Magnetic particle motion in a Poiseuille flow.

The manipulation of magnetic particles in a continuous flow with magnetic fields is central to several biomedical applications, including magnetic cell separation and magnetic drug targeting. A simplified two-dimensional (2D) equation describing the motion of particles in a planar Poiseuille flow is considered for various magnetic field configurations. Exact analytical solutions are derived for the particle motion under the influence of a constant magnetization force and a force decaying as a power of the source distance, e.g., due to a current carrying wire or a magnetized cylinder. For a source distance much larger than the transversal size of the flow, a general solution is derived and applied to the important case of a magnetic dipole. This solution is used to investigate the dependence of the particle capture efficiency on the dipole orientation. A correction factor to convert the obtained 2D results to a three-dimensional cylindrical geometry is derived and validated against computational simulations. Simulations are also used to investigate parameter ranges beyond the region of applicability of the analytical results and to investigate more complex magnetic field configurations.