I've seen a paper some years ago, where packing of circles of two different sizes on an infinite plane was considered.
The paper listed several cases with closed form expressions for the ratio of curvatures (or radii), the amount of small/large circle ratio and the density.
This was a math paper, I think it was new (after 1990 at least), but I'm not sure.
I can't find this paper right now, if you have seen it, please post a link.
So far I have only found a paper by physicists where they build a 'phase diagram' for the problem.
It's this paper:
Tom Kennedy "Compact packings of the plane with two sizes of discs", 2004
Just needed to use 'disk' instead of 'circle' when searching