Abstract
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.
Highlights
The application of magnetism in fluidic microsystems has been used since the boom of microfluidics in the early 2000 [1] with the concept of micro total analysis systems
The movement of magnetic beads in microfluidic applications is usually controlled by permanent magnets or by magnetic fields generated by electric currents
As suggested by Eq (3), the trajectories of the particles are dominated by the drag force, that is proportional to ðdpÃÞÀ2 and by the magnetic force, proportional to the non-dimensional group M, defined in Eq 11 and to the non-dimensional term ð~BÃ Á r~ÃÞ~BÃ
Summary
The application of magnetism in fluidic microsystems has been used since the boom of microfluidics in the early 2000 [1] with the concept of micro total analysis systems. To verify that all the particles are captured by the magnet we can consider that the particles located at the bottom wall of the channel should not travel along the streamwise direction a distance larger than the length of the magnet during the period of time given by Eq 14.
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