Dynamic Susceptibility of Ferrofluids: The Numerical Algorithm for the Inverse Problem of Magnetic Granulometry

The size-dependent properties of magnetic nanoparticles (MNP) are the major characteristics, determining MNP application in modern technologies and bio-medical techniques. Direct measurements of the nanosized particles, involved in intensive Brownian motion, are very complicated; so the correct mathematical methods for the experimental data processing enable to successfully predict the properties of MNP suspensions. In the present paper, we describe the fast numerical algorithm allowing to get the distribution over the relaxation time of MNP magnetic moments in ferrofluids. The algorithm is based on numerical fitting of the experimentally measured frequency spectra of the initial dynamic magnetic susceptibility. The efficiency of the algorithm in the solution of the inverse problem of magnetic granulometry is substantiated by the computer experiments for mono- and bi-fractional ferrofluids.

Effective fields in magnetic colloids and features of their magnetization kinetics

We present results of magnetization and magnetic susceptibility dependence investigations performed for undecane-based ferrofluids with dominant of Brownian relaxation for particles. A robust and effective method of fine particle size characterization is presented. It is based on the core-shell model and the analysis of the dependence of saturation magnetization on particle concentration. A novel advantage method has been used as a straightforward way to determine the concentration dependence of the effective field related to particle interaction that was calculated from the experimentally obtained concentration dependence of low field susceptibility. The computed relationship is compared with the concentration dependences of effective fields derived from several well-known theoretical models. We present some peculiarities of the real part of dynamic magnetic susceptibility on temperature. Investigated features are defined both by the magnetic state of fine particles and by crystallization of carrier at the liquid to a solid phase transition. For the first time, the dependence of the magnetization relaxation time on the colloidal particle concentration and the magnitude of bias DC magnetic field was investigated experimentally. Results are in good agreement with theoretical predictions for moderate concentration and significantly differs for concentration greater 7 vol%. It is concluded that this effect can be related either to the enhanced particle interaction or to the transition of some particles from superparamagnetic to a ferromagnetic state. These predictions are verified through the calculation in terms of Cole-Cole diagrams methods.

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 160 kHz and the field amplitude dependence of the susceptibility at a frequency of 27 kHz. The results show that the susceptibility dispersion at frequencies up to 10 kHz 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 1-100 Hz, depending on the temperature and particle concentration. Experiments at 27 kHz 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.

Magnetophoresis of particles and aggregates in concentrated magnetic fluids

Experimental and theoretical studies were carried out to investigate the problem of magnetophoresis in a thin layer of concentrated magnetic fluids, concerning the aspect of particle aggregation. A heuristic theoretical model, describing diffusion fluxes of individual and aggregated particles, is suggested. The solution of related diffusion and magnetostatic problems are compared with the experimental data. The analysis of the data shows that the aggregates essentially change the concentration profile. Good agreement between experimental and theoretical curves is observed in the case when the aggregates contain, on average, more than ten particles.

Thermomagnetic convective flows in a vertical layer of ferrocolloid: perturbation energy analysis and experimental study

Flow patterns arising in a vertical differentially heated layer of nonconducting ferromagnetic fluid placed in an external uniform transverse magnetic field are studied experimentally and discussed from the point of view of the perturbation energy balance. A quantitative criterion for detecting the parametric point where the dominant role in generating a flow instability is transferred between the thermogravitational and thermomagnetic mechanisms is suggested, based on the disturbance energy balance analysis. A comprehensive experimental study of various flow patterns is undertaken, and the existence is demonstrated of oblique thermomagnetic waves theoretically predicted by Suslov [Phys. Fluids 20, 084101 (2008)] and superposed onto the stationary magnetoconvective pattern known previously. It is found that the wave number of the detected convection patterns depends sensitively on the temperature difference across the layer and on the applied magnetic field. In unsteady regimes its value varies periodically by a factor of almost 2, indicating the appearance of two different competing wave modes. The wave numbers and spatial orientation of the observed dominant flow patterns are found to be in good agreement with theoretical predictions.