Node dynamics and cusps size distribution at the border of liquid sheets

We study the intrinsic dynamics of cusps, or indentations, moving along a liquid sheet border, and characterize their ensemble statistics. Gordillo and collaborators [J. FluidMech. 754, R1 (2014)] have shown that the symmetrical stationary cusp is the only structure accommodating for both mass and momentum conservation at a steadily receding liquid sheet rim. Cusps are also known to typically move along a sheet border, to present an asymmetry, and to be distributed in size around amean. We show here why a heterogeneous assembly of cusps traveling along the sheet rim occurs spontaneously, why big and small cusps coexist at the same time, and, more precisely, we establish a specific link between the microscopic dynamics directing their motion, and the ensemble averaged distribution of their sizes.