Effect of Closure Characteristics of Annular Jet Mixed Zone on Inspiratory Performance and Bubble System

: In the ﬂotation process, gas-liquid properties and the bubble system greatly inﬂuence bubble mineralization. In order to clarify how the mechanism applies to the closure characteristics of an annular jet mixed ﬂow zone on the inspiratory performance and the bubble system, different degrees of closure on the velocity ﬁeld and gas-liquid ratio in the mixed ﬂow zone were investigated using numerical simulation. The variations in the characteristics of bubble size distribution, rising velocity, and gas content under different closure levels were measured with a high-speed dynamic camera technology. The results conﬁrmed that when the closure degrees of the mixed ﬂow zone improved, the inlet jet could gradually overcome the static pressure outside the nozzle effectively. It formed a gas-liquid mixing zone with high turbulence ﬁrst, and a large pressure difference at the gas-liquid junction second. This helped to increase the inspiratory capacity. At the same time, the gas-liquid ratio rose gradually under conditions of constant ﬂow. When the nozzle outlet was completely closed, the gas-liquid ratio gradually stabilized. For the bubble distribution system, an enhancement in the closure degrees can effectively reduce the bubble size, and subsequently, the bubble size distribution became more uniform. Due to the improved gas-liquid shear mixing, the aspect ratio of the bubbles can be effectively changed, consequently reducing the bubble rising speed and increasing the gas content and bubble surface area ﬂux of the liquid.


Introduction
Flotation is an effective way to treat fine coal slime [1][2][3]. The suction performance of flotation equipment and the characteristics of the bubble system significantly impact the flotation effect [4][5][6]. Currently, the most commonly used slime flotation equipment includes the mechanical flotation machine and flotation column. There are two types of mechanical flotation machine: one is a mechanical stirring air suction flotation machine, and the other is a jet air suction flotation machine. The biggest difference between these types of flotation machines is that the suction mode varies. When the mechanical stirring air suction flotation machine is operating, the impeller stirs the pulp and throws the pulp around the impeller. The area under the impeller is characterized by low pressure and inhales air, which will produce a large number of bubbles [7]. When the jet air suction flotation machine is functioning, the velocity difference between the high-pressure pulp flow and the air flow makes it possible for the air to enter the jet core area under pressure. The flotation column contains no moving parts and the bubbles rely on external input. The Figure 1a shows the test system, one that is mainly composed of a submerged jet device and bubble measuring device, which can measure the suction volume, and also collect and measure bubbles. The system mainly includes the following components: (1) an observation tank, (2) an overflow tank, (3) an overflow pipe, (4) a circulation tank, (5) a circulation pump, (6) an electromagnetic flowmeter, (7) a pressure gauge, (8) an annular jet nozzle, (9) an air flow meter, (10) a high-speed dynamic camera, and (11) a light source. The annular jet nozzle, as shown in Figure 1b, has many components, for instance: (12) a feed tube, (13) nozzle exit, (14) mixed flow zone a, (15) mixed flow zone b, (16) an aspirating pipe, (17) a metallic gasket, and (18) a connection pipe. The feed pipe outlet diameter m is 8 mm while the inlet diameter n is 12 mm. The light source used in the experiment is a quartz lamp produced by OSRAM, Germany. The model of the light source is BL-1000 A and the energy is 1000 W.
