Title: Far-field theory for trajectories of magnetic ellipsoids in rectangular and circular channels,
Abstract: We report a method to control the positions of ellipsoidal magnets in flowing
channels of rectangular or circular cross section at low Reynolds number.A
static uniform magnetic field is used to pin the particle orientation, and the
particles move with translational drift velocities resulting from hydrodynamic
interactions with the channel walls which can be described using Blake's image
tensor.Building on his insights, we are able to present a far-field theory
predicting the particle motion in rectangular channels, and validate the
accuracy of the theory by comparing to numerical solutions using the boundary
element method.We find that, by changing the direction of the applied magnetic
field, the motion can be controlled so that particles move either to a curved
focusing region or to the channel walls.We also use simulations to show that
the particles are focused to a single line in a circular channel.Our results
suggest ways to focus and segregate magnetic particles in lab-on-a-chip
devices.