Non-Newtonian hydrodynamics for a dilute granular suspension under uniform shear flow.
Non-Newtonian hydrodynamics for a dilute granular suspension under uniform shear flow.
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均匀剪切流下稀颗粒悬浮液的非牛顿流体动力学。
DOI：
10.1103/physreve.92.052205
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
V. Garzó
中科院分区：
文献类型：
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作者：
M. Chamorro;F. Reyes;V. Garzó
本文研究了低密度气固悬浮液中具有零热流通量的稳定剪切层流（通常称为“均匀剪切流”）。固体颗粒被建模为具有非弹性碰撞的光滑硬球气体，而周围间隙流体对颗粒动力学的影响是在悬浮液流变模型的背景下通过体积阻力来建模的。该模型通过三种不同但互补的途径求解，其中两种是理论途径（应用于相应玻尔兹曼方程的格拉德矩法和适用于颗粒悬浮液的动力学模型的精确解），另一种是计算途径（玻尔兹曼方程的蒙特卡罗模拟）。与以往对颗粒剪切悬浮液的研究不同，与动量传递相关的碰撞力矩在Grad的解中是通过包括应力张量中的所有二次项来确定的。这种理论上的增强允许检测和评估在与层流垂直的平面上的法向应力差。此外，动力学模型的精确解给出了速度分布函数的速度矩的显式形式。我们的理论结果和数值结果的比较表明，对于非牛顿流变性能、峰度（分布函数的第四个速度矩）和动力学模型的速度分布，具有很强的非弹性和表征粘性阻力的（标度）摩擦系数值不太大的情况，总体上是很一致的。这表明我们的分析结果的准确性，使我们能够详细描述颗粒状剪切悬浮液的流动动力学。
We study in this work a steady shearing laminar flow with null heat flux (usually called "uniform shear flow") in a gas-solid suspension at low density. The solid particles are modeled as a gas of smooth hard spheres with inelastic collisions while the influence of the surrounding interstitial fluid on the dynamics of grains is modeled by means of a volume drag force, in the context of a rheological model for suspensions. The model is solved by means of three different but complementary routes, two of them being theoretical (Grad's moment method applied to the corresponding Boltzmann equation and an exact solution of a kinetic model adapted to granular suspensions) and the other being computational (Monte Carlo simulations of the Boltzmann equation). Unlike in previous studies on granular sheared suspensions, the collisional moment associated with the momentum transfer is determined in Grad's solution by including all the quadratic terms in the stress tensor. This theoretical enhancement allows for the detection and evaluation of the normal stress differences in the plane normal to the laminar flow. In addition, the exact solution of the kinetic model gives the explicit form of the velocity moments of the velocity distribution function. Comparison between our theoretical and numerical results shows in general a good agreement for the non-Newtonian rheological properties, the kurtosis (fourth velocity moment of the distribution function), and the velocity distribution of the kinetic model for quite strong inelasticity and not too large values of the (scaled) friction coefficient characterizing the viscous drag force. This shows the accuracy of our analytical results that allows us to describe in detail the flow dynamics of the granular sheared suspension.