Simple analytical model for the magnetophoretic separation of superparamagnetic dispersions in a uniform magnetic gradient

Abstract

Magnetophoresis-the motion of magnetic particles under applied magnetic gradient-is a process of great interest in novel applications of magnetic nanoparticles and colloids. In general, there are two main different types of magnetophoresis processes: cooperative magnetophoresis (a fast process enhanced by particle-particle interactions) and noncooperative magnetophoresis (driven by the motion of individual particles in magnetic fields). In the case of noncooperative magnetophoresis, we have obtained a simple analytical solution which allows the prediction of the magnetophoresis kinetics from particle characterization data (size and magnetization). Our comparison with new experimental results shows good quantitative agreement. In addition, we show the existence of a universal curve onto which all experimental results should collapse after proper rescaling. The range of applicability of the analytical solution is discussed in light of the predictions of a magnetic aggregation model [Soft Matter 7, 2336].

Two-stage kinetics of field-induced aggregation of medium-sized magnetic nanoparticles

“…At longer times, lateral aggregation dominates over tip-to-tip aggregation and the chains can merge and form either a fibrous structure "frozen" in non-equilibrium state likely by inter-particle friction 22 or column structures confined by the walls orthogonal to the applied field 29 , or unconfined ellipsoidal drop-like aggregates under pulsed magnetic field 30,31 . Theoretical studies are mainly based on Langevin dynamics simulations 19,32,33 or solution of Smoluchowsky kinetic equation 23,24,27,28,[33][34][35] . A simplified theoretical approach, so-called hierarchical model, has been developed by See and Doi 36 considering only coalescence of the chains of equal sizes and showing a satisfactory agreement with experiments on 2a , even though it predicts monodisperse particle chains instead of experimentally observed polydisperse distribution.…”

“…An excellent example is enhancement of the magnetophoresis of magnetic microbeads due to their field-induced aggregation -the phenomenon referred to as cooperative magnetophoresis [17][18][19][20] , which could be beneficial for separation and detection of biomolecules using functionalized magnetic microbeads.…”

Magnetophoresis of Superparamagnetic Nanoparticles Applied to the Extraction of Lanthanide Ions in the Presence of Magnetic Field

“…It should be noticed that at the high field limit,  a situation where the particles are very close to the magnet,  the magnetic moment (m) approaches saturation, becoming almost insensitive to changes in the field [3]. However, its contribution to our measurements is completely negligible, since the nanoparticles close to the bottom of the microtubes should undergo instantaneous deposition, without contributing to the measured magnetophoretic rates.…”

“…Its understanding is essential for the application of nanoparticles in magnetic separation processes, however, the theory involved is yet under development and has been the subject of many recent discussions [1][2][3][4][5]. In addition , the advances in the experimental procedures remain yet quite limited.…”

“…Superparamagnetic nanoparticles (MagNP) are being extensively explored in nanotechnology, and one of the recent applications deals with magnetic separations at the nanoscale (magnetophoresis) [1][2][3][4][5] and elemental processing in the mineral area [6,7] (magnetic nanohydrometallurgy) [8][9][10]. The understanding of such processes can lead to important technological advances in metal ion extraction, separation and recovery, as well as in electrowinning processes, including environmental remediation involving the capture and removal of heavy metal contaminants from industrial effluents [11,12].…”