Hydrodynamics of an inertial squirmer and squirmer dumbbell in a tube

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.