The migration and rheotaxis of elliptical squirmers (a swimmer self-propels by imposing a given tangential velocity at its surface) in a Poiseuille flow are simulated numerically. The phase diagrams are employed to illustrate the effect of the aspect ratio ([Formula: see text]) and the Reynolds number of the squirmer ([Formula: see text]), the self-propelling strength ([Formula: see text]), and the blockage ratio ([Formula: see text]) on the stable movement and orientation evolution of the elliptical squirmers. Five typical migration modes (including the stable sliding, periodic tumbling, damped swinging, periodic swimming, and chaotic migrating modes) and three rheotaxis states (including the stable, sub-stable, and unstable states) are identified. This pattern also exists for the locomotion of a pair of squirmers. It is found that, with increasing [Formula: see text] and [Formula: see text] or [Formula: see text] and [Formula: see text], the squirmers migrate in the more stable modes and rheotaxis states. With increasing Rep ([Formula: see text]), this pattern can also be found when the locomotion of two squirmers is considered, but it shows the opposite effect for an individual squirmer. In addition, a squirmer with a smaller AR is more easily to be trapped by the sidewall with [Formula: see text] because it is difficult to orient. Accordingly, a larger AR yields a migration, which is more easily along the centerline of the flow with [Formula: see text]. It is interesting that the squirmers with AR =  0.2 almost maintain upstream oriented as they are usually attracted by the sidewall.

In this paper the propulsion of elliptical objects (called squirmers) by imposed tangential velocity along the surface is studied. For a symmetric velocity distribution (a neutral squirmer), pushers (increased tangential velocity on the downstream side of the ellipse) and pullers (increased tangential velocity on the upstream side of the ellipse), the hydrodynamic characteristics, are simulated numerically using the immersed boundary-lattice Boltzmann method. The accuracy of the numerical scheme and code are validated. The effects of Reynolds number (Re) and squirmer aspect ratio (AR) on the velocity u*, power expenditure P* and hydrodynamic efficiency η of the squirmer are explored. The results show that the change of u* along radial direction r* shows the relation of u*~r*−2 for the neutral squirmer, and u*~r*−1 for the pusher and puller. With the increase of Re, u* of the pusher increases monotonically, but u* of the puller decreases from Re=0.01 to 0.3, and then increases from Re=0.3 to 3. The values of P* of the pusher and puller are the same for 0.01 ≤ Re ≤ 0.3; P* of the pusher is larger than that of the puller when Re > 0.3. η of the pusher and puller increases with increasing Re, but the pusher has a larger η than the puller at the same Re. u* and P* decrease with increasing AR, and the pusher and puller have the largest and least u*, respectively. The values of P* of the pusher and puller are almost the same and are much larger than those of the neutral squirmer. With the increase of AR, η increases for the neutral squirmer, but changes non-monotonically for the pusher and puller.

Multiphase flow with self-driven particles is ubiquitous and complex. Exploring the flow properties has both important academic meaning and engineering value. This review emphasizes some recent studies on multiphase flow with self-driven particles: the hydrodynamic interactions between self-propelled/self-rotary particles and passive particles; the aggregation, phase separation and sedimentation of squirmers; the influence of rheological properties on its motion; and the kinematic characteristics of axisymmetric squirmers. Finally, some open problems, challenges, and future directions are highlighted.

This paper simulates the locomotion of a micro-swimmer towing cargo through a shear-dependent non-Newtonian fluid. We investigate the effect of the shear-dependent rheology (refers to the power-law index n), swimming Reynolds numbers ( Re), and the relative position (refers to the distance ds and the concerning angle θ) between the swimmer and the cargoes on the assemblies' locomotion. For a swimmer towing a cargo, we find that a cargo-puller, cargo-pusher, or pusher-cargo (three typical towing models) swims faster in the shear-thickening fluids than in the shear-thinning fluids at Re ≤ 1. Moreover, the pusher-cargo swims significantly faster than the counterpart puller-cargo at Re ≤ 1. For a swimmer towing two cargoes, we find that the maximum negative swimming speeds can be achieved at θ = 30° and 150°, corresponding to two typical regular-triangle structures assembled by the squirmer and the cargoes. Interestingly, some regular-triangle assemblies (puller with θ = 30° and pusher with θ = 150°) can maintain a swimming opposite to their initial orientation. In addition, we obtain a relation of energy expenditure P ∼ Ren−1; it is also found that the assembly swimming in the shear-thinning fluids is more efficient than in the shear-thickening ones. Our results provide specified guidance in the designing of cargo-carrying micro-swimming devices.