On the oscillating shear rheometry of magnetorheological elastomers

Critical issues of the oscillating shear rheometry with disc-shaped elastomer specimens are exemplified. A torsional oscillation method to characterise magnetorheological elastomers (MREs) using a rheometer is introduced and compared to the standard procedure with disc-shaped specimens. Advantages and disadvantages of the method are identified. It is shown that the rheometry with rod-like specimens provides more reliable data, which are easier to reproduce. The method also allows characterisation of MREs in a not pre-strained condition, an aspect which importance is demonstrated. Moreover, it opens an easy way to characterise permanently magnetised MREs with a complex composition using conventional rheometers.     

Mathematical modeling of magnetorheological fluids

Magnetorheological (MR) fluids are a class of smart materials whose rheological properties may be rapidly modified by the application of a magnetic field. These materials typically consist of micron-sized ferrous particles dispersed in a fluid. In the present paper, we consider the full system of equations as well as the Clausius-Duhem inequality for moving isotropic MR fluids in an electro-magnetic field. We present the material constitutive relations for a non-Newtonian incompressible MR fluid. To illustrate the validity of the constitutive relations, the flow of a MR fluid between two parallel fixed plates under the influence of a constant magnetic field perpendicular to the flow direction is considered.Received: 14 July 2003, Accepted: 18 May 2004, Published online: 22 February 2005 Correspondence to: A. Dorfmann     

Viscoelastic properties of magnetorheological fluids

We have studied the rheological properties of some magnetorheological fluids (MRF). MRF are known to exhibit original rheological properties when an external magnetic field is applied, useful in many applications such as clutches, damping devices, pumps, antiseismic protections, etc. While exploiting parameters such as magnetic field intensity, particle concentration and the viscosity of the suspending fluid, we highlighted the importance of each one of these parameters on rheology in the presence of a magnetic field. We made this study by conducting rheological experiments in dynamic mode at very low strain which facilitates the comprehension of the influence of the structure on MRF rheology. Our results confirmed the link between the magnetic forces which ensure the cohesion of the particles in aggregates, and the elastic modulus. Moreover, we found that the loss modulus varies with the frequency in a similar manner than the elastic modulus. The system, even with the smallest deformations, was thus not purely elastic but dissipates also much energy. Moreover, we demonstrated that this dissipation of energy was not due to the matrix viscosity. Actually, we attributed viscous losses to particle movements within aggregates.     

Finite stopping time problems and rheometry of Bingham fluids

It is shown that steady channel, simple shear and Couette flows of a Bingham fluid come to rest in a finite amount of time, if either the applied pressure falls below a critical value, or the moving boundaries are brought to rest. An explicit formula for a bound on the finite stopping time in each case is derived. This bound depends on the density, the viscosity, the yield stress, a new geometric constant, and the least eigenvalue of the second order linear differential operator for the interval under consideration.     

Preparation of well-dispersed magnetorheological fluids and effect of dispersion on their magnetorheological properties

In this work, we describe methods for the preparation of suspensions of micron-sized iron particles grafted with different surfactants. The aim is to obtain well-dispersed magnetorheological (MR) fluids. The effectiveness of the surfactants as dispersants was analyzed quantitatively by means of rheological measurements. With this objective, the viscosity of the suspensions was measured, and the results were compared with the prediction of the Batchelor’s formula (Batchelor, J Fluid Mech 83:97–117, 1977). The effect of dispersion on the MR properties of the suspensions was also studied. It was found that the quality of the dispersion of a suspension does not have an important effect on the magnitude of the field-induced yield stress but does on the change of viscosity induced by the field. It was also found that the transition from the solid-like state to the liquid-like one happens very smoothly for well-dispersed suspensions, contrarily to the abrupt transition for poorly dispersed suspensions.     

Quasi-static simulations of compact polydisperse particle systems

The Discrete Element Method (DEM) was originally devised by Cundall and Strack (1979), as a technique to examine the micromechanics of granular media with the anticipation that this would lead to more physically reliable continuum theories to describe the quasi-static deformation of granular material such as sand. However, the methodology models the evolution of a system of particles as a dynamic process. Consequently there have been numerous publications of the application of DEM to an increasingly wider v...     

Static yield stress of ferrofluid-based magnetorheological fluids

In this work, the yield stress of ferrofluid-based magnetorheological fluids (F-MRF) was investigated. The fluids are composed of a ferrofluid as the liquid carrier and micro-sized iron particles as magnetic particles. The physical and magnetorheological properties of the F-MRF have been investigated and compared with a commercial mineral oil-based MR fluid. With the addition of a ferrofluid, the anti-sedimentation property of the commercial MR fluids could be significantly improved. The static yield stress of the F-MRF samples with four different weight fractions (ϕ) of micro-sized iron particles were measured using three different testing modes under various magnetic fields. The effects of weight fraction, magnetic strength, and test mode on the yielding stress have been systematically studied. Finally, a scaling relation, , was proposed for the yield stress modeling of the F-MRF system.     

