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.

Energetically favorable configurations of hematite cube chains.

Hematite at room temperature is a weak ferromagnetic material. Its permanent magnetization is three orders smaller than for magnetite. Thus, hematite colloids allow us to explore a different physical range of particle interaction parameters compared to ordinary ferromagnetic particle colloids. In this paper we investigate a colloid consisting of hematite particles with cubic shape. We search for energetically favorable structures in an external magnetic field with analytical and numerical methods and molecular dynamics simulations and analyze whether it is possible to observe them in experiments. We find that energetically favorable configurations are observable only for short chains. Longer chains usually contain kinks which are formed in the process of chain formation due to the interplay of energy and thermal fluctuations as an individual cube can be in one of two alignments with an equal probability.

Equilibrium shapes and stability of magnetic filaments.

Equilibrium shapes of magnetic rods and their stability under the action of an applied field are analyzed. The family of shapes is characterized by two magnetoelastic numbers due to the remanent magnetization and paramagnetic susceptibility of the rod. Since in experiments with flexible magnetic rods the ends are usually unfixed and unclamped, their stability is analyzed under these conditions. Solutions of the corresponding eigenvalue problems for particular cases show that under these conditions the equilibrium shapes are unstable.

Thermodiffusion anisotropy under a magnetic field in ionic liquid-based ferrofluids.

Ferrofluids based on maghemite nanoparticles (NPs), typically 10 nm in diameter, are dispersed in an ionic liquid (1-ethyl 3-methylimidazolium bistriflimide - EMIM-TFSI). The average interparticle interaction is found to be repulsive by small angle scattering of X-rays and of neutrons, with a second virial coefficient A2 = 7.3. A moderately concentrated sample at Φ = 5.95 vol% is probed by forced Rayleigh scattering under an applied magnetic field (up to H = 100 kA m-1) from room temperature up to T = 460 K. Irrespective of the values of H and T, the NPs in this study are always found to migrate towards the cold region. The in-field anisotropy of the mass diffusion coefficient Dm and that of the (always positive) Soret coefficient ST are well described by the presented model in the whole range of H and T. The main origin of anisotropy is the spatial inhomogeneities of concentration in the ferrofluid along the direction of the applied field. Since this effect originates from the magnetic dipolar interparticle interaction, the anisotropy of thermodiffusion progressively vanishes when temperature and thermal motion increase.

Rotating-field-driven ensembles of magnetic particles.

Vortex patterns in ensembles of magnetic particles driven by a rotating field are studied. The driving arises due to the lubrication forces between the rotating particles acting in the direction perpendicular to the radius vector between the particles. Since the lubrication forces cannot be equilibrated by the radial forces due to the dipolar attraction and steric repulsion, the ensemble is in a nonequilibrium state. Different regimes are found for the dynamics of the driven ensembles-solid-body rotation at low frequency of the rotating field and stick-slip motion of the external layers of the aggregate with respect to the internal structure as the frequency is increased. The relation obtained for describing the angular velocity of the solid-body rotation is in good agreement with existing experimental data.

Thermodiffusion of citrate-coated γ-Fe2O3 nanoparticles in aqueous dispersions with tuned counter-ions - anisotropy of the Soret coefficient under a magnetic field.

Under a temperature gradient, the direction of thermodiffusion of charged γ-Fe2O3 nanoparticles (NPs) depends on the nature of the counter-ions present in the dispersion, resulting in either a positive or negative Soret coefficient. Various counter-ions are probed in finely tuned and well characterized dispersions of citrate-coated NPs at comparable concentrations of free ionic species. The Soret coefficient ST is measured in stationary conditions together with the mass-diffusion coefficient Dm using a forced Rayleigh scattering method. The strong interparticle repulsion, determined by SAXS, is also attested by the increase of Dm with NP volume fraction Φ. The Φ-dependence of ST is analyzed in terms of thermophoretic and thermoelectric contributions of the various ionic species. The obtained single-particle thermophoretic contribution of the NPs (the Eastman entropy of transfer sNP) varies linearly with the entropy of transfer of the counter-ions. This is understood in terms of electrostatic contribution and of hydration of the ionic shell surrounding the NPs. Two aqueous dispersions, respectively, with ST > 0 and with ST < 0 are then probed under an applied field H[combining right harpoon above], and an anisotropy of Dm and of ST is induced while the in-field system remains monophasic. Whatever the H[combining right harpoon above]-direction (parallel or perpendicular to the gradients and ), the Soret coefficient is modulated keeping the same sign as in zero applied field. In-field experimental determinations are well described using a mean field model of the interparticle magnetic interaction.

Gravity effects on mixing with magnetic micro-convection in microfluidics.

