Rotating colloids in rotating magnetic fields: Dipolar relaxation and hydrodynamic coupling

Aligned colloidal clusters in an alternating rotating magnetic field elucidated by magnetic relaxation

Precise control at the colloidal scale is one of the most promising bottom-up approaches to fabricating new materials and devices with tunable and precisely engineered properties. Magnetically driven colloidal assembly offers great versatility because of the ability to externally tune particle-particle interactions and to construct a host of particle arrangements. However, despite previous efforts to probe the parameter space, global orientational control in conjunction with two-dimensional microstructural control has remained out of reach. Furthermore, the magnetic relaxation time of superparamagnetic beads has been largely overlooked despite being a key feature of the magnetic response. Here, we take advantage of the magnetic relaxation time of superparamagnetic beads in an alternating rotating magnetic field and show how harnessing this feature facilitates the formation of oriented clusters. The orientation of these clusters can be controlled by field parameters. Using experiments, simulations, and theory, we probe a two-particle system (dimer) under this alternating rotating magnetic field and use its dynamics to provide insights into the collective response that forms clusters. We find that the type of field has significant implications for the dipolar interactions between the colloids because of the nonnegligible magnetic relaxation. Moreover, we find that the competing time scales of the magnetic relaxation and the alternating field generate an anisotropic interaction potential that drives cluster alignment. By exploiting the magnetic relaxation time of magnetic systems, we can tailor new types of interparticle interactions, thereby expanding the capabilities of colloidal assembly in engineering unique materials and devices.

Field-Directed Motion, Cargo Capture, and Closed-Loop Controlled Navigation of Microellipsoids

Microrobots have the potential for diverse applications, including targeted drug delivery and minimally invasive surgery. Despite advancements in microrobot design and actuation strategies, achieving precise control over their motion remains challenging due to the dominance of viscous drag, system disturbances, physicochemical heterogeneities, and stochastic Brownian forces. Here, a precise control over the interfacial motion of model microellipsoids is demonstrated using time-varying rotating magnetic fields. The impacts of microellipsoid aspect ratio, field characteristics, and magnetic properties of the medium and the particle on the motion are investigated. The role of mobile micro-vortices generated is highlighted by rotating microellipsoids in capturing, transporting, and releasing cargo objects. Furthermore, an approach is presented for controlled navigation through mazes based on real-time particle and obstacle sensing, path planning, and magnetic field actuation without human intervention. The study introduces a mechanism of directing motion of microparticles using rotating magnetic fields, and a control scheme for precise navigation and delivery of micron-sized cargo using simple microellipsoids as microbots.

Microfluidic mixing by magnetic particles: Progress and prospects

Microfluidic systems have enormous potential for enabling point-of-care diagnostics due to a number of advantages, such as low sample volumes, small footprint, low energy requirements, uncomplicated setup, high surface-to-volume ratios, cost-effectiveness, etc. However, fluid mixing operations are constrained by molecular diffusion since the flow is usually in the laminar regime. The slow nature of molecular diffusion is a technological barrier to implementing fluid transformations in a reasonable time. In this context, magnetically actuated micro-mixers of different sizes, shapes, materials, and actuation techniques provide a way to enhance fluid mixing in microfluidic devices. In this paper, we review the currently existing micro-mixing technologies. From a fundamental perspective, the different magnetization models for permanent and induced dipoles are discussed. The single-particle dynamics in steady and oscillating magnetic fields is studied in order to determine the flow generated and the torque exerted on the fluid due to the magnetic particles. The effect of particle interactions, both magnetic and hydrodynamic, is examined.

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.

Superparamagnetic colloids in a rotating field: Transition state from chains to disks

When exposed to an external magnetic field, 2D layers of spherical superparamagnetic colloids form specific structures which depend on the features of the external field. If the magnetic field is constant along time, superparamagnetic colloids self-organize into chains oriented in the direction of the field. If the magnetic field is rotating in the plane of the suspension, below a critical frequency, the superparamagnetic beads still aggregate into chains, but these chains rotate with the magnetic field. When the rotation reaches a certain speed, the colloids aggregate in rotating disklike clusters. In this work, we focused on the early stages of the disklike clusters' aggregation and the dynamics of this process. In particular, we observed experimentally that before clustering into disklike structures, the colloids were aggregating into rotating chains, just as they did in suspensions submitted to a magnetic field rotating at a lower rate. Over time, the chains interact with one another and aggregate into disklike clusters, resulting in a mixture of chains and disks in the sample. Finally, we propose a model to characterize the suspension over time in terms of the proportion of chains and disklike clusters, and report its deduced temporal evolution for different frequencies and volume fractions.

