V. V. Rusakov

Modeling of the Field-Induced Plasticity of Soft Magnetic Elastomers

A phenomenological model is proposed to describe the plasticity of soft magnetic elastomer composites under an external field. Along with high elasticity, internal dry friction is introduced whose origin is attributed to the dipole-dipole interaction of the embedded particles. Numerical estimates of the model parameters are obtained from comparison with the measurements performed on iron carbonyl dispersions in soft silicon-rubber matrices.

Viscoelastic ferrogel: Dynamic magnetic susceptibilities

Theoretical model to describe magnetodynamics of a ferrogel, i.e., an assembly of ferromagnetic nanoparticles embedded in a gel, is proposed. The reorientations of the particles are determined by the influence of the elastic matrix and the rotational Brownian motion. The set of essential parameters, on which the components of the dynamic magnetic susceptibility tensor depend, is discussed. In the framework of the model, absorption of the energy of an ac field is studied. With allowance for the interaction of elastic and Brownian forces, the effective relaxation times and eigenfrequencies for the longitudinal and transverse components of the ferrogel magnetization are evaluated.

Brownian motion in a viscoelastic medium modelled by a Jeffreys fluid

The theory of Brownian motion of a particle in a viscoelastic Jeffreys fluid is extended for the case of rotational motion. The employed rheological model combines two viscous mechanisms (instantaneous and retarded) and, in contrast to the Maxwell model, does not produce artifacts and works robustly when applied to the diffusion of tracer particles in real complex fluids. With the aid of this model, specific features of the dynamic susceptibility of a magnetic Jeffreys suspension and the viscous power losses induced by an ac field are analyzed and conclusions are derived that are valid for active microrheology and magnetic hyperthermia. In general, it is shown that the developed phenomenology provides an archetypal “frame” for a number of mesoscopic models used to describe confined random walk transport processes in a variety of systems of both biological and inorganic origin.

Theory of Brownian motion in a Jeffreys fluid

We have constructed a kinetic theory of Brownian motion in a rheologically complex medium—a Jeffreys fluid that is characterized by a combination of two viscosity mechanisms: ordinary and delayed. This model is shown to be much better suited for the interpretation of experiments on the microrheology of viscoelastic media than the standard Maxwell model. In particular, no oscillations of the mean-square particle displacement arise in a Jeffreys fluid, which is a nonremovable artifact of the theory of Brownian motion in a Maxwell fluid. The developed approach can to be used also consider the diffusion of particles in other complex fluids whose rheology is described by phenomenological schemes.

Theoretical models for AC-field probing of complex magnetic fluids

Description of the magneto-orientational dynamics of single-domain ferroparticles embedded in a viscoelastic fluid or in a weak gel is constructed on the basis of the Langevin equation that takes into account the non-Newtonian properties of the matrix and the Brownian motion of the particle. For the mentioned complex media, dynamic magnetic susceptibilities are obtained and shown to possess some interesting quasi-resonance properties.

Orientational dynamics of a magnetic fluid with a viscoeleastic base

Abstract The orientational dynamics of Brownian single-domain ferroparticles suspended in a viscoelastic (Maxwellian) fluid have been studied. For a two-dimensional model, i.e., disk-like particles rotating in their plane, the Langevin equation is derived and solved approximately to yield the dynamic susceptibility. The conditions under which a resonance caused by the dynamic elasticity of the fluid matrix of the suspension would appear, are discussed.

Field-induced plasticity of soft magnetic elastomers

A phenomenological model is proposed to describe the plasticity of soft magnetic elastomer composites under an external field. Along with high-elasticity, internal dry friction is introduced whose origin is attributed to the dipole-dipole interaction of the embedded particles. Numerical estimates of the model parameters are obtained from comparison with the measurements performed on iron carbonyl dispersions in soft silicon-rubber matrices.

Plasticity of soft magnetic elastomers

A simple rheological model is introduced to describe the plasticity in soft magnetic elastomers induced by an external field. In addition to the elasticity of the polymer matrix, the effect of dry friction (plasticity), which is provided by the rearrangement of the spatial structure of a dispersed magnetic subsystem in the course of the deformation of the material by a sufficiently strong field, is taken into account in the model. Model parameters are estimated from the reported experimental data on the deformation of cylindrical samples based on a soft silicon elastomer filled with quasispherical microparticles of carbonyl iron.

Magnetic structure of a spherical cluster of monodomain particles

A numerical model is proposed for simulating the magnetic properties of a system (N-cluster) comprising a finite number N of monodomain particles uniformly distributed over a spherical surface. The calculation algorithm is based on the Monte Carlo method. In the absence of an external magnetic field, the magnetic moment of any spherical N-cluster vanishes due to the formation of vortex structures, with a measure of vorticity offered by the toroid moment Q. The results of model calculations show that the value of Q in N-clusters with 4 < N < 20 amounts to about 80% of the maximum and is virtually independent of N, while exhibiting weak even-odd oscillations.

ON THE SOLUTION OF THE FOKKER-PLANCK EQUATION FOR DIPOLAR PARTICLES IN A VISCOELASTIC FLUID

Abstract A Fokker-Planck equation (FPE) for an assembly of Brownian particles suspended in a viscoelastic fluid is studied. The particles are assumed to possess rigid dipole moments due to which their orientation is affected by an external field. The equilibrium solution of FPE in the presence of the field is constructed. With allowance for the particle inertia, the dynamic elasticity (i.e., the retarded stress) of the carrier fluid, yields a non-trivial contribution to the distribution function.