  We present the results of two-fluid hydrodynamical simulations of circumbinary discs consisting of gas and dust, with and without embedded planets, to examine the influence of the dust on the structure of the tidally truncated inner cavity and on the parking locations of migrating planets. In this proof-of-concept study, we consider Kepler-16 and -34 analogues, and examine dust fluids with Stokes numbers in the range $10^{-4} \le St \le 10^{-1}$ and dust-to-gas ratios of 0.01 and 1. For the canonical dust-to-gas ratio of 0.01, we find the inclusion of the dust has only a minor effect on the cavity and stopping locations of embedded planets compared to dust-free simulations. However, for the enhanced dust-to-gas ratio of unity, assumed to arise because of significant dust drift and accumulation, we find that the dust can have a dramatic effect by shrinking and circularising the inner cavity, which brings the parking locations of planets closer to the central binary. This work demonstrates the importance of considering both gas and dust in studies of circumbinary discs and planets, and provides a potential means of explaining the orbital properties of circumbinary planets such as Kepler-34b, which have hitherto been difficult to explain using gas-only hydrodynamical simulations. 
Dusty circumbinary discs: inner cavity structures and stopping locations   of migrating planets