Unveiling the Rolling to Kayak Transition in Propelling Nanorods with Cargo Trapping and Pumping.

Magnetic nanorods driven by rotating fields in water can be rapidly steered along any direction while generating strong and localized hydrodynamic flow fields. Here we show that, when raising the frequency of the rotating field, these nanopropellers undergo a dynamic transition from a rolling to a kayak-like motion due to the increase in viscous drag and acquire a finite inclination angle with respect to the plane perpendicular to the bottom surface. We explain these experimental observations with a theoretical model which considers the nanorod as a pair of ferromagnetic particles hydrodynamically interacting with a close stationary surface. Further, we quantify how efficiently microscopic cargoes can be trapped or expelled from the moving nanorod and use numerical simulations to unveil the generated hydrodynamic flow field. These propulsion regimes can be implemented in microfluidic devices to perform precise operations based on the selective sorting of microscopic cargoes.

Large Scale Zigzag Pattern Emerging from Circulating Active Shakers.

We report the emergence of large zigzag bands in a population of reversibly actuated magnetic rotors that behave as active shakers, namely squirmers that shake the fluid around them without moving. The shakers collectively organize into dynamic structures displaying self-similar growth and generate topological defects in the form of cusps that connect vortices of rolling particles with alternating chirality. By combining experimental analysis with particle-based simulation, we show that the special flow field created by the shakers is the only ingredient needed to reproduce the observed spatiotemporal pattern. We unveil a self-organization scenario in a collection of driven particles in a viscoelastic medium emerging from the reduced particle degrees of freedom, as here the frozen orientational motion of the shakers.

Friction Induces Anisotropic Propulsion in Sliding Magnetic Microtriangles.

In viscous fluids, motile microentities such as bacteria or artificial swimmers often display different transport modes than macroscopic ones. A current challenge in the field aims at using friction asymmetry to steer the motion of microscopic particles. Here we show that lithographically shaped magnetic microtriangles undergo a series of complex transport modes when driven by a precessing magnetic field, including a surfing-like drift close to the bottom plane. In this regime, we exploit the triangle asymmetric shape to obtain a transversal drift which is later used to transport the microtriangle in any direction along the plane. We explain this friction-induced anisotropic sliding with a minimal numerical model capable to reproduce the experimental results. Due to the flexibility offered by soft-lithographic sculpturing, our method to guide anisotropic-shaped magnetic microcomposites can be potentially extended to many other field responsive structures operating in fluid media.

Breaking action-reaction with active apolar colloids: emergent transport and velocity inversion.

Artificial active particles are autonomous agents able to convert energy from the environment into net propulsion, breaking detailed balance and the action-reaction law, clear signatures of their out-of-equilibrium nature. Here we investigate the emergence of directed motion in clusters composed of passive and catalytically active apolar colloids. We use a light-induced chemophoretic flow to rapidly assemble hybrid self-propelling clusters composed of hematite particles and passive silica spheres. By increasing the size of the passive cargo, we observe a reversal in the transport direction of the pair. We explain this complex yet rich phenomenon using a theoretical model which accounts for the generated chemical field and its coupling with the surrounding medium. We exploit further our technique to build up more complex, chemically driven, architectures capable of carrying several passive or active species, that quickly assemble and disassemble under light control.

Elastically-mediated collective organisation of magnetic microparticles.

Gels are soft elastic materials made of a three-dimensional cross-linked polymer network and featuring both elastic and dissipative responses under external mechanical stimuli. Here we investigate how such gels mediate the organization of embedded magnetic microparticles when driven by an external field. By constructing a continuum theory, we demonstrate that the collective dynamics of the embedded particles result from the delicate balance between magnetic dipole-dipole interactions, thermal fluctuations and elasticity of the polymer network, verified by our experiments. The proposed model could be extended to other soft magnetic composites in order to predict how the elastic interactions mediate the aggregation of the embedded elements, fostering technological implications for multifunctional hydrogel materials.

Hydrodynamic interactions hinder transport of flow-driven colloidal particles.

