Bubble Size Distribution Characteristics of a Jet-Stirring Coupling Flotation Device

In this study, a new jet-stirring coupling flotation device that incorporates the advantages of three conventional flotation machines (specifically, Jameson cell, mechanical flotation cell, flotation column) was designed based on jet suction. The suction capacity of a double cosine self-aspirated nozzle utilized by the device was analyzed under different feeding pressures, and the effects of frother concentration, feeding pressure, suction capacity, and height of sampling location on the bubble size distribution (BSD) were investigated using a high-speed video system. It was found that a large amount of air was sucked into the flotation cell by the self-aspirated nozzle arranged in a non-submerged manner, which met the requirements of flotation in terms of the suction amount of air. The suction capacity showed a positive linear correlation with negative pressure inside the nozzle. When the Methyl isobutyl carbinol (MIBC) concentration reached the critical coalescence concentration (CCC), the bubble size stabilized at approximately 0.31 mm, which was smaller than the bubble size produced by the conventional flotation machine. This indicated that bubbles suitable for flotation were generated. D32 linearly decreased with increasing of feeding pressures and conversely increased with increasing suction capacities and sampling location heights, independent of the frother concentration.


Introduction
Flotation devices are considered to be effective for fine coal slime separation processes [1,2], and the research and development of flotation equipment are focused on achieving a large-scale, high-efficiency, energy-saving, and environmentally friendly separation [3,4]. To date, three main types of flotation machines have been widely used in different flotation process of minerals: mechanical flotation machine [5], Jameson cell [6], and flotation column [7].
Extensive studies on the suction capacity and bubble size distribution (BSD) of traditional mechanical flotation machines have indicated that these functions are easily influenced by the structural parameters of an "impeller stator" [8], which has higher energy consumption due to mechanical agitation [9] and larger bubbles, compared to nanobubble column flotation [10]. For the Jameson cell, air in the suction mode is continuously pumped and carried by the velocity difference between the high-speed pulp flow and air flow, where air is suctioned at low pressure around the core area of the jet flow [11]; a large portion of the bubbles generated in the jet suction mode have a small size [12], such as nanobubbles, and were two orders of magnitude smaller than conventional the bottom of the axis for adjusting the dispersion of mineral particles, the uniformity of bubbles, and the degree of turbulence of the slurry; (4) a round mixing tank for mixing the slurry; (5) a draft tube for draining the slurry to the stirring impeller; and (6) a canopy hood for dispersing the slurry evenly into the stirring impeller and circulating tank.
The layout of the six double cosine self-aspirated nozzles is shown in the A-A view. The six nozzles are arranged symmetrically along the center of the upper part of the mixing tank, which cuts through the inner wall along the mixing tank. The center line of the nozzles is in the same horizontal plane as that of the driving impeller.   Figure 2 shows the structural schematic of the double cosine self-aspirated nozzle, the most important part of the flotation device, which mainly comprises three components: (1) an ejector pipe for jetting high-speed slurry and injecting air flow, (2) a suction pipe for drawing in air from the atmosphere, and (3) an outer nozzle for forming the suction and mixing zones between the ejector Minerals 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/minerals the bottom of the axis for adjusting the dispersion of mineral particles, the uniformity of bubbles, and the degree of turbulence of the slurry; (4) a round mixing tank for mixing the slurry; (5) a draft tube for draining the slurry to the stirring impeller; and (6) a canopy hood for dispersing the slurry evenly into the stirring impeller and circulating tank. The layout of the six double cosine self-aspirated nozzles is shown in the A-A view. The six nozzles are arranged symmetrically along the center of the upper part of the mixing tank, which cuts through the inner wall along the mixing tank. The center line of the nozzles is in the same horizontal plane as that of the driving impeller.   Figure 2 shows the structural schematic of the double cosine self-aspirated nozzle, the most important part of the flotation device, which mainly comprises three components: (1) an ejector pipe for jetting high-speed slurry and injecting air flow, (2) a suction pipe for drawing in air from the atmosphere, and (3) an outer nozzle for forming the suction and mixing zones between the ejector  for jetting high-speed slurry and injecting air flow, (2) a suction pipe for drawing in air from the atmosphere, and (3) an outer nozzle for forming the suction and mixing zones between the ejector pipe and outer nozzle. The cone angle of the cosine section of the ejector pipe and that of outer nozzle were both designed to be 28 . The outlet diameter of ejector pipe is 6 mm, and that of the outer nozzle is 7 mm. The distance between the ejector pipe and outer nozzle is 20 mm. The other structural parameters of the double cosine self-aspirated nozzle are given in Table 1. A stable negative pressure environment formed in the suction zone will draw in a large amount of air when a high-speed slurry jet is continuously ejected from the ejector pipe; then the air and slurry are strongly premixed in the mixing zone within the nozzle.

