A collisional model of a confined quasi-two-dimensional granular mixture is considered to analyze homogeneous steady states. The model includes an effective mechanism to transfer the kinetic energy injected by vibration in the vertical direction to the horizontal degrees of freedom of grains. The set of Enskog kinetic equations for the velocity distribution functions of each component is derived first to analyze the homogeneous state. As in the one-component case, an exact scaling solution is found where the time dependence of the distribution functions occurs entirely through the granular temperature $T$. As expected, the kinetic partial temperatures $T_i$ of each component are different and, hence, energy equipartition is broken down. In the steady state, explicit expressions for the temperature $T$ and the ratio of partial kinetic temperatures $T_i/T_j$ are obtained by considering Maxwellian distributions defined at the partial temperatures $T_i$. The (scaled) granular temperature and the temperature ratios are given in terms of the coefficients of restitution, the solid volume fraction, the (scaled) parameters of the collisional model, and the ratios of mass, concentration, and diameters. In the case of a binary mixture, the theoretical predictions are exhaustively compared with both direct simulation Monte Carlo and molecular dynamics simulations with a good agreement. The deviations are identified to be originated in the non-Gaussianity of the velocity distributions and on microsegregation patterns, which induce spatial correlations not captured in the Enskog theory.

中文翻译：

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约束准二维颗粒混合物碰撞模型中的能量非等分

考虑到有限的准二维颗粒混合物的碰撞模型来分析均匀稳态。该模型包括一种有效的机制，可将通过振动注入的动能沿垂直方向传递到晶粒的水平自由度。首先导出用于每个组件的速度分布函数的Enskog动力学方程组，以分析均匀状态。与单组分情况一样，找到了精确的缩放解决方案，其中分布函数的时间依赖性完全通过颗粒温度发生$Ť$。如预期的那样，动力学局部温度${Ť}_{\mathrm{一世}}$每个组成部分的能量均不同，因此，能量分配被打破了。在稳态下，温度的显式$Ť$ 和部分动力学温度之比 ${Ť}_{\mathrm{一世}}/{Ť}_{Ĵ}$ 通过考虑在部分温度下定义的麦克斯韦分布获得 ${Ť}_{\mathrm{一世}}$。根据恢复系数，固体体积分数，碰撞模型的（缩放）参数以及质量，浓度和直径的比率，给出（缩放的）颗粒温度和温度比。在二元混合物的情况下，将理论预测与直接模拟蒙特卡洛和分子动力学模拟进行了详尽的比较，并具有很好的一致性。偏差被确定为源自速度分布的非高斯性和微观偏析模式，这引起了Enskog理论中未捕获的空间相关性。