Clustering due to negative effective diffusion coefficients in a magnetorheological fluid.*

A magnetorheological fluid consists of magnetic particles suspended in a viscous fluid. These are used in applications requiring rapid flow control, where the suspension flows like a fluid in the absence of a field, but the particles cluster and jam the conduit in the presence of an applied field. The effect of shear flow and an applied field on the rheology is examined by incorporating the particle-particle hydrodynamic and magnetic interactions in the low Reynolds number limit. When an isolated particle is subjected to a magnetic field, the particles align in the field direction, while they rotate in `Jeffery' orbits when subjected to a shear flow. The effect of interactions in the presence of shear and an applied magnetic field is included in the dilute limit where the particle separation is much larger than the radius. In a uniform suspension, the total force due to interactions is zero. When there is a concentration modulation, there is a force on the particles which leads to a drift velocity. The effect of interactions can be expressed as an anisotropic diffusion tensor. The elements of this tensor are negative in the plane perpendicular to the field, indicating a strong clustering effect, and the are positive in the field direction, resulting in damping of concentration fluctuations. This explains the mechanism for initiation of anisotropic clusters that span the conduit and result in jamming upon application of a magnetic field.