Estimation of the Effective Permeability in Magnetorheological Fluids

Magnetorheological (MR) fluids constitute examples of controllable ("smart") fluids, whose Theological properties vary in response to an applied magnetic field. These fluids typically consist of micron-sized, magnetizable particles dispersed in a nonpermeable carrier fluid. The essential characteristic of MR fluids is that they may be continuously and reversibly varied from a state of free flowing liquids in the absence of an applied magnetic field to that of stiff semi-solids in a moderate field. Understanding the magnetic properties of MR fluids is crucial to the design of MR fluid-based devices and it also provides valuable insight into the character of the microstructure 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 this behavior that is based on the mathematical theory of homogenization. We derive effective equations that govern the magnetic response of (periodically arranged) particle-chains through magnetic saturation. Comparisons 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 fluids.