same volume filling factor (and thus $C$ value). As expected we find that the clouds evaporate faster, leading to smaller values of $\tau$.

While our discussion above indicates that $\tau$ should be roughly constant, we find that it evolves considerably over the course of SNR evolution. This is not too surprising since, especially for the 2D evolution, a small number of clouds is encountered and the location and size of the clouds affects the evaporation rate. This is demonstrated in Figures \[fig:tevap\] and \[fig:tau\_eff\] where we plot $\tau$, calculated two different ways, as a function of remnant age for a variety of our runs. The differences between the 2D runs can be attributed to the differences in the particular cloud realization for the runs with some with larger clouds placed closer to the origin and the spacing of clouds differing. As can be seen, the 3D runs show less variation between themselves and over time. This can be understood as deriving from the larger number of clouds encountered and thus more complete sampling of the cloud size distribution. A full volume 3D run would likely show an even smoother variation though the finite cloud volume would still be expected to 