Andrey Zubarev

Colloids on the frontier of ferrofluids. Rheological properties.

This paper is devoted to the steady-state rheological properties of two new kinds of ferrofluids. One of these was constituted by CoNi nanospheres of 24 nm in diameter, whereas the other by CoNi nanofibers of 56 nm in length and 6.6 nm in width. These ferrofluids were subjected to shear rate ramps under the presence of magnetic fields of different intensity, and the corresponding shear stress values were measured. From the obtained rheograms (shear stress vs shear rate curves) the values of both the static and the dynamic yield stresses were obtained as a function of the magnetic field. The magnetoviscous effect was also obtained as a function of both the shear rate and the magnetic field. The experimental results demonstrate that upon magnetic field application these new ferrofluids develop yield stresses and magnetoviscous effects much greater than those of conventional ferrofluids, based on nanospheres of approximately 10 nm in diameter. Besides some expected differences, such as the stronger magnetorheological effect in the case of ferrofluids based on nanofibers, some intriguing differences are found between the rheological behaviors of nanofiber ferrofluids and nanosphere ferrofluid. First, upon field application the rheograms of nanofiber ferrofluids present N-shaped dependence of the shear stress on the shear rate. The decreasing part of the rheograms takes place at low shear rate. These regions of negative differential viscosity, and therefore, unstable flow is not observed in the case of nanosphere ferrofluids. The second intriguing difference concerns the curvature of the yield stress vs magnetic field curves. This curvature is negative in the case of nanosphere ferrofluid, giving rise to saturation of the yield stress at medium field, as expected. However, in the case of nanofiber ferrofluid this curvature is positive, which means a faster increase of the yield stress with the magnetic field the higher the magnitude of the latter. These interesting differences may be due to the existence of strong interparticle solid friction in the case of nanofiber ferrofluids. Finally, theoretical models for the static yield stress of the ferrofluids were developed. These models consider that upon field application the ferrofluid nanoparticles are condensed in drops of dense phase. These drops tend to be aligned along the field direction, opposing the flow of the ferrofluids and being responsible for the static quasielastic deformation and the yield-stress phenomena. By considering the existence of interparticle dry friction only in the case of nanofiber ferrofluids, the developed models predicted quite well not only the magnitude of the static yield stress but also the differences in curvature of the yield stress vs magnetic field curves.

On the theory of the magnetic deformation of ferrogels

The paper deals with theoretical study of deformation of a ferrogel sample under the action of an applied magnetic field. The main goal of this work is to determine the type of deformation—either elongation or contraction in the field direction. To answer this question and to avoid artificial conclusions, we have estimated the free energy of the deformed sample by using standard methods of statistical physics. The analysis shows that the type of magnetically induced deformation significantly depends on initial shape of the sample, the applied magnetic field, as well as on the concentration and magnetic properties of the magnetic particles embedded in the gel.

Effect of gap thickness on the viscoelasticity of magnetorheological fluids

In this work, the effect of confinement distance on the magnetorheological (MR) properties of a conventional MR fluid, constituted by 30 vol % of iron microparticles dispersed in a liquid carrier, is studied. With this aim a commercial magnetorheometer supplied with parallel-plate geometry was used. The distance between the upper and the lower plate (gap thickness) was tuned from 10 to 400 μm. The steady-state and the dynamic regimes of the MR fluid in the presence of applied magnetic fields were studied as a function of the gap length. The experimental results show that in the preyield regime there is a strong increase in the magnitude of the viscoelastic moduli and the shear stress as the gap thickness is increased. The physical reason for this effect might be the influence of gap thickness on the particle structures induced by the field. This hypothesis is corroborated by microscopic observations in diluted systems. These experiments show that the aspect ratio (length/diameter) of the field-induced str...

Effect of chain-like aggregates on ferrogel magnetodeformation

This paper deals with a theoretical study of the effect of chain-like heterogeneous structures on the type of deformation of ferrogel under an applied magnetic field. The analysis shows that depending on the energy of magnetic interaction between the particles, these chains can stimulate either elongation or contraction of the sample along the field.