Mixing remains an important problem for the development of successful microfluidic and lab-on-a-chip devices, where simple and predictable systems are particularly interesting. One is magnetic micro-convection, an instability happening on the interface of miscible magnetic and non-magnetic fluids in a Hele-Shaw cell under applied field. Previous work proved that the Brinkman model quantitatively explains the experiments. However, a gravity-caused convective motion complicated the tests. Here we first improve the experimental system to exclude the parasitic convection. Afterwards, we experimentally observe the magnetic micro-convection, by finding and quantifying how gravity and laminar flow stabilizes the perturbations that create it. Accordingly, we improve our theoretical model for a zero-flow condition and perform a linear analysis. Two dimensionless quantities --magnetic and gravitational Rayleigh numbers-- are used to compare the experimental observations and theoretical predictions for the critical field of instability and the characteristic size of the emerging pattern. Finally, we discuss the conditions at which gravity plays an important role in microfluidic systems.

Dynamics of a flexible ferromagnetic filament in a rotating magnetic field.

Flexible magnetic filaments have garnered considerable attention as prospective materials for the creation of different microdevices. We describe a theoretical model of a ferromagnetic filament and derive its equations of motion by variational techniques. The numerical algorithm used to solve the filament dynamics in magnetic fields of different configurations is described. It is found that in a rotating field the filament transitions between synchronous and asynchronous regimes with respect to the rotating field, similarly to a rigid magnetic dipole. The mean angular velocity of the filament is well described by a relation valid for a rigid magnetic dipole with quantitative differences attributable to the flexibility of the filament.

Synchronized rotation in swarms of magnetotactic bacteria.

Self-organizing behavior has been widely reported in both natural and artificial systems, typically distinguishing between temporal organization (synchronization) and spatial organization (swarming). Swarming has been experimentally observed in systems of magnetotactic bacteria under the action of external magnetic fields. Here we present a model of ensembles of magnetotactic bacteria in which hydrodynamic interactions lead to temporal synchronization in addition to the swarming. After a period of stabilization during which the bacteria form a quasiregular hexagonal lattice structure, the entire swarm begins to rotate in a direction opposite to the direction of the rotation of the magnetic field. We thus illustrate an emergent mechanism of macroscopic motion arising from the synchronized microscopic rotations of hydrodynamically interacting bacteria, reminiscent of the recently proposed concept of swarmalators.

Hydrodynamics with spin in bacterial suspensions.

We describe a kind of self-propelling motion of bacteria based on the cooperative action of rotating flagella on the surface of bacteria. Describing the ensemble of rotating flagella in the framework of the hydrodynamics with spin, the reciprocal theorem of Stokesian hydrodynamics is generalized accordingly. The velocity of the self-propulsion is expressed in terms of the characteristics of the vector field of flagella orientation and it is shown that the unusually high velocities of Thiovulum majus bacteria may be explained by the cooperative action of the rotating flagella. The expressions obtained enable us to estimate the torque created by the rotary motors of the bacterium and show quantitative agreement with the existing experimental data.

Relaxation of polar order in suspensions with Quincke effect.

The Quincke effect--spontaneous rotation of dielectric particles in a liquid with low conductivity under the action of an electric field--is considered. The distribution functions for the orientation of particle rotation planes are introduced and a set of nonlinear kinetic equations is derived in the mean field approximation considering the dynamics of their orientation in the flow induced by rotating particles. As a result the nonequilibrium phase transition to the polar order, if the concentration of the particles is sufficiently high, is predicted and the condition of the synchronization of particle rotations is established. Two cases are considered: the layer of the Quincke suspension with one free boundary and the ensemble of the particles rolling on the solid wall under the action of a torque in an electric field. It is shown that in both cases the synchronization of particle rotations occurs due to the hydrodynamic interactions. In the limit of small spatial nonhomogeneity a set of nonlinear partial differential equations for the macroscopic variables--the concentration and the director of the polar order--is derived from the kinetic equation. Its properties are analyzed and compared with available recent experimental results.

Poiseuille flow of a Quincke suspension.

The controversy of models of dielectric particle suspensions with antisymmetric stress, which predict a nonphysical cusp of the velocity profile in plane Poiseuille flow under the action of the electrical field, is resolved. In the mean-field approximation, the nonlinear kinetic equation is derived for coupled due to the flow translational and rotational motion of the particles. By its numerical solution, it is shown that the velocity profile is smeared due to the translational diffusion of the particles with opposite directions of rotation. The obtained results for the velocity profiles and flow rates as a function of the electric field strength are in qualitative agreement with the existing experimental results.

Dynamics of anisotropic superparamagnetic particles in a precessing magnetic field.

A bifurcation diagram for anisotropic magnetic particles in a precessing magnetic field is analyzed. It is found that a synchronous regime in the case of a prolate particle exists for all precession angles of the magnetic field if the frequency of field rotation is below some critical value. An oblate particle has a synchronous regime in a limited range of precession angle. To understand the flow of suspensions of these particles in precessing fields, it is essential to take into account the differing dynamics of prolate and oblate particles.

