Static shear stress of electrorheological fluids

Continuum model of magnetic field induced viscoelasticity in magnetorheological fluids

An effective macroscopic model of magnetorheological fluids in the viscoelastic regime is proposed. Under the application of an external magnetic field, columns of magnetizable particles are formed in these systems. The columns are responsible for solidlike properties, such as the existence of elastic shear modulus and yield stress, and are captured by the strain field, while magnetic properties are described by the magnetization. We investigate the interplay of these variables when static shear or normal pressure is imposed in the presence of the external magnetic field. By assuming a relaxing strain field, we calculate the flow curves, i.e., the shear stress as a function of the imposed shear rate, for different values of the applied magnetic field. Focusing on the small amplitude oscillatory shear, we study the complex shear modulus, i.e., the storage and the loss moduli, as a function of the frequency. We demonstrate that already such a minimal model is capable of furnishing many of the key physical features of these systems, such as yield stress, enhancement of the shear yield stress by pressure, threshold behavior in the spirit of the frequently employed Bingham law, and several features in the frequency dependence of storage and loss moduli.

Describing magnetorheology under a colloidal glass approach

The equilibrium structure and dynamics of magnetorheological (MR) fluids are studied in this work by simulations, where particles are modeled as dipoles with a quasihard spherical core. Upon increasing the interaction strength, controlled experimentally by the magnetic field, elongated clusters grow and, for intense fields, thick columns form, aligned with the field. The dynamics of the system is monitored by the mean-squared displacement and density correlation functions, which show an increasing slowing down with the attraction strength. The correlation function shows a two-step decay, with a separation between microscopic and long time dynamics, a typical hallmark of undercooled fluids. We have therefore analyzed the dynamics of this MR fluid using the typical concepts for undercooled fluids. Thus, the second decay of the density correlation function is fitted with a stretched exponential, and the wave-vector dependence of the fitting parameters studied. Both the amplitude and the time scale oscillate in phase with the structure factor. Our results support the idea that the magnetorheological effect is in fact the manifestation of a colloidal system approaching an attractive glass transition (or gel transition).

A slender-body micromechanical model for viscoelasticity of magnetic colloids: Comparison with preliminary experimental data

The storage modulus, G', together with the yield stress, is an essential quantity characterizing the rheological properties of magnetic field-responsive suspensions (magnetorheological fluids or MRF). In this work, we present both experimental and theoretical results on the viscoelastic properties of MRFs. Two MRFs are used: In one the solid phase consists of cobalt ferrite particles + silica gel, with silicone oil as liquid phase. The second system is formed by carbonyl iron + silica gel also dispersed in silicone oil. The cobalt ferrite particles are synthesized as monodisperse colloidal spheres with an average diameter of 850 nm. We describe a new model based on the slender-body approach for hydrodynamic interactions. The predictions of the model are compared to preliminary experimental G' data obtained in a controlled stress plate-plate rheometer. It is found that the model gives the correct order of magnitude for the highest fields in iron suspensions, but underestimates the experimental results obtained in ferrite ones. In the case of high permeability materials such as carbonyl iron, by the inclusion of high-order multipolar interactions and saturation effects we also predict the order of magnitude of the experimental results. When dealing with low permeability cobalt ferrite based MRFs, other effects, such as remanence (at low fields) and saturation (at high fields), must be considered.

Linear viscoelasticity of an inverse ferrofluid

A magnetorheological fluid consisting of colloidal silica spheres suspended in an organic ferrofluid is described. Its linear viscoelastic behavior as a function of frequency, magnetic field strength, and silica volume fraction was investigated with a specially designed magnetorheometer. The storage modulus G' is at least an order of magnitude larger than the loss modulus G" at all magnetic field strengths investigated. G' does depend only weakly on frequency, and linearly on volume fraction. A model is presented for the high frequency limit of the storage modulus G'(infinity). In the model our system is treated as a collection of single noninteracting chains of particles. Assuming a dipolar magnetic interaction, theory and experiment show reasonable agreement at high frequencies.