The flow-driven transport of interacting micron-sized particles occurs in many soft matter systems spanning from the translocation of proteins to moving emulsions in microfluidic devices. Here we combine experiments and theory to investigate the collective transport properties of colloidal particles along a rotating ring of optical traps. In the corotating reference frame, the particles are driven by a vortex flow of the surrounding fluid. When increasing the depth of the optical potential, we observe a jamming behavior that manifests itself in a strong reduction of the current with increasing particle density. We show that this jamming is caused by hydrodynamic interactions that enhance the energetic barriers between the optical traps. This leads to a transition from an over- to an under-critical tilting of the potential in the corotating frame. Based on analytical considerations, the enhancement effect is estimated to increase with increasing particle size or decreasing radius of the ring of traps. Measurements for different ring radii and Stokesian dynamics simulations for corresponding particle sizes confirm this. The enhancement of potential barriers in the flow-driven system is contrasted to the reduction of barriers in a force-driven one. This diverse behavior demonstrates that hydrodynamic interactions can have a very different impact on the collective dynamics of many-body systems. Applications to soft matter and biological systems require careful consideration of the driving mechanism and of the role of hydrodynamic interactions.

Topological Boundary Constraints in Artificial Colloidal Ice.

The effect of boundaries and how these can be used to influence the bulk behavior in geometrically frustrated systems are both long-standing puzzles, often relegated to a secondary role. Here, we use numerical simulations and "proof of concept" experiments to demonstrate that boundaries can be engineered to control the bulk behavior in a colloidal artificial ice. We show that an antiferromagnetic frontier forces the system to rapidly reach the ground state (GS), as opposed to the commonly implemented open or periodic boundary conditions. We also show that strategically placing defects at the corners generates novel bistable states, or topological strings, which result from competing GS regions in the bulk. Our results could be generalized to other frustrated micro- and nanostructures where boundary conditions may be engineered with lithographic techniques.

Hydrodynamic Interactions Can Induce Jamming in Flow-Driven Systems.

Hydrodynamic interactions between fluid-dispersed particles are ubiquitous in soft matter and biological systems and they give rise to intriguing collective phenomena. While it was reported that these interactions can facilitate force-driven particle motion over energetic barriers, here we show the opposite effect in a flow-driven system, i.e., that hydrodynamic interactions hinder transport across barriers. We demonstrate this result by combining experiments and theory. In the experiments, we drive colloidal particles using rotating optical traps, thus creating a vortex flow in the corotating reference frame. We observe a jamminglike decrease of particle currents with density for large barriers between traps. The theoretical model shows that this jamming arises from hydrodynamic interactions between the particles. The impact of hydrodynamic interactions is reversed compared to force-driven motion, suggesting that our findings are a generic feature of flow-driven transport.

Collective hydrodynamic transport of magnetic microrollers.

We investigate the collective transport properties of microscopic magnetic rollers that propel close to a surface due to a circularly polarized, rotating magnetic field. The applied field exerts a torque to the particles, which induces a net rolling motion close to a surface. The collective dynamics of the particles result from the balance between magnetic dipolar interactions and hydrodynamic ones. We show that, when hydrodynamics dominate, i.e. for high particle spinning, the collective mean velocity linearly increases with the particle density. In this regime we analyse the clustering kinetics, and find that hydrodynamic interactions between the anisotropic, elongated particles, induce preferential cluster growth along a direction perpendicular to the driving one, leading to dynamic clusters that easily break and reform during propulsion.

Active apolar doping determines routes to colloidal clusters and gels.

Collections of interacting active particles, self-propelling or not, have shown remarkable phenomena including the emergence of dynamic patterns across different length scales, from animal groups to vibrated grains, microtubules, bacteria, and chemical- or field-driven colloids. Burgeoning experimental and simulation activities are now exploring the possibility of realizing solid and stable structures from passive elements that are assembled by a few active dopants. Here we show that such an elusive task may be accomplished by using a small amount of apolar dopants, namely synthetic active but not self-propelling units. We use blue light to rapidly assemble 2D colloidal clusters and gels via nonequilibrium diffusiophoresis, where microscopic hematite dockers form long-living interstitial bonds that strongly glue passive silica microspheres. By varying the relative fraction of doping, we uncover a rich phase diagram including ordered and disordered clusters, space-filling gels, and bicontinuous structures formed by filamentary dockers percolating through a solid network of silica spheres. We characterize the slow relaxation and dynamic arrest of the different phases via correlation and scattering functions. Our findings provide a pathway toward the rapid engineering of mesoscopic gels and clusters via active colloidal doping.

