  Millimeter continuum imaging of protoplanetary disks reveals the distribution
of solid particles and the presence of substructures (gaps and rings) beyond
5-10 au, while infrared (IR) spectra provide access to abundances of gaseous
species at smaller disk radii. Building on recent observational findings of an
anti-correlation between the inner disk water luminosity and outer dust disk
radius, we aim here at investigating the dynamics of icy solids that drift from
the outer disk and sublimate their ice inside the snow line, enriching the
water vapor that is observed in the IR. We use a volatile-inclusive disk
evolution model to explore a range of conditions (gap location, particle size,
disk mass, and alpha-viscosity) under which gaps in the outer disk efficiently
block the inward drift of icy solids. We find that inner-disk vapor enrichment
is highly sensitive to the location of a disk gap, yielding for each particle
size a radial "sweet spot" that reduces the inner-disk vapor enrichment to a
minimum. For pebbles of 1-10 mm in size, which carry the most mass, this sweet
spot is at 7-15 au, suggesting that inner gaps may have a key role in reducing
ice delivery to the inner disk and may not allow the formation of Earths and
super-Earths. This highlights the importance of observationally determining the
presence and properties of inner gaps in disks. Finally, we argue that the
inner water vapor abundance can be used as a proxy for estimating the pebble
drift efficiency and mass-flux entering the inner disk.