Processes 2021, 9, x FOR PEER REVIEW 3 of 15 different sealing degrees were measured. The overarching objective was to enable efficient mineralization flotation. Figure 1a shows the test system, one that is mainly composed of a submerged jet device and bubble measuring device, which can measure the suction volume, and also collect and measure bubbles. The system mainly includes the following components: (1) an observation tank, (2) an overflow tank, (3) an overflow pipe, (4) a circulation tank, (5) a circulation pump, (6) an electromagnetic flowmeter, (7) a pressure gauge, (8) an annular jet nozzle, (9) an air flow meter, (10) a high-speed dynamic camera, and (11) a light source. The annular jet nozzle, as shown in Figure 1b, has many components, for instance: (12) a feed tube, (13) nozzle exit, (14) mixed flow zone a, (15) mixed flow zone b, (16) an aspirating pipe, (17) a metallic gasket, and (18) a connection pipe. The feed pipe outlet diameter m is 8 mm while the inlet diameter n is 12 mm. The light source used in the experiment is a quartz lamp produced by OSRAM, Germany. The model of the light source is BL-1000 A and the energy is 1000 W.  The inlet pressure P of the feed pipe can be adjusted by the diverter valve so that it stays at 0.10 MPa. The nozzle distance L can be adjusted by the metallic gasket and the adjustment range is 0-20 mm. The observation tank is made of highly transparent glass,  The inlet pressure P of the feed pipe can be adjusted by the diverter valve so that it stays at 0.10 MPa. The nozzle distance L can be adjusted by the metallic gasket and the adjustment range is 0-20 mm. The observation tank is made of highly transparent glass, which is used for submerged jet and bubble collection. The length, width, and height of the glass tank are 70 cm, 15 cm, and 40 cm, respectively.

Test Device
As shown in Figure 1a, the overflow tank is located at the overflow outlet end of the observation tank, with a length of 50 mm, width of 150 mm, and height of 200 mm, respectively, and the outlet hole diameter of the overflow tank is 32 mm. Restricted by the nozzle manufacturing process, but also to ensure the full diffusion of the submerged jet, the size of the observation tank used in this measurement is larger. In the measurement, in order to ensure that the bubble measurement does not lose focus, the matching between the brightness of the backlight and focal length is debugged, so that the outline of the bubble can be photographed well. The captured and processed sample images of bubbles are shown in Figure 2. The bubble size calibration method involves placing a steel ruler with a width of 35 mm on the inner surface of the steel tank as the standard for calibrating the bubble size. The inlet pressure P of the feed pipe can be adjusted by the diverter valve so that it stays at 0.10 MPa. The nozzle distance L can be adjusted by the metallic gasket and the adjustment range is 0-20 mm. The observation tank is made of highly transparent glass, which is used for submerged jet and bubble collection. The length, width, and height of the glass tank are 70 cm, 15 cm, and 40 cm, respectively.
As shown in Figure 1a, the overflow tank is located at the overflow outlet end of the observation tank, with a length of 50 mm, width of 150 mm, and height of 200 mm, respectively, and the outlet hole diameter of the overflow tank is 32 mm. Restricted by the nozzle manufacturing process, but also to ensure the full diffusion of the submerged jet, the size of the observation tank used in this measurement is larger. In the measurement, in order to ensure that the bubble measurement does not lose focus, the matching between the brightness of the backlight and focal length is debugged, so that the outline of the bubble can be photographed well. The captured and processed sample images of bubbles are shown in Figure 2. The bubble size calibration method involves placing a steel ruler with a width of 35 mm on the inner surface of the steel tank as the standard for calibrating the bubble size.

Test Process
While the system is operating, the observation tank (1) and circulation tank (4) are filled with a foaming agent solution, the circulation pump (5) will feed water to the annular jet nozzle (8), and the negative pressure of the jet will suck air into the feed pipe (12) from the aspirating pipe (15), and mix with the solution. In this way, a large number of bubbles will be generated in the mixing flow zone of the nozzle exit (13). After the system becomes stable for about one minute, the backlight is shone on the observation surface on one side of the observation tank (1). As the light source (11) placed on one side is pasted with light cloth oil paper, the brightness distribution is uniform. On the other hand, a high-speed dynamic camera (10) is set-up and directly opposite to the light source (11). The camera focuses on capturing the clear bubble shape and change process. At the same time, the air flow rate and the outlet flow rate of the annular jet nozzle (8) are obtained by an air flowmeter and electromagnetic flowmeter, respectively.