Collective Directional Locking of Colloidal Monolayers on a Periodic Substrate.

We investigate the directional locking effects that arise when a monolayer of paramagnetic colloidal particles is driven across a triangular lattice of magnetic bubbles. We use an external rotating magnetic field to generate a two-dimensional traveling wave ratchet forcing the transport of particles along a direction that intersects two crystallographic axes of the lattice. We find that, while single particles show no preferred direction, collective effects induce transversal current and directional locking at high density via a spontaneous symmetry breaking. The colloidal current may be polarized via an additional bias field that makes one transport direction energetically preferred.

Topology Restricts Quasidegeneracy in Sheared Square Colloidal Ice.

Recovery of ground-state degeneracy in two-dimensional square ice is a significant challenge in the field of geometric frustration with far-reaching fundamental implications, such as realization of vertex models and understanding the effect of dimensionality reduction. We combine experiments, theory, and numerical simulations to demonstrate that sheared square colloidal ice partially recovers the ground-state degeneracy for a wide range of field strengths and lattice shear angles. Our method could inspire engineering a novel class of frustrated microstructures and nanostructures based on sheared magnetic lattices in a wide range of soft- and condensed-matter systems.

Dynamical modes of sheared confined microscale matter.

Based on (overdamped) Stokesian dynamics simulations and video microscopy experiments, we study the non equilibrium dynamics of a sheared colloidal cluster, which is confined to a two-dimensional disk. The experimental system is composed of a mixture of paramagnetic and non magnetic polystyrene particles, which are held in the disk by time shared optical tweezers. The paramagnetic particles are located at the center of the disk and are actuated by an external, rotating magnetic field that induces a magnetic torque. We identify two different steady states by monitoring the mean angular velocities per ring. The first one is characterized by rare slip events, where the inner rings momentarily depin from the outer ring, which is kept static by the set of optical traps. For the second state, we find a bistability of the mean angular velocities, which can be understood from the analysis of the slip events in the particle trajectories. We calculate the particle waiting- and jumping time distributions and estimate a time scale between slips, which is also reflected by a plateau in the mean squared azimuthal displacement. The dynamical transition is further reflected by the components of the stress tensor, revealing a shear-thinning behavior as well as shear stress overshoots. Finally, we briefly discuss the observed transition in the context of stochastic thermodynamics and how it may open future directions in this field.

Dynamics and clogging of colloidal monolayers magnetically driven through a heterogeneous landscape.

We combine experiments and numerical simulations to investigate the emergence of clogging in a system of interacting paramagnetic colloidal particles driven against a disordered landscape of larger obstacles. We consider a single aperture in a landscape of immobile silica particles which are irreversibly attached to the substrate. We use an external rotating magnetic field to generate a traveling wave potential which drives the magnetic particles against these obstacles at a constant and frequency tunable speed. Experimentally we find that the particles display an intermittent dynamics with power law distributions at high frequencies. We reproduce these results by using numerical simulations and show that clogging in our system arises at large frequency, when the particles desynchronize with the moving landscape. Further, we use the model to explore the hidden role of flexibility in the obstacle displacements and the effect of hydrodynamic interactions between the particles. We also consider numerically the situation of a straight wall and investigate the range of parameters where clogging emerges in such case. Our work provides a soft matter test-bed system to investigate the effect of clogging in driven microscale matter.

Propulsion and energetics of a minimal magnetic microswimmer.

In this manuscript we describe the realization of a minimal hybrid microswimmer, composed of a ferromagnetic nanorod and a paramagnetic microsphere. The unbounded pair is propelled in water upon application of a swinging magnetic field that induces a periodic relative movement of the two composing elements, where the nanorod rotates and slides on the surface of the paramagnetic sphere. When taken together, the processes of rotation and sliding describe a finite area in the parameter space, which increases with the frequency of the applied field. We develop a theoretical approach and combine it with numerical simulations, which allow us to understand the dynamics of the propeller and explain the experimental observations. Furthermore, we demonstrate a reversal of the microswimmer velocity by varying the length of the nanorod, as predicted by the model. Finally, we determine theoretically and in experiments the Lighthill's energetic efficiency of this minimal magnetic microswimmer.

