Arching effect model for particle size segregation

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Abstract
Starting from 2D experimental observations and using topological arguments, we search for the set of stable positions when a large disk is raised step by step among a 2D array of small monodisperse disks. We show and confirm experimentally that larger disks should move upward continuously via the arching effect whereas smaller disks may only climb up intermittently. We find the critical diameter ratio for a continuous ascent in 2D and 3D. Our model sheds a new light on the decisive role played by vaults in particle size segregation.