On the Apparent Yield Stress in Non-Brownian Magnetorheological Fluids

We use simulations to probe the flow properties of dense two-dimensional magnetorheological fluids. Prior results from both experiments and simulations report that the shear stress $\sigma$ scales with strain rate $\dot \gamma$ as $\sigma \sim \dot \gamma^{1-\Delta}$, with values of the exponent ranging between $2/3 <\Delta \le 1$. However it remains unclear what properties of the system select the value of $\Delta$, and in particular under what conditions the system displays a yield stress ($\Delta = 1$). To address these questions, we perform simulations of a minimalistic model system in which particles interact via long ranged magnetic dipole forces, finite ranged elastic repulsion, and viscous damping. We find a surprising dependence of the apparent exponent $\Delta$ on the form of the viscous force law. For experimentally relevant values of the volume fraction $\phi$ and the dimensionless Mason number (which quantifies the competition between viscous and magnetic stresses), models using a Stokes-like drag force show $\Delta \approx 0.75$ and no apparent yield stress. When dissipation occurs at the contact, however, a clear yield stress plateau is evident in the steady state flow curves. In either case, increasing $\phi$ towards the jamming transition suffices to induce a yield stress. We relate these qualitatively distinct flow curves to clustering mechanisms at the particle scale. For Stokes-like drag, the system builds up anisotropic, chain-like clusters as the Mason number tends to zero (vanishing strain rate and/or high field strength). For contact damping, by contrast, there is a second clustering mechanism due to inelastic collisions.