Rolling microswarms along acoustic virtual walls

Abstract

Rolling is a ubiquitous transport mode utilized by living organisms and engineered systems. However, rolling at the microscale has been constrained by the requirement of a physical boundary to break the spatial homogeneity of surrounding mediums, which limits its prospects for navigation to locations with no boundaries. Here, in the absence of real boundaries, we show that microswarms can execute rolling along virtual walls in liquids, impelled by a combination of magnetic and acoustic fields. A rotational magnetic field causes individual particles to self-assemble and rotate, while the pressure nodes of an acoustic standing wave field serve as virtual walls. The acoustic radiation force pushes the microswarms towards a virtual wall and provides the reaction force needed to break their fore-aft motion symmetry and induce rolling along arbitrary trajectories. The concept of reconfigurable virtual walls overcomes the fundamental limitation of a physical boundary being required for universal rolling movements.

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.

Fig. 2. Characterization of microchains rolling along the single acoustic virtual wall in a confined glass capillary.

a Schematic of the experimental setup. The capillary is held by a polydimethylsiloxane (PDMS) polymer substrate with two piezoelectric transducers (PZT) attached on the substrate’s lateral surfaces. The inset illustrates a cross-sectional view of the glass capillary with the microchain trapped at the pressure node of an acoustic standing wave field. b Image sequence of microchains rolling from bottom to top. The pink curved arrow, yellow arrow, and white dotted line respectively denote the clockwise magnetic rotational direction, net translational direction and displacement. Scale bar, 100 μm. c Plot characterizing the translational velocity of a single microchain (length 65.63 μm) versus magnetic rotational velocity at selected acoustic voltages. The dotted lines are the corresponding linear fits. d Plot characterizing the translational velocity of a single microchain (length 65.63 μm) versus acoustic voltage at different magnetic rotational velocities. e Plot of the translational velocity versus microchain length under an acoustic excitation voltage and frequency of 20 V_PP and 2.02 MHz, respectively. The magnetic rotational velocity and the magnetic intensity were 24 rpm and 15 mT, respectively. These fittings were performed with the linear function model, y = ax. Each data point represents the average translational velocity analyzed from 3-5 microchains (Source Data). Error bars represent the standard deviation (s.d.) of data.

Fig. 3. Bidirectional rolling of microchains along the acoustic virtual wall.

a Bidirectional rolling motion (the direction is indicated by a yellow arrow) along the x-axial acoustic virtual wall upon flipping the rotational direction of the magnetic field (green curved arrow). The white dotted line denotes the net displacement. b Bidirectional rolling motion along the y-axial acoustic virtual wall. The pink curved arrows denote the magnetic rotational direction. For both panels, the acoustic excitation voltage and frequency were 20 V_PP and 1.55 MHz, respectively. The magnetic intensity was 21 mT. The magnetic rotational velocity as depicted in panel (a) and (b) was 24 rpm and 30 rpm, respectively. Scale bar, 100 μm.

Fig. 4. Mechanism of rolling motion along the acoustic virtual wall.

a Rotation of a microchain in the absence of an acoustic field. The 1/4-cycle superimposed subfigure shows off-center rotation of the microchain, while the 2-cycle subfigure shows its final rotational profile to be like a circle. No noticeable motion is observed. b Rotation of a microchain in the presence of a one-dimensional acoustic standing wave field. The microchain exhibits off-center rotation and rolling along the acoustic pressure nodal line. The white dotted lines of (a) and (b) respectively denote the rotational centerline and the acoustic pressure nodal line. The green curved arrow denotes the rotational direction. The yellow arrow and dotted line denote the rolling direction and the net displacement, respectively. Scale bar, 50 μm. c Superimposed time-lapse images of a microchain undergoing one rotational cycle. The acoustic excitation voltage and frequency were 20 V_PP and 1.55 MHz, respectively. The magnetic rotational direction was counterclockwise, and the magnetic rotational velocity and intensity were 12 rpm and 21mT, respectively. Blue and pink curves respectively denote the tracked trajectories of the two endpoints, P₁ and P₂. The white dotted line denotes the acoustic pressure nodal line. The axis in the lower left corner denotes the rotational direction. The number refers to the overlapped frames that has the same time interval, 0.1587 s, from 1 to 32. Scale bar, 50 μm. d Trajectories of the microchain’s two endpoints (P₁ and P₂), geometric center (C), and rotational center (A) (Source data). e Plot of the variable distance between the geometric and rotational centers of the microchain against rotational time (Source data). The period of one rotational cycle was 5 s. The off-center distance was obtained by subtracting the distance ∣P₁C∣ from ∣P₁A∣ (Supplementary Fig. 9). Fitting yielded a first-order sine function of $l\left(t\right)=7.157*\sin \left(1.256t+2.518\right)$. f Schematic of the experiment-supported theoretical model. The green rod denotes the self-assembly microchain.

Fig. 5. Two-dimensional dynamic rolling manipulation.

a In situ rotation of microchains at two-dimensional acoustic pressure nodal points. b Rolling of microchains along a predesigned square path. The last subfigure is a superimposed time-lapse image showing the full path. The green curved arrow, yellow arrow, and white arrow respectively denote the rotational direction, rolling direction, and historical path. c Using reconfigurable acoustic virtual walls to write the word “ETH” with rolling microchains. The acoustic excitation frequency was 1.55 MHz and the magnetic intensity was 21 mT. Inset figures show the rolling direction. Scale bar, 100 μm.