Working Process of Flotation Device
The driving impeller was driven by a gas-containing high-speed slurry flow jetted from the double cosine self-aspirated nozzle, rotating in real time at the same angular velocity as the stirring impeller and generating centrifugal force in the mixing tank. The slurry sprayed onto the driving impeller was thrown onto the inner wall of the mixing tank to enhance the dispersion between the slurry and bubbles; the slurry was in a spiral motion within the draft tube under the action of its own gravity and centrifugal force and evenly distributed to the stirring impeller through the canopy hood. The large bubbles were again cut into microbubbles by the high-speed rotating driving impeller and the stirring impeller. In this process, the dispersion degree and collision probability of the slurry, agents (frother and collector), and bubbles were enhanced, thereby improving the effect of bubble mineralization. Figure 3 shows the overall experimental setup used in this study. The experiments for the determination of the bubble size were conducted in the jet-stirring coupling flotation device, equipped with an approximately 35 L circulating tank, provided with a false bottom in the cell; the distance between the stirring impeller and the false bottom was set to 15 mm, and that between the false bottom and circulating tank bottom was set to 10 mm. Other structural parameters of the flotation device are outlined in Table 2.

Experimental System
The view chamber was set as an inclined (15 • ) window, and used to disperse the bubbles into a near monolayer [30][31][32]. A light filter was used to improve the uniformity of the light source to provide a sharp contrast between the bubble edges and the background; the bubbles rose through a vertical sampling tube with a 12 mm inner diameter into the viewing chamber filled with the test medium (100 mm length, 150 mm width, and 20 mm depth) to observe bubbles at different points in the circulating tank.   An electromagnetic liquid flowmeter (range: 0.3-7 m 3 /h) and a diaphragm pressure gauge (range: 0-0.6 MPa) were installed on the pipeline at the outlet of the circulation pump for measuring the working parameters in real time. An LZB-6-type glass rotameter was used to measure the suction capacity (q, L/min) of the double cosine self-aspirated nozzle, and the negative pressure value (p, MPa) of the nozzle was measured by the negative pressure meter. An ACS510-01 frequency converter (ABB (China) Co., Ltd., Beijing, China) was used to control the working frequency of the circulating pump and indirectly control the feeding pressure (P, MPa).
The slurry was cyclically pumped to the double cosine self-aspirated nozzle by the circulation pump. As shown in Figure 3, the flow direction of the slurry in the flotation device and the circulating tank is represented by the black dotted arrow, while that of the slurry outside the circulating tank is represented by the black solid arrow. Since the six nozzles were of the same structure and arranged symmetrically on the upper part of the flotation device, only a single-nozzle BSD test was conducted in this study.

Experimental Conditions and Methods
Methyl isobutyl carbinol (MIBC, C6H14O, analytical pure, Shanghai Hansi Chemical Co., Ltd., Shanghai, China) was used as a frother, and its concentration is denoted as C (mmol/L). During the whole testing process, the depth of the fluid remained unchanged in the circulating tank. The vertical H coordinate axis was established for showing the sampling location height away from the horizontal center line of the stirring impeller, as shown in Figure 3. The horizontal plane where the center line of the stirring impeller is located is set as the coordinate origin, i.e., (H = 0 cm). The D32 at a different  An electromagnetic liquid flowmeter (range: 0.3-7 m 3 /h) and a diaphragm pressure gauge (range: 0-0.6 MPa) were installed on the pipeline at the outlet of the circulation pump for measuring the working parameters in real time. An LZB-6-type glass rotameter was used to measure the suction capacity (q, L/min) of the double cosine self-aspirated nozzle, and the negative pressure value (p, MPa) of the nozzle was measured by the negative pressure meter. An ACS510-01 frequency converter (ABB (China) Co., Ltd., Beijing, China) was used to control the working frequency of the circulating pump and indirectly control the feeding pressure (P, MPa).
The slurry was cyclically pumped to the double cosine self-aspirated nozzle by the circulation pump. As shown in Figure 3, the flow direction of the slurry in the flotation device and the circulating tank is represented by the black dotted arrow, while that of the slurry outside the circulating tank is represented by the black solid arrow. Since the six nozzles were of the same structure and arranged symmetrically on the upper part of the flotation device, only a single-nozzle BSD test was conducted in this study.

