Influence of vibrating wall on microswimmer migration in a channel

The migration of microorganisms or synthetic microscale robots is always affected by the local environment, such as the surrounding fluid or muscular contractions. This paper describes a numerical study and asymptotic analysis of the influence of a moving boundary on the migration of a microswimmer in a channel. The locomotion of a finite swimmer between vibrating walls is simulated with both a beating and motionless flagellum. The swimmer can be propelled by the wall vibration, and this propulsion is independent of the self-propulsion of the beating flagellum. To reveal the influence of the vibrating walls, asymptotic analysis is applied to two models, one with an infinitely long filament placed at the channel center and another with an infinitesimally small swimmer. The results show that the vibrating wall effect depends on the ratio of the distance between the walls to the wavelength. The wall effect functions for the two models are obtained for both two-dimensional and circular channels. The finite swimmer in the two-dimensional channel moves with the velocity of the flow induced by the vibrating wall, rather than the swimming speed of the infinite filament. However, in the circular channel, there is no difference between the migration speeds of the two models, and the range of the wall influence is much larger than in the two-dimensional case.