重力驱动下颗粒流中的正应力效应
Normal stress effects in the gravity driven flow of granular materials
摘要：
本文研究了两个斜面之间颗粒物质充分发展的重力驱动流动。我们假设颗粒材料可以用一种修正的二阶流体来表示，其中粘性取决于剪切速率和体积分数，法向应力系数取决于体积分数。我们还提出了应力张量的一个新的各向同性（球形）部分，它可以与（刚性）颗粒的致密性相关。这个新的术语确保了刚性固体颗粒不能被压实超过一个点，即当体积分数已经达到临界/最大填充值时。数值结果表明，新提出的应力张量对速度场和体积分数场都有明显的物理意义。
英文摘要：
In this paper, we study the fully developed gravity-driven flow of granular materials between two inclined planes. We assume that the granular materials can be represented by a modified form of the second-grade fluid where the viscosity depends on the shear rate and volume fraction and the normal stress coefficients depend on the volume fraction. We also propose a new isotropic (spherical) part of the stress tensor which can be related to the compactness of the (rigid) particles. This new term ensures that the rigid solid particles cannot be compacted beyond a point, namely when the volume fraction has reached the critical/maximum packing value. The numerical results indicate that the newly proposed stress tensor has an obvious and physically meaningful effects on both the velocity and the volume fraction fields.
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