Sliding interaction and attachment efficiency of rising bubbles in a mineral particle-laden bed

Flotation kinetics are fundamentally governed by bubble-particle collision, attachment, and detachment interactions. This study presents a novel single-bubble flotation approach and a mathematical framework based on a mineral-laden bed to analyse and quantify the attachment interaction. It directly links the flotation rate constant to bubble-particle attachment efficiency by excluding the effects of collision and detachment interactions, thus creating favourable conditions for rapid flotation kinetics. To achieve this, simple experiments were designed with single bubbles introduced at the bottom of a Hallimond tube, rising through a stationary mineral particle bed. We developed, compared, and validated mathematical models incorporating analytical (non-inertial) and numerical (inertial) solutions for Stokesian and non-Stokesian particles. Using the non-inertial model for sliding time, we derived an induction time model and an attachment efficiency model to establish a connection with flotation kinetics data. Single-bubble flotation experiments confirmed the relevance of macroscopic flotation and microscopic bubble-particle attachment mechanisms. Our numerical and analytical analyses confirmed that the sliding time model is influenced by bubble size, while five approximate models showed differences regarding particle size. Notably, within the range of theoretical applicability, fluid drag exerted a more substantial influence on sliding time than particle inertia. The kinematic parameters of particle motion on the bubble surface were successfully quantified using our models. This novel flotation system and tool provide an integrated experimental and theoretical framework to investigate bubble-particle attachment and collection mechanisms, offering valuable insights for advancing flotation theory and developing high-efficiency flotation equipment.