  We critically examine a scenario for the enrichment of the interstellar
medium (ISM) in which supernova ejecta follow a long (10^8 yr) journey before
falling back onto the galactic disk in the form of metal-rich ``droplets'',
These droplets do not become fully mixed with the interstellar medium until
they become photoionized in HII regions. We investigate the hypothesis that the
photoionization of these highly metallic droplets can explain the observed
``abundance discrepancy factors'' (ADFs), which are found when comparing
abundances derived from recombination lines and from collisionally excited
lines, both in Galactic and extragalactic HII regions. We derive bounds of
10^{13}--10^{15} cm on the droplet sizes inside HII regions in order that (1)
they should not have already been detected by direct imaging of nearby nebulae,
and (2) they should not be too swiftly destroyed by diffusion in the ionized
gas. From photoionization modelling we find that, if this inhomogeneous
enrichment scenario holds, then the recombination lines strongly overestimate
the metallicities of the fully mixed HII regions. The abundances derived from
collisionally excited lines also suffer some bias, although to a much lesser
extent. In the absence of any recipe for correcting these biases, we recommend
the discarding of all objects showing large ADFs from studies of galactic
chemical evolution. These biases must also be kept in mind when comparing the
galactic abundance gradients for elements derived from recombination lines with
those derived from collisionally excited lines. Finally, we propose a set of
observations that could be undertaken to test our scenario and improve our
understanding of element mixing in the ISM.
