  When a micron-sized magnetizable particle is introduced into a suspension of
nanosized magnetic particles, the nanoparticles accumulate around the
microparticle and form thick anisotropic clouds extended in the direction of
the applied magnetic field. This phenomenon promotes colloidal stabilization of
bimodal magnetic suspensions and allows efficient magnetic separation of
nanoparticles used in bioanalysis and water purification. In the present work,
size and shape of nanoparticle clouds under the simultaneous action of an
external uniform magnetic field and the flow have been studied in details. In
experiments, dilute suspension of iron oxide nanoclusters (of a mean diameter
of 60 nm) was pushed through a thin slit channel with the nickel microspheres
(of a mean diameter of 50$\mu$m) attached to the channel wall. The behavior of
nanocluster clouds was observed in the steady state using an optical
microscope. In the presence of strong enough flow, the size of the clouds
monotonically decreases with increasing flow speed in both longitudinal and
transverse magnetic fields. This is qualitatively explained by enhancement of
hydrodynamic forces washing the nanoclusters away from the clouds. In the
longitudinal field, the flow induces asymmetry of the front and the back
clouds. To explain the flow and the field effects on the clouds, we have
developed a simple model based on the balance of the stresses and particle
fluxes on the cloud surface. This model, applied to the case of the magnetic
field parallel to the flow, captures reasonably well the flow effect on the
size and shape of the cloud and reveals that the only dimensionless parameter
governing the cloud size is the ratio of hydrodynamic-to-magnetic forces - the
Mason number. At strong magnetic interactions considered in the present work
(dipolar coupling parameter $\alpha \geq 2$), the Brownian motion seems not to
affect the cloud behavior.
