AI 中文总结
本研究探究均匀各向同性湍流中快速沉降颗粒对的碰撞动力学，建立相关扩散模型与方程，得出理想碰撞率随重力与湍流相对强度增加而递增、碰撞效率则递减的结论。
AI 中文摘要
我们研究均匀各向同性湍流中流体动力学相互作用的无惯性球形颗粒对的碰撞动力学，分析聚焦于快速沉降极限，即颗粒穿过柯尔莫哥洛夫涡的沉降时间远小于柯尔莫哥洛夫时间尺度。我们还考虑润滑相互作用期间的连续介质破裂，这在颗粒间距与气态介质约100纳米的平均自由程可比时十分重要。由于本文考虑的颗粒尺寸小于柯尔莫哥洛夫尺度，我们将颗粒对附近的局部流场近似为背景湍流诱导的随机线性流。在快速沉降区域，湍流应变波动的累积效应较弱，因此颗粒相对运动可描述为扩散过程；此外，流体动力学相互作用会在颗粒对之间产生净相对漂移。我们沿沉降轨迹评估流体速度梯度的拉格朗日自相关函数，以获取流体动力学扩散率和相对漂移速度。快速沉降假设进一步使我们能将自相关函数与湍流能谱关联。利用这些结果，我们求解对概率密度函数的平流扩散方程以确定碰撞率。我们表明，理想碰撞率随重力与湍流相对强度的增加单调递增，而碰撞效率在相同范围内单调递减。
英文摘要
We investigate the collision dynamics of hydrodynamically interacting inertialess spherical particle pairs sedimenting in a homogeneous isotropic turbulent flow. The analysis focuses on the rapid-settling limit, in which the particle settling time across a Kolmogorov eddy is much shorter than the Kolmogorov time scale. We also consider continuum breakdown during lubrication interactions, which is important when the separation the particles is comparable to the $O(100)$ nm mean-free path of a gaseous media. Owing to the sub-Kolmogorov particle sizes considered here, we approximate the local flow field in the vicinity of a particle pair as a stochastic linear flow induced by the background turbulence. In the rapid-settling regime, the cumulative effect of turbulent strain fluctuations is weak, and the relative particle motion may therefore be described as a diffusive process. In addition, hydrodynamic interactions generate a net relative drift between the particle pairs. We obtain the hydrodynamic diffusivity and relative drift velocity from the Lagrangian autocorrelation function of the fluid velocity gradient evaluated along the settling trajectory. The rapid-settling assumption further enables us to relate the autocorrelation function to the turbulence energy spectrum. Using these results, we solve the advection-diffusion equation for the pair probability density function to determine the collision rate. We show that the ideal collision rate increases monotonically with increasing relative strength of gravity to turbulence, whereas the collision efficiency decreases monotonically over the same range.
Comments31 pages, 10 figures, and 1 table
