Settling behavior of two particles with different densities in a vertical channel

Sedimentation of two particles with different densities in a two-dimensional channel is studied using the lattice Boltzmann method. We focus on the steady state and periodic state of the settling behavior of the particles, which strongly depend on the Reynolds number Re as well as the density difference α. We show that the particles always reach a steady state if α is small enough at a large Re, while they are predicted to oscillate at a small Re. The staggered configurations in steady state for a wide range of Re and α are presented. Our results also demonstrate that the periodic state of the particles at a small Re is different from that at large Re. One significant difference is that the amplitude of oscillation decreases as α increases when Re is small, while the opposite is true when Re is large. In addition, there exists a narrow range of Re within which we can observe both of the above-mentioned periodic states. At large Re, the effect of α on the periodic motion of particles is quite significant. The phase diagram, constructed using the lateral displacements of the two particles, shows a transition to a period-doubled state on increasing α when Re is large.