Modeling the Terminal Velocity of Rising Electrocharged Microbubbles

The generation of electrocharged microbubbles is very important for several separation processes (e.g., water treatment, paper industry, and mineral processing). However, their rising terminal velocities are not fully understood. This work presents a laboratory study of the terminal velocity of single microbubbles (bubble diameter (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></semantics></math></inline-formula>) < 100 µm) rising in stagnant aqueous solutions with different pH levels (from 2 to 12) and reagent types (frother and collector; 30 ppm). The measurements were compared with the respective predicted velocities computed from the Stokes and Hadamard–Rybczynski models. It was found that the terminal velocities of electrocharged microbubbles were larger than the respective predictions from the Stokes equation. A regression equation was proposed to predict the terminal velocity as a function of the bubble diameter, which showed considerable dispersion depending on the type of reagent adsorbed on its surface, the concentration of these reagents, and the physical characteristics that the boundary layer acquires by modifying the zeta potential of the microbubbles; this effect has not yet been addressed in the literature.