Theory for nanoparticle retention time in the helical channel of quadrupole magnetic field-flow fractionation

Quadrupole magnetic field-flow fractionation (QMgFFF) is a separation and characterization technique for magnetic nanoparticles such as those used for cell labeling and for targeted drug therapy. A helical separation channel is used to efficiently exploit the quadrupole magnetic field. The fluid and sample components therefore have angular and longitudinal components to their motion in the thin annular space occupied by the helical channel. The retention ratio is defined as the ratio of the times for non-retained and a retained material to pass through the channel. Equations are derived for the respective angular and longitudinal components to retention ratio.