  We numerically model the evolution of dust in a protoplanetary disk using a
two-phase (gas+dust) Smoothed Particle Hydrodynamics (SPH) code, which is
non-self-gravitating and locally isothermal. The code follows the three
dimensional distribution of dust in a protoplanetary disk as it interacts with
the gas via aerodynamic drag. In this work, we present the evolution of a disk
comprising 1% dust by mass in the presence of an embedded planet for two
different disk configurations: a small, minimum mass solar nebular (MMSN) disk
and a larger, more massive Classical T Tauri star (CTTS) disk. We then vary the
grain size and planetary mass to see how they effect the resulting disk
structure. We find that gap formation is much more rapid and striking in the
dust layer than in the gaseous disk and that a system with a given stellar,
disk and planetary mass will have a different appearance depending on the grain
size and that such differences will be detectable in the millimetre domain with
ALMA. For low mass planets in our MMSN models, a gap can open in the dust disk
while not in the gas disk. We also note that dust accumulates at the external
edge of the planetary gap and speculate that the presence of a planet in the
disk may facilitate the growth of planetesimals in this high density region.
