Lattice Boltzmann simulation of the sedimentation of two spheres in a vertical tube

In this work the three-dimensional lattice Boltzmann simulations are performed to study the settling patterns of two spheres with different densities in a 5d (d is the diameter of sphere) tube of square-cross section. The focus is on the hydrodynamic interaction between the two spheres at the low Reynolds numbers. It has been found that the spheres will migrate to the reverse-diagonal plane of the tube even if they are initially placed in the centerline plane of the tube. The pattern suggests that the particles can only find their equilibrium positions in the diagonal plane when the Reynolds number is low. In addition, the effect of the Reynolds number on this pattern is also discussed. (paper)