Lubrication flows between spherical particles colliding in a compressible non-continuum gas
Lubrication flows between spherical particles colliding in a compressible non-continuum gas
复制标题
可压缩非连续气体中碰撞的球形颗粒之间的润滑流
作者：
A. Gopinath;Shing;D. Koch
研究了在润滑极限下，两个刚性球在理想等温气体中的低雷诺数碰撞和反弹问题。球是非布朗性质的半径远大于平均自由程的分子。颗粒间差距中的流动性质取决于最小间隙厚度h′o、整体气体分子的平均自由程λo和压缩效应变得重要的差距厚度hc的相对大小。气体的可压缩性质和差距中流动的非连续性质都包括在内，并且分别和组合地研究它们的影响。这两种效应的相对重要性由无量纲数αo（hc/λo）表征。在控制方程中加入这些效应导致差距中的压力作为时间和径向位置的函数的偏微分方程。碰撞的动力学依赖于αo、粒子斯托克斯数Sto和初始粒子间距h′o。虽然在所有分离处施加的连续不可压缩润滑力将防止颗粒接触，但包括非连续或可压缩效应允许颗粒接触。确定了粒子接触的临界Stokes数St 1，并发现其形式为St 1 = 2 [ln（h′o/l）+C（αo）]，其中C（αo）是O（1）量，l是由l <$hc（1+αo）/ αo定义的特征长度尺度.当Sto[Gt ] St 1时，两个粒子接近和反弹期间消耗的总能量也在完全弹性或非弹性固体碰撞的情况下确定。
The low-Reynolds-number collision and rebound of two rigid spheres moving in an ideal isothermal gas is studied in the lubrication limit. The spheres are non-Brownian in nature with radii much larger than the mean-free path of the molecules. The nature of the flow in the gap between the particles depends on the relative magnitudes of the minimum gap thickness, h′o, the mean-free path of the bulk gas molecules, λo, and the gap thickness at which compressibility effects become important, hc. Both the compressible nature of the gas and the non-continuum nature of the flow in the gap are included and their effects are studied separately and in combination. The relative importance of these two effects is characterized by a dimensionless number, αo≡ (hc/λo). Incorporation of these effects in the governing equations leads to a partial differential equation for the pressure in the gap as a function of time and radial position. The dynamics of the collision depend on αo, the particle Stokes number, Sto, and the initial particle separation, h′o. While a continuum incompressible lubrication force applied at all separations would prevent particle contact, the inclusion of either non-continuum or compressible effects allows the particles to contact. The critical Stokes number for particles to make contact, St1, is determined and is found to have the form St1= 2 [ln(h′o/l) +C(αo)], where C(αo) is an O(1) quantity and l is a characteristic length scale defined by l≡ hc(1+αo)/ αo. The total energy dissipated during the approach and rebound of two particles when Sto[Gt ]St1 is also determined in the event of perfectly elastic or inelastic solid-body collisions.