Abstract This paper numerically demonstrates the drafting, kissing, tumbling (DKT) phenomenon between two interacting circular, impermeable particles of different sizes in a confined medium for different scenarios using Immersed Boundary (IB) method in 2D. Two cases were considered for this particular problem. In the first case, referred to as Case 1, the trailing particle was larger in size than the leading particle and in Case 2, it was the other way round. The main emphasis of this paper was to investigate the effect of diameter ratio, γ , of the two particles, on the dynamics of the two sedimenting particles. In Case 1, it was observed that upon increasing γ from unity onwards, the particles underwent from repeated to one cycle of DKT. In Case 2, the impact of γ was more prominent. For γ 2 , the particles underwent two cycles of DKT process. For γ ≥ 2 the particles first parted away from each other, but then quickly started drafting towards each other. Subsequently, after one cycle of DKT, they permanently parted away from each other. This paper also investigated the effect of initial vertical distance between the two sedimenting particles. The results presented in here are in good agreement with other published articles on similar problems.

中文翻译：

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两种不同尺寸颗粒在密闭介质中浸入边界法牵伸、接吻和翻滚过程的研究

摘要 本文使用浸入边界 (IB) 方法在 2D 中以数值方式演示了在不同场景下在密闭介质中不同大小的两个相互作用的圆形不透水颗粒之间的牵伸、亲吻、翻滚 (DKT) 现象。针对这个特定问题考虑了两种情况。在第一种情况下，称为情况 1，尾随颗粒的尺寸大于前导颗粒的尺寸，而在情况 2 中，情况正好相反。本文的主要重点是研究两种颗粒的直径比 γ 对两种沉降颗粒动力学的影响。在案例 1 中，观察到从 1 开始增加 γ 后，粒子经历了重复到一个 DKT 循环。在案例 2 中，γ 的影响更为突出。对于 γ 2 ，粒子经历了两个循环的 DKT 过程。对于 γ ≥ 2，粒子首先彼此分开，但随后迅速开始彼此牵拉。随后，经过一个 DKT 周期后，他们永久地分道扬镳。本文还研究了两个沉降颗粒之间初始垂直距离的影响。此处显示的结果与其他已发表的关于类似问题的文章非常一致。