A finite element formulation to model the flow of flotation foams

• Published in: Chemical engineering science 2012-02, Vol.69 (1), p.279-286
• Main Authors: Brito-Parada, P.R., Kramer, S.C., Wilson, C.R., Pain, C.C., Neethling, S.J., Cilliers, J.J.
• Format: Article
• Language: English
• Subjects: Applied sciences; Chemical engineering; equations; Exact sciences and technology; Finite element methods; Flotation; Foam; foams; Hydrodynamics of contact apparatus; Mathematical modelling; mathematical models; Separations; Simulation; Solid-solid systems
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/j.ces.2011.10.047

In this paper, a numerical model for the flow of foams in flotation cells in up to three dimensions is described. By using finite elements to solve Laplace's equation for a potential scalar, the flow pattern and velocity of the foam can be obtained. This has allowed, for the first time, the carrying out of numerical investigations of foam flow patterns regardless of the symmetry of the system. The numerical model has been implemented in Fluidity, a general purpose finite element method code that allows simulations to be carried out on anisotropic unstructured meshes. Such a model is of particular interest since other phenomena occurring in flotation depend on the foam velocity. Convergence tests that verify the numerical model are presented, and simulation results that showcase important features of the present implementation are discussed. ► A finite element model for the flow of flotation foams in two and three dimensions. ► Unstructured anisotropic meshes to resolve foam velocity gradients. ► Quadratic and linear convergence for the potential and velocity fields respectively. ► Anisotropic mesh adaptivity results in an efficient use of computational resources.