Chain model of a magnetorheological suspension in a rotating field

Magnetically Enhanced Intracellular Uptake of Superparamagnetic Iron Oxide Nanoparticles for Antitumor Therapy

Superparamagnetic iron oxide nanoparticles (SPIONs) have been widely employed in biomedical fields, including targeted delivery of antitumor therapy. Conventional magnetic tumor targeting has used simple static magnetic fields (SMFs), which cause SPIONs to linearly aggregate into a long chain-like shape. Such agglomeration greatly hinders the intracellular targeting of SPIONs into tumors, thus reducing the therapeutic efficacy. In this study, we investigated the enhancement of the intracellular uptake of SPIONs through the application of rotating magnetic fields (RMFs). Based on the physical principles of SPION chain disassembly, we investigated physical parameters to predict the chain length favorable for intracellular uptake. Our prediction was validated by clear visualization of the intracellular distributions of SPIONs in tumor cells at both cellular and three-dimensional microtissue levels. To identify the potential therapeutic effects of enhanced intracellular uptake, magnetic hyperthermia as antitumor therapy was investigated under varying conditions of magnetic hyperthermia and RMFs. The results showed that enhanced intracellular uptake reduced magnetic hyperthermia time and strength as well as particle concentration. The proposed method will be useful in the development of techniques to determine the optimized physical conditions for the enhanced intracellular uptake of SPIONs in antitumor therapy.

Rotating hematite cube chains

Recently a two-dimensional chiral fluid was experimentally demonstrated. It was obtained from cubic-shaped hematite colloidal particles placed in a rotating magnetic field. Here we look at building blocks of that fluid by analyzing short hematite chain behavior in a rotating magnetic field. We find equilibrium structures of chains in static magnetic fields and observe chain dynamics in rotating magnetic fields. We find and experimentally verify that there are three planar motion regimes and one where the cube chain goes out of the plane of the rotating magnetic field. In this regime we observe interesting dynamics-the chain rotates slower than the rotating magnetic field. In order to catch up with the magnetic field, it rolls on an edge and through rotation in the third dimension catches up with the magnetic field. The same dynamics is also observable for a single cube when gravitational effects are explicitly taken into account.

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.

Optomagnetic biosensors: Volumetric sensing based on magnetic actuation-induced optical modulations

In comparison to alternative nanomaterials, magnetic micron/nano-sized particles show unique advantages, e.g., easy manipulation, stable signal, and high contrast. By applying magnetic actuation, magnetic particles exert forces on target objects for highly selective operation even in non-purified samples. We herein describe a subgroup of magnetic biosensors, namely optomagnetic biosensors, which employ alternating magnetic fields to generate periodic movements of magnetic labels. The optical modulation induced by the dynamics of magnetic labels is then analyzed by photodetectors, providing information of, e.g., hydrodynamic size changes of the magnetic labels. Optomagnetic sensing mechanisms can suppress the noise (by performing lock-in detection), accelerate the reaction (by magnetic force-enhanced molecular collision), and facilitate homogeneous/volumetric detection. Moreover, optomagnetic sensing can be performed using a low magnetic field (<10 mT) without sophisticated light sources or pickup coils, further enhancing its applicability for point-of-care tests. This review concentrates on optomagnetic biosensing techniques of different concepts classified by the magnetic actuation strategy, i.e., magnetic field-enhanced agglutination, rotating magnetic field-based particle rotation, and oscillating magnetic field-induced Brownian relaxation. Optomagnetic sensing principles applied with different actuation strategies are introduced as well. For each representative optomagnetic biosensor, a simple immunoassay strategy-based application is introduced (if possible) for methodological comparison. Thereafter, challenges and perspectives are discussed, including minimization of nonspecific binding, on-chip integration, and multiplex detection, all of which are key requirements in point-of-care diagnostics.

