Behavior of nanoparticle clouds around a magnetized microsphere under magnetic and flow fields

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

Haloing in magnetic bimodal colloids

International audienceIf a suspension of magnetic micron-sized and nano-sized particles is subjected to a homogeneous magnetic field, the nanoparticles are attracted to the microparticles and form thick anisotropic halos (clouds) around them. Such clouds can hinder approach of microparticles and result in effective repulsion between them. In the first part of this work, we present detailed experimental and theoretical studies of static nanoparticle concentration profiles and of the equilibrium shapes of nanoparticle clouds around a single magnetized microsphere taking into account interactions between nanoparticles. We show that at strong enough magnetic field, the ensemble of nanoparticles experiences a gas-liquid phase transition such that a dense liquid phase is condensed around the magnetic poles of a microsphere while a dilute gas phase occupies the rest of the suspension volume. Nanoparticle accumulation around a microsphere is governed by two dimensionless parameters - the initial nanoparticle concentration (fi_0) and the magnetic-to-thermal energy ratio (alfa) - and the three accumulation regimes are mapped onto a alfa-fi_0 phase diagram. Our local thermodynamic equilibrium approach gives a semi-quantitative agreement with the experiments on equilibrium shapes of nanoparticle clouds. In the second part of this work, we report the results of optical visualization of the flow of a dilute suspension of magnetic nanoparticles past a magnetizable microsphere in the presence of an external uniform magnetic field. Similarly to the static case, the nanopaticles are agglomerated around microspheres and built clouds, whose shape and size depend on both the parameteralfa and the ratio of hydrodynamic - to - magnetic forces, so-called Mason number Mn. With an increasing flow speed, we observe a drastic change from a smooth - to saw-tooth cloud shape, the latter inherent for Rosensweig instability. Such a transition occurs at a critical Mason number of the order of Mn=0.4 and is accompanied by a step-wise increase of the cloud size. The results of this work could be useful for the development of the bimodal magnetorheological fluids and of the magnetic separation technologies used in bio-analysis and water purification systems