Synthesis and Propulsion of Magnetic Dimers under Orthogonally Applied Electric and Magnetic Fields

Anisotropic particles have been widely used to make micro/nanomotors that convert chemical, ultrasonic, electrical, or magnetic energy into mechanical energy. The moving directions of most colloidal motors are, however, difficult to control. For example, asymmetric dimers with two lobes of different sizes, ζ-potential, or chemical composition have shown rich propulsion behaviors under alternating current (AC) electric fields due to unbalanced electrohydrodynamic flow. While they always propel in a direction perpendicular to the applied electric field, their moving directions along the substrate are hard to control, limiting their applications for cargo delivery. Inspired by two separate engine and steering wheel systems in automobiles, we use orthogonally applied AC electric field and direct current (DC) magnetic field to control the dimer's speed and direction independently. To this end, we first synthesize magnetic dimers by coating dopamine-functionalized nanoparticles on geometrically asymmetric polystyrene dimers. We further characterize their static and dynamic susceptibilities by measuring the hysteresis diagram and rotation speed experimentally and comparing them with theoretical predictions. The synthesized dimers align their long axes quickly with a planar DC magnetic field, allowing us to control the particles' orientation accurately. The propulsion speed of the dimers, on the other hand, is tunable by an AC electric field applied perpendicularly to the substrate. As a result, we can direct the particle's motion with predesigned trajectories of complex shapes. Our bulk-synthesis approach has the potential to make other types of magnetically anisotropic particles. And the combination of electric and magnetic fields will help pave the way for the assembly of magnetically anisotropic particles into complex structures.

Enhanced diffusion and magnetophoresis of paramagnetic colloidal particles in rotating magnetic fields

Dispersions of paramagnetic colloids can be manipulated with external magnetic fields to assemble structures via dipolar assembly and control transport via magnetophoresis. For fields held steady in time, the dispersion structure and dynamic properties are coupled. This coupling can be problematic when designing processes involving field-induced forces, as particle aggregation competes against and hinders particle transport. Time-varying fields drive dispersions out-of-equilibrium, allowing the structure and dynamics to be tuned independently. Rotating the magnetic field direction using two biaxial fields is a particularly effective mode of time-variation and has been used experimentally to enhance particle transport. Fundamental transport properties, like the diffusivity and magnetophoretic mobility, dictate dispersions' out-of-equilibrium responses to such time-varying fields, and are therefore crucial to understand to effectively design processes utilizing rotating fields. However, a systematic study of these dynamic quantities in rotating fields has not been performed. Here, we investigate the transport properties of dispersions of paramagnetic colloids in rotating magnetic fields using dynamic simulations. We find that self-diffusion of particles is enhanced in rotating fields compared to steady fields, and that the self-diffusivity in the plane of rotation reaches a maximum value at intermediate rotation frequencies that is larger than the Stokes-Einstein diffusivity of an isolated particle. We also show that, while the magnetophoretic velocity of particles through the bulk in a field gradient decreases with increasing rotation frequency, the enhanced in-plane diffusion allows for faster magnetophoretic transport through porous materials in rotating fields. We examine the effect of porous confinement on the transport properties in rotating fields and find enhanced diffusion at all pore sizes. The confined and bulk values of the transport properties are leveraged in simple models of magnetophoresis through tortuous porous media.

Microwheels on Microroads: Enhanced Translation on Topographic Surfaces

Microbot locomotion is challenging because of the reversible nature of microscale fluid flow, a limitation that can be overcome by breaking flowfield symmetry with a nearby surface. We have used this strategy with rotating wheel-shaped microbots, μwheels, that roll on surfaces leading to enhanced propulsion and fast translation speeds. Despite this, studies to date on flat surfaces show that μwheels roll inefficiently with significant slip. Taking inspiration from the mathematics of roads and wheels, here we demonstrate that μwheel velocities can be significantly enhanced by changing microroad topography. In this, we observe that periodic bumps in the road can be used to enhance the traction between μwheels and nearby walls. While continuous μwheel rotation with slip is observed on flat surfaces, a combination of rotation with slip and non-slip flip occurs when μwheels roll upon surfaces with periodic features, resulting in up to four-fold enhancement in translation velocity. The surprisingly fast rolling speed of μwheels on bumpy roads can be attributed to the hydrodynamic coupling between μwheels and road surface features, allowing non-slip rotation of entire wheels along one of their stationary edges. This road/wheel coupling can also be used to enhance μwheel sorting and separation where the gravitational potential energy barrier induced by topographic surfaces can lead to motion in only one direction and to different rolling speeds between isomeric wheels, allowing one to separate them not based on size but on symmetry.

