Fig. 1. Illustration of chain-shaped microswarms rolling along acoustic virtual walls.

a Virtual wall concept. To move from left to right by means of rolling in x−y plane, the gray microchain (conventional methods) has to passively follow the boundary posed by a nearby real wall; in contrast, the green microchain (our strategy) can directly roll forward along the virtual wall. b Mechanism of microchain rolling along one-dimensional acoustic virtual walls. (i) Magnetic particles are pushed to the pressure nodal line by the acoustic radiation force as the acoustic standing wave field (AF) is developed. Gray arrows denote the acoustic virtual wall effect from both sides of the acoustic pressure nodal line, which is denoted by the blue dotted line. (ii) Magnetic particles assemble into microchains and achieve rolling motion along the acoustic virtual wall as soon as the rotational magnetic field (MF) is introduced. The curved black arrow indicates the magnetic rotational direction. The red arrow shows the rolling direction. c Schematic of microchains rolling along two-dimensional dynamic acoustic virtual walls, realized by switching the orientation of the acoustic standing wave field and the rotational direction of the magnetic field. d Schematic of the experimental setup, consisting of an acoustic manipulation chamber and a magnetic manipulation system. The whole setup is mounted on an inverted microscope, and we image the rolling motion using high-speed and high-sensitivity cameras. The inset shows the piezoelectric transducer pairs A_1,2 and B_1,2.