Structure and dynamics of magnetorheological fluids in rotating magnetic fields

Assembly and manipulation of responsive and flexible colloidal structures by magnetic and capillary interactions

The long-ranged interactions induced by magnetic fields and capillary forces in multiphasic fluid-particle systems facilitate the assembly of a rich variety of colloidal structures and materials. We review here the diverse structures assembled from isotropic and anisotropic particles by independently or jointly using magnetic and capillary interactions. The use of magnetic fields is one of the most efficient means of assembling and manipulating paramagnetic particles. By tuning the field strength and configuration or by changing the particle characteristics, the magnetic interactions, dynamics, and responsiveness of the assemblies can be precisely controlled. Concurrently, the capillary forces originating at the fluid-fluid interfaces can serve as means of reconfigurable binding in soft matter systems, such as Pickering emulsions, novel responsive capillary gels, and composites for 3D printing. We further discuss how magnetic forces can be used as an auxiliary parameter along with the capillary forces to assemble particles at fluid interfaces or in the bulk. Finally, we present examples how these interactions can be used jointly in magnetically responsive foams, gels, and pastes for 3D printing. The multiphasic particle gels for 3D printing open new opportunities for making of magnetically reconfigurable and "active" structures.

Mobile mechanical signal generator for macrophage polarization

The importance of mechanical signals in regulating the fate of macrophages is gaining increased attention recently. However, the recently used mechanical signals normally rely on the physical characteristics of matrix with non-specificity and instability or mechanical loading devices with uncontrollability and complexity. Herein, we demonstrate the successful fabrication of self-assembled microrobots (SMRs) based on magnetic nanoparticles as local mechanical signal generators for precise macrophage polarization. Under a rotating magnetic field (RMF), the propulsion of SMRs occurs due to the elastic deformation via magnetic force and hydrodynamics. SMRs perform wireless navigation toward the targeted macrophage in a controllable manner and subsequently rotate around the cell for mechanical signal generation. Macrophages are eventually polarized from M0 to anti-inflammatory related M2 phenotypes by blocking the Piezo1-activating protein-1 (AP-1）-CCL2 signaling pathway. The as-developed microrobot system provides a new platform of mechanical signal loading for macrophage polarization, which holds great potential for precise regulation of cell fate.

Periodic deformation of semiflexible colloidal chains in eccentric time-varying magnetic fields

Elastic filaments driven out of equilibrium display complex phenomena that involve periodic changes in their shape. Here, the periodic deformation dynamics of semiflexible colloidal chains in an eccentric magnetic field are presented. This field changes both its magnitude and direction with time, leading to novel nonequilibrium chain structures. Deformation into S-, Z-, and 4-mode shapes arises via the propagation and growth of bending waves. Transitions between these morphologies are governed by an interplay among magnetic, viscous, and elastic forces. Furthermore, the periodic behavior leading to these structures is described by four distinct stages of motion that include rotation, arrest, bending, and stretching of the chain. These stages correspond to specific intervals of the eccentric field's period. A scaling analysis that considers the relative ratio of viscous to magnetic torques via a critical frequency illustrates how to maximize the bending energy. These results provide new insights into controlling colloidal assemblies by applying complex magnetic fields.

Increasing efficiency and accuracy of magnetic interaction calculations in colloidal simulation through machine learning

Calculating the magnetic interaction between magnetic particles that are positioned in close proximity to one another is a surprisingly challenging task. Exact solutions for this interaction exist either through numerical expansion of multipolar interactions or through solving Maxwell's equations with a finite element solver. These approaches can take hours for simple configurations of three particles. Meanwhile, across a range of scientific and engineering problems, machine learning approaches have been developed as fast computational platforms for solving complex systems of interest when large data sets are available. In this paper, we bring the touted benefits of recent advances in science-based machine learning algorithms to bear on the problem of modeling the magnetic interaction between three particles. We investigate this approach using diverse machine learning systems including physics informed neural networks. We find that once the training data has been collected and the model has been initiated, simulation times are reduced from hours to mere seconds while maintaining remarkable accuracy. Despite this promise, we also try to lay bare the current challenges of applying machine learning to these and more complex colloidal systems.

