  We study the mixing of chemical species in the interstellar medium (ISM).
Recent observations suggest that the distribution of species such as deuterium
in the ISM may be far from homogeneous. This raises the question of how long it
takes for inhomogeneities to be erased in the ISM, and how this depends on the
length scale of the inhomogeneities. We added a tracer field to the
three-dimensional, supernova-driven ISM model of Avillez (2000) to study mixing
and dispersal in kiloparsec-scale simulations of the ISM with different
supernova (SN) rates and different inhomogeneity length scales. We find several
surprising results. Classical mixing length theory fails to predict the very
weak dependence of mixing time on length scale that we find on scales of
25--500 pc. Derived diffusion coefficients increase exponentially with time,
rather than remaining constant. The variance of composition declines
exponentially, with a time constant of tens of Myr, so that large differences
fade faster than small ones. The time constant depends on the inverse square
root of the supernova rate. One major reason for these results is that even
with numerical diffusion exceeding physical values, gas does not mix quickly
between hot and cold regions.
