非弹性碰撞惯性粒子分布中的相变
Phase transitions in the distribution of inelastically colliding inertial particles
摘要：
最近有人提出，在不均匀的温度或湍流中粒子漂移的符号取决于粒子的惯性：弱惯性粒子定位在温度或湍流强度的最小值附近（称为热泳和湍流泳的效应），而强惯性粒子在无界空间中飞离最小值。湍流强度最小值附近的一个颗粒的问题与随机流中的两个颗粒的问题有关，因此前者的定域-离域转变对应于后者的路径-聚结转变。该转变由表征粒子接近最小值（其可以是壁或另一粒子）的平均速率的李雅普诺夫指数的符号变化来表示。在这里，我们解决这个问题的解析非弹性碰撞，并推导出在惯性非弹性平面的过渡相图。相图的一个重要特征是非弹性坍缩区域：如果粒子速度的恢复系数小于某个临界值，则粒子对于任何惯性都是局部化的。我们提出了直接的数值模拟，支持的理论，并揭示了依赖的流动相关时间的过渡，其特征在于由斯托克斯数。
英文摘要：
It was recently suggested that the sign of particle drift in inhomogeneous temperature or turbulence depends on the particle inertia: weakly inertial particles localize near minima of temperature or turbulence intensity (effects known as thermophoresis and turbophoresis), while strongly inertial particles fly away from minima in an unbounded space. The problem of a particle near minima of turbulence intensity is related to that of two particles in a random flow, so that the localization-delocalization transition in the former corresponds to the path-coalescence transition in the latter. The transition is signaled by the sign change of the Lyapunov exponent that characterizes the mean rate of particle approach to the minimum (which could be wall or another particle). Here we solve analytically this problem for inelastic collisions and derive the phase diagram for the transition in the inertia-inelasticity plane. An important feature of the phase diagram is the region of inelastic collapse: if the restitution coefficient of particle velocity is smaller than some critical value, then the particle is localized for any inertia. We present direct numerical simulations which support the theory and in addition reveal the dependence of the transition of the flow correlation time, characterized by the Stokes number.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
