Polydispersity exponent in homogeneous droplet growth

The homogeneous growth of D-dimensional hyperspherical droplets on a d-dimensional surface produces a bimodal distribution in the sizes of the droplets, with a roughly monodispersed distribution of larger droplets superimposed on a highly polydisperse distribution of smaller ones. The polydisperse regime is characterized by an exponent, which also determines the total droplet density. The exponent is evaluated, and it is deduced that d = 3 represents an upper critical dimensionality.