  Substructures are ubiquitous in high resolution (sub-)millimeter continuum
observations of circumstellar disks. They are possibly caused by forming
planets embedded in the disk. To investigate the relation between observed
substructures and young planets, we perform novel three-dimensional two-fluid
(gas+1-mm-dust) hydrodynamic simulations of circumstellar disks with embedded
planets (Neptune-, Saturn-, Jupiter-, 5 Jupiter-mass) at different orbital
distances from the star (5.2AU, 30AU, 50AU). We turn these simulations into
synthetic (sub-)millimeter ALMA images. We find that all but the Neptune-mass
planet open annular gaps in both the gas and the dust component of the disk. We
find that the temporal evolution of the dust density distribution is distinctly
different of the gas'. For example, the planets cause significant vertical
stirring of the dust in the circumstellar disk which opposes the vertical
settling. This creates a thicker dust disk than disks without a planet. We find
that this effect greatly influences the dust masses derived from the synthetic
ALMA images. Comparing the dust disk masses in the 3D simulations and the ones
derived from the 2D ALMA synthetic images, we find the former to be a factor of
a few (up to 10) larger, pointing to that real disks might be significantly
more massive than previously thought based on ALMA continuum images using the
optically thin assumption and equation. Finally, we analyze the synthetic ALMA
images and provide an empirical relationship between the planet mass and the
width of the gap in the ALMA images including the effects of the beam size.
