Haloing in magnetic bimodal colloids
Résumé
If 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.