A constitutive model of multiphase mixtures and its application in shearing flows of saturated solid-fluid mixtures
A constitutive model of multiphase mixtures and its application in shearing flows of saturated solid-fluid mixtures
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DOI：
10.1007/s100350050023
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发表时间：
1999
期刊：
影响因子：
2.4
通讯作者：
Yongqi Wang;K. Hutter
中科院分区：
文献类型：
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作者：
Yongqi Wang;K. Hutter
建立了多相混合物的连续介质理论。根据Goodman & Cowin [11]和Passman等人[23]，在基本平衡定律中，我们引入了平衡力的额外平衡来描述每个组分的微观结构响应。基于热力学第二定律的Müler-Liu形式，导出了一组具有微结构的粘性固-流混合物的本构方程。这些相对一般的方程，然后减少到一个系统的常微分方程，描述了一个稳定的流动的固体-流体混合物在两个水平板。由此产生的边界值问题的数值求解和结果的参数和边界条件的各种值。它表明，简单的剪切一般不会发生。典型地，对于固相，在边界附近，如果固体体积分数低，则出现高剪切速率层，其厚度几乎在5至15个粒径之间，而如果固体体积分数高，则出现互锁现象。流体速度主要取决于组分之间的拖曳力。当阻力系数足够大时，流体的流动与固体的流动几乎相同，而当阻力系数较小时，流体的剪切流动在整个流动区域内与固体的剪切流动相差很大。除此之外，存在固体颗粒在低剪切速率的区域中积聚的趋势。
A continuum theory of a multiphase mixture is formulated. In the basic balance laws we introduce an additional balance of equilibrated forces to describe the microstructural response according to Goodman & Cowin [11] and Passman et al. [23] for each constituent. Based on the Müler-Liu form of the second law of thermodynamics a set of constitutive equations for a viscous solid-fluid mixture with microstructure is derived. These relatively general equations are then reduced to a system of ordinary differential equations describing a steady flow of the solid-fluid mixture between two horizontal plates. The resulting boundary value problem is solved numerically and results are presented for various values of parameters and boundary conditions. It is shown that simple shearing generally does not occur. Typically, for the solid phase, in the vicinity of a boundary, if the solid-volume fraction is low, a layer of high shear rate occurs, whose thickness is nearly between 5 and 15 grain diameters, while if the solid-volume fraction is high, an interlock phenomenon occurs. The fluid velocity depends largely on the drag force between the constituents. If the drag coefficient is sufficiently large, the fluid flow is nearly the same as that of the solid, while for a small drag coefficient, the fluid shearing flow largely decouples from that of the solid in the entire flow region. Apart from this, there is a tendency for solid particles to accumulate in regions of low shear rate.