Break-up of bubble clusters in turbulent flow—Theory

• A model to describe the behaviour of clusters is developed.
• The model is based on the balance between the disruptive force the cohesive force.
• The Camp and Stain's equation shows a best fit to the experimental data.
• The model provides an easy way to predict the cluster size in industrial flotation cells.

The behaviour of bubble clusters in turbulent conditions has been studied theoretically. The cluster behaviour was modelled based on concept drawn from the related field of bubble breakup. It was assumed that the bubbles were bridged by particles, so the cohesive strength was determined by the capillary force between the bubbles and the particles. Two different theories were investigated for the disruptive force from the turbulent liquid: the shear rate hypothesis of Camp and Stein (1943), and the turbulent fluctuation model arising from Kolmogorov's theory of isotropic turbulence (Kolmogorov, 1941). It was found that neither method is applicable in the fragmentation stage. However, in the equilibrium stage, an equation derived from Camp and Stein's theory was more realistic than that obtained using Kolmogorov's equation.

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