Modeling and computation of the overall magnetic properties of magnetorheological fluids

Magnetorheological (MR) fluids constitute examples of controllable ("smart") fluids, whose rheological properties vary in response to an applied magnetic field. These fluids typically consist of micron-sized, magnetizable particles dispersed in an insulating medium. 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. The highly nonlinear and oscillatory nature of the magnetization of their constituents provides a challenge for the prediction of the overall magnetic response of MR composites. In this paper we initiate a study of the effective permeability of these materials by appealing to the mathematical theory of homogenization. Within this framework, we consider suspensions that display both linear as well as nonlinear magnetic behavior. For these, we derive analytic formulas for their effective permeabilities. In the case of linear materials comparisons are made with the asymptotic Rayleigh-Maxwell expressions.