Dynamics and rheology of a suspension of super-paramagnetic chains under the combined effect of a shear flow and a rotating magnetic field

This study presents an analysis of the dynamics of single and multiple chains of spherical super-paramagnetic beads suspended in a Newtonian fluid under the combined effect of an external rotating magnetic field and a shear flow. Viscosity results depend on two main non-dimensional numbers: the ratio between the shear rate and the magnetic rotation frequency and the ratio between the hydrodynamic and magnetostatic interactions (the Mason number). When the shear rate is smaller than the magnetic field frequency, the chain rotation accelerates the surrounding fluid, reducing the value of the measured suspension viscosity even below that of the solvent. In this regime, shear-thickening is observed. For values of the shear rates comparable to the rotation magnetic frequency, the viscosity reaches a maximum and non-linear coupling effects come up. If the shear rate is increased to values above the rotation frequency, the viscosity decreases and a mild shear-thinning is observed. In terms of the Mason number, the suspension viscosity reduces in line with the literature results reported for fixed magnetic fields, whereas the shear-rate/magnetic-frequency ratio parameters induce a shift of the viscosity curve towards larger values. Results at larger concentrations and multiple chains amplify the observed effects.

Motion of Particles in a Monolayer Induced by Coalescing of a Bubble with a Planar Air-Water Interface

The motion of particles in a monolayer induced by the coalescing of a bare bubble with a planar air-water interface was investigated in a modified Langmuir trough. Experiments were performed to understand the effect of particle hydrophobicity, subphase pH, packing density, the presence of a weak surfactant, and particle size distribution on the behavior of particle movement in the monolayer during the coalescence process. Video tracking software was used to track the particles and extract data based on the video footage. Visual inspection indicated that the coalescence of the bubble with the monolayer was a chaotic process which led the interface to oscillate to an extent that the particles underwent complete rearrangement. A simple analysis was carried out on the main forces involved in particle motion and rearrangement at the oscillating air-water interface. The motion characteristic of particles was evaluated by speed and mean-square displacement (MSD). The results showed that the butanol-treated particles had higher speed and MSD than the particles with a stronger affinity to the air-water interface. Similar results were also found at high subphase pH and low packing factor.

Hierarchical assemblies of superparamagnetic colloids in time-varying magnetic fields

Magnetically-guided colloidal assembly has proven to be a versatile method for building hierarchical particle assemblies. This review describes the dipolar interactions that govern superparamagnetic colloids in time-varying magnetic fields, and how such interactions have guided colloidal assembly into materials with increasing complexity that display novel dynamics. The assembly process is driven by magnetic dipole-dipole interactions, whose strength can be tuned to be attractive or repulsive. Generally, these interactions are directional in static external magnetic fields. More recently, time-varying magnetic fields have been utilized to generate dipolar interactions that vary in both time and space, allowing particle interactions to be tuned from anisotropic to isotropic. These interactions guide the dynamics of hierarchical assemblies of 1-D chains, 2-D networks, and 2-D clusters in both static and time-varying fields. Specifically, unlinked and chemically-linked colloidal chains exhibit complex dynamics, such as fragmentation, buckling, coiling, and wagging phenomena. 2-D networks exhibit controlled porosity and interesting coarsening dynamics. Finally, 2-D clusters have shown to be an ideal model system for exploring phenomena related to statistical thermodynamics. This review provides recent advances in this fast-growing field with a focus on its scientific potential.

