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.