Concentrated Ferrofluids Research Articles

Third harmonic of the dynamic magnetic susceptibility of a concentrated ferrofluid: Numerical calculation and simple approximation formula.

Information about the nonlinear magnetic response of dispersions of magnetic particles is the basis for biomedical applications. In this paper, using analytical and numerical methods, the third harmonic of the dynamic susceptibility of an ensemble of moving magnetic particles in an ac magnetic field with an arbitrary amplitude is studied, taking into account interparticle interactions. A simple approximation formula is proposed to predict the third harmonic as a function of two parameters: the Langevin susceptibility χ_{L}, which is used to estimate the particle dipole-dipole interactions, and the Langevin parameter ξ, which represents the ratio of the energy of the magnetic moment interacting with the magnetic field to the thermal energy. The derived approximation formula corresponds with the known single-particle theories in the limit case of a small particle's concentration and is valid for concentrated dispersions of magnetic particles (with the Langevin susceptibility up to χ_{L}≤3) in high-amplitude ac fields (with the Langevin parameter up to ξ≤10).

Particle correlations in concentrated aqueous ferrofluids upon dilution by small-angle X-ray scattering

Small-angle X-ray scattering is applied to study particle correlations in concentrated (up to 7.5 vol% magnetite) aqueous magnetic fluids with double-layer coating by either oleic or lauric acids. The structure of aggregates in these fluids is analyzed when diluting samples with the goal of finding out a concentration threshold at which the aggregates can be considered weakly interacting independent formations. For dilute systems, suitable models fitting experimental scattering curves are proposed, which take into account the polydispersity of both particles and aggregates. It is shown that particle correlations found in aggregates are dependent on the surfactant coating.

Influence of a bias dc field and an ac field amplitude on the dynamic susceptibility of a moderately concentrated ferrofluid.

In this paper, we study the effect of a bias dc field on the dynamic response of a moderately concentrated ferrofluid to an ac magnetic field of arbitrary amplitude. The ferrofluid is modeled by an ensemble of interacting moving magnetic particles; the reaction of particle magnetic moments to ac and dc magnetic fields occurs according to the Brownian mechanism; and the ac and dc magnetic fields are parallel. Based on a numerical solution of the Fokker-Planck equationfor the probability density of the orientation of the magnetic moment of a random magnetic particle, dynamic magnetization and susceptibility are determined and analyzed for various values of the ac field amplitude, the dc field strength, and the intensity of dipole-dipole interactions. It is shown that the system's magnetic response is formed under the influence of competing interactions, such as dipole-dipole, dipole-ac field, and dipole-dc field interactions. When the energies of these interactions are comparable, unexpected effects are observed: the system's susceptibility can either increase or decrease with increasing ac field amplitude. This behavior is associated with the formation of nose-to-tail dipolar structures under the action of the dc field, which can hinder or promote the system's dynamic response to the ac field. The obtained results provide a theoretical basis for predicting the dynamic properties of ferrofluids to improve their use in biomedical applications, such as, in magnetic induction hyperthermia.

Development of a Model and Experimental Study of Thermal Processes in a Ferrofluid Sealer

The aim of the work is to create an interconnected numerical model of the magnetic, hydrodynamic and temperature fields of a ferrofluid sealer and to analyze thermal processes occurring in highspeed seals. This goal is achieved by selecting the necessary equations, boundary conditions, assumptions and physical properties of the magnetic fluid when building the numerical model of the sealer’s working gap, verification of the developed model by the results of the physical experiment. The important results of the work are the obtained and analyzed data on the influence both of physical properties and the geometry of the working gap of the ferrofluid sealer on the heating of the ferrofluid. With a shaft radius of 140 mm and a linear velocity at the shaft surface of 25 m/s due to viscous heating the ferrofluid temperature exceeding the ambient temperature can reach values up to 80 degrees and higher, it has been shown. The use of the equation proposed by V.E. Fertman to determine the thermal conductivity of ferrofluid and the mixing rule to determine its heat capacity allows us to describe with sufficient accuracy for engineering calculations the thermophysical properties of concentrated ferrofluids, it was shown. The significance of the results consists in the possibility of using the developed numerical model in the study of interrelated physical processes in the working gap of the ferrofluid sealer of rotating shafts. The physical and concentration parameters of the synthetic oil-based magnetic fluid given in the paper and the results of its test operation as part of a ferrofluid seal can be used to verify the results of newly developed models of ferrofluid devices.

