的截留系数值带来了更大的相分离。