Predicting air recovery in flotation cells S.J. Neethling * , J.J. Cilliers Royal School of Mines, Imperial College London, London SW7 2AZ, United Kingdom article info Article history: Received 4 December 2007 Accepted 29 March 2008 Available online 16 May 2008 Keywords: Flotation froths Modelling abstract In this paper, a simple theoretical model for the fractional air recovery to the concentrate in flotation froths is presented. The model assumes that two forces are exerted on the films, one from the curvature of Plateau borders and the other from the stretching of the films. It is further assumed that there is a crit- ical pressure above which the films will fail. This model predicts that there is expected to be a maximum in the air recovery as the air rate is increased, which is indeed observed experimentally at a number of industrial flotation plants. This maximum in air recovery does not correspond to a maximum in the inher- ent stability of the films and occurs even if this stability is constant, though having a film stability that changes with air rate causes some interesting changes in the behaviour of the system. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction The recovery of air is defined as the amount of air entering a flo- tation cell that overflows the lip as unburst bubbles. It is an impor- tant, though often overlooked, factor in the performance of flotation cells. Air recovery has a direct influence on the overall recovery of the cell, seeing that it is a major factor in the amount of material becoming detached from the bubble interfaces. It also has an im- pact on the grade of the concentrate, as it is one of the parameters that dictates the amount of water, and thus gangue, recovered to the concentrate (Neethling et al., 2003). In this paper a model that couples expressions for film stability and drainage with existing models for Plateau border liquid drain- age will be used to explain some of the interesting experimental trends observed in the air recovery as the air rate into the cell is varied. 2. The model Predicting air recovery requires that the stability of the films at the froth surface be modelled. In order to do this, both the force that the film can withstand, as well as the forces exerted on the films need to be considered. In foams or froths, there is a critical pressure above which films will drain to a thickness at which they fail and below which they will not fail. This is the disjoining force that must be overcome in order for the films to fail, DP crit . In 2-phase foams this disjoining force is the result of interactions between the surfactant molecules on the air–water interfaces, typically taking the form of double layer interactions. In 3-phase systems, such as flotation froths, the stability is usually provided by the particles, with steric inter- actions between the particles keeping the interfaces apart. In flotation froths, the heterogeneous nature of the particles means that there is likely to be a distribution of pressures at which different films will fail. For the sake of simplicity, though, a single critical pressure above which films will drain to failure will be used. Two sources for the pressure exerted on the film will be consid- ered. The first comes from the curvature of the Plateau borders and the second from the stretching of the films as the flow diverges. 2.1. The capillary pressure exerted by Plateau borders The curvature of the Plateau borders exerts a pressure on the li- quid within the films. This is because the curved interface of the Plateau border means that there is a lower pressure in the liquid than in the gas. Since the lamellae have far lower curvatures than the Plateau borders, surface tension does not support the pressure difference and a force is exerted that attempts to collapse the film and is opposed by the disjoining force. The pressure exerted by the Plateau borders is proportional to the surface tension, c, and inversely proportional to the radius of curvature of the Plateau borders, r PB : DP PB ¼ c r PB ð1Þ As it is the air recovery that is being sought, it is the Plateau border curvature at the froth surface that is required. Standard foam drain- age theory will be used (e.g. Leonard and Lemlich, 1965 and Verbist et al., 1996) to estimate this curvature. In foams and froths, viscous losses occur as the liquid moves relative to the bubbles. This theory 0892-6875/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2008.03.011 * Corresponding author. Tel.: +44 2075949341. E-mail address: s.neethling@imperial.ac.uk (S.J. Neethling). Minerals Engineering 21 (2008) 937–943 Contents lists available at ScienceDirect Minerals Engineering journal homepage: www.elsevier.com/locate/mineng