Shape-induced superstructure formation in concentrated ferrofluids under applied magnetic fields.

The field-induced ordering of concentrated ferrofluids based on spherical and cuboidal maghemite nanoparticles is studied using small-angle neutron scattering, revealing a qualitative effect of the faceted shape on the interparticle interactions as shown in the structure factor and correlation lengths. Whereas a spatially disordered hard-sphere interaction potential with a short correlation length is found for ∼9 nm spherical nanoparticles, nanocubes of a comparable particle size exhibit a more pronounced interparticle interaction and the formation of linear arrangements. Analysis of the anisotropic two-dimensional pair distance correlation function gives insight into the real-space arrangement of the nanoparticles. On the basis of the short interparticle distances found here, oriented attachment, i.e. a face-to-face arrangement of the nanocubes, is likely. The unusual field dependence of the interparticle correlations suggests a field-induced structural rearrangement.

Colloidal Stability and Concentration Effects on Nanoparticle Heat Delivery for Magnetic Fluid Hyperthermia.

The heat produced by magnetic nanoparticles, when they are submitted to a time-varying magnetic field, has been used in many auspicious biotechnological applications. In the search for better performance in terms of the specific power absorption (SPA) index, researchers have studied the influence of the chemical composition, size and dispersion, shape, and exchange stiffness in morphochemical structures. Monodisperse assemblies of magnetic nanoparticles have been produced using elaborate synthetic procedures, where the product is generally dispersed in organic solvents. However, the colloidal stability of these rough dispersions has not received much attention in these studies, hampering experimental determination of the SPA. To investigate the influence of colloidal stability on the heating response of ferrofluids, we produced bimagnetic core@shell NPs chemically composed of a ZnMn mixed ferrite core covered by a maghemite shell. Aqueous ferrofluids were prepared with these samples using the electric double layer (EDL) as a strategy to maintain colloidal stability. By starting from a proper sample, ultrastable concentrated ferrofluids were achieved by both tuning the ion/counterion ratio and controlling the water content. As the colloidal stability mainly depends on the ion configuration on the surface of the magnetic nanoparticles, different levels of nanoparticle clustering are achieved by changing the ionic force and pH of the medium. Thus, the samples were submitted to two procedures of EDL destabilization, which involved dilution with an alkaline solution and a neutral pH viscous medium. The SPA results of all prepared ferrofluid samples show a reduction of up to half the efficiency of the standard sample when the ferrofluids are in a neutral pH or concentrated regime. Such results are explained in terms of magnetic dipolar interactions. Our results point to the importance of ferrofluid colloidal stability in a more reliable experimental determination of the NP heat generation performance.

Determination of the statistics of magnetically induced particle chains in concentrated ferrofluids

The paper presents the determination of the magnetic field dependence of the statistics of nanoparticle one dimensional chains in a 9.3% solid volume fraction ferrofluid, using optical dichroism experiments. It was found that, in a 300 kA/m magnetic field, 4v% of the nanoparticles are contained in one dimensional chains with 2 particles/chain on average. For this purpose, an analytical theoretical model for the influence of the magnetically induced nanoparticle chaining on the linear dichroism in ferrofluids was developed. The model is based on the statistical theory for magnetic nanoparticle chaining in ferrofluids developed by Mendelev and Ivanov. The chains statistics was obtained by means of nonlinear regression of the dichroism data with the theoretical model.