Static and dynamic behavior of magnetic particles at fluid interfaces

This perspective work reviews the current status of research on magnetic particles at fluid interfaces. The article gives both a unified overview of recent experimental advances and theoretical studies centered on very different phenomena that share a common characteristic: they involve adsorbed magnetic particles that range in size from a few nanometers to several millimeters. Because of their capability of being remotely piloted through controllable external fields, magnetic particles have proven essential as building blocks in the design of new techniques, smart materials and micromachines, with new tunable properties and prospective applications in engineering and biotechnology. Once adsorbed at a fluid-fluid interfase, in a process that can be facilitated via the application of magnetic field gradients, these particles often result sorely confined to two dimensions (2D). In this configuration, inter-particle forces directed along the perpendicular to the interface are typically very small compared to the surface forces. Hence, the confinement and symmetry breaking introduced by the presence of the surface play an important role on the response of the system to the application of an external field. In monolayers of particles where the magnetic is predominant interaction, the states reached are strongly determined by the mode and orientation of the applied field, which promote different patterns and processes. Furthermore, they can reproduce some of the dynamic assemblies displayed in bulk or form new ones, that take advantage of the interfacial phenomena or of the symmetry breaking introduce by the confining boundary. Magnetic colloids are also widely used for unraveling the guiding principles of 2D dynamic self-assembly, in designs devised for producing interface transport, as tiny probes for assessing interfacial rheological properties, neglecting the bulk and inertia contributions, as well as actuated stabilizing agents in foams and emulsions.

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.

Collective Behavior of Reconfigurable Magnetic Droplets via Dynamic Self-Assembly

Dynamic self-assembly represents an effective approach to form energy-dissipative structures by introducing interactions among multiple building blocks with a continuous energy supply. Time-dependent magnetic fields are treated as convenient energy inputs to construct such a dynamic self-assembled system. The induced interactions can be further tuned by modulating the input field, resulting in a diversity of assembled patterns. However, formation of a functional dynamic pattern with controllability remains a challenge. Herein, we report the formation and pattern control of dynamically self-assembled magnetic droplets at an air-liquid interface, energized by a precessing magnetic field. The formation process involves the assembly of magnetic microparticles into particle chains inside droplets, and then highly ordered patterns are generated by balancing the induced interactions among droplets. By modulating the input field, the interactions and collective behaviors are adjusted and the pattern can be reversibly tuned, i.e., expand and shrink, in a controlled manner. Furthermore, the assembled droplets are able to be steered in two-dimensional as an entity by applying a magnetic field gradient. Utilizing dynamic pattern control and steerability of the assembled structure, cargoes are successfully trapped, transported, and released in a noncontact fashion, indicating that the dynamically assembled droplets can act as a reconfigurable untethered robotic end-effector for manipulation.

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

Video microscopy (VM) experiments and Brownian dynamics (BD) simulations were used to measure and model superparamagnetic colloidal particles in rotating magnetic fields for interaction energies on the order of the thermal energy, kT. Results from experiments and simulations were compared for isolated particle rotation, particle rotation within doublets, doublet rotation, and separation within doublets vs field rotation frequency. Agreement between VM and BD results was obtained at all frequencies and amplitudes only by including exact two-body hydrodynamic interactions and relevant relaxation times of magnetic dipoles. Frequency-dependent particle forces and torques cause doublets to rotate at low frequencies via dipolar interactions and at high frequencies via hydrodynamic translation-rotation coupling. By matching measurements and simulations for a range of conditions, our findings unambiguously demonstrate the quantitative forms of dipolar and hydrodynamic interactions necessary to capture nonequilibrium, steady-state dynamics of Brownian colloids in magnetic fields.

Magnetic microchains and microswimmers in an oscillating magnetic field

Superparamagnetic micro-bead chains and microswimmers under the influence of an oscillating magnetic field are studied experimentally and numerically. The numerical scheme composed of the lattice Boltzmann method, immersed boundary method, and discrete particle method based on the simplified Stokesian dynamics is applied to thoroughly understand the interaction between the micro-bead chain (or swimmer), the oscillating magnetic field, and the hydrodynamics drag. The systematic experiments and simulations demonstrated the behaviors of the microchains and microswimmers as well as the propulsive efficiencies of the swimmers. The effects of key parameters, such as field strengths, frequency, and the lengths of swimmer, are thoroughly analyzed. The numerical results are compared with the experiments and show good qualitative agreements. Our results proposed an efficient method to predict the motions of the reversible magnetic microdevices which may have extremely valuable applications in biotechnology.

Colloidal Microworms Propelling via a Cooperative Hydrodynamic Conveyor Belt

We study propulsion arising from microscopic colloidal rotors dynamically assembled and driven in a viscous fluid upon application of an elliptically polarized rotating magnetic field. Close to a confining plate, the motion of this self-assembled microscopic worm results from the cooperative flow generated by the spinning particles which act as a hydrodynamic "conveyor belt." Chains of rotors propel faster than individual ones, until reaching a saturation speed at distances where induced-flow additivity vanishes. By combining experiments and theoretical arguments, we elucidate the mechanism of motion and fully characterize the propulsion speed in terms of the field parameters.

