Rheology of magnetorheological fluids: Models and measurements

Numerical and analytical models of magnetorheological fluid phenomena that account explicitly for the effects of magnetic nonlinearity and saturation are described. Finite-element analysis was used to calculate the field distribution in chains of magnetizable particles. The field-dependent stress required to shear the chains was then obtained using the Maxwell stress tenser. Three regimes are identified: at low applied fields, the stress increase quadratically, as expected from linear magnetostatics. In intermediate fields, the contact or polar regions of each particle saturate, reducing the rare of increase of the stress with increasing field. At high fields, the particles saturate completely, and the stress reaches its limiting value. Approximate analytical expressions for the yield stress and shear modulus in these regimes are also derived. The predictions of these models are compared to magnetorheological experiments in the literature and from our laboratory. These models predict successfully the magnitude of the stresses as well as their field dependence. They also suggest that particles comprised of materials with higher saturation magnetizations will exhibit the largest magnetorheological effects.