Structural characterization of concentrated aqueous ferrofluids

Structure characterizations of concentrated water-based magnetic fluids stabilized by oleic and lauric acids were done by means of small-angle neutron scattering (SANS) and complemented by dynamic light scattering and magnetization analysis. Stability of ferrofluids with time against sedimentation was concluded despite the presence of aggregates in solutions. Differences in the average sizes of individual polydisperse magnetite nanoparticles coated with surfactants and their aggregates were revealed. Structural parameters obtained from SANS have been confirmed by magnetogranulometry data. The comparative analysis of the aggregation and its change upon dilution is made basing on the data of SANS and dynamic light scattering techniques.

Dynamic susceptibility of a concentrated ferrofluid: The role of interparticle interactions.

The dynamic susceptibility of concentrated ferrofluids of magnetite-kerosene type is studied experimentally to clarify the effect of interparticle interactions on the magnetization reversal dynamics and the ferrofluid relaxation time spectrum. We synthesize six ferrofluid samples, four of which have the same wide particle size distribution with a high (more than 2kT) average energy of magnetic dipole interactions. These samples differ in particle concentration and dynamic viscosity. The two remaining samples have a lower content of large particles and a moderate energy of magnetic dipole interactions. For all samples, we measure the dynamic susceptibility in the weak probing field at frequencies up to 160kHz and the field amplitude dependence of the susceptibility at a frequency of 27kHz. The results show that the susceptibility dispersion at frequencies up to 10kHz is due to the rotational diffusion of colloidal particles and aggregates. Steric and hydrodynamic interparticle interactions are the main reason for the strong concentration dependence of the viscosity and so they also strongly influence the frequency dependence of the susceptibility. The influence of van der Waals and magnetic dipole interactions on the susceptibility is manifested indirectly, through the formation of multiparticle clusters. The contribution of clusters to the low-frequency susceptibility reaches 80%. Their large sizes (about 100 nm) shift the dispersion region to frequencies of 1-100Hz, depending on the temperature and particle concentration. Experiments at 27kHz demonstrate the increase in the dynamic susceptibility with increasing field amplitude. This growth is unexpected since all spectral amplitudes in the Debye function expansion of the dynamic susceptibility decrease monotonically with increasing field. To clarify the situation, the auxiliary problem of the magnetodynamics of a uniaxial particle in the alternating field is solved numerically. The Fokker-Planck-Brown rotational diffusion equation is used. It is shown that an increase in the field amplitude reduces the anisotropy barrier and the Néel relaxation time of particles and increases the dynamic susceptibility by one to two orders of magnitude compared to the weak-field limit. The calculation results are in qualitative agreement with the experimental data and allow us to propose a consistent interpretation of these data. We find that the increase in dynamic susceptibility with increasing amplitude is observed when two necessary conditions are met: (i) The suspension viscosity and the field frequency are high enough to cause the blocking of the rotational degrees of freedom of particles and aggregates and (ii) particles with a large magnetic anisotropy are present in the ferrofluid.

Equilibrium magnetization of a quasispherical cluster of single-domain particles

Equilibrium magnetization curve of a rigid finite-size spherical cluster of single-domain particles is investigated both numerically and analytically. The spatial distribution of particles within the cluster is random. Dipole-dipole interactions between particles are taken into account. The particles are monodisperse. It is shown, using the stochastic Landau-Lifshitz-Gilbert equation that the magnetization of such clusters is generally lower than predicted by the classical Langevin model. In a broad range of dipolar coupling parameters and particle volume fractions, the cluster magnetization in the weak field limit can be successfully described by the modified mean-field theory, which was originally proposed for the description of concentrated ferrofluids. In moderate and strong fields, the theory overestimates the cluster magnetization. However, predictions of the theory can be improved by adjusting the corresponding mean-field parameter. If magnetic anisotropy of particles is additionally taken into account and if the distribution of the particles' easy axes is random and uniform, then the cluster equilibrium response is even weaker. The decrease of the magnetization with increasing anisotropy constant is more pronounced at large applied fields. The phenomenological generalization of the modified mean-field theory, that correctly describes this effect for small coupling parameters, is proposed.

