Khalil Nagi, Garzó Vicente
Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.
J Chem Phys. 2014 Apr 28;140(16):164901. doi: 10.1063/1.4871628.
The homogeneous state of a binary mixture of smooth inelastic hard disks or spheres is analyzed. The mixture is driven by a thermostat composed by two terms: a stochastic force and a drag force proportional to the particle velocity. The combined action of both forces attempts to model the interaction of the mixture with a bath or surrounding fluid. The problem is studied by means of two independent and complementary routes. First, the Enskog kinetic equation with a Fokker-Planck term describing interactions of particles with thermostat is derived. Then, a scaling solution to the Enskog kinetic equation is proposed where the dependence of the scaled distributions φi of each species on the granular temperature occurs not only through the dimensionless velocity c = v/v0 (v0 being the thermal velocity) but also through the dimensionless driving force parameters. Approximate forms for φi are constructed by considering the leading order in a Sonine polynomial expansion. The ratio of kinetic temperatures T1/T2 and the fourth-degree velocity moments λ1 and λ2 (which measure non-Gaussian properties of φ1 and φ2, respectively) are explicitly determined as a function of the mass ratio, size ratio, composition, density, and coefficients of restitution. Second, to assess the reliability of the theoretical results, molecular dynamics simulations of a binary granular mixture of spheres are performed for two values of the coefficient of restitution (α = 0.9 and 0.8) and three different solid volume fractions (ϕ = 0.00785, 0.1, and 0.2). Comparison between kinetic theory and computer simulations for the temperature ratio shows excellent agreement, even for moderate densities and strong dissipation. In the case of the cumulants λ1 and λ2, good agreement is found for the lower densities although significant discrepancies between theory and simulation are observed with increasing density.
分析了光滑非弹性硬盘或球体二元混合物的均匀状态。该混合物由一个由两项组成的恒温器驱动：一个随机力和一个与粒子速度成正比的阻力。这两种力的联合作用试图模拟混合物与浴或周围流体的相互作用。通过两条独立且互补的途径研究该问题。首先，推导了带有描述粒子与恒温器相互作用的福克 - 普朗克项的恩斯科格动力学方程。然后，提出了恩斯科格动力学方程的一个标度解，其中每种物质的标度分布φi对颗粒温度的依赖不仅通过无量纲速度c = v/v0（v0为热速度），还通过无量纲驱动力参数。通过考虑索宁多项式展开中的主导阶来构建φi的近似形式。明确确定了动力学温度比T1/T2以及四阶速度矩λ1和λ2（分别测量φ1和φ2的非高斯性质）作为质量比、尺寸比、组成、密度和恢复系数的函数。其次，为了评估理论结果的可靠性，针对恢复系数的两个值（α = 0.9和0.8）以及三种不同的固体体积分数（ϕ = 0.00785、0.1和0.2），对球体二元颗粒混合物进行了分子动力学模拟。动力学理论与计算机模拟在温度比方面的比较显示出极好的一致性，即使对于中等密度和强耗散情况也是如此。在累积量λ1和λ2的情况下，对于较低密度发现了良好的一致性，尽管随着密度增加观察到理论与模拟之间存在显著差异。