Mixed-order phase transition in a colloidal crystal.

Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and nonequilibrium systems, but their experimental observation has remained elusive. Here, we analytically predict and experimentally realize a mixed-order equilibrium phase transition. Specifically, a discontinuous solid-solid transition in a 2D crystal of paramagnetic colloidal particles is induced by a magnetic field [Formula: see text] At the transition field [Formula: see text], the energy landscape of the system becomes completely flat, which causes diverging fluctuations and correlation length [Formula: see text] Mean-field critical exponents are predicted, since the upper critical dimension of the transition is [Formula: see text] Our colloidal system provides an experimental test bed to probe the unconventional properties of mixed-order phase transitions.

Enhancing Nanoparticle Diffusion on a Unidirectional Domain Wall Magnetic Ratchet.

The performance of nanoscale magnetic devices is often limited by the presence of thermal fluctuations, whereas in micro- and nanofluidic applications the same fluctuations may be used to spread reactants or drugs. Here, we demonstrate the controlled motion and the enhancement of diffusion of magnetic nanoparticles that are manipulated and driven across a series of Bloch walls within an epitaxially grown ferrite garnet film. We use a rotating magnetic field to generate a traveling wave potential that unidirectionally transports the nanoparticles at a frequency tunable speed. Strikingly, we find an enhancement of diffusion along the propulsion direction and a frequency-dependent diffusion coefficient that can be precisely controlled by varying the system parameters. To explain the reported phenomena, we develop a theoretical approach that shows a fair agreement with the experimental data enabling an exact analytical expression for the enhanced diffusivity above the magnetically modulated periodic landscape. Our technique to control thermal fluctuations of driven magnetic nanoparticles represents a versatile and powerful way to programmably transport magnetic colloidal matter in a fluid, opening the doors to different fluidic applications based on exploiting magnetic domain wall ratchets.

Inhomogeneous assembly of driven nematic colloids.

We present a quantitative analysis of the nonequilibrium assembly of colloidal particles dispersed in a nematic liquid crystal. The driven particles assemble into reconfigurable circular clusters by liquid-crystal-enabled electrokinetic phenomena generated by an AC electric field that provides propulsion along the local director. We identify the coexistence of different aggregation states, including a central, jammed core, where short-range elastic attraction dominates, surrounded by a liquid-like corona where particles retain their mobility but reach a mechanical equilibrium that we rationalize in terms of a balance between centripetal phoretic drive and pairwise repulsion. An analysis of the compressible liquid-like region reveals a linear density profile that can be tuned with the field frequency, and a bond-orientational order that reaches a maximum at intermediate packing densities, where elastic effects are minimized. Since the phoretic propulsion force acts also on assembled particles, we compute the mechanical pressure and show that a hard-disk equation of state can be used to describe the assembly of this driven system.

Leap-frog transport of magnetically driven anisotropic colloidal rotors.

In this article, we combine experiments and theory to investigate the transport properties of anisotropic hematite colloidal rotors that dynamically assemble into translating clusters upon application of a rotating magnetic field. The applied field exerts a torque to the particles forcing rotation close to a surface and thus a net translational motion at a frequency tunable speed. When approaching, pairs of particles are observed to assemble into stable three-dimensional clusters that perform a periodic leap-frog type dynamics and propel at a faster speed. We analyze the cluster formation and its lifetime and investigate the role of particle shape in the propulsion speed and stability. We show that the dynamics of the system results from a delicate balance between magnetic dipolar interactions and hydrodynamics, and we introduce a theoretical model that qualitatively explains the observed phenomena.

Laning, thinning and thickening of sheared colloids in a two-dimensional Taylor-Couette geometry.

We investigate the dynamics and rheological properties of a circular colloidal cluster that is continuously sheared by magnetic and optical torques in a two-dimensional (2D) Taylor-Couette geometry. By varying the two driving fields, we obtain the system flow diagram and report the velocity profiles along the colloidal structure. We then use the inner magnetic trimer as a microrheometer, and observe continuous thinning of all particle layers followed by thickening of the third one above a threshold field. Experimental data are supported by Brownian dynamics simulations. Our approach gives a unique microscopic view on how the structure of strongly confined colloidal matter weakens or strengthens upon shear, envisioning the engineering of rheological devices at the microscales.