  Various physical processes that ensue within protoplanetary disks --
including vertical settling of icy/rocky grains, radial drift of solids,
planetesimal formation, as well as planetary accretion itself -- are
facilitated by hydrodynamic interactions between H/He gas and high-$Z$ dust.
The Stokes number, which quantifies the strength of dust-gas coupling, thus
plays a central role in protoplanetary disk evolution, and its poor
determination constitutes an important source of uncertainty within the theory
of planet formation. In this work, we present a simple model for dust-gas
coupling, and demonstrate that for a specified combination of the nebular
accretion rate, $\dot{M}$, and turbulence parameter, $\alpha$, the radial
profile of the Stokes number can be calculated uniquely. Our model indicates
that the Stokes number grows sub-linearly with orbital radius, but increases
dramatically across the water-ice line. For fiducial protoplanetary disk
parameters of $\dot{M}=10^{-8}\,M_{\odot}/$year and $\alpha=10^{-3}$, our
theory yields characteristic values of the Stokes number on the order of
$\mathrm{St}\sim10^{-4}$ (corresponding to $\sim$mm-sized silicate dust) in the
inner nebula and $\mathrm{St}\sim10^{-1}$ (corresponding to $\sim$few-cm-sized
icy grains), in the outer regions of the disk. Accordingly, solids are expected
to settle into a thin sub-disk at large stellocentric distances, while
remaining vertically well-mixed inside the ice line.

Earth and Planetary Astrophysics;Solar and Stellar Astrophysics