Available online at www.sciencedirect.com ScienceDirect Mathematics and Computers in Simulation 177 (2020) 341–357 www.elsevier.com/locate/matcom Original articles Study of drafting, kissing and tumbling process of two particles with different sizes using immersed boundary method in a confined medium Sudeshna Ghosh a ,∗ , Manish Kumar b a Amity School of Applied Sciences, AUH, Gurugram , Haryana, India b NIT,Warangal, India Received 19 July 2019; received in revised form 15 April 2020; accepted 29 April 2020 Available online 16 May 2020 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. c ⃝ 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved. Keywords: Immersed boundary method; Sedimentation; Fluid–structure interaction; DKT 1. Introduction Gravitational settling of particles in a viscous fluid is encountered in many natural and industrial applications such as the petroleum and paper industries, mineral ore processing, flow of pollutants, etc. This topic has been studied extensively both theoretically and experimentally. Different numerical methods have been employed to study particulate flows involving interaction of a dynamically evolving fluid and solid suspended particles. For accurate prediction of the flow behaviour, it is very important to study the interaction between fluid and particles, as well as the interaction between particles. A pair of interacting particles in suspended flow undergoes the process of ‘drafting, kissing, tumbling’ (DKT), which has been well established experimentally [7,16] and numerically [6,11]. The physical justification of the phenomenon is well documented in the cited papers. ∗ Corresponding author. E-mail address: sudeshnagh108@gmail.com (S. Ghosh). https://doi.org/10.1016/j.matcom.2020.04.029 0378-4754/ c ⃝ 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.