Manipulation of emergent vortices in swarms of magnetic rollers

Abstract

Active colloids are an emergent class of out-of-equilibrium materials demonstrating complex collective phases and tunable functionalities. Microscopic particles energized by external fields exhibit a plethora of fascinating collective phenomena, yet mechanisms of control and manipulation of active phases often remains lacking. Here we report the emergence of unconfined macroscopic vortices in a system of ferromagnetic rollers energized by a vertical alternating magnetic field and elucidate the complex nature of a magnetic roller-vortex interactions with inert scatterers. We demonstrate that active self-organized vortices have an ability to spontaneously switch the direction of rotation and move across the surface. We reveal the capability of certain non-active particles to pin the vortex and manipulate its dynamics. Building on our findings, we demonstrate the potential of magnetic roller vortices to effectively capture and transport inert particles at the microscale.

Fig. 1

A magnetic roller vortex. a An overlay of five consecutive images showing a single roller vortex in a spherical potential well (radius of curvature 52 mm, rotating clockwise (CW). A particle grayscale intensity indicates time of the frame, light-colored particles being the initial frame and dark particles the final (see Supplementary Movie 1). Scale bar length is 2 mm. b Calculated velocity amplitude field. The white star symbol is the position of the vortex eye as determined by velocity and vorticity maps. Dashed circle around a vortex eye illustrates the core of the vortex as determined from the azimuthally averaged velocity profile of the vortex shown in d. Scale bar is 2 mm. c Potential energy U of the vortex eye in the spherical well has a harmonic dependence on distance from center r. U was calculated using Eq. 1 from scatter plots of the vortex eye positions (insets). Scale bars are 1. Error bars are the standard deviation of the measurements. As indicated by the order parameter ϕ_R in e the vortex spontaneously switched rotation direction during the course of the experiment. For scatter plots only frames with |ϕ_R| > 0.3 were chosen. d Azimuthally averaged vortex tangential velocity profile versus distance from the center for the vortex shown in b. Dashed line marks the boundary of the defined vortex core where the rollers speed reaches maximum. e Time evolution of the polar order parameter ϕ_R in a roller vortex demonstrating a spontaneous switch of the vortex chirality. f The pair correlation function for the rollers forming the vortex. g(r) has a single peak, implying the presence of a characteristic spacing between rollers. a–e The magnetic field direction is aligned with the gravity and oscillates in- and out-of-plane (amplitude B₀ = 5.78 mT, frequency f_B = 40 Hz)

Fig. 2

Chirality switching statistics of a roller vortex. a Chirality switching events illustrated by the polar order parameter of a roller vortex formed in a soft harmonic gravitational confinement. B₀ = 5.78 mT, f_B = 40 Hz. b Events of the flock intermittency not resulted in a roller vortex chirality switch. c Probability distribution functions for the roller vortex to have no chirality switching events (P₀) or have one successful chirality change (P₁). Error bars are the standard deviation of the measurements

Fig. 3

Potential stiffness manipulation with passive scatterers. a Trapping potential stiffness as a function of number of magnetic rollers comprising the vortex N_Ni. The number of rollers has a weak influence on the trapping potential. Black solid line is a linear fit. B₀ = 5.78 mT, f_B = 40 Hz. b Effect of small scatterers (d_bead = 150 ± 9 μm) on the vortex trapping potential k_p (blue triangles, dashed line marks the value for a pristine vortex). Vortex angular speed ω (inset) decreases with the scatterers number. Black solid lines are linear fits. B₀ = 5.78 mT, f_B = 40 Hz, N_Ni = 214. c Pinning of the roller vortex by intermediate bead sizes. Three-fold increase in stiffness of the trapping potential k_p for intermediate sized scatterers (red squares, dashed line marks the value for a pristine vortex). The blue region indicates the system response as in b and the green area shows the bead sizes, where even a single scatterer destroys the vortex state. B₀ = 7.54 mT, f_B = 43 Hz, N_Ni = 271. Error bars in all panels are the standard deviation of the measurements

Fig. 4

Inert bead capture and transport by a roller vortex. a–c The snapshots demonstrate the capture and transport of a passive glass bead (d_bead = 500 ± 25 μm). See also Supplementary Movie 2. The red curve marks the path traveled by the passive bead and the blue circle encloses the particles that are a part of the vortex. The arrow denotes the direction of the vortex rotation. b the scatterer is captured by the vortex through intermittent flocking. The passive particle is transported by the vortex for about 14 s. The vortex spontaneously disintegrates (frame c) to release the bead. The energizing field: B₀ = 6.07 mT, f_B = 43 Hz. The scale bars are 2 mm