Understanding Froth Behaviour with Cfd

This paper will discuss the use of CFD in foam and froth modelling. The physics of froths is introduced and the methodology of combining the models for each phase into a complete description is reviewed. The utility of the CFD model is illustrated in two ways: First the equations are solved explicitly, giving a clear interpretation of process variables and their importance. Second, an example of the use of froth CFD for equipment design is given. Both cases are compared with experimental data. The paper concludes by highlighting a number of important issues that remain to be addressed. INTRODUCTION Froth flotation is a particle separation process used for collecting selectively the small fraction of valuable mineral from a mixed ore. Froth flotation is based on differences in particle hydrophobicity and is the largest tonnage separation process worldwide. In flotation, the particles, after being finely ground and suspended in water (the pulp), are treated with a surfactant to make the sulphurbearing minerals hydrophobic. Air is blown into the pulp mixture, and the particles attach to the bubbles, rise to the surface and are collected continuously in an overflowing froth (the concentrate). Modern flotation tanks have a volume of 100m to 300m, and plants have 3 or 4 flotation stages, each with 6 to 10 tanks. Although occupying less than 10% of the flotation cell volume, the froth behaviour largely determines the fractional and relative recoveries of the valuable and waste minerals from the pulp to the concentrate. Design issues have included froth flow modification and addition of water to enhance the separation. To date, operating and design variables have been changed largely by empirical observation and trialand-error. This is not cost-effective and the potential for a CFD-model approach to froth flotation design and optimisation is significant. However, froths have unique properties that make their modelling difficult and which must be considered. This paper will describe first foam structure and the physics of flotation froths. The significant structural changes in the froth will be detailed. Models for the motion of the bubbles, the liquid and the solids will be introduced, and how they are combined to give a CFD-type description. The utility of the approach will be illustrated by extracting an explicit solution for the overflowing water rate that allows interpretation of observed industrial behaviour. Full CFD simulations will compare surface and internal wash-water distribution. The paper will also discuss the key outstanding issues in froth modelling, and the potential of implementing these. FOAM STRUCTURE AND PHYSICS The Structural Components: Lamellae, Plateau borders and Vertices Foams and froths structure is well-defined by the physics of minimal surfaces (Weaire and Huzler, 1999). Consider a vertical cross-section through a typical two-phase foam. The foam is formed by bubbles freely rising through the liquid until they meet the foam-liquid interface (Figure 1). Figure 1: Vertical cross-section through a typical flowing foam showing rapid decrease in liquid content and bubble growth In the lowest part of the foam, the bubbles are round and essentially a collection of close-packed spheres. The liquid content very rapidly drops above the interface and within a few bubble diameters the foam is significantly drier, where the bubbles take on an angular shape. These polyhedral bubbles coalesce when the lamella separating two bubbles fails. Plateau borders are channels formed where three lamellae meet. Because of surface tension, the angle between three lamellae forming a Plateau border is always 120o, and only three lamellae form a stable Plateau border. Plateau borders have a well defined shape, with a curvature determined by the liquid content and bubble size. Figure 2 shows the shape of a Plateau border. Four Plateau borders meet in a vertex, at the tetrahedral angle. Figure 2 shows a micrograph of a solidified liquid foam and for comparison the simulated shape of a vertex, based on minimum surface area calculations. The Plateau borders and vertices form an interconnected network of channels through the foam. The network of Plateau borders and vertices contains virtually all the liquid in a foam. The gasliquid interface curvature exerts a negative pressure on the lamellae and draws liquid into Plateau borders and vertices. Flotation froths should therefore be regarded as a network of liquid channels, the dimensions of which vary with liquid content and bubble size. The bubble size determines the Plateau border length per volume, λ, and is inversely proportional to the square of the bubble radius, R.