The depletion potential in one, two and three dimensions

We study the behavior of the depletion potential in binary mixtures of hard particles in one, two, and three dimensions within the framework of a general theory for depletion potential using density functional theory. By doing so we extend earlier studies of the depletion potential in three dimensions to the cases of d=1 and 2 about which little is known, despite their importance for experiments. We also verify scaling relations between depletion potentials in sphere--sphere and wall--sphere geometries in d=3 and in disk--disk and wall--disk geometries in d=2.