Application of hydrodynamic lubrication in discrete element method (DEM) simulations of wet bead milling chambers

Abstract

Fine grinding in wet stirred media mills is a key operation in numerous industrial processes. During wet milling, grinding beads (typically millimetre scale) collide with each other under rapid agitation. These collisions transfer energy into the surrounding medium, a feed stream comprising a premixed slurry (a suspension of micron-sized particles), leading to a reduced particle size. Numerical simulation provides an opportunity to gain mechanistic insight by modelling the influences of grinding media, agitator speed and slurry rheology on the breakage. The multiphase nature of wet milling necessitates models that account for both the solid grinding beads and the slurry feed. Established fluid-particle coupled methods are in principle capable of doing this, but the need to resolve the large hydrodynamic lubrication forces between near-contacting beads demands extremely high fluid field resolution, leading to proliferating simulation size and cost. To address this challenge, a Discrete Element Method (DEM) simulation for a lab scale mill is presented in which the bead-bead interaction includes pairwise hydrodynamic lubrication in addition to frictional contact forces. The model accounts for multiphase effects in a simplified yet physically well-motivated way, circumventing the computational cost of a fully fluid-resolved model. A systematic model calibration against the laboratory mill is presented, and thereafter the model provides a good estimation for the empirical power draw across the full range of rotation speeds and considered feed viscosities. The differences in energy dissipation modes and the local distribution of collisions along the mill chamber are examined for the extreme viscosity condition, revealing that most energy dissipation is due to inter-particle forces acting tangentially (shearing and rolling) while highly energetic collisions (impact and torsion), relying on free flows and inter-bead mobility, are relatively unimportant.