Pareto distribution in the system of polyamide particle clusters on the water surface

The present article considers a theoretical model of the formation of the Pareto distribution in a system of two-dimensional polyamide structures on the water surface. Complexes of polyamide granules collide with each other on the surface, moving in background liquid flows caused by random thermal gradients in the liquid bulk. Small complexes with a size of fractions of mm become organized into clusters with a complex structure and a size of a few cm under the action of surface tension forces. Numerical calculation taking into account the decomposition of large clusters provides power-law distribution of the density of complexes over their area. The results of the theoretical calculation are confirmed by the experimental data.