A Criterion for the Complete Deposition of Magnetic Beads on the Walls of Microchannels

This paper analyzes numerical simulations of the trajectories of magnetic beads in a microchannel, with a nearby permanent cubical magnet, under different flow and magnetic conditions. Analytically derived local fluid velocities and local magnetic forces have been used to track the particles. A centered position and a lateral position of the magnet above the microchannel are considered. The computed fractions of deposited particles on the walls are compared successfully with a new theoretically derived criterion that imposes a relation between the sizes of the magnet and the microchannel and the particle Stokes and Alfvén numbers to obtain the complete deposition of the flowing particles on the wall. In the cases in which all the particles, initially distributed uniformly across the section of the microchannel, are deposited on the walls, the simulations predict the accumulation of the major part of particles on the wall closest to the magnet and near the first half of the streamwise length of the magnet.