  A magnetorheological fluid, which consists of magnetic particles suspended in
a viscous fluid, flows freely with well-dispersed particles in a the absence of
a magnetic field, but particle aggregation results in flow cessation when a
field is applied. The mechanism of dynamical arrest is examined by analysing
interactions between magnetic particles in a magnetic field subject to a shear
flow. An isolated spherical magnetic particle undergoes a transition between a
rotating state at low magnetic field and a static orientation at high magnetic
field. The effect of interactions for spherical dipolar and polarisable
particles with static orientation is examined for a dilute viscous suspension.
There are magnetic interactions due to the magnetic field disturbance at one
particle caused by the dipole moment of another, hydrodynamic interactions due
to the antisymmetric force moment of a non-rotating particle in a shear flow,
and a modification of the magnetic field due to the particle magnetic moment
density. When there is a concentration variation, the torque balance condition
results in a disturbance to the orientation of the particle magnetic moment.
The net force and the drift velocity due to these disturbances is calculated,
and the collective motion generated is equivalent to an anisotropic diffusion
process. When the magnetic field is in the flow plane, the diffusion
coefficients in the two directions perpendicular to the field direction are
negative, implying that concentration fluctuations are unstable in these
directions. This instability could initiate field-induced dynamical arrest in a
magnetorheological fluid.
