https://doi.org/10.1140/epje/s10189-026-00573-z
Research - Flowing Matter
Formation of cylindrical shells via sphere packing from fluidized beds
1
Faculdade de Engenharia Mecânica, UNICAMP-Universidade Estadual de Campinas, Rua Mendeleyev, 200, Campinas, SP, Brazil
2
Laboratoire PIMM, CNRS, Arts et Métiers Institute of Technology, 151 boulevard de l’Hôpital, Paris, France
3
Faculty of Physics, Duisburg, Germany
a
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Received:
13
November
2025
Accepted:
27
February
2026
Published online:
3
April
2026
Abstract
The results of a numerical investigation of fluidized beds of spherical particles in a narrow vertical cylindrical pipe, with particular attention to the spontaneous settling along the wall, are reported. Starting from a steady fluidized state, the particles fluctuate because of fluid-particle, particle-particle, and particle-wall interactions. The particles are heavier than the fluid, with diameters d yielding ratios of pipe to particle diameters 
and 4.7. For given ranges of flow velocities and bed sizes, particles settle on the wall, with a decrease in the bed height and particle fluctuations. Either a glass- or crystal-like shell forms along the pipe wall, in qualitative agreement with previous experiments. The polydispersity and the particle-particle friction are varied to test the stability of the particulate shell formation. The shell structure is analyzed by unwrapping it in a plane and locating all particles and their contact points, and we find that it exhibits a hexagonal lattice with a defects density that increases with polydispersity. The shell formation is hindered by polydispersity, and there exists a critical point for polydispersity above which a crystal-like shell is unstable. In a particular case of bidisperse beds, the crystal-like shell only appears when the particle-particle friction is high enough. Finally, we compute the contact forces within particle-particle chains and in particle-wall contacts, which sustain the cylindrical shell, highlighting the dominant role of particle-particle forces.
© The Author(s) 2026
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