Quantification of Attachment behavior of Hydrophobic Mineral Surface to Air Bubble in Flotation

Abstract

The attachment of air bubbles to hydrophobic mineral surfaces in water is an important factor in the flotation process. Therefore, a quantitative analysis of bubble-hydrophobic mineral surface attachment interactions would be beneficial for improving flotation efficiency. The attachment process consists of three steps: drainage of the liquid film between the bubble and the surface, liquid film rupture, and three-phase contact line (TPCL) expansion. Many previus studies experimentally quantified the attachment interactions between hydrophobic minerals and air bubbles by measuring the surface forces generated in the drainage step, or the attachment time, which is the time required for completion of the entire attachment process. However, theoretical quantification relevant to the attachment of hydrophobic mineral surfaces to bubbles remains challenging, as the hydrophobic force (or hydrophobic attraction) cannot be described by the foundational DLVO theory. It has recently been observed that in water, hydrophobic surfaces adsorb dissolved gases to form an interfacial gas enrichment (IGE) layer. Additionally, the IGE of dissolved gases significantly contributes to attractive forces between solid hydrophobic surfaces, increasing in thickness as the hydrophobicity of the surface increases. Therefore, it has been suggested that the surface force of a hydrophobic surface can be calculated using the multilayer dispersion force (advanced van der Waals), after taking IGE layer thickness into account. In this study, the attachment time was quantitatively analyzed by employing the film drainage model and surface force, which include the advanced multilayer van der Waals and electro-double layer forces. The attachment times of hydrophobic glass slides and hydrophobic galena surfaces were measured as a function of hydrophobicity, and were accurately determined from either the transient force curves, or transient film thickness as a function of time. The transient-force and transient-liquid film curves may be obtained using a tensiometer and high-speed camera, respectively. Critically, it was possible to accurately quantify the attachment time of bubbles attached to hydrophobic mineral surfaces using the transient force or transient film curves, and the advanced multilayer dispersion theory incorporating the IGE layer. In this study, the attachment behavior of the hydrophobic mineral surface and air bubble was quantified by the attachment force instead of the surface force. The attachment force is defined as the maximum force determined from the Laplace pressure and capillary forces, generated in the rupture and TPCL extension steps. The capillary force and Laplace pressure are strongly influenced by hydrophobicity, because they are governed by the contact angle, surface tension, TPCL, and curvature radius. Therefore, presumably it is possible to quantify the attachment behavior of the hydrophobic surface and the bubble by the attachment force. The attachment forces were measured between the air bubble and mineral surface, which were modified with surfactants to exhibit a range of hydrophobicities. Chalcopyrite and galena were used as the mineral surfaces, and their hydrophobicity was controlled by surface-adsorbed xanthates with variable hydrocarbon chain lengths. Hydrophobicity is represented by the static contact angle of water on the mineral surface. When the static contact angle is smaller than 90° the attachment force increases exponentially with increasing surface static contact angles, irrespective of mineral type or hydrocarbon chain length of the adsorbed xanthate. The hydrophobicity of the mineral surface was found to be the dominant factor for determining the attachment force. To quantify the measured attachment force theoretically, the attachment force model was developed using capillary forces and the Laplace pressure equation. The measured attachment forces were in good agreement with those calculated based on the derived attachment force model. As a result, attachment forces can provide quantitative information on attachment interactions between an air bubble and a hydrophobic mineral surface. Finally, micro-flotation experiments were performed to examine the relationship between the attachment force, time, and flotation kinetics, employing the same conditions as those of the attachment interaction experiments, to control surface hydrophobicity. The correlation between the flotation rate constant and the attachment time was exponential, while a linear relationship was observed between the flotation rate constant and the attachment force. That is, the measured and simulated attachment force and time can represent attachment interactions between a bubble and the hydrophobic mineral surface. This study allows for attachment interactions between a hydrophobic surface and bubble to be quantified by the attachment time and force. Furthermore, it enables evaluation of the effect of hydrophobicity on attachment of the hydrophobic surface to the bubble, and provides a rationale for the attachment mechanism. These findings can be applied to reagent choice and the optimization of operating conditions for the flotation process. Furthermore, as the theoretical attachment time and surface force calculated from the advanced van der Waals theory can be employed in the flotation performance model, it is possible to theoretically predict flotation efficiency.