Experimental Conditions and Methods
Methyl isobutyl carbinol (MIBC, C 6 H 14 O, analytical pure, Shanghai Hansi Chemical Co., Ltd., Shanghai, China) was used as a frother, and its concentration is denoted as C (mmol/L). During the whole testing process, the depth of the fluid remained unchanged in the circulating tank. The vertical H coordinate axis was established for showing the sampling location height away from the horizontal center line of the stirring impeller, as shown in Figure 3. The horizontal plane where the center line of the stirring impeller is located is set as the coordinate origin, i.e., (H = 0 cm). The D 32 at a different height of the sampling location were studied by moving the inlet of the sampling tube vertically up. All tests were performed at room temperature (20 ± 1 • C) using tap water of pH 6.8 [33,34].
Images of the bubbles sliding up the inclined view chamber were captured using an i-SPEED 3 high-speed camera (CINV Optical Instruments Co., Ltd., Nanjing, China) at a rate of 4000 frames per second and a typical image resolution of 768 × 576 px. To increase the accuracy of the BSD, a minimum of 5000 bubbles were measured for each condition tested. Professional image analysis software, Image-pro-plus, was used for correctly identifying bubble sizes, recording, and analyzing the data.

Data Processing
The Sauter mean diameter (D 32 ) is commonly used to evaluate the average value of the bubble swarm, which was determined using Equation (1) [13,35].
where n is the total number of bubbles sampled; d i represents the diameter of the ith bubble.

Effect of Feeding Pressure on Suction Capacity and Negative Pressure in a Double Cosine Self-Aspirated Nozzle
The suction capacity and negative pressure as a function of the feeding pressure in a double cosine self-aspirated nozzle are presented in Figure 4. Within the studied feeding pressure range, the suction capacity and absolute value of the negative pressure generally increased on increasing the feeding pressure; this indicates that increasing the feeding pressure results in an increase in the speed difference between the liquid and gas, as shown in Figure 5. It can be seen from Table 3 that the high-speed liquid carries away a considerable amount of air from the suction pipe and creates a stable negative pressure environment inside the nozzle. It can be seen from Figure 5 that once the feeding pressure rises higher than 0.16 MPa, the velocity difference of liquid-air exceeds 14 m/s, indicating that the ejection ability of liquid is greatly enhanced. height of the sampling location were studied by moving the inlet of the sampling tube vertically up. All tests were performed at room temperature (20 ± 1 °C) using tap water of pH 6.8 [33,34]. Images of the bubbles sliding up the inclined view chamber were captured using an i-SPEED 3 high-speed camera (CINV Optical Instruments Co., Ltd., Nanjing, China) at a rate of 4000 frames per second and a typical image resolution of 768 × 576 px. To increase the accuracy of the BSD, a minimum of 5000 bubbles were measured for each condition tested. Professional image analysis software, Image-pro-plus, was used for correctly identifying bubble sizes, recording, and analyzing the data.

Data Processing
The Sauter mean diameter (D32) is commonly used to evaluate the average value of the bubble swarm, which was determined using Equation (1) [13,35].
where n is the total number of bubbles sampled; di represents the diameter of the ith bubble.

Effect of Feeding Pressure on Suction Capacity and Negative Pressure in a Double Cosine Self-Aspirated Nozzle
The suction capacity and negative pressure as a function of the feeding pressure in a double cosine self-aspirated nozzle are presented in Figure 4. Within the studied feeding pressure range, the suction capacity and absolute value of the negative pressure generally increased on increasing the feeding pressure; this indicates that increasing the feeding pressure results in an increase in the speed difference between the liquid and gas, as shown in Figure 5. It can be seen from Table 3 that the highspeed liquid carries away a considerable amount of air from the suction pipe and creates a stable negative pressure environment inside the nozzle. It can be seen from Figure 5 that once the feeding pressure rises higher than 0.16 MPa, the velocity difference of liquid-air exceeds 14 m/s, indicating that the ejection ability of liquid is greatly enhanced.     There is a linear positive correlation between the suction capacity and negative pressure, as seen in Figure 6. The curve was fitted using a linear function, and the coefficient of determination is as high as 0.9815. The suction capacity increased with the increase in negative pressure, suggesting that the improvement in the negative pressure environment inside the suction zone caused the nozzle to draw in a large amount of gas required for flotation. This demonstrates the feasibility of arranging the nozzle in a non-submerged manner and the rationality of the nozzle parameter design.  There is a linear positive correlation between the suction capacity and negative pressure, as seen in Figure 6. The curve was fitted using a linear function, and the coefficient of determination is as high as 0.9815. The suction capacity increased with the increase in negative pressure, suggesting that the improvement in the negative pressure environment inside the suction zone caused the nozzle to draw in a large amount of gas required for flotation. This demonstrates the feasibility of arranging the nozzle in a non-submerged manner and the rationality of the nozzle parameter design.

