scholarly journals A Cascading Mean-Field Approach to the Calculation of Magnetization Fields in Magnetoactive Elastomers

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1372
Author(s):  
Dirk Romeis ◽  
Marina Saphiannikova
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Mean Field ◽  
Magnetic Interactions ◽  
Interacting Particles ◽  
Precise Calculation ◽  
Magnetization Field ◽  
Individual Particles ◽  
Composite Samples ◽  
Magnetoactive Elastomer

We consider magnetoactive elastomer samples based on the elastic matrix and magnetizable particle inclusions. The application of an external magnetic field to such composite samples causes the magnetization of particles, which start to interact with each other. This interaction is determined by the magnetization field, generated not only by the external magnetic field but also by the magnetic fields arising in the surroundings of interacting particles. Due to the scale invariance of magnetic interactions (O(r−3) in d=3 dimensions), a comprehensive description of the local as well as of the global effects requires a knowledge about the magnetization fields within individual particles and in mesoscopic portions of the composite material. Accordingly, any precise calculation becomes technically infeasible for a specimen comprising billions of particles arranged within macroscopic sample boundaries. Here, we show a way out of this problem by presenting a greatly simplified, but accurate approximation approach for the computation of magnetization fields in the composite samples. Based on the dipole model to magnetic interactions, we introduce the cascading mean-field description of the magnetization field by separating it into three contributions on the micro-, meso-, and macroscale. It is revealed that the contributions are nested into each other, as in the Matryoshka’s toy. Such a description accompanied by an appropriate linearization scheme allows for an efficient and transparent analysis of magnetoactive elastomers under rather general conditions.

Particle Orientational Properties and Viscosity of a Dense Colloidal Dispersion Composed of Ferromagnetic Spherocylinder Particles: Analysis by Means of Mean Field Approximation for a Simple Shear

2005 ◽  
Author(s):  
Akira Satoh
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Mean Field ◽  
Magnetic Interaction ◽  
Colloidal Dispersion ◽  
Field Approximation ◽  
Magnetic Interactions ◽  
Mean Field Approximation ◽  
Particle Interactions ◽  
Orientational Distribution

We have theoretically investigated the particle orientational distribution and viscosity of a dense colloidal dispersion composed of ferromagnetic spherocylinder particles under circumstances of an applied magnetic field. The mean field approximation has been applied to take into account the magnetic interactions of the particle of interest with the other ones which belong to the neighboring clusters, besides its own cluster. The basic equation of the orientational distribution function, which is an integro-differential equation, has approximately been solved by Galerkin’s method and the method of successive approximation. Even when the magnetic interaction between particles is of the order of the thermal energy, the effect of particle-particle interactions on the orientational distribution comes to appear more significantly with increasing the volumetric fraction of particles. This effect comes to appear more significantly when the influence of the applied magnetic field is not relatively so strong compared with magnetic particle-particle interactions.

scholarly journals Exactly solvable model of three interacting particles in an external magnetic field

2003 ◽  
Vol 67 (20) ◽  
Author(s):  
E. P. Nakhmedov ◽  
K. Morawetz ◽  
M. Ameduri ◽  
A. Yurtsever ◽  
C. Radehaus
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Solvable Model ◽  
Interacting Particles ◽  
Exactly Solvable Model ◽  
Exactly Solvable

Influences of Magnetic Particle-Particle Interactions on Orientational Distributions and Rheological Properties of a Semi-Dense Colloidal Dispersion Composed of Rod-Like Hematite Particles: Analysis by Means of Mean Field Approximation for an External Magnetic Field Parallel to the Angular Velocity Vector of a Simple Shear Flow

2007 ◽  
Author(s):  
Ryo Hayasaka ◽  
Masayuki Aoshima ◽  
Toshinori Suzuki ◽  
Akira Satoh
Keyword(s):  
Magnetic Field ◽  
Magnetic Moment ◽  
Mean Field ◽  
Field Approximation ◽  
Field Direction ◽  
Magnetic Interactions ◽  
Mean Field Approximation ◽  
Magnetic Field Direction ◽  
Orientational Distribution ◽  
The Magnetic Field

We have investigated mainly the influences of magnetic particle-particle interactions on orientational distributions and viscosity of a semi-dense dispersion, which is composed of rod-like particles with a magnetic moment magnetized normal to the particle axis. In addition, the influences of the magnetic field strength, shear rate, and random forces on the orientational distribution and rheological properties have been clarified. The mean field approximation has been applied to take into account magnetic interactions between rod-like particles. The basic equation of the orientational distribution function has been derived from the balance of torques and solved by the numerical analysis method. The results obtained here are summarized as follows. For a strong magnetic field, the rotational motion of the rod-like particle is restricted in a plane normal to the shearing plane because the magnetic moment of the particle is restricted in the magnetic field direction. Under circumstances of a very strong magnetic interaction between particles, the magnetic moment is strongly restricted in the magnetic field direction, so that the particle has a tendency to incline in the flow direction with the magnetic moment pointing to the magnetic field direction. For a strong shear flow, a directional characteristic of rod-like particles is enhanced, and this leads to a more significant one-peak-type distribution of the orientational distribution function. Magnetic interactions between particles do not contribute to the viscosity because the mean-field vector has only a component along the magnetic field direction.

