The Stefan-Reynolds Model and the Modified Stefan-Reynolds Model for Studying Bubble-Particle Attachment Interactions in the Context of Flotation.

Bubble-particle attachment is the key step for successful flotation. Modeling of attachment interactions between air bubbles and particles after their collision can be analyzed using the Stefan-Reynolds model (immobile bubble surfaces) and the modified Stefan-Reynolds model (mobile bubble surfaces). However, these models have been rarely used, and the limitations of these models have not yet been reported. The objective of this paper is to address this matter under a wide range of experimental flotation conditions. It was found that the Stefan-Reynolds model can be used to determine the real bubble-particle hydrophobic constants at low surfactant concentrations. However, at high surfactant concentrations, the real bubble-particle hydrophobic constants cannot be determined, but the fictive bubble-particle hydrophobic constants can be obtained by using the linear extrapolation method. The same analysis was also performed using the modified Stefan-Reynolds model. The results showed that the attachment of quartz particles to air bubbles in the presence of dodecyl amine hydrochloride is accelerated due to the mobility of the air-water interface. This paper demonstrated that the limitations of the Stefan-Reynolds model and the modified Stefan-Reynolds model to analyze the bubble-particle attachment interactions can be addressed by introducing the fictive bubble-particle hydrophobic constants.