Nonlinear response of a concentrated ferrofluid to a low-frequency magnetic field

Nonlinear response of a concentrated ferrofluid to a low-frequency magnetic field

Modified mean-field theory of the magnetic properties of concentrated, high-susceptibility, polydisperse ferrofluids.

The effects of particle-size polydispersity on the magnetostatic properties of concentrated ferrofluids are studied using theory and computer simulation. The second-order modified mean-field (MMF2) theory of Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)1063-651X10.1103/PhysRevE.64.041405] has been extended by calculating additional terms of higher order in the dipolar coupling constant in the expansions of the initial magnetic susceptibility and the magnetization curve. The theoretical predictions have been tested rigorously against results from Monte Carlo simulations of model monodisperse, bidisperse, and highly polydisperse ferrofluids. Comparisons have been made between systems with the same Langevin susceptibility and the same saturation magnetization. In all cases, the new theoretical magnetization curve shows better agreement with simulation data than does the MMF2 theory. As for the initial susceptibility, MMF2 theory is most accurate for the monodisperse model, while the new theory works best for polydisperse systems with a significant proportion of large particles. These results are important for the analysis and characterization of recently synthesized polydisperse ferrofluids with record-breaking values of the initial magnetic susceptibility.

Magnetoviscoelastic characteristics of superparamagnetic oxides (Fe, Ni) based ferrofluids

Ferrofluids have been popular among the academic and scientific communities owing to their intelligent physical characteristics under external stimuli and are in fact among the first nanotechnology products to be employed in real world applications. However, studies on the magnetoviscoelastic behavior of concentrated ferrofluids, especially of superparamagnetic oxides of iron and nickel are rare. The present article comprises the formulation of magneto-colloids utilizing the three various metal oxides nanoparticles viz. Iron (II, III) oxide (Fe3O4), Iron (III) oxide (Fe2O3) and Nickel oxide (NiO) in oil. Iron (II, III) oxide based colloids demonstrate high magnetoviscous characteristics over the other oxides based colloids under external magnetic fields. The maximum magnitude of yield stress and viscosity is found to be 3.0kPa and 2.9kPa.s, respectively for iron (II, III) oxide based colloids at 2.6vol% particle concentration and 1.2T magnetic field. Experimental investigations reveal that the formulated magneto-nanocolloids are stable, even in high magnetic fields and almost reversible when exposed to rising and drop of magnetic fields of the same magnitude. Observations also reveal that the elastic behavior dominates over the viscous behavior with enhanced relaxation and creep characteristics under the magnetic field. The effect of temperature on viscosity and yield stress of magneto-nanocolloids under magnetic fields has also been discussed. Thus, the present findings have potential applications in various fields such as electromagnetic clutch and brakes of automotive, damping, sealing, optics, nanofinishing etc.

Visualization and comparative investigations of pulsating ferro-fluid heat pipe

Pulsating heat pipes (PHPs) are among the best solutions for the electronics cooling due to their low cost, effectiveness and being passive. Experiments to study the effective factors on heat transfer performance have been designed and as a result, improvement of ferrofluid PHP performance has been achieved. Two different heat pipes made of copper and glass were prepared to investigate the behavior of magnetic nanofluids. In order to find the best condition for heat transfer performance, different concentrations of nanofluid with a filling ratio of 50% were tested in 3 different cases of magnetic field. The results indicated that the ferrofluid is more stable in the glass PHP. It also shows that the presence of magnetic field in the copper PHP has the best outcome while in the glass PHP, the absence of magnetic field results better. It was detected that using a more concentrated ferrofluid causes a better performance in the copper PHP only when the magnetic field is applied, while in the glass PHP, increasing the concentration of ferrofluid improves the performance of the PHP in all conditions of applying the magnetic field.

