Chain model of a magnetorheological suspension in a rotating field

We develop an athermal chain model for magnetorheological suspensions in rotating magnetic fields. This model is based on a balance of hydrodynamic and magnetostatic forces and focuses on the mechanical stability of chains. Using a linear approximation of the chain shape, we compute the orientation and size of a critical chain in a rotating magnetic field as a function of the Mason number Mn, which is the ratio of dipolar to hydrodynamic forces between two particles in contact. The critical chain length is found to scale with the inverse square root of Mn, and its orientation relative to the instantaneous field is independent of Mn. The actual nonlinear shape of a chain in a rotating field is then computed self-consistently. Finally, the effect of local fields on the dipolar interaction force is considered, leading to predictions for the chain shape and orientation that depend rather strongly on the magnetic permeability of the particles. A principal finding is the possibility of brittle or ductile chain fracture, depending on the permeability of the particles. Single-chain simulations confirm this prediction, as do experimental measurements.