Dust crystallinity in protoplanetary disks: the effect of diffusion/viscosity ratio

The process of turbulent radial mixing in protoplanetary disks has strong relevance to the analysis of the spatial distribution of crystalline dust species in disks around young stars and to studies of the composition of meteorites and comets in our own solar system. A debate has gone on in the recent literature on the ratio of the effective viscosity coefficient $\nu$ (responsible for accretion) to the turbulent diffusion coefficient $D$ (responsible for mixing). Numerical magneto-hydrodynamic simulations have yielded values between $\nu/D\simeq 10$ (Carballido, Stone & Pringle, 2005) and $\nu/D\simeq 0.85$ (Johansen & Klahr, 2005}). Here we present two analytic arguments for the ratio $\nu/D=1/3$ which are based on elegant, though strongly simplified assumptions. We argue that whichever of these numbers comes closest to reality may be determined {\em observationally} by using spatially resolved mid-infrared measurements of protoplanetary disks around Herbig stars. If meridional flows are present in the disk, then we expect less abundance of crystalline dust in the surface layers, a prediction which can likewise be observationally tested with mid-infrared interferometers.