论文标题
评估中等密度颗粒二元混合物的动力学理论：剪切粘度系数
Assessment of kinetic theories for moderately dense granular binary mixtures: Shear viscosity coefficient
论文作者
论文摘要
两种不同的动力学理论[J. Solsvik和E. Manger（SM理论），物理。流体\ textbf {33}，043321（2021）和V.Garzó，J。W。Dufty和C. M. Hrenya（GDH-theory），Phys。 e \ e \ textbf {76}，031303（2007）]被认为是为了确定剪切粘度$η$，用于中等密集的光滑硬球的中等密集的颗粒二进制混合物。将混合物经过简单的剪切流，并通过外部驱动力（高斯恒温器）的作用加热，该驱动力（高斯恒温器）准确地补偿了碰撞中消散的能量。一组endkog动力学方程是获得$η$对混合物控制参数的依赖性的起点：固体分数，浓度，质量和直径比以及正常恢复的系数。虽然SM理论中发现的$η$的表达是基于麦克斯韦分布在每个物种的速度分布函数的假设，但GDH理论通过Chapman-enskog方法求解了enskog方程。为了评估这两种动力学理论的准确性，通过直接模拟蒙特卡洛（DSMC）方法来求解恩科方程。使用恒温器控制冷却效果，在简单的剪切流下进行混合物进行模拟。鉴于SM理论预测了动力学对剪切粘度的消失，因此理论与仿真之间的比较基本上是在碰撞贡献$η_c$对剪切粘度的层面上进行的。结果清楚地表明，GDH理论与模拟的比较比SM理论要比恢复系数的广泛值，体积分数和混合物的参数（质量，直径和浓度）要好得多。
Two different kinetic theories [J. Solsvik and E. Manger (SM-theory), Phys. Fluids \textbf{33}, 043321 (2021) and V. Garzó, J. W. Dufty, and C. M. Hrenya (GDH-theory), Phys. Rev. E \textbf{76}, 031303 (2007)] are considered to determine the shear viscosity $η$ for a moderately dense granular binary mixture of smooth hard spheres. The mixture is subjected to a simple shear flow and heated by the action of an external driving force (Gaussian thermostat) that exactly compensates the energy dissipated in collisions. The set of Enskog kinetic equations is the starting point to obtain the dependence of $η$ on the control parameters of the mixture: solid fraction, concentration, mass and diameter ratios, and coefficients of normal restitution. While the expression of $η$ found in the SM-theory is based on the assumption of Maxwellian distributions for the velocity distribution functions of each species, the GDH-theory solves the Enskog equation by means of the Chapman--Enskog method to first order in the shear rate. To assess the accuracy of both kinetic theories, the Enskog equation is numerically solved by means of the direct simulation Monte Carlo (DSMC) method. The simulation is carried out for a mixture under simple shear flow, using the thermostat to control the cooling effects. Given that the SM-theory predicts a vanishing kinetic contribution to the shear viscosity, the comparison between theory and simulations is essentially made at the level of the collisional contribution $η_c$ to the shear viscosity. The results clearly show that the GDH-theory compares with simulations much better than the SM-theory over a wide range of values of the coefficients of restitution, the volume fraction, and the parameters of the mixture (masses, diameters, and concentration).
