  Stellar and nebular abundance indicators reveal that there exists significant
abundance fluctuations in the interstellar medium (ISM) of gas-rich galaxies.
It is shown that at the present observed solar level of O/H $\sim 6 \times
10^{-4}$, abundance differences of a factor of two, such as existing between
the Sun and the nearby Orion Nebula, are many times larger than expected.
  We examine a variety of hydrodynamical processes operating at scales ranging
from 1 pc to greater than 10 kpc, and show that the ISM should appear better
homogenized chemically than it actually is: $(i)$ on large galactic scales (1
$\geq\ l\ \geq$ 10 kpc), turbulent diffusion of interstellar clouds in the
shear flow of galactic differential rotation is able to wipe out azimuthal O/H
fluctuations in less than $10^9$ yrs; $(ii)$ at the intermediate scale (100
$\geq\ l\ \geq$ 1000 pc), cloud collisions and expanding supershells driven by
evolving associations of massive stars, differential rotation and triggered
star formation will re-distribute and mix gas efficiently in about $10^8$ yrs;
$(iii)$ at small scales (1 $\geq\ l\ \geq$ 100 pc), turbulent diffusion may be
the dominant mechanism in cold clouds, while Rayleigh-Taylor and
Kelvin-Helmhotz instabilities quickly develop in regions of gas ionized by
massive stars, leading to full mixing in