Short-time self-diffusion, collective diffusion and effective viscosity of dilute hard sphere magnetic suspensions

2016 ◽  
Vol 791 ◽  
pp. 237-259
Author(s):  
Krzysztof A. Mizerski ◽  
Eligiusz Wajnryb
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Effective Viscosity ◽  
Hard Spheres ◽  
Magnetic Interactions ◽  
Point Dipole ◽  
Basic Principles ◽  
Self Diffusion ◽  
Viscosity Coefficients ◽  
Short Time

The virial corrections to short-time self- and collective diffusion coefficients as well as the effective viscosity are calculated for suspensions of hard spheres with the same radii and constant (blocked within the particle) magnetization modelled by a point dipole. Analytic, integral formulae derived from basic principles of statistical mechanics are provided for both cases – in the absence and in the presence of an external magnetic field. In the former case the diffusion and viscosity coefficients are evaluated numerically as a function of the strength of magnetic interactions between the particles and it is reported that the translational collective diffusion coefficient is significantly greater than all the other coefficients. In the presence of an external magnetic field the coefficients become anisotropic and are evaluated in the asymptotic regime of weak interparticle magnetic interactions.

scholarly journals Effect of external magnetic field on the co-existence of superconductivity and antiferromagnetism in rare earth nickel borocarbides (RNi2B2C)

2016 ◽  
Vol 30 (08) ◽  
pp. 1650044
Author(s):  
Salila Das ◽  
Prakash Chandra Padhi
Keyword(s):  
Magnetic Field ◽  
Rare Earth ◽  
External Magnetic Field ◽  
Energy Gap ◽  
Density Wave ◽  
Spin Density Wave ◽  
Mean Field ◽  
Antiferromagnetic Order ◽  
Superconducting Energy Gap ◽  
Nickel Borocarbides

In this paper, we have studied the effect of external magnetic field in the co-existing phase of superconducting and antiferromagnetism (AFM) of rare earth nickel borocarbides. The AFM in these systems might have originated due to both localized “f” electrons as well as itinerant electrons which are responsible for conduction. On the other hand, superconductivity (SC) is due to spin density wave, arising out of Fermi surface instability. The AFM order is mostly influenced by hybridization of the “f” electron with the conduction electron. Here, we have obtained the dependence of superconducting energy gap as well as staggered magnetic field on temperature T and energy [Formula: see text] in a framework based on mean field Hamiltonian using double time electron Green’s function. We have shown in our calculation the effect of external magnetic field on superconducting and antiferromagnetic order parameters for [Formula: see text] in the presence of hybridization. The ratio of the calculated effective gap and [Formula: see text] is close to BCS value which agrees quite well with experimental results.

scholarly journals Modeling of Magnetorheological Fluids by the Discrete Element Method

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Mickaël Kargulewicz ◽  
Ivan Iordanoff ◽  
Victor Marrero ◽  
John Tichy
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Discrete Element Method ◽  
Discrete Element ◽  
Magnetic Interactions ◽  
Time Interval ◽  
Mr Fluid ◽  
Carrier Fluid ◽  
Mr Fluids ◽  
Element Method

Magnetorheological (MR) fluids are fluids whose properties vary in response to an applied magnetic field. Such fluids are typically composed of microscopic iron particles (~1-20μm diameter, 20-40% by volume) suspended in a carrier fluid such as mineral oil or water. MR fluids are increasingly proposed for use in various mechanical system applications, many of which fall in the domain of tribology, such as smart dampers and clutches, prosthetic articulations, and controllable polishing fluids. The goal of this study is to present an overview of the topic to the tribology audience, and to develop an MR fluid model from the microscopic point of view using the discrete element method (DEM), with a long range objective to better optimize and understand MR fluid behavior in such tribological applications. As in most DEM studies, inter-particle forces are determined by a force-displacement law and trajectories are calculated using Newton’s second law. In this study, particle magnetization and magnetic interactions between particles have been added to the discrete element code. The global behavior of the MR fluid can be analyzed by examining the time evolution of the ensemble of particles. Microscopically, the known behavior is observed: particles align themselves with the external magnetic field. Macroscopically, averaging over a number of particles and a significant time interval, effective viscosity increases significantly when an external magnetic field is applied. These preliminary results would appear to establish that the DEM is a promising method to study MR fluids at the microscopic and macroscopic scales as an aid to tribological design.

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