Toward Accumulation of Magnetic Nanoparticles into Tissues of Small Porosity

Magnetic concentration of drug-laden magnetic nanoparticles has been proven to increase the delivery efficiency of treatment by 2-fold. In these techniques, particles are concentrated by the presence of a magnetic source that delivers a very high magnetic field and a strong magnetic field gradient. We have found that such magnetic conditions cause even 150 nm particles to aggregate significantly into assemblies that exceed several micrometers in length within minutes. Such assembly sizes exceed the effective intercellular pore size of tumor tissues preventing these drug-laden magnetic nanoparticles from reaching their target sites. We demonstrate that by using dynamic magnetic fields instead, we can break up these magnetic nanoparticles while simultaneously concentrating them at target sites. The dynamic fields we investigate involve precessing the field direction while maintaining a field gradient. Manipulating the field direction drives the particles into attractive and repulsive configurations that can be tuned to assemble or disassemble these particle clusters. Here, we develop a simple analytic model to describe the kinetic thresholds of disassembly and we compare both experimental and numerical results of magnetic particle suspensions subjected to dynamic fields. Finally we apply these methods to demonstrate penetration in a porous scaffold with a similar pore size to that expected of a tumor tissue.

Malaria pigment crystals as magnetic micro-rotors: key for high-sensitivity diagnosis

The need to develop new methods for the high-sensitivity diagnosis of malaria has initiated a global activity in medical and interdisciplinary sciences. Most of the diverse variety of emerging techniques are based on research-grade instruments, sophisticated reagent-based assays or rely on expertise. Here, we suggest an alternative optical methodology with an easy-to-use and cost-effective instrumentation based on unique properties of malaria pigment reported previously and determined quantitatively in the present study. Malaria pigment, also called hemozoin, is an insoluble microcrystalline form of heme. These crystallites show remarkable magnetic and optical anisotropy distinctly from any other components of blood. As a consequence, they can simultaneously act as magnetically driven micro-rotors and spinning polarizers in suspensions. These properties can gain importance not only in malaria diagnosis and therapies, where hemozoin is considered as drug target or immune modulator, but also in the magnetic manipulation of cells and tissues on the microscopic scale.

Numerical and experimental study of a rotating magnetic particle chain in a viscous fluid

A simple and fast numerical method is developed capable of accurately determining the 3D rotational dynamics of a magnetic particle chain in an infinite fluid domain. The focus is to control the alternating breakup and reformation of the bead chain which we believe is essential to achieve effective fluid mixing at small scales. The numerical scheme makes use of magnetic dipole moments and extended forms of the Oseen-Burgers tensor to account for both the magnetic and hydrodynamic interactions between the particles. It is shown that the inclusion of hydrodynamic interaction between the particles is crucial to obtain a good description of the particle dynamics. Only a small error of deviation is observed when benchmarking the numerical scheme against a more computationally intensive method, the direct simulation method. The numerical results are compared with experiments and the simulated rotational dynamics correspond well with those obtained from video-microscopy experiments qualitatively and quantitatively. In addition, a dimensionless number (R(T)) is derived as the sole control parameter for the rotational bead chain dynamics. Numerically and experimentally, R(T)≈ 1 is the boundary between rigid "rod" and dynamic "breaking and reformation" behaviors.

Superparamagnetic particle dynamics and mixing in a rotating capillary tube with a stationary magnetic field

The dynamics of superparamagnetic particles subject to competing magnetic and viscous drag forces have been examined with a uniform, stationary, external magnetic field. In this approach, competing drag and magnetic forces were created in a fluid suspension of superparamagnetic particles that was confined in a capillary tube; competing viscous drag and magnetic forces were established by rotating the tube. A critical Mason number was determined for conditions under which the rotation of the capillary prevents the formation of chains from individual particles. The statistics of chain length were investigated by image analysis while varying parameters such as the rotation speed and the viscosity of the liquid. The measurements showed that the rate of particle chain formation was decreased with increased viscosity and rotation speed ; the particle dynamics could be quantified by the same dimensionless Mason number that has been demonstrated for rotating magnetic fields. The potential for enhancement of mixing in a bioassay was assessed using a fast chemical reaction that was diffusion-limited. Reducing the Mason below the critical value, so that chains were formed in the fluid, gave rise to a modest improvement in the time to completion of the reaction.

