Formation of cylindrical shells via sphere packing from fluidized beds

TL;DR

This numerical study investigates how spherical particles in fluidized beds spontaneously form stable, hexagonally ordered cylindrical shells along the pipe wall, influenced by polydispersity and friction.

Contribution

It reveals the conditions under which crystal-like shells form or break down, including effects of polydispersity and friction, and analyzes the contact forces maintaining these structures.

Findings

Shells form along the pipe wall with hexagonal lattice structure.

Polydispersity increases defect density and can destabilize shells.

High particle-particle friction enables shell formation in bidisperse beds.

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 D/d=4.3 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.