Department of Mechanical Engineering, University of Minnesota, 111 Church Street S.E., Minneapolis, Minnesota 55455, USA.
Phys Rev E. 2017 Sep;96(3-1):032911. doi: 10.1103/PhysRevE.96.032911. Epub 2017 Sep 18.
Like and oppositely charged particles or dust grains in linear shear flows are often driven to collide with one another by fluid and/or electrostatic forces, which can strongly influence particle-size distribution evolution. In gaseous media, collisions in shear are further complicated because particle inertia can influence differential motion. Expressions for the collision rate coefficient have not been developed previously which simultaneously account for the influences of linear shear, particle inertia, and electrostatic interactions. Here, we determine the collision rate coefficient accounting for the aforementioned effects by determining the collision area, i.e., the area of the plane perpendicular to the shear flow defining the relative initial locations of particles which will collide with one another. Integration of the particle flux over this area yields the collision rate. Collision rate calculations are parametrized as an enhancement factor, i.e., the ratio of the collision rate considering potential interactions and inertia to the traditional collision rate considering laminar shear only. For particles of constant surface charge density, the enhancement factor is found dependent only on the Stokes number (quantifying particle inertia), the electrostatic energy to shear energy ratio, and the ratio of colliding particle radii. Enhancement factors are determined for Stokes numbers in the 0-10 range and energy ratios up to 5. Calculations show that the influences of both electrostatic interactions and inertia are significant; for inertialess (St=0) equal-sized and oppositely charged particles, we find that even at energy ratios as low as 0.2, enhancement factors are in excess of 2. For the same situation but like-charged particles, enhancement factors fall below 0.5. Increasing the Stokes number acts to mitigate the influence of electrostatic potentials for both like and oppositely charged particles; i.e., inertia reduces the enhancement factor for oppositely charged particles and increases it for like-charged particles. Uniquely, at elevated Stokes numbers with attractive potentials we find collisionless "pockets" within the collision area, which are regions completely bounded by the collision area but within which collisions do not occur. Regression equations to results are provided, enabling calculation of the enhancement factor as a function of energy ratio and Stokes number. In total, this study both leads to insight into the collision dynamics of finite-inertia, charged particles in shear flows, and provides a means to simply calculate the particle-particle collision rate coefficient.
在直线剪切流中，带相同或相反电荷的粒子或尘粒通常会受到流体和/或静电力的驱动而相互碰撞，这会强烈影响颗粒尺寸分布的演化。在气态介质中，由于颗粒惯性会影响差异运动，剪切碰撞会变得更加复杂。之前尚未开发出同时考虑线性剪切、颗粒惯性和静电相互作用影响的碰撞速率系数表达式。在这里，我们通过确定碰撞面积来确定同时考虑上述影响的碰撞速率系数，即垂直于剪切流的平面的面积，该面积定义了将相互碰撞的颗粒的相对初始位置。对该区域内的颗粒通量进行积分即可得到碰撞速率。碰撞速率的计算被参数化为增强因子，即考虑潜在相互作用和惯性的碰撞速率与仅考虑层流剪切的传统碰撞速率的比值。对于具有恒定表面电荷密度的颗粒，增强因子仅取决于斯特克斯数（量化颗粒惯性）、静电能与剪切能的比值以及碰撞颗粒半径之比。为 0-10 范围内的斯特克斯数和高达 5 的能量比确定了增强因子。计算表明，静电相互作用和惯性的影响都很显著；对于无惯性（St=0）、等大小和带相反电荷的颗粒，即使在能量比低至 0.2 的情况下，增强因子也超过 2。对于相同情况但带相同电荷的颗粒，增强因子低于 0.5。增加斯特克斯数可以减轻静电势对带相反和相同电荷的颗粒的影响；即，惯性会降低带相反电荷的颗粒的增强因子，并增加带相同电荷的颗粒的增强因子。独特的是，在具有吸引力的势的高斯特克斯数下，我们在碰撞区域内发现了无碰撞的“口袋”，这些区域完全被碰撞区域包围，但其中不会发生碰撞。提供了回归方程的结果，可以将增强因子作为能量比和斯特克斯数的函数进行计算。总的来说，这项研究不仅深入了解了剪切流中有限惯性带电颗粒的碰撞动力学，还提供了一种简单计算颗粒-颗粒碰撞速率系数的方法。
