Modelling the transient drainage of liquid in foams

Froth flotation is the largest tonnage separation process worldwide and is used for paper deinking, water purification and, particularly, mineral separation. One of the key aspects of the performance of flotation cells is the behaviour of the liquid within the froth, as it is crucial to the purity of the product and a major influence on the overall recovery. Nonlinearities in models for liquid motion in the froth make them complex to solve and existing numerical solutions have been in two dimensions at most. In order to predict the performance of industrial flotation cell designs, a three-dimensional solution for these equations is desirable. Moreover, the understanding of the process would be enhanced if a transient model were used to predict the dynamics of foam drainage. In this work, the equations for the liquid drainage have been rearranged in order to make them analogous to a compressible version of the Navier-Stokes equations, coupled to an equation of state. A model for predicting the movement of the flowing foam has also been developed, which is able to solve for the foam velocity in two and three dimensions. This has allowed the transient behaviour of liquid in flotation foams to be modelled using Fluidity, a general purpose finite element method code that allows simulations to be carried out on unstructured adaptive meshes. This is an important feature for improving the computational cost of modelling these systems, as there are boundary layers present in the process, whose size is independent of the scale of the flotation system being modelled. These models have allowed, for the first time, to carry out numerical investigations of drainage for arbitrary flotation tank geometries in up to three dimensions, and have been verified against analytical solutions and compared to laboratory scale experiments with satisfactory agreement.