(242e) An Anisotropic Clustering Instability Due to Inter-Particle Hydrodynamic and Magnetic Interactions in a Sheared Magnetorheological Fluid Subject to a Magnetic Field

A magnetorheological fluid is made of magnetic particles, with permanent of induced dipole moments, suspended in a viscous liquid. These fluids exhibit a transition between a flowing state in the absence of a magnetic field and a jammed state with sample-spanning particle aggregates when a magnetic field is applied. The formation of aggregates in a static suspension is considered to be due to the magnetic interaction between particles. However, the dynamical arrest of the flowing state requires the interactions between well dispersed particles subject to a shear flow, leading to rapid aggregation of particles. The mechanism of the concentration amplification in a well-dispersed suspension of magnetic particles under shear subject to a magnetic field is considered here.

The initiation of dynamical arrest of an initially well-dispersed sheared suspension is examined by considering the effect of inter-particle hydrodynamic and magnetic interactions. In a dilute suspension at low Reynolds number, there is a disturbance due to the magnetic field around one particle due to the magnetic moment of neighbouring particles, and a velocity disturbance due to the hydrodynamic torque exerted by neighbouring particles on the fluid. There is a correction to the particle angular velocity due to the net torque resulting from the hydrodynamic and magnetic interactions. The total force and the drift velocity due to these interactions is zero in a uniform suspension. In the presence of concentration fluctuations, there is a net force exerted on the particles due to both magnetic and hydrodynamic interactions, and the disturbance to the particle orientation due to the torque on the particles. There is also a change in the magnetic permeability due to the change in the magnetic moment density of the particles. The collective effect of all of these interactions is shown to be equivalent to an anisotropic diffusion process. The components of the diffusion tensor are calculated as a function of the strain rate, the magnetic field, and the particle diameter and particle and fluid properties. The diffusion coefficients in the directions perpendicular to the magnetic field are negative, indicating a strong clustering tendency in these directions. The diffusion coefficient in the magentic field direction is positive, and this results in the damping of concentration fluctuations in the direction of the field. This instability could initiate the formation of sample-spanning clusters along the field direction, leading to dynamical arrest upon application of a magnetic field.