Hydrodynamics of an inertial squirmer and squirmer dumbbell in a tube

Abstract

We study the hydrodynamics of a spherical and dumbbell-shaped microswimmer in a tube. Combined with a squirmer model generating tangential surface waves for self-propulsion, a direct-forcing fictitious domain method is employed to simulate the swimming of the microswimmers. We perform the simulations by considering the variations of the swimming Reynolds numbers (Re), the blockage ratios (κ) and the relative distances (ds) between the squirmers of the dumbbell. The results show that the squirmer dumbbell weakens the inertia effects of the fluid more than an individual squirmer. The constrained tube can speed up an inertial pusher (propelled from the rear) and an inertia pusher dumbbell; a greater distance ds results in a slower speed of an inertial pusher dumbbell but a faster speed of an inertial puller (propelled from the front) dumbbell. We also illustrate the swimming stability of a puller (stable) and pusher (unstable) swimming in the tube at Re = 0. At a finite Re, we find that the inertia and the tube constraint competitively affect the swimming stability of the squirmers and squirmer dumbbells. The puller and puller dumbbells swimming in the tube become unstable with increasing Re, whereas an unstable–stable–unstable evolution is found for the pusher and pusher dumbbells. With increasing κ, the puller and puller dumbbells become stable while the pusher and pusher dumbbells become unstable. In addition, we find that a greater ds yields a higher hydrodynamic efficiency η of the inertial squirmer dumbbell.

Cargo carrying with an inertial squirmer in a Newtonian fluid

“…The DF-FDM simulation of squirmer dynamics has been shown to be accurate when compared with the theoretical solution at Re = 0 (Lin & Gao 2019) and other numerical results at a finite Re (Ouyang et al. 2022). Note that the swimming Reynolds number in this study is defined as Re = ρ f aU 0 / μ , and the velocities and the time are normalized by the velocity scale U 0 and time scale a / U 0 , respectively.…”

“…2011; Ouyang et al. 2022). The pusher-cargo assemblies with different-shaped cargoes maintain the same decay as | u | ≈ O ( r −4 ) at the first stage ( r / a < 2.5); by further increasing r / a , the velocity decay for the pusher-cargo model 2 is faster than that for the pusher-cargo model 1.…”

“…This pattern is different from that of an individual squirmer because the carried cargoes change the structure of the flow field for these assemblies. However, this result indicates that a more rapid decay leads to larger efficiency (Zhu et al 2011;Ouyang et al 2022). The pusher-cargo assemblies with different-shaped cargoes maintain the same decay as |u| ≈ O(r −4 ) at the first stage (r/a < 2.5); by further increasing r/a, the velocity decay for the pusher-cargo model 2 is faster than that for the pusher-cargo model 1.…”

“…In addition, the assemblies with a larger d s (d s = 3a) tend to become unstable more easily, similar to the pattern of the stability for a puller dumbbell (two pullers assembled in tandem). This is because the body with a larger d s suffers the effect of the flows it induced in pushing away from the original orbit more significantly than that with a smaller d s (Ouyang & Lin 2021;Ouyang et al 2022). This mechanism may also cause the stability of a squirmer carrying a cargo with different geometries -an assembly with an oblate cargo is more stable than that with prolate cargo, because the former (as the case with a larger d s ) is more slender than the latter one.…”

“…More recently, Ouyang et al. (2022) considered the inertial swimming of a squirmer dumbbell inside a tube and found that the constrained tube could counterintuitively hasten an inertial pusher dumbbell.…”