  We present a numerical study of the effect that fluid and particle inertia
have on the motion of suspended spherical particles through a geometric
constriction to understand analogous microfluidic settings, such as pinched
flow fractionation devices. The particles are driven by a constant force in a
quiescent fluid, and the constriction (the pinching gap) corresponds to the
space between a plane wall and a second, fixed sphere of the same size (the
obstacle). The results show that, due to inertia and/or the presence of a
geometric constriction the particles attain smaller separations to the
obstacle. We then relate the minimum surface-to-surface separation to the
effect that short-range, repulsive non-hydrodynamic interactions (such as
solid-solid contact due to surface roughness, electrostatic double layer
repulsion, etc.) would have on the particle trajectories. In particular, using
a simple hard-core repulsive potential model for such interactions, we infer
that the particles would experience larger lateral displacements moving through
the pinching gap as inertia increases and/or the aperture of the constriction
decreases. Thus, separation of particles based on differences in density is in
principle possible, owing to the differences in inertia associated with them.
We also discuss the case of significant inertia, in which the presence of a
small construction may hinder separation by reducing inertia effects.
