Measuring and modeling the magnetic settling of superparamagnetic nanoparticle dispersions

In this paper, we present settling experiments and mathematical modeling to study the magnetic separation of superparamagnetic iron-oxide nanoparticles (SPIONs) from a brine. The experiments were performed using SPIONs suspensions of concentration between 3 and 202g/L dispersed in water and separated from the liquid under the effect of a permanent magnet. A 1D model was developed in the framework of the sedimentation theory with a conservation law for SPIONs and a mass flux function based on the Newton's law for motion in a magnetic field. The model describes both the hindering effect of suspension concentration (n) during settling due to particle collisions and the increase in settling rate due to the attraction of the SPIONs towards the magnet. The flux function was derived from the settling experiments and the numerical model validated against the analytical solution and the experimental data. Suspensions of SPIONs were of 2.8cm initial height, placed on a magnet, and monitored continuously with a digital camera. Applying a magnetic field of 0.5T of polarization, the SPION's velocity was of approximately 3·10(-5)m/s close to the magnet and decreases of two orders of magnitude across the domain. The process was characterized initially by a classical sedimentation behavior, i.e., an upper interface between the clear water and the suspension slowly moving towards the magnet and a lower interface between the sediment layer and the suspension moving away from the magnet. Subsequently, a rapid separation of nanoparticle occured suggesting a non-classical settling phenomenon induced by magnetic forces which favor particle aggregation and therefore faster settling. The rate of settling decreased with n and an optimal condition for fast separation was found for an initial n of 120g/L. The model agrees well with the measurements in the early stage of the settling, but it fails to describe the upper interface movement during the later stage, probably because of particle aggregation induced by magnetization which is not accounted for in the model.