Effect of Frother Concentration on Bubble Size Distribution
D 32 as a function of the MIBC concentration for a constant suction capacity of 0.5 L/min, P = 0.10 MPa, and H = 0 cm is shown in Figure 7. It can been seen from Figure 7 that D 32 decreased with the increase in the MIBC concentration until the CCC value of 0.111 mmol/L was reached [36,37]; above this value, D 32 was almost constant at approximately 0.31 mm. The comparison of D 32 in flotation machines at CCC is shown in Table 4. It can be seen from Table 4 that D 32 of this device was smaller than that of the conventional flotation machines.

Effect of Frother Concentration on Bubble Size Distribution
D32 as a function of the MIBC concentration for a constant suction capacity of 0.5 L/min, P = 0.10 MPa, and H = 0 cm is shown in Figure 7. It can been seen from Figure 7 that D32 decreased with the increase in the MIBC concentration until the CCC value of 0.111 mmol/L was reached [36,37]; above this value, D32 was almost constant at approximately 0.31 mm. The comparison of D32 in flotation machines at CCC is shown in Table 4. It can be seen from Table 4 that D32 of this device was smaller than that of the conventional flotation machines.
The BSDs of three representative frother concentrations of 0.096, 0.111, and 0.127 mmol/L are presented in the inset of Figure 7. As observed, the percentage of small bubbles increases with the frother concentration, and the peak position of each curve gradually shifts toward the smaller bubble size with an increasing MIBC concentration.   Figure 8 presents the orientation of the frother molecules at the air/water interface, and effect of different frother concentrations adsorbed on the surface of bubbles during the collision, coalescence, and separation of bubbles. It can be seen from Figure 8 that a lower frother concentration adsorbed on the surface of bubbles easily, causing them to coalesce and generate larger bubbles from smaller bubbles during bubble collision; conversely, a higher frother concentration effectively prevents bubble coalescence during the process of bubble collision. It was demonstrated that MIBC reduced the surface tension of the solution [26]; its molecular structure consists of a hydrophilic polar group and a hydrophobic hydrocarbon chain. When the polar groups are arranged in the liquid phase and non-polar groups are arranged in the gas phase [24], the MIBC molecules are adsorbed on the surface of bubbles as an oriented layer to form a more stable "protective layer" at the air/water interface. The number of molecules adsorbed on the surface of the bubbles increases with the MIBC concentration, resulting in further reduction in the solution surface tension; hence, D32 also further reduced. At lower frother concentrations, the bubbles are easily affected by external forces and merge into larger bubbles. As the concentration reaches the CCC, the number of molecules on the surface of the bubbles remains essentially constant, and the surface tension of the solution can resist the influence of external forces. Bubbles will collide, deform, and then bounce away; therefore, the possibility of bubble coalescence is reduced.   [39,40] The BSDs of three representative frother concentrations of 0.096, 0.111, and 0.127 mmol/L are presented in the inset of Figure 7. As observed, the percentage of small bubbles increases with the frother concentration, and the peak position of each curve gradually shifts toward the smaller bubble size with an increasing MIBC concentration. Figure 8 presents the orientation of the frother molecules at the air/water interface, and effect of different frother concentrations adsorbed on the surface of bubbles during the collision, coalescence, and separation of bubbles. It can be seen from Figure 8 that a lower frother concentration adsorbed on the surface of bubbles easily, causing them to coalesce and generate larger bubbles from smaller bubbles during bubble collision; conversely, a higher frother concentration effectively prevents bubble coalescence during the process of bubble collision. It was demonstrated that MIBC reduced the surface tension of the solution [26]; its molecular structure consists of a hydrophilic polar group and a hydrophobic hydrocarbon chain. When the polar groups are arranged in the liquid phase and non-polar groups are arranged in the gas phase [24], the MIBC molecules are adsorbed on the surface of bubbles as an oriented layer to form a more stable "protective layer" at the air/water interface. The number of molecules adsorbed on the surface of the bubbles increases with the MIBC concentration, resulting in further reduction in the solution surface tension; hence, D 32 also further reduced. At lower frother concentrations, the bubbles are easily affected by external forces and merge into larger bubbles. As the concentration reaches the CCC, the number of molecules on the surface of the bubbles remains essentially constant, and the surface tension of the solution can resist the influence of external forces. Bubbles will collide, deform, and then bounce away; therefore, the possibility of bubble coalescence is reduced.   Figure 9 presents the variation of D32 with the feeding pressure for three typical frother concentrations at q = 0.5 L/min and H = 0 cm. Overall, with an increasing feeding pressure, D32 gradually decreased at each frother concentration. Lower frother concentrations caused a higher decrease in D32, and the D32 difference between two adjacent curves also decreased with the feeding pressure increased. From another perspective, for a fixed volumetric input rate of the gas, this decrease in bubble size represents an increase in the number of bubbles, which in turn signifies an increase in the total surface area available for coal particle attachment [41]. The change in the feeding pressure mainly increased the turbulence intensity in the nozzle mixing zone, which led to an increase in the gas-liquid interaction frequency. Moreover, the increase in the feeding pressure also caused an increase in the flow