An anisotropic clustering instability in a sheared suspension of magnetic particles subject to a magnetic field.

A suspension of magnetic particles in a viscous fluid exhibits 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 initiation of dynamical arrest of an initially well-dispersed sheared suspension is examined by considering the effect of inter-particle hydrodynamic and magnetic interactions. There is a disturance 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, the collective effect of inter-particle interactions is shown to be equivalent to an anisotropic diffusion process. 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 concetration fluctuations in the direction fo the field.