A Rheological Model for Magneto-rheological Fluids

Magneto-rheological fluids (MRF) are suspensions of particles which can be magnetized. MRF exhibit fast, strong and reversible changes in their rheological properties when a magnetic field is applied. A commercially available damping system that takes full advantage of the controllable technology of MRF and delivers valveless damping control appeared on passenger vehicles in 2003. Further commercial systems are e.g. a MRF brake, „steer-by-wire” vehicle control, controllable friction damper that decreases the noise and vibrations in washing machines, above-the-knee prosthesis, and seismic mitigation MRF damping systems protecting buildings and bridges from earthquakes and windstorms. Goncalves et al. [6] present a recent review of the state of the art in magnetorheological technology. Since their invention in 1948, MR fluid development has made significant advancements. Throughout this time, MR fluids have been faced with many challenges and today MR fluid formulations appear to have overcome many of these challenges. Goncalves et al [6] focus thei review on strength (i.e. the achievable yield stress), stability and durability of the fluid, since when using a MR fluid in a particular application these three areas fall under the greatest scrutiny. The viscoelastic properties of a magneto-rheological fluid can be variably controlled using a magnetic field. Wollny et al. [13] have developed a new experimental method allowing an accurate determination of a magneto-rheological fluid’s viscoelastic properties as a function of the preset magnetic field strength. Carletto and Bossis [2] attempt to correlate the rheological characteristics of a magnetic colloidal suspension subjected to a unidirectional magnetic field with the structures formed within the fluid. As far as the MRF yield stress is concerned, Bossis et al. conclude that the aggregates do not break but begin to slip on the wall, then they begin to rotate and no longer touch the plates. At some critical strain the hydrodynamic shear force will break the aggregates. This particular behaviour is found in the experimental results we present in this paper, and it is captured in the mathematical model we propose