  We construct a boundary integral representation for the low-Reynolds-number
flow in a channel in the presence of freely-suspended particles (or droplets)
of arbitrary size and shape. We demonstrate that lubrication theory holds away
from the particles at horizontal distances exceeding the channel height and
derive a multipole expansion of the flow which is dipolar to the leading
approximation. We show that the dipole moment of an arbitrary particle is a
weighted integral of the stress and the flow at the particle surface, which can
be determined numerically. We introduce the equation of motion that describes
hydrodynamic interactions between arbitrary, possibly different, distant
particles, with interactions determined by the product of the mobility matrix
and the dipole moment. Further, the problem of three identical interacting
spheres initially aligned in the streamwise direction is considered and the
experimentally observed "pair exchange" phenomenon is derived analytically and
confirmed numerically. For non-aligned particles, we demonstrate the formation
of a configuration with one particle separating from a stable pair. Our results
suggest that in a dilute initially homogeneous particulate suspension flowing
in a channel the particles will eventually separate into singlets and pairs.
