School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York, USA.
Langmuir. 2011 Oct 4;27(19):11813-23. doi: 10.1021/la202138t. Epub 2011 Sep 7.
The collision of particles influences the behavior of suspensions through the formation of aggregates for adhesive particles or through the contributions of solid-body contacts to the stress for nonadhesive particles. The simplest estimate of the collision rate, termed the ideal collision rate, is obtained when particles translate and rotate with the flow but have no hydrodynamic or colloidal interactions. Smoluchowski calculated the ideal collision frequency of spherical particles in 1917. So far, little work has been done to understand rate of collision for nonspherical particles. In this work, we calculate the ideal collision rate for cylindrical particles over a broad range of particle aspect ratios r defined as the ratio of length to diameter. Monte Carlo simulations are performed with initial relative positions and orientations that model the rate of approach of noninteracting particles following Jeffery orbits with several choices of the orbit distribution. The role of rotational motion of particles on collision frequency is elucidated by comparing the ideal collision rate calculations with similar calculations for nonrotating particles. It is shown that the ratio of the collision rate of cylinders to that of spheres that circumscribe the cylinders is proportional to 1/rr(e) for r ≫ 1 and r(e) for r ≪ 1. Here, r(e) is the effective aspect ratio defined as the aspect ratio of a spheroid having the same period of rotation as the cylinder. The effective aspect ratio of the cylindrical particles was determined using finite element calculations of the torque on nonrotating cylinders with their axes parallel to the velocity and velocity gradient directions. In addition to deriving the total collision rate, we categorize collisions as side-side, edge-side, and face-edge based on the initial point of contact. Most collisions are found to be side-edge for r ≫ 1 and face-edge for r ≪ 1, suggesting that nonlinear aggregates will develop if particles stick at the point of first contact.
颗粒碰撞通过形成粘性颗粒的聚集体或通过非粘性颗粒的固体质点接触对应力的贡献来影响悬浮液的行为。最简单的碰撞速率估计，即理想碰撞速率，是在颗粒随流平移和旋转但没有流体动力或胶体相互作用时获得的。Smoluchowski 在 1917 年计算了球形颗粒的理想碰撞频率。到目前为止，对于非球形颗粒的碰撞速率，几乎没有工作来理解。在这项工作中，我们计算了在广泛的颗粒纵横比 r（定义为长度与直径的比）范围内的圆柱形颗粒的理想碰撞速率。使用初始相对位置和取向进行蒙特卡罗模拟，这些位置和取向模拟了非相互作用颗粒遵循 Jeffery 轨道的接近速率，其中选择了几种轨道分布。通过将理想碰撞速率计算与非旋转颗粒的类似计算进行比较，阐明了颗粒旋转运动对碰撞频率的作用。结果表明，圆柱的碰撞速率与圆柱所包围的球体的碰撞速率之比与 r ≫ 1 和 r ≪ 1 时的 1/rr(e)成正比。这里，r(e)是有效纵横比，定义为与圆柱具有相同旋转周期的旋转椭球体的纵横比。使用有限元计算平行于速度和速度梯度方向的非旋转圆柱的扭矩，确定了圆柱形颗粒的有效纵横比。除了推导总碰撞速率外，我们还根据初始接触点将碰撞分类为侧面-侧面、边缘-侧面和面-边缘。对于 r ≫ 1，大多数碰撞被发现为侧面-边缘，对于 r ≪ 1，大多数碰撞被发现为面-边缘，这表明如果颗粒在第一次接触时粘住，将形成非线性聚集体。
