We simulated the sedimentations of two unequal spheres with different densities in a square tube for Galileo numbers (Ga) from 5 to 25, resulting in a Reynolds number range of $0.8\leqslant Re_{T}\leqslant 17.3$ based on the terminal settling velocity. The sedimentation of spheres with different densities is dynamically more complex than that of identical spheres. At high Ga the spheres oscillate in the centreline plane of the tube, where they are initially released from rest. By contrast, the spheres move to the diagonal or reverse–diagonal plane of the tube at low Ga, reaching a steady or periodic state depending on the density difference between them. A phase diagram illustrates the transitions between different sedimentation behaviours depending on Ga and the density difference. A possible mechanism for these behaviours is also presented. Furthermore, we compare two-dimensional (2-D) and three-dimensional computations for our system to attain a better understanding of the hydrodynamic interactions between two unequal spheres at low but finite Reynolds number. Comparing relative trajectories, periods of oscillation and flow features shows that 2-D circular cylinders oscillate much more strongly and frequently than spheres under the same flow conditions. In particular, spheres do not have the discontinuity in period that arises in the 2-D case from the change in rotation sign of a heavy particle.

We simulated the motions and interactions of circular squirmers under gravity in a two-dimensional channel at finite fluid inertia, aiming to provide a comprehensive analysis of the dynamic features of swimming microorganisms or engineered microswimmers. In addition to a squirmer-type factor (β), another control parameter (α) was introduced, representing ratio of the self-propelling strength to the sedimentation strength of squirmers. Simulations were performed at 0.4 ≤ α ≤ 1.2 and −5 ≤ β ≤ 5. We first considered the sedimentation of a single squirmer. Five patterns were revealed, depending on both α and β: steady downward falling, steady inclined falling or rising and small-scale or large-scale oscillating. Compared with a pusher (β < 0, gaining thrust from rear), a puller (β > 0, gaining thrust from front) is more likely to break down its symmetrical structure and subsequently lose stability, owing to the high-pressure regions on its lateral sides. Typically, a pusher settles faster than a puller, whereas a neutral squirmer (β = 0) settles in between. This is related to the ‘trailing negative flow’ behind a pusher and ‘leading negative flow’ before a puller. We then placed two squirmers in line with the gravity direction to study their interactions. Results show pullers attract each other and come into contact as a result of the low-pressure regions between them, whereas the opposite is observed for pushers. The interactions between two pullers are illustrated by their respective patterns. In contrast, pushers never come into contact and maintain distance from each other with increasing separation. We finally examined how a puller interacts with a pusher.

In this paper, we propose a lattice Boltzmann (LB) method coupled with a direct-forcing fictitious domain (DF/FD) method for the simulation of particle suspen- sions. This method combines the good features of the LB and the DF/FD methods by using two unrelated meshes, namely, an Eulerian mesh for the flow domain and a Lagrangian mesh for the solid domain, which avoids the re-meshing procedure and does not need to calculate the hydrodynamic forces at each time step. The non-slip boundary condition is enforced by introducing a forcing term into the lattice Boltz- mann equation, which preserves all remarkable advantages of the LBM in simulating fluid flows. The present LB-DF/FD method has been validated by comparing its re- sults with analytical results and previous numerical results for a single circular particle and two circular particles settling under gravity. The interaction between particle and wall, the process of drafting-kissing-tumbling (DKT) of two settling particles will be demonstrated. As a manifestation of the efficiency of the present method, the settling of a large number (128) of circular particles is simulated in an enclosure.

We simulated the sedimentation of two self-propelled particles in a two-dimensional (2D) vertical channel using the lattice Boltzmann method. A 2D squirmer model was employed to simulate the microswimmers, and five typical locomotive modes were obtained for a single squirmer, namely, central steady sedimentation, near-wall steady motion, wall-attracted oscillation, large-amplitude oscillation, and small-amplitude oscillation. The locomotive modes of two squirmers are obtained by combinations of different locomotive modes of a single squirmer. It was found that the motion of two squirmers was much more complex than that of a single squirmer, and this complex locomotive mode could be explained by the pressure distribution of the two squirmers. Moreover, we performed a comprehensive analysis of the obtained locomotive modes and determined that the angle at which the two squirmers separated from each other and swimming speed were crucial, which may be the reason for the different locomotive modes of the squirmers that switch from each other.

Direct Numerical Simulation of Multiple Particles Sedimentation at an Intermediate Reynolds Number - Volume 16 Issue 3 - Deming Nie, Jianzhong Lin, Mengjiao Zheng