Experimental determination of the random-parking limit in two dimensions

Abstract

The two-dimensional random-parking limit is the area fraction of a plane covered by circles when the circles are added sequentially in a random way, without overlap, until no further circles can be added. As yet, no analytical solution exists for this limit. Several computer simulations and one experimental study have been carried out in the past, with results varying from 50% to 62% for the parking limit. In our work, we carry out an experimental determination of this parking limit, utilizing a spherical colloid that sticks irreversibly to a flat substrate. The experimental value obtained is 0.55±0.01, which agrees with two of the most recent, computer-generated values. © 1986 The American Physical Society.