Steady and oscillatory shear 3-D simulations of electro- and magnetorheology in uniaxial and biaxial fields are presented, and compared to the predictions of the chain model. These large scale simulations are three dimensional, and include the effect of Brownian motion. In the absence of thermal fluctuations, the expected shear thinning viscosity is observed in steady shear, and a striped phase is seen to rapidly form in a uniaxial field, with a sher slip zone in each sheet. However, as the influence of Brownian motion increases, the fluid stress decreases, especially at lower Mason numbers, and the striped phase eventually disappears, even when the fluid stres is still high. In a biaxial field, an opposite trend is seen, where Brownian motion decreases the stress most significantly at higher Mason numbers. To account for the uniaxial steady shear data we propose a microscopic chain model of the role played by thermal fluctuations on the rheology of ER and MR fluids tht delineates the regimes where an applied field can impact the fluid viscosity, and gives an analytical prediction for the thermal effect. In oscillatory shear,. a striped phase again appears in a uniaxial field, at strain amplitudes greater than approx 0.15, and the presence of a shear slip zone creates strong stress nonlinearities at low strain amplitudes. In a biaxial field, a shear slip zone is not created, and so the stress nonlinearities develop only at expected strain amplitudes. The nonlinear dynamics of these systems is shown to be in good agreement with the Kinetic Chain Model.
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