During the test, the submergence depth of the annular jet nozzle (8) is 150 mm, while the pressure of the pressure gauge (7) remains unchanged. The closure degree of the inlet jet to the nozzle exit outlet is adjusted by adjusting the distance between the feed pipe (12) and the nozzle exit (13) outlet. The opening of the liquid level-regulating valve serves to control the liquid level in the observation tank (1), in order for it to be filled with clear water medium.
Because it is difficult to measure the bubble production process in the gas-liquid mixing state in the annular jet nozzle (8), the bubbles produced are released into the tank and then measured. Due to the effect of the bubble group dissolving and merging in the tank, this will affect the measurement and characterization of the bubble system generated by the annular jet nozzle (8). In order to better understand the influence of the annulus jet on the characteristics of the bubble system in the observation tank (1), the effect of the bubble merger was minimized by using a foaming agent concentration greater than the critical coalescence concentration. The experimental solution with a concentration greater than the critical coalescence concentration was prepared by deionized water serving as the medium. Subsequently, the concentration was 0.13 mmol/L and the average temperature required for the test was 25 • C.
When shooting bubbles, the image acquisition frequency was 1000 frames/s, and ProAnalyst software (2-D Professional, Woburn, MA, USA) was used for processing. At least 2000 bubbles were analyzed in each group.
Considering that the same bubbles may be captured in continuous images, the shooting time in each case lasted 2 min or more, and an area of 80 mm by 80 mm was effectively focused on and photographed. As the rising velocity of bubbles was distributed between 260 and 290 cm/s, the interval between the two selected pictures in shooting time should be at least 0.04 s when selecting the pictures for bubbles recognition and statistics, to ensure that the same bubble is not measured repeatedly. At the same time, 50 pictures in each case were selected to ensure that the number of bubbles reached 2000. Figure 2 depicts the captured and processed sample image of bubbles. Figure 2a shows the original image while Figure 2b shows the bubbles' contour image processed by the software.
The Sauter diameter helped to characterize the bubble size characteristics in the test, which can be calculated by the following formula [27]: where d bi is the bubble diameter and n i is the number of bubbles. The suction characteristics of the annular jet nozzle can be evaluated by the relationship curve q between the gas-liquid ratio and suction volume: where Q g and Q l are the volume flows of gas and water, respectively. The suction capacity Q g can be obtained by a gas flow meter (9), and the volume flow quantity Q l can be obtained by an electromagnetic flow meter. The model type of the gas flow meter (9) was LZB-4, which is manufactured by China Hongqi Instrument Co., Ltd. (Wenzhou, China) and the measuring range is 25-250 L/h.

Reagents
The foaming agent used in this study was MIBC, which is produced by Shanghai Hans Chemical Co., Ltd. (Shanghai, China). The molecular formula is (CH3)2CHCH2CH(OH)CH3 and the molecular weight is 102.18. The density, viscosity, and surface tension of the foaming agent were, respectively, 0.8033, 4.59 mPa·s, and 25.3 dyne/cm.

Numerical Model Model Establishment
The three-dimensional model for the annular jet nozzle and observation slot was established. In order to improve the model's mesh quality, a structured mesh was used in the ejector pipe, nozzle, mixing zone, and slot, while an unstructured tetrahedral mesh was employed in other parts of the annular jet device, such as the intersection of the slot and nozzle. The number of meshes used in the three-dimensional method was 980784. Figure 3 shows the meshing diagram of the nozzle and observation tank. Figure 3a shows the combined meshing diagram of the observation tank and annular jet nozzle, while Figure 3b shows the meshing diagram of the annular jet nozzle.
