The force acting on a superparamagnetic bead due to an applied magnetic field

This paper describes a model of the motion of superparamagnetic beads in a microfluidic channel under the influence of a weak magnetic field produced by an electric current passing through a coplanar metal wire. The model based on the conventional expression for the magnetic force experienced by a superparamagnetic bead (suspended in a biologically relevant medium) and the parameters provided by the manufacturer failed to match the experimental data. To fit the data to the model, it was necessary to modify the conventional expression for the force to account for the non-zero initial magnetization of the beads, and to use the initial magnetization and the magnetic susceptibility of the beads as adjustable parameters. The best-fit value of susceptibility deviated significantly from the value provided by the manufacturer, but was in good agreement with the value computed using the magnetization curves measured independently for the beads from the same vial as those used in the experiment. The results of this study will be useful to researchers who need an accurate prediction of the behavior of superparamagnetic beads in aqueous suspensions under the influence of weak magnetic fields. The derivation of the force on a magnetic bead due to a magnetic field also identifies the correct treatment to use for this interaction, and resolves discrepancies present throughout the literature.