Dust in disks behave differently from the gas. They tend to drift to the pressure maximum.

In Zhu et al. 2012, we carried out two-dimensional two-fluid global simulations and have studied the response of dust to gap formation by a single planet in the gaseous component of a protoplanetary disk - the so-called dust filtration'' mechanism.  We have found that a gap opened by a giant planet at 20 AU in a $\alpha$=0.01, $\dot{M}=10^{-8}\msunyr$ disk can effectively stop dust particles larger than 0.1 mm drifting inwards, leaving a sub-millimeter dust cavity/hole. However, smaller particles are difficult to filter by a planet-induced gap due to 1) dust diffusion, and 2) a high gas accretion velocity at the gap edge. Based on these simulations, an analytic model is derived to understand what size particles can be filtered by the planet-induced gap edge. We show that a dimensionless parameter $T_{s}/\alpha$, which is the ratio between the dimensionless dust stopping time and the disk viscosity parameter, is important for the dust filtration process. Finally, with our updated understanding of dust filtration, we have computed Monte-Carlo radiative transfer models with variable dust size distributions to generate the spectral energy distributions (SEDs) of disks with gaps.  By comparing with transitional disk observations (e.g. GM Aur), we have found that dust filtration alone has difficulties to deplete small particles sufficiently to explain the near-IR deficit of moderate $\dot{M}$ transitional disks, except under some extreme circumstances.The scenario of gap opening by multiple planets studied previously suffers the same difficulty. One possible solution is by invoking both dust filtration and dust growth in the inner disk. In this scenario,  a planet induced gap filters  large dust particles in the disk, and the remaining small dust particles passing to the inner disk can grow efficiently without replenishment from fragmentation of large grains. Predictions for ALMA have also been made based on all these scenarios. We conclude that dust filtration with planet(s) in the disk is a promising mechanism to explain submm observations of transitional disks but it may need to be combined with other processes (e.g. dust growth) to explain the near-IR deficit of some systems.

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