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We study the mixing of chemical species in the interstellar medium (ISM).Recent observations suggest that the distribution of species such as deuteriumin the ISM may be far from homogeneous. This raises the question of how long ittakes for inhomogeneities to be erased in the ISM, and how this depends on thelength scale of the inhomogeneities. We added a tracer field to thethree-dimensional, supernova-driven ISM model of Avillez (2000) to study mixingand dispersal in kiloparsec-scale simulations of the ISM with differentsupernova (SN) rates and different inhomogeneity length scales. We find severalsurprising results. Classical mixing length theory fails to predict the veryweak dependence of mixing time on length scale that we find on scales of25--500 pc. Derived diffusion coefficients increase exponentially with time,rather than remaining constant. The variance of composition declinesexponentially, with a time constant of tens of Myr, so that large differencesfade faster than small ones. The time constant depends on the inverse squareroot of the supernova rate. One major reason for these results is that evenwith numerical diffusion exceeding physical values, gas does not mix quicklybetween hot and cold regions.Comment: 23 pages, 14 figures that include 7 simulation images and 19 plots,  accepted for publication at Ap

Mixing Timescales in a Supernova‐driven Interstellar Medium