field turbulence intensity in the circulating tank due to an increase in the impeller speed, as shown in Figure 10. The bubble size and feeding pressure were approximately linear, and the data were linearly fitted, as presented in Table 5. It can be seen from Table 5 that the absolute value of the slope of the curve, the intercept, and ΔD32 gradually decreased with the increasing frother concentration. When the concentration of the frother increased from 0.096 to 0.111 mmol/L, the slope changed by 1.98; when the concentration increased from 0.111 to 0.127 mmol/L, the slope changed by 0.18, indicating that the size of the bubbles is significantly affected by the feeding pressure at lower frother concentrations. However, when the concentration reached or exceeded the CCC, the rigidity of the bubble surfaces increased owing to an increase in the amount of frother adsorbed on the surface of the bubble; almost no merger occurred between the bubbles, and the size of the bubble was reduced owing to the influence of the feeding pressure.   Figure 9 presents the variation of D 32 with the feeding pressure for three typical frother concentrations at q = 0.5 L/min and H = 0 cm. Overall, with an increasing feeding pressure, D 32 gradually decreased at each frother concentration. Lower frother concentrations caused a higher decrease in D 32 , and the D 32 difference between two adjacent curves also decreased with the feeding pressure increased. From another perspective, for a fixed volumetric input rate of the gas, this decrease in bubble size represents an increase in the number of bubbles, which in turn signifies an increase in the total surface area available for coal particle attachment [41]. The change in the feeding pressure mainly increased the turbulence intensity in the nozzle mixing zone, which led to an increase in the gas-liquid interaction frequency. Moreover, the increase in the feeding pressure also caused an increase in the flow field turbulence intensity in the circulating tank due to an increase in the impeller speed, as shown in Figure 10. The bubble size and feeding pressure were approximately linear, and the data were linearly fitted, as presented in Table 5. It can be seen from Table 5 that the absolute value of the slope of the curve, the intercept, and ∆D 32 gradually decreased with the increasing frother concentration. When the concentration of the frother increased from 0.096 to 0.111 mmol/L, the slope changed by 1.98; when the concentration increased from 0.111 to 0.127 mmol/L, the slope changed by 0.18, indicating that the size of the bubbles is significantly affected by the feeding pressure at lower frother concentrations. However, when the concentration reached or exceeded the CCC, the rigidity of the bubble surfaces increased owing to an increase in the amount of frother adsorbed on the surface of the bubble; almost no merger occurred between the bubbles, and the size of the bubble was reduced owing to the influence of the feeding pressure.   Figure 9 presents the variation of D32 with the feeding pressure for three typical frother concentrations at q = 0.5 L/min and H = 0 cm. Overall, with an increasing feeding pressure, D32 gradually decreased at each frother concentration. Lower frother concentrations caused a higher decrease in D32, and the D32 difference between two adjacent curves also decreased with the feeding pressure increased. From another perspective, for a fixed volumetric input rate of the gas, this decrease in bubble size represents an increase in the number of bubbles, which in turn signifies an increase in the total surface area available for coal particle attachment [41]. The change in the feeding pressure mainly increased the turbulence intensity in the nozzle mixing zone, which led to an increase in the gas-liquid interaction frequency. Moreover, the increase in the feeding pressure also caused an increase in the flow field turbulence intensity in the circulating tank due to an increase in the impeller speed, as shown in Figure 10. The bubble size and feeding pressure were approximately linear, and the data were linearly fitted, as presented in Table 5. It can be seen from Table 5 that the absolute value of the slope of the curve, the intercept, and ΔD32 gradually decreased with the increasing frother concentration. When the concentration of the frother increased from 0.096 to 0.111 mmol/L, the slope changed by 1.98; when the concentration increased from 0.111 to 0.127 mmol/L, the slope changed by 0.18, indicating that the size of the bubbles is significantly affected by the feeding pressure at lower frother concentrations. However, when the concentration reached or exceeded the CCC, the rigidity of the bubble surfaces increased owing to an increase in the amount of frother adsorbed on the surface of the bubble; almost no merger occurred between the bubbles, and the size of the bubble was reduced owing to the influence of the feeding pressure.     Figure 11 presents the D32 values as a function of suction capacity at P = 0.10 MPa and H = 0 cm. Within the studied range of the suction capacity, D32 increased for each frother concentration as the suction capacity increased, indicating that the bubble size can be effectively controlled by adjusting the suction capacity. The bubble size was relatively small for a suction capacity of 0.1 to 0.3 L/min at frother concentrations of 0.111 and 0.127 mmol/L; the bubble size at 0.111 mmol/L was larger than that at 0.127 mmol/L when the suction capacity was greater than 0.3 L/min. When the suction capacity increased from 0.1 to 0.9 L/min, the bubble size increased by 0.261 mm (0.096 mmol/L), 0.096 mm (0.111 mmol/L), and 0.047 mm (0.127 mmol/L) respectively; i.e., the difference in D 32 between the two random concentration curves appeared to increase with increasing suction capacity. For a fixed energy input (feeding pressure P = 0.10 MPa), the energy allocated to the unit air was reduced as the amount of suction capacity increased; therefore, the ability of energy to disperse the unit air was diminished.

