Electro- and magnetorheological (ER and MR) fluids are particulate suspensions whose rheological properties are dramatically altered by electric and magnetic fields, respectively. The applied fields also alter the suspension microstructure, causing the formation of particulate columns oriented in the field direction in quiescent suspensions, and the formation of concentrated particulate stripes oriented in the flow direction in sheared suspensions. These structural changes are intimately connected to the rheological phenomena. The formation of particulate columns is known to cause the dramatic rheological changes. The appearance of stripes is associated with the onset of a transient rheological response, where the shear stress slowly increases as the stripes coalesce, coarsen, and densify. ER and MR fluids are being exploited in the development of such applications as shock absorbers, clutches, and brakes, with MR applications recently reaching commercialization. Understanding and modeling the transient structural and rheological behavior is crucial for the design, optimization and control of ER and MR fluids and devices.
Particle-level simulations have been valuable for understanding the relationships between particle properties, interactions, and macroscopic behavior. However, these approaches are computationally expensive, and thus ill-suited for modeling the behavior of an entire device. Other modeling strategies must be developed to complement particle-level simulations and overcome their inherent limitations. We have developed a continuum description of the structure evolution in ER suspensions, as characterized by the time and position-dependent particle volume fraction _(x; t). The particle flux is related to the particle contribution to the stress via a momentum balance. Using this two-fluid approach, one predicts the patterns observed experimentally-column formation in quiescent suspensions, and stripe formation in sheared suspensions- without the computational expense of following the motion of individual particles.
Although this continuum model can successfully reproduce certain features of structure evolution, assumptions employed for the constitutive behavior limit its predictive power. Most notably, assuming a form for the electrostatic stress appropriate for an isotropic suspension precludes an estimate for the field-induced shear stress and thus the associated rheological transients; and the neglect of nonlocal polarization gives little insight into the long-time transients. The main goal of the proposed work is to combine the strengths of the two modeling approaches to obtain a multiscale description of ER/MR fluids and devices, overcoming the limitations of our prior continuum modeling effort. We will employ particle-level simulations (i.e., Stokesian dynamics simulations) to determine the appropriate constitutive behavior for particle stress and particle flux for use in the continuum model. Employing this constitutive behavior will allow us to probe both the evolution of structure and shear rheology from a continuum perspective. We will also extend a selfconsistent field model of ER fluids to model nonlocal polarization contributions in the continuum model, in order to describe the long-time transient phenomena. The proposed work will yield a complete continuum description of the rheology and mass transport in ER and MR fluids that can be used in the design, optimization and control of ER and MR fluids and devices.
Simulation studies will be performed by Klingenberg, Morris, and students, with continuing consultation with Ulicny at General Motors. Experiments for verification will be performed at both UW and GM. GM will also provide experimental results for clutch performance from measurements on a clutch test rig at GM.
Intellectual Merit and Broader Impact. The proposed work will specifically benefit the design, optimization and control of sheared ER and MR devices by providing a models for both the rheology and mass transport. Such information is necessary as particle transport appears to be ubiquitous in sheared ER and MR fluids, and impacts the apparent rheology. More generally, the proposed work will benefit suspension mechanics research as we further develop continuum methods for describing the flow of suspensions.
The broader impact of this work includes an educational component through the training of undergraduate and graduate students in the technical modeling aspects of this work, as well as the experimental techniques. Results from this work will be available to the scientific community through submission of manuscripts to refereed journals, and presentations at scientific meetings.
