Abstract This paper presents a study on the drafting, kissing, tumbling (DKT) phenomenon between two circular and impermeable interacting particles of different sizes and densities in a confined medium in 2D using Immersed Boundary (IB) method. There are two different cases considered in this study. The first case, Case 1, deals with the scenario when the trailing particle was larger in size than the leading particle and in the second case, it was the other way round (Case 2). In both cases, apart from the size difference, the particles were assumed to have different densities. The paper investigated the effect of diameter ratio, as well as the effect of density differential on the dynamics of the settling particles. The obtained results clearly indicated that the size and the density of particles play an important role in the dynamics of the two interacting particles. The results suggested when the larger particle in both the cases was chosen to have higher density than the smaller particles, irrespective of diameter ratio and density difference, the particles went through one complete cycle of DKT. On the other hand, when the larger particle, irrespective of its initial position- leading or trailing, was having less density than the smaller particles, the results obtained was specific to diameter ratio as well as density difference.

中文翻译：

---

用浸入边界法研究密闭介质中两种不同尺寸和密度颗粒的牵伸、接吻和翻滚过程

摘要 本文使用浸入边界 (IB) 方法研究了二维受限介质中两个不同尺寸和密度的圆形和不可渗透的相互作用粒子之间的牵伸、亲吻、翻滚 (DKT) 现象。本研究考虑了两种不同的情况。第一种情况，情况 1，处理尾随粒子的尺寸大于前导粒子的情况，而在第二种情况下，情况正好相反（情况 2）。在这两种情况下，除了尺寸差异外，假设颗粒具有不同的密度。该论文研究了直径比的影响，以及密度差异对沉降颗粒动力学的影响。所得结果清楚地表明，粒子的大小和密度在两个相互作用粒子的动力学中起着重要作用。结果表明，当在两种情况下选择较大的颗粒比较小的颗粒具有更高的密度时，无论直径比和密度差异如何，颗粒都经历了一个完整的 DKT 循环。另一方面，当较大颗粒的密度低于较小颗粒时，无论其初始位置是领先还是落后，所获得的结果都特定于直径比和密度差异。粒子经历了一个完整的 DKT 循环。另一方面，当较大颗粒的密度低于较小颗粒时，无论其初始位置是领先还是落后，所获得的结果都特定于直径比和密度差异。粒子经历了一个完整的 DKT 循环。另一方面，当较大颗粒的密度低于较小颗粒时，无论其初始位置是领先还是落后，所获得的结果都特定于直径比和密度差异。