Magnetically powered metachronal waves induce locomotion in self-assemblies

The study investigates a bio-inspired approach to creating many-particle swimming strategies, drawing inspiration from the metachronal rhythms observed in ciliates and some arthropods like Volvox. These organisms achieve locomotion through the coordinated beating of numerous cilia. The researchers aim to replicate this efficient movement using a simple system of self-assembled magnetic particles at a liquid interface. This system offers the potential to understand fundamental principles of collective locomotion and create micro-scale devices without complex microfabrication processes. The research's significance lies in its potential to create miniature, bio-inspired robots for various applications, such as targeted drug delivery or environmental monitoring. The self-assembly of magnetic particles at liquid interfaces, driven by the balance between capillary attraction and magnetic repulsion, is a well-established phenomenon, allowing for the creation of different patterns based on particle size and magnetic field strength. This study builds upon previous research in magnetocapillary self-assembly, but goes further to investigate and control the collective motion of these assemblies, thus introducing a novel approach for micro-robotics.

The paper reviews existing literature on artificial microswimmers, highlighting various propulsion methods like bacterial flagella mimicry, biohybrid systems, and plant-based designs. It discusses the challenges in creating efficient and controllable locomotion at low Reynolds numbers, a regime typical of microscale systems. The literature on metachronal waves in biological systems is also reviewed, focusing on the coordinated movement of cilia in organisms like Volvox and the underlying mechanisms. This review sets the stage by establishing the current state of the art in artificial microswimmers and biological locomotion strategies, demonstrating a gap in the development of versatile and easily controlled many-particle swimming systems.

The researchers utilized self-assembled rafts composed of soft ferromagnetic beads (diameters of 400, 500, and 800 µm) placed at a water-air interface within a tri-axis Helmholtz coil system. A constant vertical magnetic field (B_z) was applied, causing the beads to self-assemble into various structures (e.g., hexagonal, octagonal). To induce locomotion, a time-dependent horizontal magnetic field (B_x, B_y) was added, controlled by a multichannel arbitrary function generator. The researchers used two types of horizontal magnetic fields: a precessing field (rotating in the horizontal plane), resulting in rotational motion, and a Lissajous figure-8 pattern, resulting in translational motion. The motion of the beads was recorded using a camera with a macro lens, and the trajectories were analyzed using image processing techniques (Hough transform). Experiments were conducted in both water and a higher-viscosity water-glycerol mixture to investigate the effect of Reynolds number. A theoretical model based on the dipole-dipole interaction between beads was used to analyze the observed deformations and relate them to the applied magnetic fields. Data filtering via Fourier transform was implemented to analyze particle trajectories by emphasizing the dominant frequency component and thereby improving visibility of phase shifts.

The study's key findings demonstrate that applying a precessing magnetic field induces a metachronal wave around the periphery of the self-assembled rafts, causing them to rotate. The rotation occurs in a direction opposite to the direction of the applied magnetic field's rotation. Using a Lissajous figure-8 pattern for the horizontal magnetic field generated two counter-propagating waves, leading to translational motion of the assembly. This translational motion was found to be controllable and could be directed in various directions by changing the orientation of the Lissajous figure. The researchers observed that the speed of the self-assembled rafts depends on the number of particles (N), scaling approximately as 1/N, suggesting that the phase shift between neighboring particles is the dominant factor in locomotion, with the efficiency of each 'motor' particle scaling with 1/N. Experiments using a water-glycerol mixture demonstrated that the locomotion strategy remains effective even at significantly lower Reynolds numbers (down to 10^-3), confirming its low-Reynolds-number robustness. Individual particle trajectories reveal the existence of effective and recovery strokes, analogous to those observed in biological cilia, contributing to the overall locomotion.

The results demonstrate a novel method for generating controlled locomotion in many-particle systems at low Reynolds numbers. This method successfully mimics the natural process of metachronal wave-induced locomotion seen in biological systems. The simplicity and robustness of the method are highlighted by its effectiveness across different assembly sizes and symmetries, while also being effective even at very low Reynolds numbers. The 1/N scaling of the speed suggests that inter-particle phase shifts are crucial to the locomotion mechanism. This work opens up new avenues for the design of micro-robots with customizable movement patterns, potentially applicable to diverse fields such as targeted drug delivery or environmental monitoring. Future research could explore optimizing the swimming speed by adjusting field parameters, particle properties, and liquid interfaces.

This study successfully demonstrates a bio-inspired approach to generating controlled locomotion in self-assembled magnetic micro-robots. The use of precessing and figure-8 magnetic fields induces metachronal waves, leading to rotational and translational motion, respectively, at low Reynolds numbers. The method's versatility and effectiveness across different assembly sizes and symmetries make it a promising platform for creating complex micro-scale devices. Future work should focus on optimizing the swimming speed and exploring different magnetic field configurations and particle properties to expand the capabilities of these systems.

The study primarily focuses on specific self-assembled structures, and the generality of the approach for highly irregular or unstable assemblies requires further investigation. While the 1/N scaling is observed, a more comprehensive theoretical model accounting for all inter-particle interactions and hydrodynamic effects is needed to fully understand the locomotion mechanism. The current experimental setup uses uniform magnetic fields; exploring non-uniform fields could potentially enhance the controllability and speed of locomotion. The limited range of particle sizes and materials explored might restrict the generalizability of the findings.