Anomalous transport and nonlinear reactions in spiny dendrites

We present a mesoscopic description of the anomalous transport and reactions of particles in spiny dendrites. As a starting point we use two-state Markovian model with the transition probabilities depending on residence time variable. The main assumption is that the longer a particle survives inside spine, the smaller becomes the transition probability from spine to dendrite. We extend a linear model presented in Fedotov [Phys. Rev. Lett. 101, 218102 (2008)] and derive the nonlinear Master equations for the average densities of particles inside spines and parent dendrite by eliminating residence time variable. We show that the flux of particles between spines and parent dendrite is not local in time and space. In particular the average flux of particles from a population of spines through spines necks into parent dendrite depends on chemical reactions in spines. This memory effect means that one cannot separate the exchange flux of particles and the chemical reactions inside spines. This phenomenon does not exist in the Markovian case. The flux of particles from dendrite to spines is found to depend on the transport process inside dendrite. We show that if the particles inside a dendrite have constant velocity, the mean particles position increases as t(μ) with μ<1 (anomalous advection). We derive a fractional advection-diffusion equation for the total density of particles.

Behavior of nanoparticle clouds around a magnetized microsphere under magnetic and flow fields.

When a micron-sized magnetizable particle is introduced into a suspension of nanosized magnetic particles, the nanoparticles accumulate around the microparticle and form thick anisotropic clouds extended in the direction of the applied magnetic field. This phenomenon promotes colloidal stabilization of bimodal magnetic suspensions and allows efficient magnetic separation of nanoparticles used in bioanalysis and water purification. In the present work, the size and shape of nanoparticle clouds under the simultaneous action of an external uniform magnetic field and the flow have been studied in detail. In experiments, a dilute suspension of iron oxide nanoclusters (of a mean diameter of 60 nm) was pushed through a thin slit channel with the nickel microspheres (of a mean diameter of 50 μm) attached to the channel wall. The behavior of nanocluster clouds was observed in the steady state using an optical microscope. In the presence of strong enough flow, the size of the clouds monotonically decreases with increasing flow speed in both longitudinal and transverse magnetic fields. This is qualitatively explained by enhancement of hydrodynamic forces washing the nanoclusters away from the clouds. In the longitudinal field, the flow induces asymmetry of the front and the back clouds. To explain the flow and the field effects on the clouds, we have developed a simple model based on the balance of the stresses and particle fluxes on the cloud surface. This model, applied to the case of the magnetic field parallel to the flow, captures reasonably well the flow effect on the size and shape of the cloud and reveals that the only dimensionless parameter governing the cloud size is the ratio of hydrodynamic-to-magnetic forces-the Mason number. At strong magnetic interactions considered in the present work (dipolar coupling parameter α≥2), the Brownian motion seems not to affect the cloud behavior.

Experimental, numerical, and theoretical investigation on the concentration-dependent Soret effect in magnetic fluids

