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 _ { 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 .