An analog to Bond number for pendant nanodrops

It is argued that the Bond number, which is widely used for the qualitative description of the shape and stability of a pendant macroscopic drop, is not appropriate to characterize a nanodrop. The new number, called Rb, is introduced in a heuristic manner using the results obtained for nanodrops on the basis of density functional theory. Unlike the Bond number which involves surface tension of the liquid, Rb depends on microscopic parameters of the liquid-liquid and liquid-solid interactions. It also involves gravitational acceleration G, number of molecules in the system, as well as roughness of the solid surface. Some possible applications of Rb are discussed. In particular, it is shown that Rb can be used for estimation of the range of the nanodrop stability with respect to the magnitude of G.