Drafting, kissing, and tumbling of a pair of particles settling in non-Newtonian fluids

The drafting, kissing, and tumbling (DKT) of a pair of particles in Newtonian fluids are frequently observed in particle sedimentations and have been well studied. However, sedimentation shows distinct behaviors when the particle pair is released in non-Newtonian fluids, and dynamics of the DKT have still not been completely understood. In this paper, the immersed boundary-lattice Boltzmann method with a hybrid multiple-relaxation-time scheme is used to examine the dynamics of the DKT of a pair of particles settling in non-Newtonian fluids. The particle pair is released in a confined channel filled with non-Newtonian fluids, in which the non-Newtonian behaviors of shear-thinning/shear-thickening and yield stress are considered. The results demonstrate that the horizontal migration direction at the initial stage of the separation state in a shear-thinning fluid is totally different from that happening in a Newtonian fluid. It is attributed to the asymmetrical fluid viscosity on both sides of the pair of particles. Our findings also show that yield stress plays a dominant role in the sedimentation velocity and separation distance between the particles forming this pair. Under the effect of yield stress, three sedimentation structures, which correspond to different dynamic behaviors of the pair of particles, are also identified during the sedimentation. Furthermore, some critical conditions, regarding horizontal migration toward the right or left side, DKT/non-DKT and kissing/non-kissing states are established through the Bingham number (Bn)-power-law index (n) diagrams and tables. Also, the effect of the diameter ratio between two particles on the DKT is studied.