Swimming of an inertial squirmer array in a Newtonian fluid

An immersed boundary-lattice Boltzmann method is employed to simulate a squirmer (a classical self-propelled model) array swimming in a Newtonian fluid. The swimming Reynolds number Re-s is set in the range 0.05 <= Re-s <= 5 to study three typical arrays (i.e., the two-squirmer, triangular-squirmer, and quadrilateral-squirmer arrays) in their swimming speed, their power expenditure (P), and their hydrodynamic efficiency (eta). Our results show that the two-pusher array with a smaller d(s) (the distance between the squirmers) yields a slower speed in contrast to the two-puller array, where a smaller d(s) yields a faster speed at Re-s > 1 (pusher is propelled from the rear and puller from the front). The regular triangular-pusher (triangular-puller) array with theta = -60 degrees (the included angle between the squirmers) swims faster (slower) than that with theta = 60 degrees; the quadrilateral-pusher (quadrilateral-puller) array with model 2 swims faster (slower) than model 1 (the models are to be defined later). It is also found that a two-puller array with a larger d(s) is more likely to become unstable than that with a smaller d(s). The triangular-puller array with theta = 60 degrees is more likely to become unstable than that with theta = 60 degrees; the quadrilateral-puller array with model 1 becomes unstable easier than that with model 2. In addition, a larger d(s) generally results in a less energy expenditure. A faster squirmer array yields a higher eta, except for two extraordinarily puller arrays. A quantitative relation for eta with Re-U > 1 is obtained approximately, in that the increasing ratio of eta is proportional to an exponent of the motion Reynolds number Re-U. Published under an exclusive license by AIP Publishing.

Automated summary

An immersed boundary-lattice Boltzmann method is used to study the swimming behavior of a squirmer array in a Newtonian fluid. The results show that the array configuration and spacing have significant effects on the swimming speed, power expenditure, and hydrodynamic efficiency. It is also found that larger spacings tend to result in instability and higher energy efficiency can be achieved with smaller spacings.