Controlling collective rotational patterns of magnetic rotors

Topological phase locking in stochastic oscillators

The dynamics of many nanoscale biological and synthetic systems such as enzymes and molecular motors are activated by thermal noise, and driven out-of-equilibrium by local energy dissipation. Because the energies dissipated in these systems are comparable to the thermal energy, one would generally expect their dynamics to be highly stochastic. Here, by studying a thermodynamically-consistent model of two coupled noise-activated oscillators, we show that this is not always the case. Thanks to a novel phenomenon that we term topological phase locking (TPL), the coupled dynamics become quasi-deterministic, resulting in a greatly enhanced average speed of the oscillators. TPL is characterized by the emergence of a band of periodic orbits that form a torus knot in phase space, along which the two oscillators advance in rational multiples of each other. The effectively conservative dynamics along this band coexists with the basin of attraction of the dissipative fixed point. We further show that TPL arises as a result of a complex, infinite hierarchy of global bifurcations. Our results have implications for understanding the dynamics of a wide range of systems, from biological enzymes and molecular motors to engineered nanoscale electronic, optical, or mechanical oscillators.

Active transport of cargo-carrying and interconnected chiral particles

Directed motion up a concentration gradient is crucial for the survival and maintenance of numerous biological systems, such as sperms moving towards an egg during fertilization or ciliates moving towards a food source. In these systems, chirality-manifested as a rotational torque-plays a vital role in facilitating directed motion. While systematic studies of active molecules in activity gradients exist, the effect of chirality remains little studied. In this study, we examine the simplest case of a chiral active particle connected to a passive particle in a spatially varying activity field. We demonstrate that this minimal setup can exhibit rich emergent tactic behaviors, with the chiral torque serving as the tuning parameter. Notably, when the chiral torque is sufficiently large, even a small passive particle enables the system to display the desired accumulation behavior. Our results further show that in the dilute limit, this desired accumulation behavior persists despite the presence of excluded volume effects. Additionally, interconnected chiral active particles exhibit emergent chemotaxis beyond a critical chain length, with trimers and longer chains exhibiting strong accumulation at sufficiently high chiral torques. This study provides valuable insights into the design principles of hybrid bio-molecular devices of the future.

Femtosecond Laser Fabrication of Three-Dimensional Bubble-Propelled Microrotors for Multicomponent Mechanical Transmission

Inspired by the reverse thrust generated by fuel injection, micromachines that are self-propelled by bubble ejection are developed, such as microrods, microtubes, and microspheres. However, controlling bubble ejection sites to build micromachines with programmable actuation and further enabling mechanical transmission remain challenging. Here, bubble-propelled mechanical microsystems are constructed by proposing a multimaterial femtosecond laser processing method, consisting of direct laser writing and selective laser metal reduction. The polymer frame of the microsystems is first printed, followed by the deposition of catalytic platinum into the desired local site of the microsystems by laser reduction. With this method, a variety of designable microrotors with selective bubble ejection sites are realized, which enable excellent mechanical transmission systems composed of single and multiple mechanical components, including a coupler, a crank slider, and a crank rocker system. We believe the presented bubble-propelled mechanical microsystems could be extended to applications in microrobotics, microfluidics, and microsensors.

Wireless Magnetoelectrochemical Induction of Rotational Motion

Electromagnetically induced rotation is a key process of many technological systems that are used in daily life, especially for energy conversion. In this context, the Lorentz force-induced deviation of charges is a crucial physical phenomenon to generate rotation. Herein, they combine the latter with the concept of bipolar electrochemistry to design a wireless magnetoelectrochemical rotor. Such a device can be considered as a wet analog of a conventional electric motor. The main driving force that propels this actuator is the result of the synergy between the charge-compensating ion flux along a bipolar electrode and an external magnetic field applied orthogonally to the surface of the object. The trajectory of the wirelessly polarized rotor can be controlled by the orientation of the magnetic field relative to the direction of the global electric field, producing a predictable clockwise or anticlockwise motion. Fine-tuning of the applied electric field allows for addressing conducting objects having variable characteristic lengths.

