Soni, V. H.,Ketisch, P. M.,Rodriguez, J. D.,Shpunt, A.,Hubler, A. W.
Under an electric field, spherical conducting particles in a dielectric liquid assemble into a dendritic tree in order to dissipate charge. Several topological measures characterize such networks, including degree distributions, Strahler numbers, and total external pathlengths. Here, scaling laws relating these measures to the number of nodes in the system are presented and shown to match diffusion limited aggregation (DLA) structures. Experimental bifurcation and stream-length ratios in this easily reproducible laboratory experiment are found to agree with DLA simulations and Horton's laws for river networks. Certain scaling relations in transportation networks are known to originate from general features of networks. Here we find the experimental structures share properties with hydrological drainage networks.