A broad perspective to particle-laden fluid interfaces systems: from chemically homogeneous particles to active colloids

Particles adsorbed to fluid interfaces are ubiquitous in industry, nature or life. The wide range of properties arising from the assembly of particles at fluid interface has stimulated an intense research activity on shed light to the most fundamental physico-chemical aspects of these systems. These include the mechanisms driving the equilibration of the interfacial layers, trapping energy, specific inter-particle interactions and the response of the particle-laden interface to mechanical perturbations and flows. The understanding of the physico-chemistry of particle-laden interfaces becomes essential for taking advantage of the particle capacity to stabilize interfaces for the preparation of different dispersed systems (emulsions, foams or colloidosomes) and the fabrication of new reconfigurable interface-dominated devices. This review presents a detailed overview of the physico-chemical aspects that determine the behavior of particles trapped at fluid interfaces. This has been combined with some examples of real and potential applications of these systems in technological and industrial fields. It is expected that this information can provide a general perspective of the topic that can be exploited for researchers and technologist non-specialized in the study of particle-laden interfaces, or for experienced researcher seeking new questions to solve.

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.

Gauge invariant and gauge dependent aspects of topological walking colloidal bipeds

Paramagnetic colloidal spheres assemble to colloidal bipeds of various length in an external magnetic field. When the bipeds reside above a magnetic pattern and we modulate the direction of the external magnetic field, the rods perform topologically distinct classes of protected motion above the pattern. The topological protection allows each class to be robust against small continuous deformations of the driving loop of the external field. We observe motion of the rod from a passive central sliding and rolling motion for short bipeds toward a walking motion with both ends of the rod alternately touching down on the pattern for long bipeds. The change of character of the motion occurs in form of discrete topological transitions. The topological protection makes walking a form of motion robust against the breaking of the non symmorphic symmetry. In patterns with non symmorphic symmetry walking is reversible. In symmorphic patterns lacking a glide plane the walking can be irreversible or reversible involving or not involving ratchet jumps. Using different gauges allows us to unravel the active and passive aspects of the topological walks.

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.

Distribution model of the surface roughness in magnetorheological jet polishing

Magnetorheological jet polishing (MJP) plays an important role in polishing complex cavities and special optical elements with high precision. However, the roughness distribution function that describes the variation with polishing time of the roughness value of every area in the polishing area has not been studied deeply. In this paper, the influence of the roughness distribution on the removal function of MJP in optics (with a roughness of less than 10 nm) and its evolution model in the spatial and time domains are studied. With the increase of polishing time, the surface roughness of the central area linearly increases, forming surface defects, such as pits. The roughness of the polishing area exhibits a limited growth trend. Verification experiments are carried out on BK7 glass. The results of the roughness distribution on the removal function prove the correctness of the model. The model laid a foundation; therefore, it has important guidance and reference value for the application to the whole aperture polishing.

Cohesive self-organization of mobile microrobotic swarms

Mobile microrobots are envisioned to be useful in a wide range of high-impact applications, many of which require cohesive group formation to maintain self-bounded swarms in the absence of confining boundaries. Cohesive group formation relies on a balance between attractive and repulsive interactions between agents. We found that a balance of magnetic dipolar attraction and multipolar repulsion between self-assembled particle chain microrobots enables their self-organization into cohesive clusters. Self-organized microrobotic clusters move above a solid substrate via a hydrodynamic self-propulsion mechanism. Cluster velocity increases with cluster size, resulting from collective hydrodynamic effects. Clustering is promoted by the strength of cohesive interactions and is hindered by the heterogeneities of individual microrobots. The scalability of cohesive interactions allows the formation of larger groups, whose internal spatiotemporal organization undergoes a transition from solid-like ordering to a liquid-like behavior with increasing cluster size. Our work elucidates the dynamics of clustering under cohesive interactions, and presents an approach for addressing the operation of microrobots as localized collectives.

Continuum model of magnetic field induced viscoelasticity in magnetorheological fluids

An effective macroscopic model of magnetorheological fluids in the viscoelastic regime is proposed. Under the application of an external magnetic field, columns of magnetizable particles are formed in these systems. The columns are responsible for solidlike properties, such as the existence of elastic shear modulus and yield stress, and are captured by the strain field, while magnetic properties are described by the magnetization. We investigate the interplay of these variables when static shear or normal pressure is imposed in the presence of the external magnetic field. By assuming a relaxing strain field, we calculate the flow curves, i.e., the shear stress as a function of the imposed shear rate, for different values of the applied magnetic field. Focusing on the small amplitude oscillatory shear, we study the complex shear modulus, i.e., the storage and the loss moduli, as a function of the frequency. We demonstrate that already such a minimal model is capable of furnishing many of the key physical features of these systems, such as yield stress, enhancement of the shear yield stress by pressure, threshold behavior in the spirit of the frequently employed Bingham law, and several features in the frequency dependence of storage and loss moduli.

