Magnetic Separation and Hydrodynamic Interactions in Microfluidic Systems

Abstract

Magnetic bead manipulation, in particular separation, in microfluidic systems is a tech- nique which offers to simplify and integrate separation and rinsing procedures for minute samples of biological material. We study the physics of magnetic bead motion in such systems. The force on a body in a magnetic field is determined from principles of thermody- namics. From that result, the force between two spherical linearly paramagnetic particles immersed in an external magnetic field is derived provided that they are well separated. Furthermore, we find the magnetic dipole moments that two linearly paramagnetic spher- ical particles induce in one another; both being immersed in an external magnetic field. The leading magnetic interaction force decays as particle separation to the power 3. The hydrodynamic interaction, which stems from the fluid motion set about by par- ticles moving in a viscous fluid, is shown to decay with separation to the power 1 by means of hydrodynamic Greens functions. The magnetic interaction decays much faster with separation. This significantly influences the dynamics of magnetic bead motion which is illustrated through numerical simulations that study individual beads. Instead of adding more and more beads on an individual basis, we go on to treat the beads as a continuum described by a distribution that is coupled to the problem of fluid flow in a model microfluidic channel. This shows that hydrodynamic interactions help the capturing of magnetic beads and that this depends on the concentration of beads. An effort is underway to test this prediction in experiments. Finally, we have derived an analytic framework for the description of the slow motion of spherical particles in a viscous fluid in confined geometries. This enables us to derive a first approximation to the mobility of a spherical particle at the centre of a cube filled with viscous fluid.

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