Microhydrodynamic analysis of nanogrinding in stirred media mills

The dynamics of the milling media in a turbulent flow is considered. The mean velocity of the milling beads is calculated on the assumption that the power spent on stirring is transferred into the energy of turbulent eddies. The energy spent on stirring dissipates as a result of media-liquid viscous friction, lubrication, and by inelastic collisions of the beads with each other. The maximum force at which the milling beads can compress particles between them is calculated by the Hertzian theory of elastic impact. The frequency of compressions for a single particle is evaluated by probabilistic analysis. A criterion of milling efficiency, based on calculating the energy spent on the plastic particle deformation, is proposed. A numerical study of the milling bead dynamics and their interactions with the particles in the mixing tank is performed. The numerical results are in qualitative agreement with the experimental data. Both the numerical and experimental analyses show that, from the perspective of hydrodynamics, an optimization of stirred media mills can be achieved bv choosing the optimum size and concentration of the milling media.