Analytical model of batch magnetophoretic separation.

Magnetophoresis (the motion of magnetic particles driven by the nonuniform magnetic field), that for a long time has been used for extracting magnetically susceptible objects in diverse industries, now attracts interest to develop more sophisticated microfluidic and batch techniques for separation and manipulation of biological particles, and magnetically assisted absorption and catalysis in organic chemistry, biochemistry, and petrochemistry. A deficiency of magnetic separation science is the lack of simple analytical models imitating real processes of magnetic separation. We have studied the motion of superparamagnetic (generally, soft magnetic) particles in liquid in the three-dimensional field of the diametrically polarized permanent cylindrical magnet; this geometry is basically representative of the batch separation mode. In the limit of the infinite-length magnet, we found the particle magnetophoresis proceeds independently of the magnet polarization direction, following the simple analytical relation incorporating all the relevant physical and geometrical parameters of the particle-magnet system. In experiments with a finite-length magnet we have shown applicability of the developed theory as to analyze the performance of the real batch separation systems in the noncooperative mode, and finally, we have presented an example of such analysis for the case of immunomagnetic cell separation and developed a criterion of the model limitation imposed by the magnetic aggregation of particles.