By employing a torque sensor to measure energy input in a flotation machine, this paper investigates the flotation behavior of modified quartz particles with different sizes but similar surface hydrophobicity under various energy input conditions. Numerical simulations of the mechanical flotation machine were conducted to obtain the fluid dynamic characteristics including the flow velocity, turbulence kinetic energy, and turbulent eddy scale. With the flotation results and numerical simulations combined, the potential collision, attachment, and detachment behaviors of fine particles (―45 µm), intermediate particles (45―74 µm), and coarse particles (74―125 µm) were analyzed. The results demonstrate that under different conditions of energy input, the recovery of intermediate-sized particles was optimal for the above size fractions. As the particle size increases, the energy input required to achieve optimal recovery decreases. The flotation rate constants increase nearly linearly with energy input. Compared to the medium-sized particles in the range of 45―74 µm, finer and larger particles exhibit lower floatability. When the energy input exceeds a certain range, no stagnation zone is observed. The rupture of bubble-particle aggregates becomes more pronounced, which may be a reason why flotation recovery begins to decrease. Increasing energy input enhances turbulence energy dissipation and reduces the Kolmogorov turbulence length scale, in this study, the ―45 µm, 45―74 µm, and 74―125 µm particle sizes reached the optimal flotation performance at dp / η values of 1.35, 1.83, 2.54, respectively. The particle diameter-to-integral length scale ratio (dp/L) is also discussed as an important parameter for turbulent dispersion.
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