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The two-dimensional lattice Boltzmann method (LBM) was used to study the motion of two interacting particles with different densities (ρ_1 and ρ_2) and diameters (d_1 and d_2), which were placed in a vertical channel under gravity. Both the density ratio (λ=ρ_2/ρ_1) and diameter ratio (r=d_2/d_1) between the particles were considered. The transition boundaries between the regime where the particles settle separately and the regime where the particles interact are identified by λ_mar) and λ_min(r); they exhibit excellent power-law rela
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