tablished. In order to improve the model's mesh quality, a structured mesh was used in the ejector pipe, nozzle, mixing zone, and slot, while an unstructured tetrahedral mesh was employed in other parts of the annular jet device, such as the intersection of the slot and nozzle. The number of meshes used in the three-dimensional method was 980784. Figure 3 shows the meshing diagram of the nozzle and observation tank. Figure 3a shows the combined meshing diagram of the observation tank and annular jet nozzle, while Figure 3b shows the meshing diagram of the annular jet nozzle. The boundary conditions were as follows: the turbulent intensity was 5%, and the turbulent viscosity ratio was 10. The turbulent viscosity ratio refers to the ratio of turbulent viscosity to dynamic viscosity. The inlet of the feed tube and the aspirating tube was a pressure inlet, and the outlet of the nozzle was also a pressure outlet. The inlet pressure of the feed tube was 0.10 MPa, the inlet pressure of the aspirating tube was 0 MPa, and outlet pressure of the nozzle was 0 MPa. The wall of the nozzle was a stationary wall and no slip shear condition. The numerical calculation of the annular jet device used a realizable turbulence model; the pressure velocity coupling term used the SIMPLEC algorithm [28,29]. For the multi-phase flow model, the VOF model can be used for the system where air and water cannot be integrated with each other. In this paper, the VOF model simulated the gas-liquid two-phase flow [30][31][32]. The coordinate origin of the geometric model was located in the center of the intersection of the nozzle and the ejector tube, with the exit direction of the ejector tube as the positive x direction. Meanwhile, the Z-axis was parallel to the suction tube and perpendicular to the X-axis. The boundary conditions were as follows: the turbulent intensity was 5%, and the turbulent viscosity ratio was 10. The turbulent viscosity ratio refers to the ratio of turbulent viscosity to dynamic viscosity. The inlet of the feed tube and the aspirating tube was a pressure inlet, and the outlet of the nozzle was also a pressure outlet. The inlet pressure of the feed tube was 0.10 MPa, the inlet pressure of the aspirating tube was 0 MPa, and outlet pressure of the nozzle was 0 MPa. The wall of the nozzle was a stationary wall and no slip shear condition. The numerical calculation of the annular jet device used a realizable turbulence model; the pressure velocity coupling term used the SIMPLEC algorithm [28,29]. For the multi-phase flow model, the VOF model can be used for the system where air and water cannot be integrated with each other. In this paper, the VOF model simulated the gas-liquid two-phase flow [30][31][32]. The coordinate origin of the geometric model was located in the center of the intersection of the nozzle and the ejector tube, with the exit direction of the ejector tube as the positive x direction. Meanwhile, the Z-axis was parallel to the suction tube and perpendicular to the X-axis.

Evaluating the Reliability of Numerical Simulation
The suction capacity and gas-liquid ratio of the annular jet nozzle with different tube-nozzle distances were measured by the test system when the inlet pressure was 0.10 MPa, and they were compared with the simulation test results. The outcomes are shown in Table 1.  The equation between nozzle distance L and suction capacity is obtained via cubic polynomial regression analysis: The cubic polynomial regression equation between nozzle distance L and gas-liquid ratio q is as follows: The subscript sum represents the numerical analysis value and the experimental value, respectively. The prediction error of numerical calculation and experiment is obtained by using a dimensionless equation: The nozzle distance ranged from 0 to 20 mm, the corresponding α Qg value was about 5.2%, and the α q value was about 4.8%. Consequently, it can be stated that the numerical model had high reliability. Figure 4 illustrates the comparison between the numerical simulation and experimental test. It is observed that with the increase in nozzle distance, the suction capacity and gas-liquid ratio increased as the inlet pressure also increased. The suction capacity rose from 0.063 m 3 /h when the nozzle distance was 0 mm to 0.173 m 3 /h when the nozzle distance was 20 mm, with an increase of 174.60%. The gas-liquid ratio also rose from 0.149 to 0.309, with an increase of 107.38%. This confirms that the nozzle distance and inlet pressure had an important influence on the adjustment of suction volume and gas-liquid ratio.  