Bubble shape in the prediction of terminal velocities in flotation

Abstract

Minerals flotation is a process that involves the formation of a population of bubbles to produce a concentrate by selective capture and separation of particles of valuable hydrophobic minerals on the surface of bubbles. The bubble rising velocity is a crucial piece of information for developing operating and control strategies, and for estimating metallurgical performance of flotation circuits. Bubble rising velocities depend on their size and on the physicochemical characteristics of the surrounding liquid medium. Velocities in pure liquids are the largest possible because gas-liquid interfaces remain clean and fully mobile allowing circulation of the gas phase, but when surfactants and ions from soluble mineral species are present (contaminated liquid), which is the case in minerals flotation, a molecular arrangement of adsorbed molecules develops on the surface of the bubbles. This structure reduces bubble surface mobility as internal gas circulation is restricted, velocity is reduced, and shape evolves from oblate spheroidal to spherical. Models proposed to predict the terminal velocity of bubbles have been devised, in general, for working at two extreme sets of conditions: bubbles rising either with fully mobile surfaces in pure liquids, or with rigid surfaces in highly contaminated liquids. The purpose of this work was the assessment of bubble velocity predictions of models that have been used in flotation applications; a data set of simultaneous measurement of velocity and shape of rising single bubbles under a broad set of conditions relevant for minerals flotation was used. The results demonstrated that bubble velocity and aspect ratio were intrinsically linked, and for bubbles of the same size, consistent trends between terminal velocity and aspect ratio that included measurements in frother and polymer solutions. Measurements in solutions of four frothers showed, as expected, significantly different terminal-velocity reduction trends as the frother concentrations were increased. This was considered as a demonstration that the frother molecular structure and the extent of equilibrium coverage were frother dependent. Model assessment demonstrated that prediction of terminal velocities was not possible for contaminated solutions with frother concentrations below the levels that get bubble surfaces fully covered. The measurements collected in this work were used to develop an empirical model for predicting bubble velocities as a function of aspect ratio; the comparison of measured and predicted velocities had a correlation coefficient of 0.9987.