发表机构
Universidad de Extremadura; Instituto de Computación Científica Avanzada (ICCAEx)（埃斯特雷马杜拉大学; 高级计算科学研究所 (ICCAEx)）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过恩斯柯格动力学理论，在Δ模型下确定了受限稠密颗粒混合物的热通量输运系数，并证明均匀稳态线性稳定且量化了昂萨格关系的违反。
AI 中文摘要
本工作基于$\Delta$-模型框架，研究中等密度受限颗粒混合物的恩斯柯格动力学理论。$\Delta$-模型是一种有效的碰撞模型，通过在碰撞过程中引入额外的速度增量，考虑了颗粒能量从垂直自由度向水平自由度的转移。主要目标是通过显式确定热通量输运系数（即杜福尔系数和热导率系数），以及颗粒温度和冷却速率的一阶贡献，完善稠密二元颗粒混合物的纳维-斯托克斯流体动力学描述。这些量在稳态下通过查普曼-恩斯柯格方法从恩斯柯格动力学方程中确定，并以颗粒的质量和直径、混合物组成、密度和恢复系数的函数形式表达。结果表明，有限密度效应对输运有显著影响，导致与稀薄区域观察到的行为明显不同的现象。完整的输运系数集合被进一步用于研究两个不同问题。首先，我们对均匀稳态（HSS）进行线性稳定性分析。分析表明，在所探索的参数空间中，未发现不稳定的横向或纵向流体动力学模式，这表明即使在中等密度下，HSS也是线性稳定的。作为第二个问题，我们量化了受限稠密颗粒混合物中昂萨格互易关系的违反程度，并以问题的参数空间为函数进行表述。
英文摘要
This work considers the Enskog kinetic theory for moderately dense confined granular mixtures within the framework of the $Δ$-model, an effective collisional model that accounts for the transfer of energy from the vertical to the horizontal degrees of freedom of grains through an additional velocity increment during collisions. The main objective is to complete the Navier--Stokes hydrodynamic description of dense binary granular mixtures by explicitly determining the heat-flux transport coefficients, namely the Dufour and thermal conductivity coefficients, together with the first-order contributions to the partial temperatures and the cooling rate. These quantities are determined in the steady state from the Enskog kinetic equation by means of the Chapman--Enskog method and are expressed in terms of the masses and diameters of the particles, mixture composition, density, and coefficients of restitution. The results show that finite-density effects have a significant influence on transport, leading to behaviors that differ markedly from those observed in the dilute regime. The complete set of transport coefficients is considered further to study two different problems. First, we perform a linear stability analysis of the homogeneous steady state (HSS). The analysis demonstrates that no unstable transverse or longitudinal hydrodynamic modes are found over the parameter space explored, indicating that the HSS is linearly stable even at moderate densities. As a second problem, the violation of the Onsager reciprocal relations for a confined dense granular mixture is quantified in terms of the parameter space of the problem.
Comments27 pages; 8 figures
