  The presence of planets in binary systems poses interesting problems for
planet formation theories, both in cases where planets must have formed in very
compact discs around the individual stars and where they are located near the
edge of the stable circumbinary region, where in situ formation is challenging.
Dust dynamics is expected to play an important role in such systems, since dust
trapping at the inner edge of circumbinary discs could aid in situ formation,
but would simultaneously starve the circumstellar discs of the solid material
needed to form planets. Here we investigate the dynamics of dust in binary
systems using Smooth Particle Hydrodynamics. We find that all our simulations
tend towards dust trapping in the circumbinary disc, but the timescale on which
trapping begins depends on binary mass ratio ($q$) and eccentricity as well as
the angular momentum of the infalling material. For $q \gtrsim 0.1$, we find
that dust can initially accrete onto the circumstellar discs, but as the
circumbinary cavity grows in radius, dust eventually becomes trapped in the
circumbinary disc. For $q = 0.01$, we find that increasing the binary
eccentricity increases the time required for dust trapping to begin. However,
even this longer timescale is likely to be shorter than the planet formation
timescale in the inner disc and is insufficient to explain the observed
pre-transitional discs. This indicates that increase in companion eccentricity
alone is not enough to allow significant transfer of solids from the outer to
the inner disc.