Note: design of a novel rotating magnetic field device

A novel device to produce a rotating magnetic field was designed, constructed, and tested. The system consists of a Helmholtz coil pair which is mechanically coupled to a dc electric motor whose angular velocity is controlled. The coil pair generates a uniform magnetic field; the whole system is rotated maintaining the coils energized using brushes. The magnetic field strength is uniform (≈5.8 mT) for a workspace of about 100 mm along the rotation axis. The system remains free of undesirable high amplitude mechanical vibrations for rotation frequencies below 10 Hz. We verified the performance of the apparatus by conducting experiments with magnetic swimmers.

Cluster-cluster aggregations of superparamagnetic particles in a rotational magnetic field

We investigate the cluster-cluster aggregations of superparamagnetic particles in a rotational magnetic field numerically by the Brownian dynamics method, focusing on the cases of ϕ = 0.01 and 0.03 and Ma = 0, 0.001, 0.01, and 0.1, where ϕ is the area fraction of superparamagnetic particles and Ma is the Mason number, i.e., the ratio of viscous drag to magnetic force acting on a magnetic particle. We clarify the effect of ϕ and Ma on the cluster-cluster aggregation process from the point of view of dynamic scaling law.

Characterization of magnetic nanoparticles using programmed quadrupole magnetic field-flow fractionation

Quadrupole magnetic field-flow fractionation is a relatively new technique for the separation and characterization of magnetic nanoparticles. Magnetic nanoparticles are often of composite nature having a magnetic component, which may be a very finely divided material, and a polymeric or other material coating that incorporates this magnetic material and stabilizes the particles in suspension. There may be other components such as antibodies on the surface for specific binding to biological cells, or chemotherapeutic drugs for magnetic drug delivery. Magnetic field-flow fractionation (MgFFF) has the potential for determining the distribution of the magnetic material among the particles in a given sample. MgFFF differs from most other forms of field-flow fractionation in that the magnetic field that brings about particle separation induces magnetic dipole moments in the nanoparticles, and these potentially can interact with one another and perturb the separation. This aspect is examined in the present work. Samples of magnetic nanoparticles were analysed under different experimental conditions to determine the sensitivity of the method to variation of conditions. The results are shown to be consistent and insensitive to conditions, although magnetite content appeared to be somewhat higher than expected.

Colour-barcoded magnetic microparticles for multiplexed bioassays

Encoded particles have a demonstrated value for multiplexed high-throughput bioassays such as drug discovery and clinical diagnostics. In diverse samples, the ability to use a large number of distinct identification codes on assay particles is important to increase throughput. Proper handling schemes are also needed to readout these codes on free-floating probe microparticles. Here we create vivid, free-floating structural coloured particles with multi-axis rotational control using a colour-tunable magnetic material and a new printing method. Our colour-barcoded magnetic microparticles offer a coding capacity easily into the billions with distinct magnetic handling capabilities including active positioning for code readouts and active stirring for improved reaction kinetics in microscale environments. A DNA hybridization assay is done using the colour-barcoded magnetic microparticles to demonstrate multiplexing capabilities.

Magneto-mechanical mixing and manipulation of picoliter volumes in vesicles

Superparamagnetic beads in giant unilamellar vesicles are used to facilitate magnetic manipulation, positioning, agitation and mixing of ultrasmall liquid volumes. Vesicles act as leakproof picoliter reaction vessels in an aqueous bulk solution and can be deliberately conveyed by an external magnetic field to a designated position. Upon application of an external magnetic field the beads align to form extended chains. In a rotating magnetic field chains break up into smaller fragments caused by the interplay of viscous friction and magnetic attraction. This process obeys a simple relationship and can be exploited to enhance mixing of the vesicle content and the outer solution or adjacent vesicle volumes exactly at the position of release.

