动力学理论应用于刚性粗糙平面间无摩擦球体的压力控制剪切流动
Kinetic theory applied to pressure-controlled shear flows of frictionless spheres between rigid, bumpy planes
AI总结：
本研究通过离散元模拟和动力学理论，分析了粗糙平面间无摩擦球体在固定载荷下的剪切流动，首次验证了扩散率和碰撞耗散的本构关系，并提出了预测结晶临界载荷的准则。
摘要：
我们通过离散元模拟，在无重力及固定法向载荷条件下，数值研究了在两平行粗糙平面间受剪切的相同无摩擦球体的稳态流动。我们测量了固体体积分数、平均速度、搅拌强度和应力的空间分布，并证实了先前关于颗粒气体动力学理论所预测的状态方程和粘度有效性的结果。作为首次尝试，我们还直接测量了扩散率和脉动动能的碰撞耗散率的空间分布，并成功检验了动力学理论中相关的本构关系。随后，我们构建并数值积分了一个控制该流动的微分方程组，施加适当的边界条件，并展示了在流体动力学场分布、剪切应力与压力之比以及粗糙平面间距对碰撞恢复系数、施加载荷和平面粗糙度的依赖关系上，与离散模拟结果在定性和定量上均具有显著的一致性。最后，我们基于边值问题的解，提出了一个准则，用于预测可能发生结晶的施加载荷临界值。这显著重现了我们在离散模拟中观察到的现象。
英文摘要：
We numerically investigate, through discrete element simulations, the steady flow of identical, frictionless spheres sheared between two parallel, bumpy planes in the absence of gravity and under a fixed normal load. We measure the spatial distributions of solid volume fraction, mean velocity, intensity of agitation and stresses, and confirm previous results on the validity of the equation of state and the viscosity predicted by the kinetic theory of granular gases. In a first, we also directly measure the spatial distributions of the diffusivity and the rate of collisional dissipation of the fluctuation kinetic energy, and successfully test the associated constitutive relations of the kinetic theory. We then phrase and numerically integrate a system of differential equations governing the flow, with suitable boundary conditions, and show a remarkable qualitative and quantitative agreement with the results of the discrete simulations in terms of the dependence of the profiles of the hydrodynamic fields, the ratio of shear stress-to-pressure and the gap between the bumpy planes on the coefficient of collisional restitution, the imposed load and the bumpiness of the planes. Finally, we propose a criterion to predict, on the basis of the solution of the boundary-valued problem, the critical value of the imposed load above which crystallization may occur. This notably reproduces what we observe in the discrete simulations.
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