I was reading about random close packing of spheres on Wikipedia and Wolfram Mathworld, and if I did not interpret both incorrectly, the conclusion is that if I pack a volume V randomly with spheres, the spheres will occupy a volume of approximately 0.6V.
I feel like I am missing something because I would expect the volume fraction occupied by the spheres to be larger if the spheres were smaller (in the extreme case, if each sphere were the size of a water molecule, packing with spheres would be the same as filling the volume with a fluid). Is there something I'm missing in the definition of packing density that gives a size dependence?
The volume fraction constant is not dependent on the size of the spheres because the scaling transformation which transforms larger spheres into smaller ones scales the volume of the spheres with exactly the same constant that it scales the volume of the spaces between the spheres (the "voids" of the packing) --- so the ratio is unaffected.
Your intuition is only correct when the volume being packed is finite and and not very large compared to the volume of an individual sphere. The references you cite discuss instead the case of the limit as V becomes all of $\mathbb R^3$, which has infinite volume.