Determination of the mass transfer rate constant in a laboratory column flotation using the bubble active surface coefficient

This study aimed to introduce a new approach to determine the mass transfer rate constant in a laboratory column flotation through an analogy to a mass transfer process. The RTD of the column at two separate bubble sizes were modeled using both conventional N-mixer and N-mixer with back-mixing flow models. The number of perfect mixers (N) and the corresponding backflow coefficients (λ) were optimized using MINLP solver in MATLAB environment where N = 5 with λ = 0.567 at the bubble size of 1.8 mm and N = 8 with λ = 0.643 at the bubble size of 0.8 mm were obtained. The bubble active surface coefficient was introduced as a new parameter to study the flotation kinetics. Thus, the mass transfer rate constant was determined for various operational conditions based on the bubble active surface coefficient and bubble loading measurements. Results showed that the mass transfer rate depends on the physical and surface properties such as particle size, particle surface hydrophobicity, and the carrying capacity. At the fine particle size, the mass transfer continues such that a long bubble retention time is required. However, for the coarse particles, bubbles reach their maximum loading capacity prior to the pulp-froth interface so that any additional retention time does not contribute to the flotation. Besides, at the coarse particle size, due to the poor stability of the aggregates, especially for particles with low surface hydrophobicity, the mass transfer rate and thereupon the bubble loading decreases remarkably. Moreover, the fine particles show lower flotation kinetics in the presence of the large bubbles.