Study of magnetorheological fluids at high shear rates

The tunable rheological properties of magnetorheological (MR) materials at high shear rates are studied using a piston-driven flow-mode-type rheometer. The proposed method provides measurement of the apparent viscosity and yield stress of MR fluids for a shear rate range of 50 to 40,000 s⁻¹. The rheological properties of a commercial MR fluid, as well as a newly developed MR polymeric gel, and a ferrofluid-based MR fluid are investigated. The results for apparent viscosity and dynamic and static shear stresses under different applied magnetic fields are reported.     

Compressible rubber materials: experiments and simulations

Porous rubber materials are often used in automotive industries. In this paper, a carbon black-filled one is investigated, which is used, for example, as sealing. Such materials are distinguished by viscoelastic behaviour and by a structural compressibility induced by the porous structure. To identify the material behaviour, uniaxial tension tests and hydrostatic compression tests are performed. Therein the main focus of attention lies on the basic elasticity and on the viscoelasticity in the whole loading range. An important observation of these tests is the viscoelastic behaviour under hydrostatic compression, which has to be included in the material model. Because of the two-phase character of cellular rubber, the theory of porous media is taken into account. To model the structural compressibility, a volumetric–isochore split of the deformation gradient is used. Therein the volumetric part includes the aspect of the point of compaction. Finally, the concept of finite viscoelasticity is applied introducing an intermediate configuration. Because of the viscoelastic behaviour under hydrostatic compression, the volumetric–isochore split is taken into account for the nonequilibrium parts, too. Nonlinear relaxation functions are used to model the process-dependent relaxation times and the highly nonlinear behaviour with respect to the deformation and feedrate. The material parameters of the model are estimated using a stochastic identification algorithm.     

Comparison of squeeze flow and vane rheometry for yield stress and viscous fluids

Two principal squeeze flow modes are investigated for yield stress and Newtonian materials squeezed by a constant force, F, between plates of equal or unequal diameters. In mode A, the material fills the space between the plates and is extruded at their periphery as their separation decreases. Experiments are described to measure the contribution to F from the extrudate. In mode B, all the material remains in contact with the planes of the plates as their separation decreases; there is no extrudate. The results of mode B experiments agree closely with the predictions of theory and give rheological parameters in fair agreement with those measured by the rotational vane method. The material properties and extrusion behaviour which complicate mode A experiments are discussed.     

Discrete element study of viscous flow in magnetorheological fluids

Using discrete element simulations, we gain insight into the structure of a magnetorheological fluid (MRF) under shear. In simulations with flat walls, the particles arrange in chains, sheet-like structures, or columns along the magnetic field lines, depending on the strength of the applied external magnetic field. Corresponding to the structure formation, three different types of failure mechanisms can be identified. For the characterization of the different regimes, specific particle coordination numbers are introduced. The three structural regimes can be distinguished and described by means of these coordination numbers. To analyze the contact between the MRF particles and the walls of the shear cell, additional simulations with rough walls have been conducted. The resulting structure formation could be successfully classified by the introduced coordination numbers. Based on the analysis of the shear stress transmission both in the case of flat and rough walls, possibilities for shear stress enhancement for technological applications are discussed.     

Compression behaviors of magnetorheological fluids under nonuniform magnetic field

This work is concerned with an experimental and theoretical study on compression properties of magnetorheological fluids under the nonuniform field. Experimental tests of unidirectional monotonic compression were firstly carried out under constant area operation using a commercial plate–plate magneto-rheometer where the magnetic field radial distribution was nonuniform. Normal forces increased with decreasing of the gap distance, and two regions were found through the normal force versus gap distance curves: elastic deformation and plastic flow. High normal forces could be obtained in the case of high magnetic field, high compression velocity, low initial gap distance, high volume fraction, and high medium viscosity. In the plastic flow region, the normal force with the gap distance could be fitted with a power law relation $F_{\textrm {N}} \propto h^n$ , and the index n was around well in the range (?3, ?2). Taking nonuniform magnetic field into account, the theoretical modeling in the plastic flow was then developed to calculate the normal force under compression based on the continuum media theory. Compared to the uniform field, there existed a magnetic field gradient-induced normal force under nonuniform field. Considering the sealing and squeeze strengthening effect, the gap distance-dependent shear yield stress was proposed, and a good correspondence between the theoretical and experimental results was obtained.     

Aging, rejuvenation, and thixotropy in yielding magnetorheological fluids

The yielding behavior of dilute magnetorheological (MR) fluids has been investigated using creep–recovery tests. At very low stress levels, MR fluids behave in the linear viscoelastic regime as demonstrated by the fact that the instantaneous strain equals the instantaneous (elastic) recovery. In this region, gap-spanning field-induced structures support the stress levels applied. Upon increasing the stress value, the MR fluid evolves towards a nonlinear viscoelastic response. Here, the retarded elastic and viscous strain decrease, and the plastic contribution to the instantaneous strain grows probably due to the appearance of unattached field-induced structures. A larger stress value results in a viscoplastic solid behavior with negligible retarded and viscous strain and a fully plastic instantaneous strain. Finally, a plastic fluid behavior is found when the stress value is larger than the so-called yield stress. MR fluids exhibit an intermediate behavior between non-thixotropic (simple) and highly thixotropic model yield stress fluids.     

