Estimation of the Eeective Permeability in Magnetorheological Fluids

Magnetorheological (MR) uids constitute examples of controllable (\smart") u-ids, whose rheological properties vary in response to an applied magnetic eld. These uids typically consist of micron-sized, magnetizable particles dispersed in a non-permeable carrier uid. The essential characteristic of MR uids is that they may be continuously and reversibly varied from a state of free owing liquids in the absence of an applied magnetic eld to that of stii semi-solids in a moderate eld. Understanding the magnetic properties of MR uids is crucial to the design of MR uid-based devices and it also provides valuable insight into the character of the microstructure responsible for their eld-dependent rheology. Prediction of the overall magnetic properties of MR composites is a challenging task, however, due to the highly nonlinear and os-cillatory nature of the magnetization of the constituents. In this paper we propose a model for this behavior that is based on the mathematical theory of homogenization. We derive eeective equations that govern the magnetic response of (periodically arranged) particle-chains through magnetic saturation. Comparison of numerical results for these equations with experimental data show good agreement which suggests that our approach could be useful in the design of improved MR uids.