On-Demand Breaking of Action-Reaction Reciprocity between Magnetic Microdisks Using Global Stimuli

Coupled physical interactions induce emergent collective behaviors of many interacting objects. Nonreciprocity in the interactions generates unexpected behaviors. There is a lack of experimental model system that switches between the reciprocal and nonreciprocal regime on demand. Here, we study a system of magnetic microdisks that breaks action-reaction reciprocity via fluid-mediated hydrodynamic interactions, on demand. Via experiments and simulations, we demonstrate that nonreciprocal interactions generate self-propulsion-like behaviors of a pair of disks; group separation in collective of magnetically nonidentical disks; and decouples a part of the group from the rest. Our results could help in developing controllable microrobot collectives. Our approach highlights the effect of global stimuli in generating nonreciprocal interactions.

Self-Sustained Rotation of Lorentz Force-Driven Janus Systems

Rotation is an interesting type of motion that is currently involved in many technological applications. In this frame, different and sophisticated external stimuli to induce rotation have been developed. In this work, we have designed a simple and original self-propelled bimetallic Janus rotor powered by the synergy between a spontaneous electric and ionic current, produced by two coupled redox reactions, and a magnetic field, placed orthogonal to the surface of the device. Such a combination induces a magnetohydrodynamic vortex at each extremity of the rotor arm, which generates an overall driving force able to propel the rotor. Furthermore, the motion of the self-polarized object can be controlled by the direction of the spontaneous electric current or the orientation of the external magnetic field, resulting in a predictable clockwise or anticlockwise motion. In addition, these devices exhibit directional corkscrew-type displacement, when representing their displacement as a function of time, producing time-space specular behavior. The concept can be used to design alternative self-mixing systems for a variety of (micro)fluidic equipment.

High-performance Marangoni hydrogel rotors with asymmetric porosity and drag reduction profile

Miniaturized rotors based on Marangoni effect have attracted great attentions due to their promising applications in propulsion and power generation. Despite intensive studies, the development of Marangoni rotors with high rotation output and fuel economy remains challenging. To address this challenge, we introduce an asymmetric porosity strategy to fabricate Marangoni rotor composed of thermoresponsive hydrogel and low surface tension anesthetic metabolite. Combining enhanced Marangoni propulsion of asymmetric porosity with drag reduction of well-designed profile, our rotor precedes previous studies in rotation output (~15 times) and fuel economy (~34% higher). Utilizing thermoresponsive hydrogel, the rotor realizes rapid refueling within 33 s. Moreover, iron-powder dopant further imparts the rotors with individual-specific locomotion in group under magnetic stimuli. Significantly, diverse functionalities including kinetic energy transmission, mini-generator and environmental remediation are demonstrated, which open new perspectives for designing miniaturized rotating machineries and inspire researchers in robotics, energy, and environment.

A DNA origami rotary ratchet motor

To impart directionality to the motions of a molecular mechanism, one must overcome the random thermal forces that are ubiquitous on such small scales and in liquid solution at ambient temperature. In equilibrium without energy supply, directional motion cannot be sustained without violating the laws of thermodynamics. Under conditions away from thermodynamic equilibrium, directional motion may be achieved within the framework of Brownian ratchets, which are diffusive mechanisms that have broken inversion symmetry^1-5. Ratcheting is thought to underpin the function of many natural biological motors, such as the F₁F₀-ATPase^6-8, and it has been demonstrated experimentally in synthetic microscale systems (for example, to our knowledge, first in ref. ³) and also in artificial molecular motors created by organic chemical synthesis^9-12. DNA nanotechnology¹³ has yielded a variety of nanoscale mechanisms, including pivots, hinges, crank sliders and rotary systems^14-17, which can adopt different configurations, for example, triggered by strand-displacement reactions^18,19 or by changing environmental parameters such as pH, ionic strength, temperature, external fields and by coupling their motions to those of natural motor proteins^20-26. This previous work and considering low-Reynolds-number dynamics and inherent stochasticity^27,28 led us to develop a nanoscale rotary motor built from DNA origami that is driven by ratcheting and whose mechanical capabilities approach those of biological motors such as F₁F₀-ATPase.