Programmable Collective Behavior in Dynamically Self-Assembled Mobile Microrobotic Swarms

Collective control of mobile microrobotic swarms is indispensable for their potential high-impact applications in targeted drug delivery, medical diagnostics, parallel micromanipulation, and environmental sensing and remediation. Without integrated electronics for sensing and actuation, current microrobotic systems should rely on physical interactions among individual microrobots for local communication and cooperation. Here, it is shown that mobile microrobotic swarms with well-defined collective behavior can be designed by engineering magnetic interactions among individual units. Microrobots, dynamically self-assembled from magnetic microparticles into linear chains, locomote on surfaces in response to a precessing magnetic field. Control over precessing magnetic field allows engineering attractive and repulsive interactions among microrobots and, thus, collective order with well-defined spatial organization and stable parallel operation over macroscale distances (≈1 cm) and through confining obstacles. The design approach described here addresses programmable assembly, propulsion, and collective behavior of dense mobile microrobot swarms simultaneously by engineering magnetic interactions and dynamic actuation of microrobots. The presented approach will advance swarm microrobotics by enabling facile and rapid formation of self-organized and reconfigurable microrobotic swarms with programmable collective order and stability.

Paramagnetic colloids: Chaotic routes to clusters and molecules

We present computer simulations and experiments on dilute suspensions of superparamagnetic particles subject to rotating magnetic fields. We focus on chains of four particles and their decay routes to stable structures. At low rates, the chains track the external field. At intermediate rates, the chains break up but perform a periodic (albeit complex) motion. At sufficiently high rates, the chains generally undergo chaotic motion at short times and decay to either closely packed clusters or more dispersed, colloidal molecules at long times. We show that the transition out of the chaotic states can be described as a Poisson process in both simulation and experiment.

Magnetic Microlassos for Reversible Cargo Capture, Transport, and Release

Microbot propulsion has seen increasing interest in recent years as artificial methods that overcome the well-established reversible and challenging nature of microscale fluid mechanics. While controlled movement is an important feature of microbot action, many envisioned applications also involve cargo transport where microbots must be able to load and unload contents on command while tolerating complex solution chemistry. Here we introduce a physical method that uses flexible and linked superparamagnetic colloidal chains, which can form closed rings or "lassos" in the presence of a planar rotating magnetic field. By adding an additional AC magnetic field along the direction perpendicular to the substrate, we can orient the lasso at a tilted camber angle. We show that these magnetic lassos can roll at substantial velocities, with precise spatial control by manipulating both field strength and phase lag. Moreover, the lasso can curl around and capture cargo tightly and transport it based on a wheel-type mechanism. At the targeted destination, cargo is easily released upon field removal and the lasso can be readily reused. Since the entire process is physically controlled with no chemistry for attachment or disengagement involved, our system can potentially be used for transporting diverse types of cargo under different solution conditions.

Modified Mason number for charged paramagnetic colloidal suspensions

The dynamics of magnetorheological fluids have typically been described by the Mason number, a governing parameter defined as the ratio between viscous and magnetic forces in the fluid. For most experimental suspensions of magnetic particles, surface forces, such as steric and electrostatic interactions, can significantly influence the dynamics. Here we propose a theory of a modified Mason number that accounts for surface forces and show that this modified Mason number is a function of interparticle distance. We demonstrate that this modified Mason number is accurate in describing the dynamics of a rotating pair of paramagnetic colloids of identical or mismatched sizes in either high or low salt solutions. The modified Mason number is confirmed to be pseudoconstant for particle pairs and particle chains undergoing a stable-metastable transition during rotation. The interparticle distance term can be calculated using theory or can be measured experimentally. This modified Mason number is more applicable to magnetorheological systems where surface forces are not negligible.

