Microscale Magneto-Elastic Composite Swimmers at the Air-Water and Water-Solid Interfaces Under a Uniaxial Field

Self-propulsion of magneto-elastic composite microswimmers is demonstrated under a uniaxial field at both the air-water and the water-substrate interfaces. The microswimmers are made of elastically linked magnetically hard $\mathrm{Co}\text{−}\mathrm{Ni}\text{−}\mathrm{P}$ and soft $\mathrm{Co}$ ferromagnets, fabricated using standard photolithography and electrodeposition. Swimming speed and direction are dependent on the field frequency and amplitude, reaching a maximum of 95.1 µm/s on the substrate surface. Fastest motion occurs at low frequencies via a spinning (air-water interface) or tumbling (water-substrate interface) mode that induces transient inertial motion. Higher frequencies result in low Reynolds number propagation at both interfaces via a rocking mode. Therefore, the same microswimmer can be operated as either a high or a low Reynolds number swimmer. Swimmer pairs agglomerate to form a faster superstructure that propels via spinning and rocking modes analogous to those seen in isolated swimmers. Microswimmer propulsion is driven by a combination of dipolar interactions between the $\mathrm{Co}$ and $\mathrm{Co}\text{−}\mathrm{Ni}\text{−}\mathrm{P}$ magnets and rotational torque due to the applied field, combined with elastic deformation and hydrodynamic interactions between different parts of the swimmer, in agreement with previous models.

Figure 1

Flow diagram of the fabrication process. (a) Evaporation of $\mathrm{Cr}/\mathrm{Au}$ on glass. (b) Preparation of alignment markers and the hard $\mathrm{Co}\text{−}\mathrm{Ni}\text{−}\mathrm{P}$ particles. To minimize systematic error, alignment marker lithography is performed prior to particle lithography. (c) Preparation of soft $\mathrm{Co}$ particles. (d) Preparation of the PDMS links.

Figure 2

(a) Optical microscopy image of a two-particle ferromagnetic swimmer with soft $\mathrm{Co}$ and hard $\mathrm{Co}\text{−}\mathrm{Ni}\text{−}\mathrm{P}$ particles labeled (body length of 68 µm). Swimmer orientation defined by the rotation of the vector from the $\mathrm{Co}$ particle to the $\mathrm{Co}\text{−}\mathrm{Ni}\text{−}\mathrm{P}$ particle from the field axis. (b) Vibrating sample magnetometer hysteresis loops of arrays of $\mathrm{Co}$ and $\mathrm{Co}\text{−}\mathrm{Ni}\text{−}\mathrm{P}$ particles.

Figure 3

Field frequency dependence of (a) swimming speed and (b) propagation direction (with respect to the field axis) of the two-particle ferromagnetic swimmer at the air-water interface under field amplitudes of 3.5, 7.0, and 14.0 mT. Data points represent the average of 24 measurements taken regularly over a 2 min period (error bars represent the standard deviation). The grayed area in (a) indicates data below the average drift speed. Directional data from these points in (b) have been neglected.

Figure 4

(a) Representative images of spinning mode motion on the air-water interface. The phase angle within one field cycle is indicated in each image. (b) Differential images of the spinning mode, showing the change in swimmer position between the phase indicated and the previous frame (taken 0.67 ms earlier). Blue (red) contrast indicates regions that the swimmer has entered (left). The circled region highlights the initial distortion of the swimmer prior to rotation. (c) The time variation of the swimmer orientation and the instantaneous Reynolds number (Re) calculated from the tangential speed in the spinning mode (averaged over 10 field cycles). All data shown under a 15 Hz, 7.0 mT field, B, applied along the axis indicated by the arrows.

Figure 5

(a–d) Schematic diagram of swimmer motion during the spinning: (a) magnetic particles are initially aligned with the field, (b) when the field changes direction, the torque from the field acts initially on the magnetic particles (for simplicity, we neglect the torque acting on the soft particle in this description), resulting in a localized elastic deformation and small flow around the particle, (c) rotation of the whole structure occurs, with a chirality determined by the elastic deformation and resultant flow, (d) as the particle aligns with the field, the elastic deformation relaxes and the structure unbends.

Figure 6

(a) Representative images of rocking mode motion on the air-water interface at different phases of the field cycle (25 Hz, 7.0 mT field, B, applied along the axis indicated by the arrow). (b) Measurement of the center-to-center particle separation during rocking motion. (c) The time variation of the swimmer orientation and the instantaneous Re calculated from the tangential speed in the rocking mode (averaged over eight field cycles).

Figure 7

(a–d) Schematic diagram of swimmer motion during the rocking mode: (a) magnetic particles are aligned with each other, causing a contraction of the swimmer (the dashed circle represents the unstrained link shape), (b) when the field changes direction, the swimmer initially rotates in the contracted state, (c) the magnetization of the soft particle reverses before the swimmer has aligned with the field, causing the swimmer to expand, (d) when the field returns to the original direction, the swimmer rotates back in the expanded state. Subsequently, the soft particle reverses again to align with the field.

Figure 8

(a) Swimmer orientation during propagation. Data points show the average orientation measured during speed and propagation direction measurements (shown in Fig. 3). Error bars indicate the range of angles the swimmer passes through (measured separately using 1500 fps images). Note that in the spinning mode, the swimmer orientation rotates through 360°. (b) Initial orientation of the swimmer, measured immediately before the fields indicated are applied. No field is applied in (b). The field conditions shown correspond to the matching data points in (a). Orientations at 90° correspond to alignment with the Earth’s magnetic field.

Figure 9

(a) Frequency dependence of the swimmer speed close to the water-substrate interface. Data average of five measurements, error bars show standard deviation. Arrows denoted “f” mark the critical frequency above which the data indicates switches from the synchronous to the asynchronous mode. (b) Images of swimmer motion in the synchronous mode on the water-substrate interface (20 Hz, 5.1 mT field). The angles indicate the phase of each image within one field cycle. The arrow shows the applied field axis. (c) Relationship between the instantaneous Re calculated from the tangential speed of in-plane rotation and the azimuthal swimmer orientation (data taken over nine field cycles).

Figure 10

Optical images of the two-particle ferromagnetic swimmer moving in the asynchronous rocking mode at the water-substrate surface, overlaid with the trace of the 45 Hz, 5.1 mT field applied along the axis indicated by the red arrow (B). The images are taken at the time points indicated in sequential frames of the 75 fps video shown in Video 6, and the angles indicate the phase of the field cycle in which each image is taken. The rocking mode can be resolved when motion is viewed over several cycles as a function of phase angle.

Figure 11

(a) Spinning and (b) rocking modes exhibited by two interacting swimmers on the air-water interface under (a) 2 Hz, 2.00 mT and (b) 25 Hz, 3.48 mT fields. Numerals indicate the sequence of time.