3D waveforms and patterning behavior in thin monodisperse and multidisperse vertically-vibrated layers

Vibrofluidization in monodisperse granular materials is a hierarchical phenomenon involving different spatial and temporal behaviors, known to produce macroscopic structures with well-defined properties and high reproducibility. However, as witnessed by the paucity of relevant results in the literature, investigating the collective organization of particles across such different length and time scales becomes particularly challenging when multi-component systems are considered, i.e. if the considered vibrated material is not monodisperse. In this work, this problem is addressed through numerical simulation of the governing equations accounting for (dissipative) inelastic and frictional effects in the framework of a DEM (Discrete Element Method) method. Binary and ternary particle distributions are considered and, in order to filter out possible density-driven particle segregation or mixing mechanisms, particles are assumed to be iso-dense. The problem is initially analyzed through the coarse-grained lens of patterning behavior (supported by a Voronoi analysis for many representative cases) and then from a micromechanical level in which statistical data based on particle collisions and related dissipative effects are used to gain additional insights into the observed macroscopic trends. It is found that, starting from the initial traditional monodisperse case, the addition of particles with smaller sizes (while keeping the overall mass and depth of the considered layer almost unchanged) generally leads to a corrugation in the otherwise perfect symmetry of the original patterns, which is similar to that already seen in companion situations related to viscoelastic fluids. Moreover, while in the case of an initially hexagonal pattern, this topology is generally retained, in other situations, the initial perfection is taken over by less regular waveforms. Specific circumstances also exist where the initial square symmetry is lost in favor of a triangular symmetry. In all cases, segregation effects simply manifest as a preferential concentration of particles with larger size in an intermediate layer, which apparently behaves as a cohesive entity during each vibration cycle.