Self-Assembled Magnetic Surface Swimmers

We report studies of novel self-assembled magnetic surface swimmers (magnetic snakes) formed from a dispersion of magnetic microparticles at a liquid-air interface and energized by an alternating magnetic field. We show that under certain conditions the snakes spontaneously break the symmetry of surface flows and turn into self-propelled objects. Parameters of the driving magnetic field tune the propulsion velocity of these snakelike swimmers. We find that the symmetry of the surface flows can also be broken in a controlled fashion by attaching a large bead to a magnetic snake (bead-snake hybrid), transforming it into a self-locomoting entity. The observed phenomena have been successfully described by a phenomenological model based on the amplitude equation for surface waves coupled to a large-scale hydrodynamic mean flow equation.

Figure 1

Magnetic swimmers generated by a vertical alternating magnetic field. (a) Surface flow velocity field in the vicinity of the snake’s tail. Arrows depict the surface velocity field obtained by PIV and the background colors show relative magnitudes of flow velocities. (b) Self-propelled magnetic swimmer energized by a 100 Oe, 140 Hz vertical magnetic field. (c) The vortex structure of a self-propelled snake. Arrow shows the direction of swimming. The bottom image illustrates the amplitude of surface flows around the swimming snake. Dark blue (dark gray) color corresponds to low velocities of flows; a long jet stream emanates from one of the snake’s tails. (d) Self-propelled snake-particle hybrid, $f=80\mathrm{Hz}$, $H_0=100\mathrm{Oe}$, 1.5 mm spherical glass bead is used.

Figure 2

Mean swimming velocity of the snake-bead hybrid vs amplitude of the magnetic field at $f=140\mathrm{Hz}$. The dashed line is a fit to quadratic dependence of the swimmer velocity on the amplitude of the external field, $V\sim H^2$. Insert: flow velocity at the tail of the stable snake generated at $f=140\mathrm{Hz}$. The swimming velocity is of the same order as the maximum flow velocity of a stationary snake.

Figure 3

Numerical studies of a self-propelled snake showing the onset of the snake’s symmetry breaking and swimming. The solid line is a fit to a $(\gamma -{\gamma }_c{)}^{1/2}$ dependence. Inset: spontaneous symmetry breaking of the snake’s quadrupole vortex flows (colors represent the values of the stream function $\Omega$) obtained from Eqs. (1, 2, 3). Arrow shows the direction of swimming, note the asymmetry between vortex pairs. Parameters in Eqs. (1, 2, 3) are: $\epsilon =1$, $b=5$, $\gamma =3.32$, $D=0.2$, $\beta =60$, $\omega =3$, ${\alpha }_1=100$, ${\alpha }_2=500$, $\nu =1.5$, $\zeta =-7$ in a domain of water-air $200\times 200$ dimensionless units.

Figure 4

Velocity field of a snake-particle hybrid (arrows), colors show the value of $|\psi {|}^2$. The simulation is performed at $\omega =2.95$, $\gamma =3.20$. The gray circle in the image depicts the area where the forcing term $\mathbf{F}$ in Eq. (3) is suppressed.