Non-equilibrium steady-state colloidal assembly dynamics

Simulations and experiments are reported for nonequilibrium steady-state assembly of small colloidal crystal clusters in rotating magnetic fields vs frequency and amplitude. High-dimensional trajectories of particle coordinates from image analysis of experiments and from Stokesian Dynamic computer simulations are fit to low-dimensional reaction coordinate based Fokker-Planck and Langevin equations. The coefficients of these equations are effective energy and diffusivity landscapes that capture configuration-dependent energy and friction for nonequilibrium steady-state dynamics. Two reaction coordinates that capture condensation and anisotropy of dipolar chains folding into crystals are sufficient to capture high-dimensional experimental and simulated dynamics in terms of first passage time distributions. Our findings illustrate how field-mediated nonequilibrium steady-state colloidal assembly dynamics can be modeled to interpret and design pathways toward target microstructures and morphologies.

Measurement of Anisotropic Particle Interactions with Nonuniform ac Electric Fields

Optical microscopy measurements are reported for single anisotropic polymer particles interacting with nonuniform ac electric fields. The present study is limited to conditions where gravity confines particles with their long axis parallel to the substrate such that particles can be treated using quasi-2D analysis. Field parameters are investigated that result in particles residing at either electric field maxima or minima and with long axes oriented either parallel or perpendicular to the electric field direction. By nonintrusively observing thermally sampled positions and orientations at different field frequencies and amplitudes, a Boltzmann inversion of the time-averaged probability of states yields kT-scale energy landscapes (including dipole-field, particle-substrate, and gravitational potentials). The measured energy landscapes show agreement with theoretical potentials using particle conductivity as the sole adjustable material property. Understanding anisotropic particle-field energy landscapes vs field parameters enables quantitative control of local forces and torques on single anisotropic particles to manipulate their position and orientation within nonuniform fields.

Energy landscapes for ellipsoids in non-uniform AC electric fields

We report a closed-form analytical model for energy landscapes of ellipsoidal particles in non-uniform high-frequency AC electric fields to identify all possible particle positions and orientations. Three-dimensional equilibrium positions and orientations of prolate (r_x = r_y < r_z), oblate (r_x = r_z > r_y), and scalene (r_x≠r_y≠r_z) ellipsoids are reported vs. field frequency and amplitude, which are determined from energy landscape minima. For ellipsoids within non-uniform electric fields between co-planar parallel electrodes, the number of configurations of position and orientation is 6 for prolate, 5 for oblate, and 9 for scalene ellipsoids. In addition, for coplanar electrodes, conditions are identified when particles can be treated using a quasi-2D analysis in the plane of their most probable elevation near an underlying surface. The reported expressions are valid for time-averaged interactions of ellipsoid particles in arbitrary AC electric field configurations, such that our results are applicable to electromagnetic tweezers interacting with particles having an appropriate material property contrast with the medium in the frequency range of interest.

Enhanced Fibrinolysis with Magnetically Powered Colloidal Microwheels

Thrombi that occlude blood vessels can be resolved with fibrinolytic agents that degrade fibrin, the polymer that forms between and around platelets to provide mechanical stability. Fibrinolysis rates however are often constrained by transport-limited delivery to and penetration of fibrinolytics into the thrombus. Here, these limitations are overcome with colloidal microwheel (µwheel) assemblies functionalized with the fibrinolytic tissue-type plasminogen activator (tPA) that assemble, rotate, translate, and eventually disassemble via applied magnetic fields. These microwheels lead to rapid fibrinolysis by delivering a high local concentration of tPA to induce surface lysis and, by taking advantage of corkscrew motion, mechanically penetrating into fibrin gels and platelet-rich thrombi to initiate bulk degradation. Fibrinolysis of plasma-derived fibrin gels by tPA-microwheels is fivefold faster than with 1 µg mL^-1 tPA. µWheels following corkscrew trajectories can also penetrate through 100 µm sized platelet-rich thrombi formed in a microfluidic model of hemostasis in ≈5 min. This unique combination of surface and bulk dissolution mechanisms with mechanical action yields a targeted fibrinolysis strategy that could be significantly faster than approaches relying on diffusion alone, making it well-suited for occlusions in small or penetrating vessels not accessible to catheter-based removal.