Effect of hydrodynamic parameters on particle-bubble interactions in flotation

The current thesis studies the impact of particle and bubble characteristics as well as cell hydrodynamic properties on particle-bubble interactions. Additionally, it investigates the estimation and optimization of the encounter probability of particle-bubble (Ec) and flotation rate constant (k) in the presence and absence of turbulence by means of response surface method (RSM). The present work comprehensively compiles the previous studies implemented on determination and assessment of Ec in laminar and turbulent fluid flows by means of analytical (streamline-based concepts), numerical (CFD and DEM) and practical methods (direct and indirect approaches). The effects of some significant factors such as particle size (1-100µm), particle density (1.3-7.1g/cm3), bubble size (0.05-0.15cm) and velocity (10-30cm/s), bubble surface mobility (contaminated and non-contaminated) and turbulence dissipation rate (18, 21, 24, 27, 30m2/s3) on the Ec and k are investigated in detail. The comparison between three common methods for estimation of Ec revealed that the analytical modeling mainly disregard the microhydrodynamic (µHM) resistance forces and particle trajectory together with its angle of tangency in greater Stokes values. However, the best correlation among numerical and analytical modeling is obtained in the rangee of fine and ultra-fine particles due to low impact of inertial forces. Initially, it is found in this work that omitting water inertial forces results in two to four times greater estimation of flotation rate constant as a function of particle diameter (dp), particle density (ρ_p) and their synergetic effects. For the first-time, the intersection of three collision models (i.e. Sutherhland, Schulze and Dukhin) is suggested as an alternative method for estimating the critical Stokes number (Stcr) as a function of bubble surface properties (bubble size, its diameter and mobility). The results of the presented approach highly comply the data given by Stokes. Also, the exact thresholds for identifying the positive and negative effects of particle inertia are reported. It is found from optimization processes that particle density plays an opposite role on Ec which implies further studies for more clarification. Also, under a limited hydrodynamic circumstances in a flotation cell, particle inertial effect can be solely ignored to a certain extent. The predicted Ec values are sub-classified in three main zones, i.e. low (0-4%), intermediate (4-8%) and high (8-14%) regions with respect to the role of bubble size (dB) and its velocity (vB). Using a combination of Yoon-Luttrell's collision (E_c^YL) and attachment (E_a^YL) models leads to overestimation of collection efficiencies in comparison with generalized Sutherland equation (E_c^GSE) and modified Dobby–Finch (E_a^DF) models. Moreover, the relative significance of key factors (particle size, bubble diameter, bubble velocity, particle density and turbulence) on Ec and k is shown for the first time to be incoherent in the literature.