  We study dust concentration in axisymmetric gas rings in protoplanetary
disks. Given the gas surface density, we derived an analytical total dust
surface density by taking into account the differential concentration of all
the grain sizes. This model allows us to predict the local dust-to-gas mass
ratio and the slope of the particle size distribution, as a function of radius.
We test this analytical model comparing it with a 3D magneto-hydrodynamical
simulation of dust evolution in an accretion disk. The model is also applied to
the disk around HD 169142. By fitting the disk continuum observations
simultaneously at $\lambda = 0.87$, 1.3, 3.0 mm, we obtain a global dust-to-gas
mass ratio $\epsilon_{\rm global} = 1.05 \times 10^{-2}$ and a viscosity
coefficient $\alpha = 1.35 \times 10^{-2}$. This model can be easily
implemented in numerical simulations of accretion disks.