Applying a temperature gradient to a layer of a binary fluid establishes a diffusive transport mechanism called thermophoresis or Soret effect which separates the two fluid’s components and is measured by the Soret coefficient. Recent investigations carried out on concentrated magnetic fluids showed that the intensity of the Soret effect depends on the concentration of the nanoparticles transported. The present article, therefore, deals with the concentration-dependence of the Soret coefficient using five equally composed magnetic fluids only varying in the concentration of the particles from 2 vol. % to 10 vol. % of magnetic material. The current investigations point out that the determination of the Soret coefficient and especially its dependence on the particles’ concentration is based on the determination of the thermal and particle diffusion coefficient. The article, therefore, presents a theoretical approach for the determination of the thermal diffusion coefficient and adapts a commonly used Ansatz for the particle diffusion coefficient for the present case of concentrated magnetic fluids. It is thereby possible to determine a theoretical Soret coefficient in dependence on an empirical parameter α. The coefficient is compared with the experimental approaches which have been previously used, these will be referred to as “analytical approach” throughout the text. A second comparison is achieved with a hybrid Soret coefficient which fits the experimentally detected separation curves numerically. Within the investigations, the hydrodynamic concentration of the particles is used, assuming a surfactant layer’s thickness of 2 nm per magnetic particle which leads to concentrations between approximately 11 vol. % and 47 vol. %. The diffusion coefficient ranges from 0.6 × 10−11 m2/s to 2.5 × 10−11 m2/s depending on the analytical model used. The theoretical Soret coefficient decreases with increasing particles’ concentration; the experimental values derived from the analytical approach decrease from 0.06 K−1 to 0.01 K−1 for increasing particles’ concentration. The numerically determined coefficient ranges from 0.11 K−1 to 0.022 K−1. The experimental values are smaller than former experimental results suggest (0.16 K−1), which is due to the fact that in former works, only magnetic concentrations had been considered. All three current investigations prove what could also be partly seen in former experiments that the higher the particles’ concentration the weaker is thermophoresis. The particle diffusion coefficient has to be known for the determination of the Soret coefficient. It is carried out a proof of principle in the article showing that the horizontal thermophoresis cell can also be used to determine the rehomogenisation process which takes place after separating the fluid by applying a homogeneous temperature to the fluid. The diffusion coefficients that could be determined experimentally range from 1 × 10−11 m2/s to 6 × 10−11 m2/s.

Stress relaxation in a ferrofluid with clustered nanoparticles

The formation of structures in a ferrofluid by an applied magnetic field causes various changes in the rheological behaviour of the ferrofluid. A ferrofluid based on clustered iron nanoparticles was investigated. We experimentally and theoretically consider stress relaxation in the ferrofluid under the influence of a magnetic field, when the flow is suddenly interrupted. It is shown that the residual stress observed in the fluid after the relaxation is correlated with the measured and theoretically predicted magnetic field-induced yield stress. Furthermore, we have shown that the total macroscopic stress in the ferrofluid after the flow is interrupted is defined by the presence of both linear chains and dense, drop-like bulk aggregates. The proposed theoretical approach is consistent with the experimentally observed behaviour, despite a number of simplifications which have been made in the formulation of the model. Thus, the obtained results contribute a lot to the understanding of the complex, magnetic field-induced rheological properties of magnetic colloids near the yield stress point.

Two-stage kinetics of field-induced aggregation of medium-sized magnetic nanoparticles

The present paper is focused on the theoretical and experimental study of the kinetics of field-induced aggregation of magnetic nanoparticles of a size range of 20-100 nm. Our results demonstrate that (a) in polydisperse suspensions, the largest particles could play a role of the centers of nucleation for smaller particles during the earliest heterogeneous nucleation stage; (b) an intermediate stage of the aggregate growth (due to diffusion and migration of individual nanoparticles towards the aggregates) is weakly influenced by the magnetic field strength, at least at high supersaturation;

Persistent random walk of cells involving anomalous effects and random death.

The purpose of this paper is to implement a random death process into a persistent random walk model which produces sub-ballistic superdiffusion (Lévy walk). We develop a stochastic two-velocity jump model of cell motility for which the switching rate depends upon the time which the cell has spent moving in one direction. It is assumed that the switching rate is a decreasing function of residence (running) time. This assumption leads to the power law for the velocity switching time distribution. This describes the anomalous persistence of cell motility: the longer the cell moves in one direction, the smaller the switching probability to another direction becomes. We derive master equations for the cell densities with the generalized switching terms involving the tempered fractional material derivatives. We show that the random death of cells has an important implication for the transport process through tempering of the superdiffusive process. In the long-time limit we write stationary master equations in terms of exponentially truncated fractional derivatives in which the rate of death plays the role of tempering of a Lévy jump distribution. We find the upper and lower bounds for the stationary profiles corresponding to the ballistic transport and diffusion with the death-rate-dependent diffusion coefficient. Monte Carlo simulations confirm these bounds.