Preparation and characterization of carbonyl iron/strontium hexaferrite magnetorheological fluids

The heat transfer oil-based magnetorheological fluid (MRF) was prepared using oleic acid-modified micron carbonyl iron powder as a magnetic dispersed phase and strontium hexaferrite (SrFe₁₂O₁₉) nanoparticles as an additive. The sedimentation stability of MRFs was studied. The results indicated that the stability of MRFs was improved remarkably by adding SrFe₁₂O₁₉ nanoparticles and the sedimentation ratio was only 0.88 in 20 days when the content of nanoparticles reached 10 wt%. The rheological properties were characterized by a HAAKE rheometer without a magnetic field and a capillary rheometer with and without a magnetic field. The effects of SrFe₁₂O₁₉ nanoparticles, the temperature, and magnetic field strength were investigated. In addition, the rheological properties could be predicted well using the improved Herschel–Bulkley model, even under a magnetic field. A theoretical model was also proposed to predict the yield stress based on the microstructure of the MRF under an applied magnetic field.     

Preparation and characterization of carbonyl iron/strontium hexaferrite magnetorheological fluids

The heat transfer oil-based magnetorheological fluid(MRF) was prepared using oleic acid-modified micron carbonyl iron powder as a magnetic dispersed phase and strontium hexaferrite(SrFe_(12)O_(19))nanoparticles as an additive.The sedimentation stability of MRFs was studied.The results indicated that the stability of MRFs was improved remarkably by adding SrFe_(12)O_(19) nanoparticles and the sedimentation ratio was only 0.88 in 20 days when the content of nanoparticles reached 10 wt%.The Theological properties were characterized by a HAAKE rheometer without a magnetic field and a capillary rheometer with and without a magnetic field.The effects of SrFe_(12)O_(19) nanoparticles,the temperature,and magnetic field strength were investigated.In addition,the rheological properties could be predicted well using the improved Herschel-Bulkley model,even under a magnetic field.A theoretical model was also proposed to predict the yield stress based on the microstructure of the MRF under an applied magnetic field.     

Aerodynamics of ski jumping: experiments and CFD simulations

The aerodynamic behaviour of a model ski jumper is investigated experimentally at full-scale Reynolds numbers and computationally applying a standard RANS code. In particular we focus on the influence of different postures on aerodynamic forces in a wide range of angles of attack. The experimental results proved to be in good agreement with full-scale measurements with athletes in much larger wind tunnels, and form a reliable basis for further predictions of the effects of position changes on the performance. The comparison of CFD results with the experiments shows poor agreement, but enables a clear outline of simulation potentials and limits when accurate predictions of effects from small variations are required.     

Microstructural investigations of the yielding behaviour of bidisperse magnetorheological fluids

Particle level simulations were used to investigate the effects of size bidispersity and particle size ratios on the static and yielding behaviour of magnetorheological fluids (MRF). The MRF were treated as linearly magnetisable, neutrally buoyant particles dispersed in a viscous carrier liquid. In the quiescent mode (static structures), the bidisperse suspensions were found to have a higher tendency to form straight chains than the monodisperse suspensions; this is consistent with previous findings. Under steady shearing, the bidisperse suspensions exhibited higher stress enhancement than the monodisperse systems. The stress enhancement in bidisperse suspensions is likely to be due to the population and orientation of interacting large particles in the bidisperse suspensions.     

Rheometry for large-particulated fluids: analysis of the ball measuring system and comparison to debris flow rheometry

For large-particulated fluids encountered in natural debris flow, building materials, and sewage treatment, only a few rheometers exist that allow the determination of yield stress and viscosity. In the present investigation, we focus on the rheometrical analysis of the ball measuring system as a suitable tool to measure the rheology of particulated fluids up to grain sizes of 10 mm. The ball measuring system consists of a sphere that is dragged through a sample volume of approximately 0.5 l. Implemented in a standard rheometer, torques exerted on the sphere and the corresponding rotational speeds are recorded within a wide measuring range. In the second part of this investigation, six rheometric devices to determine flow curve and yield stress of fluids containing large particles with maximum grain sizes of 1 to 25 mm are compared, considering both rheological data and application in practical use. The large-scale rheometer of Coussot and Piau, the building material learning viscometer of Wallevik and Gjorv, and the ball measuring system were used for the flow curve determination and a capillary rheometer, the inclined plane test, and the slump test were used for the yield stress determination. For different coarse and concentrated sediment–water mixtures, the flow curves and the yield stresses agree well, except for the capillary rheometer, which exhibits much larger yield stress values. Differences are also noted in the measuring range of the different devices, as well as for the required sample volume that is crucial for application.     

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.