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arXiv 2107.00282cond-mat.soft
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含时二元颗粒悬浮液的均匀状态

Time-dependent homogeneous states of binary granular suspensions

Rubén Gómez González, Vicente Garzó

摘要:

在Enskog动力学方程的背景下,研究了均匀双分散颗粒悬浮液的时间演化。周围的粘性气体对固体颗粒的影响是通过一个确定性的粘性阻力加上随机Langevin类项建模。首先发现,无论初始条件,系统达到(经过短暂的持续几个碰撞每个粒子)一个普遍的非定常流体动力学制度,每个物种的分布函数不仅取决于无量纲速度(如在均匀冷却状态),但也对瞬时温度相对于背景温度缩放。为了证实这一结果,随时间变化的局部温度的理论预测进行了比较,对直接模拟蒙特卡罗(DSMC)的结果,比较显示出良好的协议,确认流体力学在颗粒悬浮液中的适用性。此外,在瞬态制度,所谓的Mpemba样效应(即,当一个最初较热的样品比冷的一个更快地冷却)进行了分析的非弹性碰撞。Mpemba效应的理论分析进行的初始状态接近和远离渐近稳定状态。在这两种情况下,一个很好的协议之间的理论和DSMC结果再次发现。作为对前人研究的补充,本文确定了悬架动力学特性的稳态值对系统参数空间的依赖关系。更具体地说,我们把注意力集中在温度比$T_1/T_2$和四阶累积量$c_1$和$c_2$(测量速度分布$f_1$和$f_2$与它们的麦克斯韦形式的偏离)。最后,对稳态解进行了线性稳定性分析,表明稳态总是线性稳定的。

英文摘要:

The time evolution of a homogeneous bidisperse granular suspension is studied in the context of the Enskog kinetic equation. The influence of the surrounding viscous gas on the solid particles is modeled via a deterministic viscous drag force plus a stochastic Langevin-like term. It is found first that, regardless of the initial conditions, the system reaches (after a transient period lasting a few collisions per particle) a universal unsteady hydrodynamic regime where the distribution function of each species not only depends on the dimensionless velocity (as in the homogeneous cooling state) but also on the instantaneous temperature scaled with respect to the background temperature. To confirm this result, theoretical predictions for the time-dependent partial temperatures are compared against direct simulation Monte Carlo (DSMC) results; the comparison shows an excellent agreement confirming the applicability of hydrodynamics in granular suspensions. Also, in the transient regime, the so-called Mpemba-like effect (namely, when an initially hotter sample cools sooner than the colder one) is analyzed for inelastic collisions. The theoretical analysis of the Mpemba effect is performed for initial states close to and far away from the asymptotic steady state. In both cases, a good agreement is found again between theory and DSMC results. As a complement of the previous studies, we determine in this paper the dependence of the steady values of the dynamic properties of the suspension on the parameter space of the system. More specifically, we focus on our attention in the temperature ratio $T_1/T_2$ and the fourth degree cumulants $c_1$ and $c_2$ (measuring the departure of the velocity distributions $f_1$ and $f_2$ from their Maxwellian forms). Finally, a linear stability analysis of the steady state solution is also carried out showing that the steady state is always linearly stable.

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