Time of gas–solid–liquid three-phase contact expansion in flotation

Abstract The elementary step of gas–solid–liquid three-phase contact (TPC) expansion in bubble–particle attachment is theoretically and experimentally investigated. The TPC expansion is theoretically described using the extended molecular-kinetic theory [Nguyen, A.V., Stechemesser, H., Zobel, G., Schulze, H.J., 1997a. Order of three-phase (solid–liquid–gas) contact line as probed by simulation of three-phase contact line expansion on small hydrophobic spheres. J. Colloid Interface Sci., 187: 547–550.], which involves the effect of three-phase contact line tension on the TPC expansion with a small wetting radius. A theoretical model for the time of the TPC expansion is proposed and compared with the experimental data. Our data shows that the TPC expansion kinetics in flotation is strongly controlled by line tension, along with particle hydrophobicity. This is consistent with the results of the earlier investigation of the line tension effect on flotation by Scheludko et al. [Scheludko, A., Toshev, B., Bogadiev, B., 1976. Attachment of particles to a liquid surface (Capillary theory of flotation). J. Chem. Soc., Faraday Trans. 1, 72: 2815–2828.]. The line tension obtained in this paper is close to the reported data for similar systems [Li, D., Neumann, A.W., 1990. Determination of line tension from the drop size dependence of contact angles. Colloids Surfaces, 43: 195–206; Duncan, D., Li, D., Gaydos, J., Neumann, A.W., 1995. Correlation of line tension and solid–liquid interfacial tension from the measurements of the drop size dependence of contact angles. J. Colloid Interface Sci., 169: 256–261.] and depends on the interfacial energies of the solid–liquid and gas–liquid interfaces. TPC expansion is an important elementary step in particle-bubble attachment and has to be taken into consideration in modelling and predicting the probability of particle-bubble attachment in flotation.