Heinrich Schubert

On the turbulence-controlled microprocesses in flotation machines

Abstract In flotation machines, the operation takes place in a highly turbulent flow. Therefore, the modelling as well as the optimization of a flotation process necessitate the application of essential results of the statistical turbulence theory, where an extensive simplification of the complicated laws is typical for the application in processing. Three effects of turbulence are important in flotation: the turbulent transport phenomena (suspension of particles), the turbulent dispersion of air and the turbulent particle–bubble collisions. While the transport phenomena are mainly caused by the macroturbulence, the microturbulence controls the two last-named microprocesses. In the paper a brief introduction of the theoretical background is given as far as it is necessary for modelling. The effect of turbulence damping by fine particles is also discussed. Models of the microprocesses air dispersion and particle–bubble collisions are presented, and it is clearly demonstrated that the particle–bubble attachment almost exclusively occurs in the zone of high energy dissipation rates, i.e., in the impeller stream. Further on, it is shown that the entrainment of fine particles into the froth lamellae is a result of the suspension state and, therefore, can be influenced by the design of the turbulence generating system (impeller–stator system). Finally, it is demonstrated that there is no feasibility to achieve optimum hydrodynamics for all particle sizes simultaneously. For coarse particle flotation, the power input should be minimized (generation of coarser bubbles; stronger buoyancy and lower turbulent stresses acting on the particle–bubble agglomerates!). In contrast to this, fine particle flotation requires high turbulent collision rates, i.e., a higher power input.

On the microprocesses air dispersion and particle-bubble attachment in flotation machines as well as consequences for the scale-up of macroprocesses

Abstract By means of considerations, experimental results as well as high-speed photographs it is shown that in flotation machines the zone of high local energy dissipation, i.e. the impeller stream, is the active region for the realization of the microprocesses bubble dispersion and particle-bubble attachment. Because of the pressure differences as well as the turbulent pressure fluctuations existing there, it is not unlikely that gas precipitation influences the attachment events substantially. Outside of the impeller stream, the local energy dissipation is so far reduced below the mean dissipation ϵ = P m that the preconditions for realizing these microprocesses, which are controlled by turbulence, are no more met. However, these phenomena call for further explanation. It seems to be very likely that the widespread and too simplistic ideas on the course of the particle-bubble attachment need substantial adjustments and/or completions. Moreover, the consequences which result from these findings for the hydrodynamic scale-up are discussed.

On the Origin of “Anomalous” Shapes of the Separation Curve in Hydrocyclone Separation of Fine Particles

In hydrocyclone separation, the fine end of the separation curve T(d) frequently becomes a line parallel to the abscissa of the diagram at T > 0, which is caused by the turbulent flow character of the hydrocyclone flow. But in the classification of feeds <100 µm in small-diameter cyclones, several authors have found curve shapes that show a minimum in the range of about 10 µm or below and a rising of the curve again towards the finest end. This phenomenon is called the fishhook effect. Toward this end, a model is presented based on the flow forces having an effect on fine particles in the zones of the shear gradients (boundary layers) around settling coarser particles. These forces have an attractive component so that “swarms” enriched by fine particles can form around coarser ones. As a first approximation, the Reynolds range of the settling coarse particles where swarm formation can occur is suggested as Re P ≈ 0.5 to 25. The upper limit is given by beginning separation of the flow around the coarse particles, the lower limit by the requirement of inertia effects. Such a swarm is a dynamic association, which is in continuous exchange with its vicinity by particle motions (directed and diffusive motions). From the influence of dynamic lift force F D, a reduction of the mobility of the fine particles results in the swarms; consequently, an increase of their retention time as well as concentration is observed. The presented approach of swarm formation is verified by extensive test results using quartzite of different size distributions as materials. Finally, on the basis of the new approach an explanation can be given why this effect could only be found in almost every case at the classification in small-diameter hydrocyclones.