Strong intrinsic mixing in vortex magnetic fields

We report a method of magnetic mixing wherein a "vortex" magnetic field applied to a suspension of magnetic particles creates strong homogeneous mixing throughout the fluid volume. Experiments designed to elucidate the microscopic mechanism of mixing show that the torque is quadratic in the field, decreases with field frequency, and is optimized at a vortex field angle of approximately 55 degrees . Theory and simulations indicate that the field-induced formation of volatile particle chains is responsible for these phenomena. This technique has applications in microfluidic devices and is ideally suited to applications such as accelerating the binding of target biomolecules to biofunctionalized magnetic microbeads.

Overdamped dynamics of paramagnetic ellipsoids in a precessing magnetic field

We report on the dynamical behavior of paramagnetic ellipsoidal particles dispersed in water and floating above a flat plane when subjected to an external precessing magnetic field. When the magnetic field and the long axis of the particles are on the same plane, two clear regimes are distinguished in which the particles follow the magnetic modulation synchronously or asynchronously. Both regimes are also observed when the field precesses at an angle theta<90 degrees with respect to the normal to the confining plane, while the transition frequency increases with decreasing precession angle. We combine experimental observations with a theoretical model to characterize the particle dynamics. The possibility to control and/or reorient microscopic elongated particles by changing the frequency or strength of the applied field makes them suitable in microfluidic devices such as microgates for microchannels or active fluid mixers when placed close to channel junctions.

Tumbling motion of magnetic particles on a magnetic substrate induced by a rotational magnetic field

We analyze the dynamics of paramagnetic particles on a paramagnetic substrate under a rotational magnetic field. When the paramagnetic particles are subjected to a rotational magnetic field, the rotational plane of which is perpendicular to the substrate surface, the particles form chain clusters caused by the dipole-dipole interaction between the particles and these clusters display a tumbling motion under certain conditions. In this case, the angular momentum of the clusters is converted to a translational one through the force of friction acting between the particles and substrate and, as a result, the clusters move along the surface of the substrate. We analyze the conditions under which the tumbling motion occurs and the dependence of the translational velocity of a cluster on the control parameters by the Stokesian dynamics method. Based on the dynamics of magnetic particles, we propose a method of manipulating nano- and microparticles using a rotational magnetic field. We demonstrate the manipulation of magnetic and nonmagnetic particles, a carbon nanotube, and a biological cell.

Chaotic mixing induced by a magnetic chain in a rotating magnetic field

Chaotic mixing, induced by breakup and reformation of a magnetic chain under the influence of a rotating magnetic field, is studied. A direct simulation method combining the Maxwell stress tensor and a fictitious domain method is employed to solve flows with suspended magnetic particles. The motion of the chain is significantly dependent on the Mason number (Ma), the ratio of viscous force to magnetic force. The degree of chaos is characterized by the maximum Lyapunov exponents. We also track the interface of two fluids in time and calculate the rate of stretching as it is affected by the Mason number. The progress of mixing is visualized via a tracer particle-tracking method and is characterized by the discrete intensity of segregation. Within a limited range of Mason number, a magnetic chain rotates and breaks into smaller chains, and the detached chains connect again to form a single chain. The repeating topological changes of the chain lead to the most efficient way of chaotic mixing by stretching at chain breakup and folding due to rotational flows.

Transient behaviour of magnetic micro-bead chains rotating in a fluid by external fields

Magnetic micro-beads can facilitate many functions in lab-on-a-chip systems, such as bio-chemical labeling, selective transport, magnetic sensing and mixing. In order to investigate potential applications of magnetic micro-beads for mixing in micro fluidic systems, we developed a pin-jointed mechanism model that allows analysing the behaviour of rotating superparamagnetic bead chains. Our numerical model revealed the response of the chains on a rotating magnetic field over time. We could demonstrate that the governing parameters are the Mason number and number of beads in the chain. The results are in agreement with the simplified analytical model, assuming a straight chain, but also allow prediction of the transient chain shape. The modelled chains develop an anti-symmetric S-shape that is stable, if the Mason number for a given chain length does not surpass a critical value. Above that value, rupture occurs in the vicinity of the chain centre. However, variations in bead susceptibility can shift the location of rupture. Moreover, we performed experiments with superparamagnetic micro-beads in a small fluid volume exposed to a uniform rotating magnetic field. Our simulation could successfully predict the observed transient chain form and the time for chain rupture. The developed model can be used to design optimised bead based mixers in micro fluidic systems.

