  A flowing pair of particles in inertial microfluidics gives important
insights into understanding and controlling the collective dynamics of
particles like cells or droplets in microfluidic devices. They are applied in
medical cell analysis and engineering. We study the dynamics of a pair of solid
particles flowing through a rectangular microchannel using lattice Boltzmann
simulations. We determine the inertial lift force profiles as a function of the
two particle positions, their axial distance, and the Reynolds number.
Generally, the profiles strongly differ between particles leading and lagging
in flow and the lift forces are enhanced due to the presence of a second
particle. At small axial distances, they are determined by viscous forces,
while inertial forces dominate at large separations. Depending on the initial
conditions, the two-particle lift forces in combination with the Poiseuille
flow give rise to three types of unbound particle trajectories, called
moving-apart, passing, and swapping, and one type of bound trajectories, where
the particles perform damped oscillations. The damping rate scales with
Reynolds number squared, since inertial forces are responsible for driving the
particles to their steady-state positions.