Diagrammatics of tunable interactions in anisotropic colloids in rotating electric or magnetic fields: New kind of dipole-like interactions

Anisotropic particles are widely presented in nature, from colloidal to bacterial systems, and control over their interactions is of crucial importance for many applications, from self-assembly of novel materials to microfluidics. Placed in rapidly rotating external electric fields, colloidal particles attain a tunable long-range and many-body part in their interactions. For spherical colloids, this approach has been shown to offer rich capabilities to construct the tunable interactions via designing the internal structure of particles and spatial hodographs of external rotating fields, but in the case of anisotropic particles, the interactions remain poorly understood. Here, we show that tunable interactions between anisotropic rod-like and spheroidal colloidal particles in rotating electric or magnetic fields can be calculated and analyzed with the diagrammatic technique we developed in the present work. With this technique, we considered an in-plane rotating electric field, obtained the long-range asymptotics of the anisotropic interactions, calculated the tunable interactions between particles rotating synchronously, and found conditions for rotator repulsion. We compared the mechanisms providing tunable interactions to those for orientational (Keesom), induction (Debye), and dispersion (London) interactions in molecular systems and found that the tunable interactions between anisotropic particles represent a novel kind of dipole-like interaction. The method can be directly generalized for magnetically induced interactions, 3D systems, and fields with spatial hodographs. The results provide significant advance in theoretical methods for tunable interactions in colloids and, therefore, are of broad interest in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

How rotating ATP synthases can modulate membrane structure

F1Fo-ATP synthase (ATP synthase) is a central membrane protein that synthetizes most of the ATP in the cell through a rotational movement driven by a proton gradient across the hosting membrane. In mitochondria, ATP synthases can form dimers through specific interactions between some subunits of the protein. The dimeric form of ATP synthase provides the protein with a spontaneous curvature that sustain their arrangement at the rim of the high-curvature edges of mitochondrial membrane (cristae). Also, a direct interaction with cardiolipin, a lipid present in the inner mitochondrial membrane, induces the dimerization of ATP synthase molecules along cristae. The deletion of those biochemical interactions abolishes the protein dimerization producing an altered mitochondrial function and morphology. Mechanically, membrane bending is one of the key deformation modes by which mitochondrial membranes can be shaped. In particular, bending rigidity and spontaneous curvature are important physical factors for membrane remodelling. Here, we discuss a complementary mechanism whereby the rotatory movement of the ATP synthase might modify the mechanical properties of lipid bilayers and contribute to the formation and regulation of the membrane invaginations.

Driving a Microswimmer with Wall-Induced Flow

Active walls such as cilia and bacteria carpets generate background flows that can influence the trajectories of microswimmers moving nearby. Recent advances in artificial magnetic cilia carpets offer the potentiality to use a similar wall-generated background flow to steer bio-hybrid microrobots. In this paper, we provide some ground theoretical and numerical work assessing the viability of this novel means of swimmer guidance by setting up a simple model of a spherical swimmer in an oscillatory flow and analysing it from the control theory viewpoint. We show a property of local controllability around the reference free trajectories and investigate the bang-bang structure of the control for time-optimal trajectories, with an estimation of the minimal time for suitable objectives. By direct simulation, we have demonstrated that the wall actuation can improve the wall-following transport by nearly 50%, which can be interpreted by synchronous flow structure. Although an open-loop control with a periodic bang-bang actuation loses some robustness and effectiveness, a feedback control is found to improve its robustness and effective transport, even with hydrodynamic wall-swimmer interactions. The results shed light on the potentialities of flow control and open the way to future experiments on swimmer guidance.

Conditions for metachronal coordination in arrays of model cilia

Motile cilia can coordinate with each other to beat in the form of a metachronal wave, which can facilitate the self-propulsion of microorganisms such as Paramecium and can also be used for fluid transport such as mucus removal in trachea. How can we predict the collective behavior of arrays of many cilia coordinated by hydrodynamic interactions, and in particular, the properties of the emerging metachronal waves, from the single-cilium characteristics? We address this question using a bottom-up coarse-graining approach and present results that contribute to understanding how the dynamical self-organization of ciliary arrays can be controlled, which can have significant biological, medical, and engineering implications.

