Abstract 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.

中文翻译：

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使用气泡活性表面系数确定实验室柱浮选中的传质速率常数

摘要 本研究旨在引入一种新方法，通过类比传质过程来确定实验室柱浮选中的传质速率常数。使用传统的 N 型混合器和带返混流动模型的 N 型混合器对两种不同气泡尺寸下的塔的 RTD 进行建模。在 MATLAB 环境中使用 MINLP 求解器对完美混合器的数量 (N) 和相应的回流系数 (λ) 进行了优化，其中 N = 5 且 λ = 0.567，气泡尺寸为 1.8 mm，N = 8，气泡尺寸为 λ = 0.643获得了 0.8 毫米的尺寸。引入气泡活性表面系数作为研究浮选动力学的新参数。因此，基于气泡活性表面系数和气泡负载测量，针对各种操作条件确定传质速率常数。结果表明，传质速率取决于物理和表面性质，如粒径、颗粒表面疏水性和承载能力。在细粒度下，传质继续进行，因此需要较长的气泡停留时间。然而，对于粗颗粒，气泡在纸浆-泡沫界面之前达到其最大负载能力，因此任何额外的停留时间都不会对浮选产生影响。此外，在粗粒径下，由于聚集体的稳定性差，特别是对于表面疏水性低的颗粒，传质速率和气泡载荷显着降低。此外，细颗粒在大气泡的存在下表现出较低的浮选动力学。