  We present a systematic simulation campaign to investigate the pairwise
interaction of two mobile, monodisperse particles submerged in a viscous fluid
and subjected to monochromatic oscillating flows. To this end, we employ the
immersed boundary method to geometrically resolve the flow around the two
particles in a non-inertial reference frame. We neglect gravity to focus on
fluid-particle interactions associated with particle inertia and consider
particles of three different density ratios aligned along the axis of
oscillation. We systematically vary the initial particle distance and the
frequency based on which the particles show either attractive or repulsive
behavior by approaching or moving away from each other, respectively. This
behavior is consistently confirmed for the three density ratios investigated,
although particle inertia dictates the overall magnitude of the particle
dynamics. Based on this, threshold conditions for the transition from
attraction to repulsion are introduced that obey the same power law for all
density ratios investigated. We furthermore analyze the flow patterns by
suitable averaging and decomposition of the flow fields and find competing
effects of the vorticity induced by the fluid-particle interactions. Based on
these flow patterns, we derive a circulation-based criterion that provides a
quantitative measure to categorize the different cases. It is shown that such a
criterion provides a consistent measure to distinguish the attractive and
repulsive arrangements.