On surfaces with many motile cilia, beats of the individual cilia coordinate to form metachronal waves. We present a theoretical framework that connects the dynamics of an individual cilium to the collective dynamics of a ciliary carpet via systematic coarse graining. We uncover the criteria that control the selection of frequency and wave vector of stable metachronal waves of the cilia and examine how they depend on the geometric and dynamical characteristics of a single cilium, as well as the geometric properties of the array. We perform agent-based numerical simulations of arrays of cilia with hydrodynamic interactions and find quantitative agreement with the predictions of the analytical framework. Our work sheds light on the question of how the collective properties of beating cilia can be determined using information about the individual units and, as such, exemplifies a bottom-up study of a rich active matter system.

Ciliary chemosensitivity is enhanced by cilium geometry and motility

Cilia are hairlike organelles involved in both sensory functions and motility. We discuss the question of whether the location of chemical receptors on cilia provides an advantage in terms of sensitivity and whether motile sensory cilia have a further advantage. Using a simple advection-diffusion model, we compute the capture rates of diffusive molecules on a cilium. Because of its geometry, a non-motile cilium in a quiescent fluid has a capture rate equivalent to a circular absorbing region with ∼4× its surface area. When the cilium is exposed to an external shear flow, the equivalent surface area increases to ∼6×. Alternatively, if the cilium beats in a non-reciprocal way in an otherwise quiescent fluid, its capture rate increases with the beating frequency to the power of 1/3. Altogether, our results show that the protruding geometry of a cilium could be one of the reasons why so many receptors are located on cilia. They also point to the advantage of combining motility with chemical reception.

Magnetic Microswimmers Exhibit Bose-Einstein-like Condensation

We study an active matter system comprised of magnetic microswimmers confined in a microfluidic channel and show that it exhibits a new type of self-organized behavior. Combining analytical techniques and Brownian dynamics simulations, we demonstrate how the interplay of nonequilibrium activity, external driving, and magnetic interactions leads to the condensation of swimmers at the center of the channel via a nonequilibrium phase transition that is formally akin to Bose-Einstein condensation. We find that the effective dynamics of the microswimmers can be mapped onto a diffusivity-edge problem, and use the mapping to build a generalized thermodynamic framework, which is verified by a parameter-free comparison with our simulations. Our work reveals how driven active matter has the potential to generate exotic classical nonequilibrium phases of matter with traits that are analogous to those observed in quantum systems.

Microfluidic devices powered by integrated elasto-magnetic pumps

We show how an asymmetric elasto-magnetic system provides a novel integrated pumping solution for lab-on-a-chip and point of care devices. This monolithic pumping solution, inspired by Purcell's 3-link swimmer, is integrated within a simple microfluidic device, bypassing the requirement of external connections. We experimentally prove that this system can provide tuneable fluid flow with a flow rate of up to 600 μL h-1. This fluid flow is achieved by actuating the pump using a weak, uniform, uniaxial, oscillating magnetic field, with field amplitudes in the range of 3-6 mT. Crucially, the fluid flow can be reversed by adjusting the driving frequency. We experimentally prove that this device can successfully operate on fluids with a range of viscosities, where pumping at higher viscosity correlates with a decreasing optimal driving frequency. The fluid flow produced by this device is understood here by examining the non-reciprocal motion of the elasto-magnetic component. This device has the capability to replace external pumping systems with a simple, integrated, lab-on-a-chip component.

Degenerate states, emergent dynamics and fluid mixing by magnetic rotors

We investigate the collective motion of magnetic rotors suspended in a viscous fluid under a uniform rotating magnetic field. The rotors are positioned on a square lattice, and low Reynolds hydrodynamics is assumed. For a 3 × 3 array of magnets, we observe three characteristic dynamical patterns as the external field strength is varied: a synchronized pattern, an oscillating pattern, and a chessboard pattern. The relative stability of these depends on the competition between the energy due to the external magnetic field and the energy of the magnetic dipole-dipole interactions among the rotors. We argue that the chessboard pattern can be understood as an alternation in the stability of two degenerate states, characterized by striped and spin-ice configurations, as the applied magnetic field rotates. For larger arrays, we observe propagation of slip waves that are similar to metachronal waves. The rotor arrays have potential as microfluidic devices that can mix fluids and create vortices of different sizes.