The effect of polydispersity on the magnetostatic properties of concentrated ferrofluids

A statistical model of highly concentrated polydisperse ferrocolloids is proposed. The study approach is based on the second-order modified mean-field theory (MMF2) [A.O. Ivanov, O.B. Kuznetsova, Magnetic properties of dense ferrofluids: an influence of interparticle correlations, Phys. Rev. E 64 (2001) 041405-1–12]. To increase the accuracy of the analytical expression of the magnetization we calculate the contribution of the dipole–dipole interaction energy up to the 2nd order in the pair distribution function for ferroparticles system. The obtained expression of magnetization corresponds to the theoretical expression of initial magnetic susceptibility proposed by the new polydisperse theory [A.O. Ivanov, E.A. Elfimova, Low-temperature magnetic susceptibility of concentrated ferrofluids: the influence of polydispersity, J. Magn. Magn. Matter. 374 (2015) 327–332] exactly. In conjunction it can be applied for magnetogranulometric analysis of polydisperse concentrated ferrofluids.

Ferrofluid-based magnetorheological fluids: tuning the properties by varying the composition at two hierarchical levels

The magnetorheological behavior of three sets of ferrofluid-based magnetorheological (MR) fluids is investigated to determine the dependence of the static and dynamic yield stresses, as well as of the magnetoviscous effect on the volume fraction of magnetite nanoparticles φ and of the added Fe particles Φ Fe , at different values of the magnetic induction B in the MR cell. A wide range of the magnetic particle volume fractions were considered at the two hierarchical levels involved: at the nanometer level, φ = 2.75, 11.67, and 22.90 %, and at the micrometer level, Φ Fe = 5–40 %. Taking into account also the oleic acid monolayer coating of the magnetite nanoparticles, the hydrodynamic volume fraction of the most concentrated ferrofluid results to be 65 % and, consequently, the highest value of the effective total volume fraction of the investigated extremely bidisperse MR fluids attains 85 %. The diagrams of the static and dynamic (Bingham) yield stresses and of the magnetoviscous effect offer an adequate choice of the nanometer and micrometer range particle volume fractions to fulfill the specific requirements of high-pressure rotating seals and of various MR devices.

Nano-micro composite magnetic fluids: Magnetic and magnetorheological evaluation for rotating seal and vibration damper applications

In this paper, static magnetic properties and magnetorheological behavior of a set of 12 nano-micro composite magnetic fluids (CMFs) were studied. The samples with a ferromagnetic particle volume fraction ranging in a large interval φFe=(1÷44)% were prepared by adding carbonyl iron powder in a highly concentrated transformer oil-based ferrofluid (FF). The ferrofluid has the magnetite volume fraction of φFe3O4=22.90% and saturation magnetization of Ms=74kA/m (930 Gs). No further additives were used in order to prevent sedimentation. It was noticed an increase of the static yield stress, of about 3 orders of magnitude, with the increase of the total solid volume fraction of samples and with the increase of the magnetic field, which varied between 0 kA/m and 950 kA/m. The dynamic yield stress (Herschel-Bulkley model) τHB of the samples strongly increases with the magnetic field and shows a slight tendency of saturation for higher intensities of the magnetic field. There is a less pronounced increase of τHB, about an order of magnitude with the increasing volume fraction of the iron particles. The relative viscosity increase induced by the magnetic field reaches a maximum for both considered shear rates: γ⋅=7.85s-1 and γ⋅=88.41s-1 and it was revealed an optimal volume fraction of Fe particles, φFe=20%, corresponding to a total volume fraction of φtot≈38%, at which the magnetoviscous effect has its maximum value. The magnetic properties and also the magnetorheological and the magnetoviscous behavior of highly concentrated ferrofluid-based CMFs can be controlled by the addition of iron microparticles in order to attain the optimal concentration for the envisaged engineering applications, rotating seals and magnetorheological vibration dampers.