Rigid, superparamagnetic chains of permanently linked beads coated with magnetic nanoparticles. Synthesis and rotational dynamics under applied magnetic fields

An inexpensive and versatile approach is reported for the synthesis of monodisperse magnetoresponsive rods of desired diameter, length, and magnetic susceptibility based on the confined alignment of magnetic beads in microchannels of selected channel height, followed by localized hydrolysis of sol-gel precursors within polyelectrolyte shells adsorbed on the beads. The layer-by-layer technique was used to coat the polystyrene beads with polyelectrolytes of alternating charge and with charged magnetic nanoparticles, and the polystyrene cores could be removed either by solvent dissolution or by calcination to form hollow-shelled chains. The reorientation dynamics of single and clustered chains following the application of an external magnetic field was evaluated theoretically, with favorable comparisons with the experimental data.

CFD analysis of paramagnetic particle containment in microwells

Designs for a flow-through biochemical sensor based on rotating chains of paramagnetic particles are analyzed with computational fluid dynamics and theoretical relations for particles in fluids. The sensor is based on the behaviour of paramagnetic particles--n particular, their tendency to align themselves into chain-like structures when subjected to a magnetic field. Paramagnetic particles can be prepared onto which fluorescently tagged analytes will attach. Rotating magnetic fields rotate the particle chains providing the opportunity to selectively acquire the signal associated with chains, through well known lock-in amplifier techniques. Commercially available CFD software can be used to address some basic questions in the design of such a sensor. Computational and experimental results suggest that a trade-off exists between the efficiency of delivering the analyte to the particle chains and the difficulty of holding the chains in the desired location.

Dynamics of disklike clusters formed in a magnetorheological fluid under a rotational magnetic field

We investigate the cluster formations and dynamics in a magnetorheological fluid under a rotational magnetic field focusing on the case of a relatively high volume fraction. We find that isotropic disklike clusters, which rotate more slowly than the field rotation, are formed at low Mason numbers (the ratio of viscous to magnetic forces) and, what is more, we show short rod clusters, which rotate stably thanks to the low Mason numbers and circulate along the surface of the disklike clusters. The circulation velocity of the surface particles is much higher than the rotational surface velocity of the rigid disklike clusters.

Micromixing with Linked Chains of Paramagnetic Particles

Paramagnetic colloidal particles aggregate into linear chains under an applied external magnetic field. These particles can be chemically linked to create chains that can be magnetically actuated to manipulate microscopic fluid flow. The flexibility of the chain can be adjusted by varying the length of the linker molecule. In this paper, we describe the use of a suspension of linked paramagnetic chains in a rotating magnetic field to perform microscale mixing. The effect of chain rotation and flexibility on the diffusion of molecules is studied by observing the mixing of an acid and base in a microchannel. We show that, as the chain rotation frequency increases, there is marked increase in the effective mixing between fluid streams; however, a maximum frequency exists and above this frequency the chains are no longer effective in mixing. More flexible chains are more effective at mixing over a larger range of frequencies.

Bending of flexible magnetic rods

The flexible inextensible magnetic rod model is applied for the study of bending and buckling deformations of the paramagnetic particle chains linked by polymer molecules. It is shown that the existing experimental results can be reasonably well described by this model which takes into account the normal magnetic forces arising at chain bending deformation. By matching the experimentally observed shapes with our numerical simulation results different physical properties of the linked paramagnetic particle chains are determined.

Rotational dynamics of semiflexible paramagnetic particle chains

Paramagnetic particles have the unique ability to reversibly form magnetic chains. We have taken advantage of this property by permanently linking the chains with three linking chemistries to create flexible chains whose behavior changes with the application of a magnetic field. We study the behavior of these chains in a rotating magnetic field and model them as elastic rods. Rigid chains rotate as a solid body while flexible chains deform under the influence of magnetic, viscous, and elastic stresses. We find that the shapes chains assume in rotating magnetic fields confirm the chain flexibility determined from previous micromechanics measurements.

