Gravitational sedimentation and the collision of particles play key roles in various natural and engineering processes. In practice, particles are often non-spherical in shape with non-uniform mass distribution. In this study we investigate how the mass eccentricity influences the settling and gravitational collision of non-spherical particles in a quiescent fluid. Firstly, we theoretically analyse the effect of mass centre offset on the settling motion of a single spheroid under the low-Reynolds-number assumption. We find that the competition of fluid-inertia torque and gravitational torque determines the terminal settling mode of the spheroid. As the mass centre offset increases from zero to a critical value, the orientation of a settling spheroid undergoes a transition from the broad-side-on to narrow-side-on alignment. With an intermediate mass centre offset, the settling spheroid prefers an oblique orientation with a horizontal drift. Secondly, we investigate the gravitational collision rate of settling spheroids. With the change of particle orientation, the collision kernel exhibits a non-monotonic variation with a maximum when particles settle with an intermediate oblique orientation. Therefore, adjusting the mass centre offset to alter particle orientation can indirectly affect the collision rate of settling spheroidal particles. In summary, our findings reveal the significance of the mass eccentricity on particle dynamics in fluid flows, and suggest a potential approach for manipulating the settling motion and collision rate of non-spherical particles by adjusting their mass centre position.

中文翻译：

---

静止流体中具有偏移质心的球状颗粒的沉降和碰撞

重力沉降和颗粒碰撞在各种自然和工程过程中发挥着关键作用。在实践中，颗粒通常是非球形且质量分布不均匀。在这项研究中，我们研究质量偏心率如何影响静态流体中非球形颗粒的沉降和重力碰撞。首先，我们从理论上分析了低雷诺数假设下质心偏移对单个球体沉降运动的影响。我们发现流体惯性力矩和重力力矩的竞争决定了球体的最终沉降模式。随着质心偏移从零增加到临界值，沉降球体的方向经历从宽边对准到窄边对准的转变。具有中等质心偏移时，沉降球体更喜欢具有水平漂移的倾斜方向。其次，我们研究了沉降球体的重力碰撞率。随着粒子方向的变化，碰撞核表现出非单调变化，当粒子以中间倾斜方向沉降时碰撞核达到最大值。因此，调整质心偏移以改变颗粒方向可以间接影响沉降球体颗粒的碰撞率。总之，我们的研究结果揭示了质量偏心率对流体流动中颗粒动力学的重要性，并提出了一种通过调整非球形颗粒的质心位置来操纵非球形颗粒的沉降运动和碰撞率的潜在方法。