At the same time, it can be seen that due to the closure of the nozzle outlet by the diffusion water beam, an effective mixed flow zone formed, which improved the suction capacity. Therefore, the gas-liquid ratio can be effectively adjusted by controlling the suction capacity from the outside, and then the gas holdup of the slurry can be controlled. At the same time, as the nozzle distance continued to increase, the gas-liquid ratio and suction rate diminished. This is due to the fall in velocity difference on the one hand, and the backmixing of the feed on the inner wall of the nozzle on the other. At the same time, it can be seen that due to the closure of the nozzle outlet by the diffusion water beam, an effective mixed flow zone formed, which improved the suction capacity. Therefore, the gas-liquid ratio can be effectively adjusted by controlling the suction capacity from the outside, and then the gas holdup of the slurry can be controlled. At the same time, as the nozzle distance continued to increase, the gas-liquid ratio and suction rate diminished. This is due to the fall in velocity difference on the one hand, and the backmixing of the feed on the inner wall of the nozzle on the other. Based on what is shown in the velocity vector diagram, it appears that when there was a larger nozzle distance, the range of the mixed flow zone increased. At this time, the maximum water velocity in the core of the feed flow did not change, but the water velocity in the radial direction gradually reduced with the increase in axial distance.  There is a certain diffusivity of the water beam in the process of the submerged jet. According to the schematic diagram of the water beam sealing process at the nozzle outlet ( Figure 6), when the nozzle distance was short, the diffusivity of the water beam close to the outlet was low, and the water beam failed to prevent the water in the water tank from entering the nozzle. The mixed flow area a was very small, so it was impossible to form an effective pressure difference at the junction of mixed flow area a and mixed flow area b, as shown in Figure 6a. With the increase in nozzle distance, the increase in water beam cross-sectional area can effectively seal the nozzle outlet. This helps to overcome the static pressure of water in the tank and form a large velocity difference at the junction of mixed There is a certain diffusivity of the water beam in the process of the submerged jet. According to the schematic diagram of the water beam sealing process at the nozzle outlet ( Figure 6), when the nozzle distance was short, the diffusivity of the water beam close to the outlet was low, and the water beam failed to prevent the water in the water tank from entering the nozzle. The mixed flow area a was very small, so it was impossible to form an effective pressure difference at the junction of mixed flow area a and mixed flow area b, as shown in Figure 6a. With the increase in nozzle distance, the increase in water beam cross-sectional area can effectively seal the nozzle outlet. This helps to overcome the static pressure of water in the tank and form a large velocity difference at the junction of mixed flow area a and mixed flow area b, effectively forming a large pressure difference. At the same time, the more obvious the ejection effect is in the mixed flow zone b, the more air suction can be obtained by forming an air flow belt, as shown in Figure 6b. This is consistent with the direction of the jet. It can also be seen from the vector diagram of the junction of mixed flow area a and mixed flow area b shown in Figure 5b that the gas region and velocity vector in the radial direction gradually increased. Based on the gas-liquid two-phase volume division diagram at different tube-nozzle distances shown in Figure 7, it can be observed that as the tube-nozzle distance increased, the nozzle mixing zone a and mixing zone b within the volume of the liquid phase gradually diminished. The gas phase volume accounted for more and more, and the airflow band gradually formed in mixing zone b, and while the suction volume and gas-liquid ratio increased, the gas interacted directly with the feed stream in mixing zone a. This produced small bubble clusters after shearing and breaking, and then initially forming a bubble system, which helps bubbles disperse better in the tank carried by the jet. Based on the gas-liquid two-phase volume division diagram at different tube-nozzle distances shown in Figure 7, it can be observed that as the tube-nozzle distance increased, the nozzle mixing zone a and mixing zone b within the volume of the liquid phase gradually diminished. The gas phase volume accounted for more and more, and the airflow band gradually formed in mixing zone b, and while the suction volume and gas-liquid ratio increased, the gas interacted directly with the feed stream in mixing zone a. This produced small bubble clusters after shearing and breaking, and then initially forming a bubble system, which helps bubbles disperse better in the tank carried by the jet. Figure 8 depicts the change curve of bubble particle size distribution under different tube-nozzle distances, and Figure 8a highlights the bubble probability density distribution at 0.10 MPa. As the tube-nozzle distance increased, the distribution range of bubble size gradually decreased, the probability of smaller bubble particle size also increased, and the average bubble size decreased. For example, when the nozzle distance was 0 mm, the range of the bubble particle size distribution with a probability greater than 60% was 0.75~1.59 mm, and the particle size fluctuation range was 0.84 mm. When the nozzle distance increased to 20 mm, the bubble particle size distribution range was 0.47~1.22 mm with a probability greater than 60%, and the particle size fluctuation range was 0.75 mm. It is known that as the nozzle distance increased, the particle size shrank and became more uniform.

