Cooperative magnetophoresis of superparamagnetic colloids: theoretical aspects

Superparamagnetic colloids have a great practical interest for their applications to processes ranging from biomedicine to environmental waste and pollutants removal. A fast and efficient separation of these particles from the solvent constitutes a key step in the practical implementation of this technology. Recent experiments show fast magnetophoretic separation using relatively small magnetic gradients and high magnetic fields. The mechanism underlying this fast separation was shown to be the reversible aggregation of the magnetic beads induced by the external field. In this paper, we analyze theoretically the physicochemical conditions under which reversible aggregation can be typically achieved, the timescale at which aggregates form, and their shape. In the case of colloids stabilized electrostatically, for reasonable surface potentials (approximately −70 mV), we find that the interaction potential between two superparamagnetic particles displays a barrier with a minimum so that reversible aggregates can form. We also show that the aggregation of particles is quite fast (typically less than a second for usual concentrations) and that lateral aggregation is more energetically stable than tip-to-tip aggregation for long chains (larger than 14 microspheres). This is consistent with experimental observations and very relevant for a fast magnetophoresis since thick aggregates move faster than thin ones.