入侵者在加热颗粒稠密气体中的分凝
Segregation of an intruder in a heated granular dense gas
摘要：
重新审视了最近的分离准则[V. Garzó，Phys. Rev. E \textbf{78}，020301（R）（2008）]，该准则基于由非弹性Enskog方程描述的加热颗粒气体中入侵者的热扩散因子$Λ$。$Λ$的符号提供了巴西坚果效应（BNE）和反向巴西坚果效应（RBNE）之间过渡的判据。目前的理论包括两个额外的成分没有考虑到以前的理论尝试。首先，该理论是基于对入侵者质量通量输运系数的第二Sonine近似。第二，温度比（入侵者的温度超过主机粒状气体）对固体体积分数的依赖性被考虑在第一和第二Sonine近似。为了检验Sonine近似的准确性，还采用直接模拟蒙特卡罗（DSMC）方法对Enskog方程进行了数值求解，得到了动力学扩散系数$D_0$。理论和模拟之间的比较表明，第二Sonine近似的$D_0$产生的第一Sonine近似的改进时，入侵者比气体粒子在大的非弹性范围内轻。相对于BNE/RBNE过渡的相图的形式，因子$Λ$的动力学理论结果表明，虽然这些图的形式敏感地依赖于考虑当重力不存在时的Sonine近似的阶数，但在相反的极限（重力主导热梯度）中，两个Sonine解之间没有显着差异。在前一种情况下（无重力），第一Sonine近似高估了RBNE区域和耗散对热扩散偏析的影响。
英文摘要：
A recent segregation criterion [V. Garzó, Phys. Rev. E \textbf{78}, 020301(R) (2008)] based on the thermal diffusion factor $Λ$ of an intruder in a heated granular gas described by the inelastic Enskog equation is revisited. The sign of $Λ$ provides a criterion for the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE). The present theory incorporates two extra ingredients not accounted for by the previous theoretical attempt. First, the theory is based upon the second Sonine approximation to the transport coefficients of the mass flux of intruder. Second, the dependence of the temperature ratio (intruder temperature over that of the host granular gas) on the solid volume fraction is taken into account in the first and second Sonine approximations. In order to check the accuracy of the Sonine approximation considered, the Enskog equation is also numerically solved by means of the direct simulation Monte Carlo (DSMC) method to get the kinetic diffusion coefficient $D_0$. The comparison between theory and simulation shows that the second Sonine approximation to $D_0$ yields an improvement over the first Sonine approximation when the intruder is lighter than the gas particles in the range of large inelasticity. With respect to the form of the phase diagrams for the BNE/RBNE transition, the kinetic theory results for the factor $Λ$ indicate that while the form of these diagrams depends sensitively on the order of the Sonine approximation considered when gravity is absent, no significant differences between both Sonine solutions appear in the opposite limit (gravity dominates the thermal gradient). In the former case (no gravity), the first Sonine approximation overestimates both the RBNE region and the influence of dissipation on thermal diffusion segregation.
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