Dynamics of a flexible magnetic chain in a rotating magnetic field

The model of an elastic magnetic rod is applied for a study of a behavior of the flexible magnetic particle chain in a rotating magnetic field. By numerical simulation it is shown that behavior of a flexible magnetic chain is characterized by the existence of a critical frequency beyond which the dynamics of the rod is periodic with subsequent stages of bending and straightening. The value of the critical frequency found is explained by a simple model. Below the critical frequency the chain is bent and rotates synchronously with a field. It is illustrated that in particular cases the considered model reproduces phenomena observed experimentally and numerically for the magnetic particle chains in magnetorheological suspensions. It is emphasized that the present approach gives the general framework for the description of different phenomena in magnetorheological suspensions.

Fractal patterns, cluster dynamics, and elastic properties of magnetorheological suspensions

We study pattern formation and the aggregation processes in magnetorheological suspensions in the presence of a static magnetic field, and some of their associated physical properties. In particular, we analyze the elastic modes as a function of the intensity of the applied field and for several particle concentrations. We observe that the clusters formed in these systems have multifractal characteristics, which are the result of three well defined stages of the aggregation process. In these stages three generations of clusters are produced sequentially. The structure of the suspension can be well characterized by its mass fractal dimensions and the mass radial distribution. The size distribution of the second-generation clusters written in terms of their mass fractal dimension allows us to calculate the sound speed of the longitudinal modes in the large wavelength regime. This multifractal analysis applied to several kinds of aggregates reveals that the occurrence of at least three stages of aggregation is a common feature to several physical aggregation processes.

Microstructure evolution in magnetorheological suspensions governed by Mason number

The spatiotemporal evolution of field-induced structures in very dilute polarizable colloidal suspensions subject to rotating magnetic fields has been experimentally studied using video microscopy. We found that there is a crossover Mason number (ratio of viscous to magnetic forces) above which the rotation of the field prevents the particle aggregation to form chains. Therefore, at these high Mason numbers, more isotropic clusters and isolated particles appear. The same behavior was also found in recent scattering dichroism experiments developed in more concentrated suspensions, which seems to indicate that the dynamics does not depend on the volume fraction. Scattering dichroism experiments have been used to study the role played by the volume fraction in suspensions with low concentration. As expected, we found that the crossover Mason number does not depend on the volume fraction. Brownian particle dynamics simulations are also reported, showing good agreement with the experiments.

Rotational magnetic endosome microrheology: viscoelastic architecture inside living cells

The previously developed technique of magnetic rotational microrheology [Phys. Rev. E 67, 011504 (2003)] is proposed to investigate the rheological properties of the cell interior. An endogeneous magnetic probe is obtained inside living cells by labeling intracellular compartments with magnetic nanoparticles, following the endocytosis mechanism, the most general pathway used by eucaryotic cells to internalize substances from an extracellular medium. Primarily adsorbed on the plasma membrane, the magnetic nanoparticles are first internalized within submicronic membrane vesicles (100 nm diameter) to finally concentrate inside endocytotic intracellular compartments (0.6 microm diameter). These magnetic endosomes attract each other and form chains within the living cell when submitted to an external magnetic field. Here we demonstrate that these chains of magnetic endosomes are valuable tools to probe the intracellular dynamics at very local scales. The viscoelasticity of the chain microenvironment is quantified in terms of a viscosity eta and a relaxation time tau by analyzing the rotational dynamics of each tested chain in response to a rotation of the external magnetic field. The viscosity eta governs the long time flow of the medium surrounding the chains and the relaxation time tau reflects the proportion of solidlike versus liquidlike behavior (tau=eta/G, where G is the high-frequency shear modulus). Measurements in HeLa cells show that the cell interior is a highly heterogeneous structure, with regions where chains are embedded inside a dense viscoelastic matrix and other domains where chains are surrounded by a less rigid viscoelastic material. When one compound of the cell cytoskeleton is disrupted (microfilaments or microtubules), the intracellular viscoelasticity becomes less heterogeneous and more fluidlike, in the sense of both a lower viscosity and a lower relaxation time.