Extending the concept of machine acceleration used to model the bubble-particle detachment in flotation. Part 2 – Machine acceleration of solid particles in water

Abstract

The machine acceleration introduced by H. J. Schulze has been a cornerstone of the bubble-particle (BP) detachment theory. It connects the mean dissipation rate of turbulence energy of water in a flotation machine with the BP detachment. In a recent paper, we scrutinized the theory and recommended its extension to cover both the longitudinal (centrifugation) and transverse (shear) effects of water turbulence. Since there is a significant difference in the densities of water, solid particles, and air bubbles, it is unknown if the available determination of the machine acceleration using the “water particles” is a good approximation for the bubble-particle aggregates. This paper aims to provide an answer to this fundamental question. For simplicity, this paper focuses on the acceleration of solid particles in water. Specifically, we use the Basset-Boussinesq-Oseen equation to quantify the particle acceleration. The correlation method in combination with the isotropic turbulence theory is applied to predict the particle acceleration components for the full range of turbulence length scale. Comparing with Schulze’s model, our recent model shows that the particle inertia should be considered in calculating the machine acceleration, especially for large and/or heavy particles and high energy dissipation rate. Our numerical results show that the machine acceleration decreases with increasing particle size and density and increases with increasing dissipation rate of turbulent kinetic energy and turbulence intensity.