Parametric excitation of bending deformations of a rod by periodic twist.

A model of a semiflexible magnetic filament with magnetization frozen in the direction perpendicular to the tangent of its center line is formulated. It is shown that if the rod is magnetized at its ends in opposite directions, an AC magnetic field causes parametric excitation of bending deformations. Neutral curves of parametric excitation are calculated both analytically and numerically. The shapes arising upon parametric excitation of bending deformations are chiral. Periodic rotation of the chiral filament due to nonhomogeneous twist in a nonhomogeneous AC field causes its unidirectional motion.

Bilayer properties of giant magnetic liposomes formed by cationic pyridine amphiphile and probed by active deformation under magnetic forces.

We synthesize giant magnetic liposomes by a reverse-phase evaporation method (REV) using a new self-assembling Cationic Pyridine Amphiphile (CPA) derived from 1,4-dihydropyridine as liposome-forming agent and a magnetic ferrofluid based on γ-Fe(2)O(3) nanoparticles. Having in view the potential interest of CPA in targeted transport by magnetic forces, the mechanical elastic properties of such bilayers are here directly investigated in vesicles loaded with magnetic nanoparticles. Bending elastic modulus K(b) ∼ 0.2 to 5k(B)T and pre-stress τ ∼ 3.2 to 12.10(-6) erg/cm(2) are deduced from the under-field deformations of the giant magnetic liposomes. The obtained K(b) values are discussed in terms of A. Wurgers's theory.

Magnetic wire-based sensors for the microrheology of complex fluids.

We propose a simple microrheology technique to evaluate the viscoelastic properties of complex fluids. The method is based on the use of magnetic wires of a few microns in length submitted to a rotational magnetic field. In this work, the method is implemented on a surfactant wormlike micellar solution that behaves as an ideal Maxwell fluid. With increasing frequency, the wires undergo a transition between a steady and a hindered rotation regime. The study shows that the average rotational velocity and the amplitudes of the oscillations obey scaling laws with well-defined exponents. From a comparison between model predictions and experiments, the rheological parameters of the fluid are determined.

Three-dimensional dynamics of a particle with a finite energy of magnetic anisotropy in a rotating magnetic field.

A model of a single ferromagnetic particle with a finite coupling energy of the magnetic moment with the body of the particle is formulated, and regimes of its motion in a rotating magnetic field are investigated. Regimes are possible that are synchronous and asynchronous with the field. In a synchronous regime the easy axis of the particle is in the plane of the rotating magnetic field at low frequencies (a planar regime) and on the cone at high frequencies (a precession regime). The stability of these regimes is investigated, and it is shown that the precession regime is stable for field strengths below the critical value. In a particular range of field strength value, irreversible jumps of the magnetic moment take place in the asynchronous planar regime. The stability of this regime is investigated, and it is shown that it is stable for field strengths above the critical value, which depends on the frequency. The implications of these results for the energy dissipation in a rotating field are analyzed, and it is shown that the maximum of the heat production near the transition to the synchronous regime is flattened out by the transition to the precession regime.

Coupled stochastic dynamics of magnetic moment and anisotropy axis of a magnetic nanoparticle.

An algorithm is developed for numerical simulation of coupled stochastic dynamics of magnetic moment and magnetic anisotropy axis of a nanoparticle. Time-correlation functions of the magnetic moment and its components longitudinal and transverse to the magnetic anisotropy axis are calculated by averaging along the stochastic trajectory. The longitudinal and transverse relaxation times are found by fitting the time correlation functions. Existing theoretical relations derived by the effective field approach in the limit of small fields are confirmed. The time-correlation functions of magnetic moments of nanoparticles in dependence on their properties are calculated numerically for arbitrary large magnetic fields and it is shown that they may be approximated by a sum of several exponentials. These results are applied for the calculation of relaxivity parameters of nuclear magnetic resonance (NMR) imaging in dependence on the field strength.

Dynamics of superparamagnetic filaments with finite magnetic relaxation time.

In this paper we formulate a model of superparamagnetic filaments with internal dissipative torques due to the action of a rotating magnetic field. It is shown that spirals are formed at both ends of the filament due to the action of the internal torques. These spirals propagate to the center of the filament and collide, forming a compact cluster that rotates in accordance with the rotating magnetic field. These results are in agreement with recent experiments with chains of superparamagnetic beads in a rotating magnetic field.

Ferromagnetic microswimmer.

The self-propelling motion of the flexible ferromagnetic swimmer is described. Necessary symmetry breaking is achieved by the buckling instability at field inversion. The characteristics of self-propulsion are in good agreement with the numerical calculations of the Floquet multipliers for the ferromagnetic filament under the action of ac magnetic field. In the low frequency range the power stroke of self-propelling motion is similar to that used by the unicellular green algae chlamydomonas and in the high frequency region the self-propulsion is due to the undulation waves propagating from the free ends perpendicularly to ac magnetic field.