Micro-mutual-dipolar model for rapid calculation of forces between paramagnetic colloids

Typically, the force between paramagnetic particles in a uniform magnetic field is calculated using either dipole-based models or the Maxwell stress tensor combined with Laplace's equation for magnetostatics. Dipole-based models are fast but involve many assumptions, leading to inaccuracies in determining forces for clusters of particles. The Maxwell stress tensor yields an exact force calculation, but solving Laplace's equation is very time consuming. Here, we present a more elaborate dipole-based model: the micro-mutual-dipolar model. Our model has a time complexity that is similar to that of other dipole-based models but is much more accurate especially when used to calculate the force of small aggregates. Using this model, we calculate the force between two paramagnetic spheres in a uniform magnetic field and a circular rotational magnetic field and compare our results with those of other models. The forces for three-particle and ten-particle systems dispersed in two-dimensional (2D) space are examined using the same model. We also apply this model to calculate the force between two paramagnetic disks dispersed in 2D space. The micro-mutual-dipolar model is demonstrated to be useful for force calculations in dynamic simulations of small clusters of particles for which both accuracy and efficiency are desirable.

Configurations and control of magnetic fields for manipulating magnetic particles in microfluidic applications: magnet systems and manipulation mechanisms

The use of a magnetic field for manipulating the motion of magnetic particles in microchannels has attracted increasing attention in microfluidic applications. Generation of a flexible and controllable magnetic field plays a crucial role in making better use of the particle manipulation technology. Recent advances in the development of magnet systems and magnetic field control methods have shown that it has great potential for effective and accurate manipulation of particles in microfluidic systems. Starting with the analysis of magnetic forces acting on the particles, this review gives the configurations and evaluations of three main types of magnet system proposed in microfluidic applications. The interaction mechanisms of magnetic particles with magnetic fields are also discussed.

Numerical calculation of interaction forces between paramagnetic colloids in two-dimensional systems

Typically the force between paramagnetic particles in a uniform magnetic field is described using the dipolar model, which is inaccurate when particles are in close proximity to each other. Instead, the exact force between paramagnetic particles can be determined by solving a three-dimensional Laplace's equation for magnetostatics under specified boundary conditions and calculating the Maxwell stress tensor. The analytical solution to this multi-boundary-condition Laplace's equation can be obtained by using a solid harmonics expansion in conjunction with the Hobson formula. However, for a multibody system, finite truncation of the Hobson formula does not lead to convergence of the expansion at all points, which makes the approximation physically unrealistic. Here we present a numerical method for solving this Laplace's equation for magnetostatics. This method uses a smoothed representation to replace all the boundary conditions. A two-step propagation is used to dramatically accelerate the calculation without losing accuracy. Using this method, we calculate the force between two paramagnetic particles in a uniform and a rotational external field and compare our results with other models. Furthermore, the many-body effects for three-particle, ten-particle, and 24-particle systems are examined using the same method. We also calculate the interaction between particles with different magnetic susceptibilities and particle diameters. The Laplace's equation solver method described in this article that is used to determine the force between paramagnetic particles is shown to be very useful for dynamic simulations for both two-particle systems and a large cluster of particles.

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.

Accelerated immunoassays based on magnetic particle dynamics in a rotating capillary tube with stationary magnetic field

A rapid and simple magnetic particle-based immunoassay has been demonstrated in a capillary mixing system. Antibody-coated micrometer size superparamagnetic polystyrene (SPP) particles were used in an assay for rabbit IgG in a sandwich (noncompetitive) format. The kinetics of the assay was compared between a plate-based system and a single capillary tube. The interaction between the antigen (R-IgG) and the antibody (anti-R-IgG) that was carried by the SPP particles in a rotating capillary was tested under a stationary magnetic field. Competing magnetic and viscous drag forces helped to enhance the interaction between the analyte and the capture antibodies on the particles. The dimensionless Mason number (Mn) was employed to characterize the magnetic particle dynamics; a previously determined critical Mason number (Mn(c)) was employed as a guide to the appropriate experimental conditions of magnetic field strength and rotational speed of the capillary. The advantage of the rotating capillary system included a short assay time and a reduced reactive volume (20 μL). The results show that the immunoassay kinetics were improved by the formation of chains of the SPP particles for the conditions that corresponded to the critical Mason number.

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.

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.

