  We study the accretion of dust particles of various sizes onto embedded
massive gas giant planets, where we take into account the structure of the gas
disk due to the presence of the planet. The accretion rate of solids is
important for the structure of giant planets: it determines the growth rate of
the solid core that may be present as well as their final enrichment in solids.
We use the RODEO hydrodynamics solver to solve the flow equations for the gas,
together with a particle approach for the dust. The solver for the particles'
equations of motion is implicit with respect to the drag force, which allows us
to treat the whole dust size spectrum. We find that dust accretion is limited
to the smallest particle sizes. The largest particles get trapped in outer
mean-motion resonances with the planet, while particles of intermediate size
are pushed away from the orbit of the planet by the density structure in the
gas disk. Only particles smaller than approximately s_max =10 micron may
accrete on a planet with the mass of Jupiter. For a ten times less massive
planet s_max=100 micron. The strongly reduced accretion of dust makes it very
hard to enrich a newly formed giant planet in solids.