Influence of Inflow Pressure on Bubble Size Distribution
Based on the gas-liquid two-phase volume division diagram at different tube-nozzle distances shown in Figure 7, it can be observed that as the tube-nozzle distance increased, the nozzle mixing zone a and mixing zone b within the volume of the liquid phase gradually diminished. The gas phase volume accounted for more and more, and the airflow band gradually formed in mixing zone b, and while the suction volume and gas-liquid ratio increased, the gas interacted directly with the feed stream in mixing zone a. This produced small bubble clusters after shearing and breaking, and then initially forming a bubble system, which helps bubbles disperse better in the tank carried by the jet.   Figure 8a highlights the bubble probability density distribution at 0.10 MPa. As the tube-nozzle distance increased, the distribution range of bubble size gradually decreased, the probability of smaller bubble particle size also increased, and the average bubble size decreased. For example, when the nozzle distance was 0 mm, the range of the bubble particle size distribution with a probability greater than 60% was 0.75~1.59 mm, and the particle size fluctuation range was 0.84 mm. When the nozzle distance increased to 20 mm, the bubble particle size distribution range was 0.47~1.22 mm with a probability greater than 60%, and the particle size fluctuation range was 0.75 mm. It is known that as the nozzle distance increased, the particle size shrank and became more uniform.  Figure 8b shows the variation curve of the bubble Sauter diameter, in which it can be seen that when the tube-nozzle distance increased, the Sauter diameter of the bubble decreased, while the particle size changed more when it switched from 0 to 7 mm. When the tube-nozzle distance reached 15 mm, the particle size of a bubble tended to be stable. Under the large nozzle distance, when the vortex formed at the mixing zone was large, the  Figure 8b shows the variation curve of the bubble Sauter diameter, in which it can be seen that when the tube-nozzle distance increased, the Sauter diameter of the bubble decreased, while the particle size changed more when it switched from 0 to 7 mm. When the tube-nozzle distance reached 15 mm, the particle size of a bubble tended to be stable. Under the large nozzle distance, when the vortex formed at the mixing zone was large, the higher the degree of turbulence, the stronger the shearing effect, and the smaller the diameter of the bubbles formed.

Effect of Tube-Nozzle Distances on Bubble Motion Characteristics
The aspect ratio of the bubbles and the rising speed of the bubbles in water are directly related to the gas content and adsorption effect with the agent [19]. This study also discovered that the bubble rise velocity declined linearly with the increase in the aspect ratio, independent of the reagent type, concentration, and mixing. It is therefore necessary to study the influence of the nozzle outlet closure degree on the aspect ratio and bubble rise velocity at different tube-nozzle distances, in order to regulate the bubble system. Figure 9 shows the influence curve of different tube-nozzle distances on the bubble aspect ratio and rising speed. As the tube-nozzle distance gradually increased, the gasliquid mixing zone also gradually increased, and the incidence of the jet to the nozzle outlet closure enhanced, so the cutting and crushing effect on the bubble was reinforced. The bubble particle size reduced while the resistance to deformation strengthened, so the aspect ratio gradually increased, first from 0.74 of 0 mm to 0.93 of 20 mm. Eventually, they converged to the spherical variation range, while the bubble rising speed decreased with the tube-nozzle distance. Furthermore, the gas velocity decreased progressively and moderately when the tube-nozzle distance was greater than 7 mm. A lower bubble rising speed helps to improve the gas content of the pulp, which is then conducive to regulating the bubble mineralization time. discovered that the bubble rise velocity declined linearly with the increase in the aspect ratio, independent of the reagent type, concentration, and mixing. It is therefore necessary to study the influence of the nozzle outlet closure degree on the aspect ratio and bubble rise velocity at different tube-nozzle distances, in order to regulate the bubble system. Figure 9 shows the influence curve of different tube-nozzle distances on the bubble aspect ratio and rising speed. As the tube-nozzle distance gradually increased, the gasliquid mixing zone also gradually increased, and the incidence of the jet to the nozzle outlet closure enhanced, so the cutting and crushing effect on the bubble was reinforced. The bubble particle size reduced while the resistance to deformation strengthened, so the aspect ratio gradually increased, first from 0.74 of 0 mm to 0.93 of 20 mm. Eventually, they converged to the spherical variation range, while the bubble rising speed decreased with the tube-nozzle distance. Furthermore, the gas velocity decreased progressively and moderately when the tube-nozzle distance was greater than 7 mm. A lower bubble rising speed helps to improve the gas content of the pulp, which is then conducive to regulating the bubble mineralization time. Aspect ratio Aspect ratio Figure 9. Effect of tube-nozzle distance on bubble aspect ratio and rise velocity.