Magneto-optical biosensing platform based on light scattering from self-assembled chains of functionalized rotating magnetic beads

We describe a simple protocol for the rapid, highly sensitive, and quantitative measurement of the concentration of biomolecules in a solution by monitoring light scattered by self-assembled chains of functionalized superparamagnetic beads (SBs) rotating in the solution. A rotating external field (H(ex)) applied to an aqueous solution containing 250 nm diameter biotinylated SBs produced linear chains of SBs rotating in phase with Hex due to magnetically induced self-assembly. At constant Hex, the addition of avidin to the solution led to the formation of longer SB-chains than without the presence of avidin. The generation of longer SB-chains was revealed by increases in the amplitude of the oscillating optical transmittance signal of the magnetic colloid solution. Monitoring changes in the amplitude of the optical transmittance of the solution enabled quantitative determination of the concentration of avidin added to the solution with a sensitivity of 100 pM (6.7 ng/mL) and a dynamic range of at least 3 orders of magnitude. The rotating chains acted as biomolecule probes and micromagnetic mixers, enabling detection of biomolecular recognition in less than 30 s. This approach offers a rapid, highly sensitive, inexpensive, and homogeneous means for detecting biorecognition processes.

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.

Hydrodynamics of chains in ferrofluid-based magnetorheological fluids under rotating magnetic field

Ferrofluid-based magnetorheological (MR) fluid is prepared by dispersing micron-size magnetic spheres in a ferrofluid. We report here the mechanism of chain formation in ferrofluid based MR fluid, which is quite different from conventional MR fluid. Some of the nanomagnetic particles of ferrofluid filled inside the microcavities are formed due to association of large particles, and some of them are attached at the end of large particles. Under rotating magnetic field, fragmentation of a single chain into three parts is observed. Two of them are chains of micron-size magnetic particles which are suspended in a ferrofluid, and the third one is the chain of nanomagnetic particles of ferrofluid, which may be the connecting bridge between the two chains of larger magnetic particles. The rupture of a single chain provides evidence for the presence of nanomagnetic particles within the magnetic field-induced chainlike structure in this bidispersed MR fluid.

Theory of strong intrinsic mixing of particle suspensions in vortex magnetic fields

Recent experiments have shown that a type of triaxial magnetic field we call a vortex field can induce strong mixing in a magnetic particle suspension. A vortex triaxial field consists of a rotating magnetic field in a horizontal plane, with a dc field applied normal to this. The mixing torque is found to be independent of the field frequency and fluid viscosity over a broad range; scales as the square of the applied field; and is strongest for a balanced triaxial field-one in which the root-mean-square amplitudes of the three field components are equal. In this paper we show that these anomalous effects are consistent with the formation of volatile particle chains that have a precessionlike motion. Theoretical results are given for both particle chains and magnetic rods for arbitrary vortex field angles. A key conclusion is that the mixing torque is independent of particle size, making this mixing technique scale adaptive, and thus suitable for microfluidics applications.

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.

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.

Nonlinear ac responses of electro-magnetorheological fluids

We apply a Langevin model to investigate the nonlinear ac responses of electro-magnetorheological (ERMR) fluids under the application of two crossed dc magnetic (z axis) and electric (x axis) fields and a probing ac sinusoidal magnetic field. We focus on the influence of the magnetic fields which can yield nonlinear behaviors inside the system due to the particles with a permanent magnetic dipole moment. Based on a perturbation approach, we extract the harmonics of the magnetic field and orientational magnetization analytically. To this end, we find that the harmonics are sensitive to the degree of anisotropy of the structure as well as the field frequency. Thus, it is possible to real-time-monitor the structure transformation of ERMR fluids by detecting the nonlinear ac responses.

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.

Statistical-mechanical theory of the overall magnetic properties of mesocrystals

The mesocrystal showing both electrorheological and magnetorheological effects is called electro-magnetorheological (EMR) solids. Prediction of the overall magnetic properties of the EMR solids is a challenging task due to the coexistence of the uniaxially anisotropic behavior and structural transition as well as long-range interaction between the suspended particles. To consider the uniaxial anisotropy effect, we present an anisotropic Kirkwood-Fröhlich equation for calculating the effective permeabilities by adopting an explicit characteristic spheroid rather than a characteristic sphere used in the derivation of the usual Kirkwood-Fröhlich equation. Further, by applying an Ewald-Kornfeld formulation we are able to investigate the effective permeability by including the structural transition and long-range interaction explicitly. Our theory can reduce to the usual Kirkwood-Fröhlich equation and Onsager equation naturally. To this end, the numerical simulation shows the validity of monitoring the structure of EMR solids by detecting their effective permeabilities.

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.

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.