Abstract
In present study, the drafting, kissing and tumbling (DKT) phenomenon of two spheres sedimenting in a long container filled with an incompressible fluid is numerically investigated by using the immersed-boundary technique. The main emphasis of this study is to investigate the effect of the initial gap sizes and diameter ratio between two spheres on the flow pattern during sedimentation. The method is first validated with flows induced by a sphere settling under gravity in a small container for which experimental data are available. For sedimentation of two spheres with different sizes, three initial configurations are considered: in Setup-A, the larger sphere is initially located above the regular one; in Setup-B, there are two identical regular spheres; in Setup-C, the regular sphere is initially located above the larger one. The results show that, for all three initial configurations, the kissing time delays as the initial gap size increases. For Setup-A, the duration of kissing decreases with the increase of diameter ratio. Instead, for Setup-C, the duration of kissing increases with the increase of diameter ratio and there is no DKT phenomenon beyond threshold initial gap size and diameter ratio. For both Setup-A and Setup-C, the gaps between two spheres at terminal velocity increase, whereas for Setup-B that remain constant because of the same terminal velocity of two spheres. Finally, the effects of initial gap size and diameter ratio on the occurrence of DKT process are investigated. By changing these two parameters, the results reveal the transitions between the DKT phenomena.