Determination of the collision frequency between bubbles and particles in flotation

Collision efficiency for a spherical bubble rising in a uniform concentration of small non-inertial particles is studied by direct numerical simulations (DNS). The Stokes number of the particles is negligibly small so that the particle trajectories follow the streamlines. The effect of the bubble interface contamination is studied for the flow surrounding the bubble using the spherical cap model. Numerical results are obtained for a wide range of bubble Reynolds number (based on bubble diameter dbdb) ranging from 0.01 to 1000 and for different angles of contamination ranging from 0∘0∘ to 180∘180∘. The collision efficiency is found to be increased with the Reynolds number and significantly decreased with the level of contamination. Correlations of the numerical results are proposed for efficiencies versus dp/dbdp/db (dpdp being the particle diameter), bubble Reynolds number and interface contamination degree. For clean (respectively, fully contaminated) spherical bubbles, the efficiency evolves as dp/dbdp/db (respectively (dp/db)2)(dp/db)2) whatever the bubble Reynolds number and the particle size. For partially contaminated bubbles, efficiency can be scaled with dp/dbdp/db or (dp/db)2(dp/db)2 depending on both the level of contamination and the particle size.