Analysis of the Effect of Bubble Surface Area Flux
The surface area flux of bubbles expresses the surface area of bubbles passing through a unit cross-sectional area of the tank per unit time. It is important for the meas- Figure 9. Effect of tube-nozzle distance on bubble aspect ratio and rise velocity.

Analysis of the Effect of Bubble Surface Area Flux
The surface area flux of bubbles expresses the surface area of bubbles passing through a unit cross-sectional area of the tank per unit time. It is important for the measurement of the bubble gas capacity and the adsorption surface of the agent. For the effect of bubble surface area, fluxes S b were used [33]: where J g denotes the surface gas velocity and D 32 denotes the Sauter diameter. The surface area flux of bubbles expresses the surface area of bubbles passing through a unit crosssectional area of the tank per unit time. The surface flux can be used to characterize the number and diameter of bubbles. The increase in surface area flux means that there are more small-diameter bubbles in the liquid phase at a certain superficial gas velocity. The comparative plots of bubble surface fluxes are derived from Equation (3) for the tube-nozzle distances of 0 mm and 20 mm, respectively, as shown in Figure 10.  The bubble surface area flux decreased and then stabilized to 23.11 s −1 with increasing tube-nozzle distance at smaller inflow pressures, while it increased and then stabilized to more than 30.00 s −1 with increasing tube-nozzle distance at larger inflow pressures. As indicated in Figure 8, when the tube-nozzle distance was 0 mm, the gas flux decreased, and the bubble surface area flux was low as the inflow pressure increased, remaining at about 23.00 s −1 . When the tube-nozzle distance was 20 mm, the bubble surface area flux increased as the inlet pressure rose and stabilized at about 30.55 s −1 ; this occurred when the nozzle distance reached 7 mm. Based on the above analysis, it can be stated here that a smaller tube-nozzle distance was not conducive to improving the bubble surface area flux, while a higher tube-nozzle distance was certainly conducive to improving the bubble surface area flux. This is linked to the surface energy required for bubble rupture, and also indicates that the best parameter conditions will improve the surface area flux with the least energy consumption and provide the best results. The bubble surface area flux decreased and then stabilized to 23.11 s −1 with increasing tube-nozzle distance at smaller inflow pressures, while it increased and then stabilized to more than 30.00 s −1 with increasing tube-nozzle distance at larger inflow pressures. As indicated in Figure 8, when the tube-nozzle distance was 0 mm, the gas flux decreased, and the bubble surface area flux was low as the inflow pressure increased, remaining at about 23.00 s −1 . When the tube-nozzle distance was 20 mm, the bubble surface area flux increased as the inlet pressure rose and stabilized at about 30.55 s −1 ; this occurred when the nozzle distance reached 7 mm. Based on the above analysis, it can be stated here that a smaller tube-nozzle distance was not conducive to improving the bubble surface area flux, while a higher tube-nozzle distance was certainly conducive to improving the bubble surface area flux. This is linked to the surface energy required for bubble rupture, and also