Estimation of the effective permeability in magnetorheological fluids

Magnetorheological (MR) fluids constitute examples of controllable ("smart" ) fluids, whose rheological properties vary in response to an applied magne tic field. These fluids typically consist of micron-sized, magnetizable par ticles dispersed in a nonpermeable carrier fluid. The essential characteris tic of MR fluids is that they may be continuously and reversibly varied fro m a state of free flowing liquids in the absence of an applied magnetic fie ld to that of stiff semi-solids in a moderate field. Understanding the magn etic properties of MR fluids is crucial to the design of MR fluid-based dev ices and it also provides valuable insight into the character of the micros tructure responsible for their field-dependent rheology. Prediction of the overall magnetic properties of MR composites is a challenging task, however , due to the highly nonlinear and strongly spatially variable nature of the magnetization of the constituents. In this paper we propose a model for th is behavior that is based on the mathematical theory of homogenization. We derive effective equations that govern the magnetic response of(periodicall y arranged) particle-chains through magnetic saturation. Comparisons of num erical results for these equations with experimental data show good agreeme nt which suggests that our approach could be useful in the design of improv ed MR fluids.