The capillary force between a bubble and a cubical particle

The force of attraction between a bubble and a captured particle in flotation, is determined by the behaviour at the three-phase contact line on the surface of the particle. Capillary forces provide stability to bubble-particle aggregates in flotation. Although the force of attraction can be found analytically for spheres, no such calculation is available for cubes or other shapes with sharp corners or edges. At a sharp edge, the angle between the gas–liquid interface and solid–liquid surfaces is not generally the same as the contact angle due to pinning. The capillary force on a particle at a free surface has been calculated using Surface Evolver software to find the shape of the gas–liquid interface by minimising the surface energy subject to specified constraints. The simulation results compare very well with experimental data. The results show that pinning of the three-phase contact line on sharp-edged particles such as cubes and hexagons provides greater stability than is found with spherical particles of the same wetted perimeter. The technique can readily be extended to particles of greater complexity, such as composite partially liberated particles, that are generally found in flotation.

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► Method presented for calculating the capillary force of attraction between bubble and cubical particle.
► Shape of gas–liquid interface near a hydrophobic surface is found by minimising energy of the system.
► Model incorporates pinning of contact line at corners and edges.
► Excellent agreement between theory and experiment.
► Method can be used to calculate force between bubbles and composite particles.