Microstructural Analysis and Control of Magneto-Rheological Fluid

Characteristic phenomenological behavior of MR fluids is typically modeled by Bingham’s equation, which has no fundamental connection to the microstructure of MR fluid and the fully coupled mechanical-electrical-magnetic equations. In this paper microstructurally, kinetic theory-based model of MR fluids (consisting of micro-sized ferrous particles suspended in a Newtonian fluid) are developed. For modeling these composite systems, dumbbell models in which two beads joined by an elastic connector are investigated. In these models the distributed forces from the carrier fluid and from the magnetic field on the suspended particle are idealized as being localized on beads. Microscale constitutive equations relating flow, stress, and particle orientation are produced by integrating the coupled equations governing forces, flow, and orientation over a representative volume of particles and carrier fluid. Coefficients in the constitutive equations are specified not by a fit to macroscale experimental flow measurement but rather in terms of primitive measurements of particle microstructure, carrier fluid, viscosity and density, and temperature. These new models for MR fluids are three dimensional and applicable to any flow geometry, while the Bingham plastic model is in general applicable only to shear flow. The models in this paper reduce to forms similar to Bingham’s model in a simple shear flow, but with coefficients which arise from fundamental electromagnetic considerations and microstructural features such as geometrical, magnetic and mechanical characterization of the particles, quantities measured primitively from the carrier fluid, magnetic field and temperature.