The effects of polydispersity on the initial susceptibilities of ferrofluids

The effects of particle-size polydispersity on the initial susceptibilities of concentrated ferrofluids are analyzed using a combination of theory and computer simulation. The study is focused on a model ferrofluid with a prescribed magnetic-core diameter distribution, a fixed non-magnetic surface layer (corresponding to a demagnetized layer and adsorbed surfactant) and a combination of dipolar and hard-core interactions. The non-trivial effects of polydispersity are identified by comparing the initial susceptibilities of monodisperse and polydisperse ferrofluids with the same Langevin susceptibility. The theory is based on a correction to the second-order modified mean-field theory arising from a formal Mayer-type cluster expansion; this correction is dependent on a parameter similar to the normal dipolar coupling constant, except that it contains a complicated double average over the particle-size distribution, which means that the initial susceptibility should depend significantly on polydispersity. Specifically, the theory predicts that the initial susceptibility is enhanced significantly by polydispersity. This prediction is tested rigorously against results from Monte Carlo simulations and is found to be robust. The qualitative agreement between theory and simulation is already satisfactory, but the quantitative agreement could be improved by a systematic extension of the cluster expansion. The overall conclusion is that polydispersity should be accounted for carefully in magnetogranulometric analyses of real ferrofluids.

Low-temperature magnetic susceptibility of concentrated ferrofluids: The influence of polydispersity

In this paper we address the question of theoretical explanation of extremely high low-temperature initial magnetic susceptibility of concentrated ferrofluids . These laboratory synthesized samples [A.F. Pshenichnikov, A.V. Lebedev, J. Chem. Phys. 121(11) (2004) 5455; Colloid J. 67(2) (2005) 189] demonstrated the record-breaking values χ ~ 120 – 150 at temperatures ~ 230–240 K. The existing models predict such high susceptibility only under the assumption of unreasonably large dipolar coupling constant, which is out of the range of applicability. Here we calculate the second virial contribution to susceptibility for polydisperse ferrofluid, modeled by the dipolar hard sphere fluid. In the resulting expression there exists the parameter, which plays a part of dipolar coupling constant and which is defined in a form of double averaging of high powers of particle sizes over the granulometric distribution. For real particle size distribution this effective parameter at least twice exceeds the commonly defined polydisperse dipolar coupling constant. We show that the low-temperature magnetic susceptibility of the record-breaking ferrofluids could be explained theoretically on the basis of the first terms of the polydisperse second virial contribution in combination with the second-order modified mean field model. • Record-breaking magnetic susceptibility of ferrofluids at low temperatures. • Second virial contribution to magnetic susceptibility of polydisperse ferrofluids. • Interparticle dipole correlations are more pronounced in dense ferrofluids. • Presented model describes the ferrofluid susceptibility χ ~ 120 at temperature 240 K.

Yield stress and flow behavior of concentrated ferrofluid-based magnetorheological fluids: the influence of composition

In this paper, the magnetorheological (MR) and magnetoviscous properties of ferrofluid-based iron particle suspensions were investigated. The 2.1-µm mean size Fe particles were dispersed in high-concentration transformer oil-based ferrofluid, the iron particle volume fraction in the resulting nano-micro composite magnetorheological fluid samples varying from Φ Fe = 5 to 40 %. The ferrofluid carrier has φ p = 23 % solid volume fraction of magnetic nanoparticles stabilized with chemisorbed oleic acid monolayer and without any excess surfactant. In the absence of the field, the ferrofluid has a quasi-Newtonian behavior with a weak shear thinning tendency. The static yield stress shows an increase of about 3 orders of magnitude for an iron particle content of approx. Φ Fe = 25 % (Φ tot = 42.25 %), while above this value, a saturation tendency is observed. The dynamic yield stress (Bingham model) also increases with the magnetic induction and the particle volume fraction; however, the saturation of the MR effect is less pronounced. The relative viscosity change has a maximum at Φ Fe = (10–15) % due to the accelerated increase of the effective viscosity of the composite for higher Fe content. Addition of micrometer-sized iron particles to a concentrated ferrofluid without any supplementary stabilizing agent proved to be a direct and simple way to control the magnetorheological and magnetoviscous behavior, as well as the saturation magnetization of the resulting nano-micro composite fluid to fulfill the requirements of their use in various MR control and rotating seal devices.