Polydispersity exponent in homogeneous droplet growth

The homogeneous growth of D-dimensional hyperspherical droplets on a d-dime nsional surface produces a bimodal distribution in the sizes of the droplet s, with a roughly monodispersed distribution of larger droplets superimpose d on a highly polydisperse distribution of smaller ones. The polydisperse r egime is characterized by an exponent, which also determines the total drop let density. The exponent is evaluated, and it is deduced that d = 3 repres ents an upper critical dimensionality.