# Gas-Liquid Mixability Study in a Jet-Stirred Tank for Mineral Flotation
## 1 Introduction  
The significance of mineral resources to economic and social development is indisputable. However, many mineral resources cannot be utilized directly after mining; they must undergo a series of sorting and processing procedures [1]. Among these procedures, flotation stands out as one of the most crucial and widely applied mineral sorting technologies [2]. The principle of flotation is based on the selective attachment between mineral particles and bubbles. During flotation, the slurry (a mixture of minerals and water) is introduced into a flotation cell, and air is injected through a gas-liquid two-phase mixing system, generating a large number of fine bubbles. Hydrophobic mineral particles preferentially attach to the surface of the bubbles and rise with them to the surface of the slurry, forming mineralized froth, thus separating from the hydrophilic minerals. This process takes full advantage of the differences in the surface properties of minerals to achieve mineral separation [3]. In stirred tank flotation operations, traditional stirred tanks utilize mechanical stirring, leading to challenges like high energy consumption, control difficulties, and bubble crushing [4]. To tackle these issues, jet-stirring technology was introduced. This innovative approach leverages the kinetic effect of high-speed jets. By generating numerousmicro- and nano-bubbles through high-pressure jets, the stirred tank efficiently mixes them with suspended matter and colloids in the slurry, ultimately boosting the recovery rate of concentrates [5]. Research on jet mixing began as early as the 1950s [6], and, by the end of the 20 th century, jet-mixing technology had been further developed. Researchers subsequently began to systematically study the flow characteristics of jets [7]. In the past 20 years, with the development and application of computational fluid dynamics (CFDs) technology, analyses of different mixing situations have become increasingly comprehensive [8]. In 2002, [PERSON] [9] predicted the mixing time and concentration distribution in a jet-mixing system using jet velocity, nozzle angle, and geometry as variables. In 2009, [PERSON] [10; 11; 12] simulated and analyzed gas mixing and stirring, proposing a design of a stirring device from a multifaceted perspective. [PERSON] et al. [13] experimentally investigated the effect of jet position on the neutralization performance of alkali streams. Experiments on the mixing of the neutralization reaction were conducted at optimal and worst positions, revealing that the jet position significantly affected neutralization performance. In 2017, [PERSON] et al. [14] proposed a rotary jet-mixing device for the mixing of multiphase streams containing oxygenated air, lime slurry, and limestone particles to optimize the removal of sulfur dioxide. In 2019, [PERSON]'s team [15] calculated residence time and mixing within a jet-stirred reactor at different flow rates using a large eddy simulation, focusing on non-reacting mixtures under ambient conditions. In 2023, [PERSON] et al. [4] explored fluid flow and mass transfer patterns in a loop jet reactor, correlating these properties to guide reactor design. Current research on jet mixing primarily examines the influence of operating parameters on performance, with a limited focus on structural parameters. Gas-liquid mixing uniformity is a critical parameter for evaluating the effectiveness of jet-stirred tanks, as improving this uniformity enhances production efficiency and reduces energy consumption, which is vital for effective jet stirring [16; 17]. Many studies have explored this area, particularly in traditional mixing tanks where impeller design significantly affects hydrodynamic behavior. [PERSON] et al. [18] designed a new type of impeller with a gridded structure, which demonstrated superior gas dispersion performance and lower energy consumption compared to conventional impellers. [PERSON] et al. [19] introduced a fan impeller into the gas-liquid mixing process and found it enhanced oxygen delivery efficiency.