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

Abstract

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. KeywordsField-flow fractionation; magnetic field-flow fractionation; MgFFF; magnetic nanoparticles; nanoparticle characterization; quadrupole magnetic field; helical channelThe field-flow fractionation (FFF) techniques are for the separation and characterization of particulate and macromolecular materials suspended or dissolved in a liquid medium. They are similar to chromatography in that different components of a small sample elute from a separation channel at different times [1]. Chromatography exploits differences in partition between mobile and stationary phases to separate sample components as they are carried along a column, but FFF separation is achieved within the flowing mobile phase and does not utilize a stationary phase. The separation channel optimally has a uniform thickness and a high aspect ratio, i.e., it is much thinner than it is broad. The fluid velocity profile is therefore parabolic, or close to parabolic, with the fastest velocity close to the center and zero velocity at the walls. The small perturbation due to the viscous drag of the side-walls may be ignored for a channel of high aspect ratio. A field of some type is applied across the channel thickness, perpendicular to the direction of fluid flow. The materials to be separated (we restrict our consideration to submicron particles in this work) interact with the field and are driven toward one of the walls, known as the accumulation wall. The resulting increase in concentration adjacent to the accumulation wall is opposed by Brownian diffusion, and dynamic steady-state distributions are approached where the concentration of each species is highest adjacent to the wall and decays exponentially away from the wall. Furthermore, the rate of exponential decay is related *Corresponding

Magnetic Nanoparticle Drug Carriers and Their Study by Quadrupole Magnetic Field-Flow Fractionation

“…If it is assumed that there is no interaction between particles, as for other forms of FFF, then the dependence of R on λ for the helical channel would deviate only to a small extent from that shown in eq 3 which is valid for the parallelplate channels. 209 The dependence converges to the relationship in eq 3 as w/r o f 0. QMgFFF separates magnetic nanoparticles according to their response to the magnetic field gradient.…”

“…The magnitude of the magnetic field is therefore constant and maximized at the outer channel wall, and the field gradient across the channel thickness is constant throughout the channel. If is assumed that there is no interaction between particles, as for other forms of FFF, then the dependence of R on λ for the helical channel would deviate only to a small extent from that shown in eq (3) which is valid for the parallel-plate channels 209. The dependence converges to the relationship in eq (3) as w / r o → 0.…”

“…Quadrupole Magnetic Field-Flow Fractionation. Quadrupole magnetic field-flow fractionation (QMgFFF) [205][206][207][208][209] makes use of a quadrupole magnetic field that has the property of being axisymmetric. Inside the aperture of the quadrupole, the magnitude of the magnetic field increases in direct proportion to the distance from the axis.…”

Characterization of magnetic nanoparticles using programmed quadrupole magnetic field-flow fractionation

“…We can therefore assume the force experienced by the particles across the zone thickness corresponds to that at the accumulation wall, without introducing significant error. The steady-state concentration profile across the channel thickness is found to be given by (Williams et al 2009b)…”