Microstructural Analysis and Control of Magneto-Rheological Fluid

Abstract

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.

The development of variably compliant haptic systems using magnetorheological fluids

“…Substituting equations (16) and (17) in equation (15) (18) Rewriting equation (12) with respect to the input voltage V in results in…”

“…These models are extremely successful in deducing macroscale viscoelastic properties of nanoparticle/Newtonian fluid systems that agree with experiments from microstructural measurements. We comment that the models we deduce for MR fluids are fully three dimensional and applicable to any flow geometry [18].…”

“…The research outlined in this document is subdivided into two parts: microstructural, kinetic theory based modeling and actuator design. A microstructural, kinetic theory-based model of MR fluids has been developed [18]. For modeling these composite systems, dumbbell models in which two beads joined by an elastic connector were investigated.…”

A Constitutive Equation for Magnetorheological Fluid Characterization

“…Equation 12 can be applied to predict the stress tensor for magnetorheological fluids flowing through complex geometries. Stress tensor predictions for simple shear flow of spherical particles in contact are presented in the following paragraph.…”

“…For dilute suspensions and quasi-static conditions the equation can predict either the structure evolution in quiescent suspensions (chain formation) or structure evolution in sheared suspensions for low shear rates (lamellae formation). Bechtel et al [12] developed a set of constitutive equations based on the dumbbell model, assuming that the hydrodynamic and the magnetic forces act only on beads, and that no short or long range hydrodynamic interactions occur. For simple shear flow their constitutive equations reduce to a form similar to the Bingham model.…”