Effect of sampling location on bubble size
D32 as a function of sampling location at P = 0.10 MPa and q = 0.5 L/min is shown in Figure 12. D32 almost linearly increased with the height of the sampling location for each MIBC concentration; Figure 10. The rotating speed of the impeller (n) as a function of feeding pressure (P)  Figure 11 presents the D 32 values as a function of suction capacity at P = 0.10 MPa and H = 0 cm. Within the studied range of the suction capacity, D 32 increased for each frother concentration as the suction capacity increased, indicating that the bubble size can be effectively controlled by adjusting the suction capacity. The bubble size was relatively small for a suction capacity of 0.1 to 0.3 L/min at frother concentrations of 0.111 and 0.127 mmol/L; the bubble size at 0.111 mmol/L was larger than that at 0.127 mmol/L when the suction capacity was greater than 0.3 L/min. When the suction capacity increased from 0.1 to 0.9 L/min, the bubble size increased by 0.261 mm (0.096 mmol/L), 0.096 mm (0.111 mmol/L), and 0.047 mm (0.127 mmol/L) respectively; i.e., the difference in D 32 between the two random concentration curves appeared to increase with increasing suction capacity. For a fixed energy input (feeding pressure P = 0.10 MPa), the energy allocated to the unit air was reduced as the amount of suction capacity increased; therefore, the ability of energy to disperse the unit air was diminished.  Figure 10. The rotating speed of the impeller (n) as a function of feeding pressure (P)  Figure 11 presents the D32 values as a function of suction capacity at P = 0.10 MPa and H = 0 cm. Within the studied range of the suction capacity, D32 increased for each frother concentration as the suction capacity increased, indicating that the bubble size can be effectively controlled by adjusting the suction capacity. The bubble size was relatively small for a suction capacity of 0.1 to 0.3 L/min at frother concentrations of 0.111 and 0.127 mmol/L; the bubble size at 0.111 mmol/L was larger than that at 0.127 mmol/L when the suction capacity was greater than 0.3 L/min. When the suction capacity increased from 0.1 to 0.9 L/min, the bubble size increased by 0.261 mm (0.096 mmol/L), 0.096 mm (0.111 mmol/L), and 0.047 mm (0.127 mmol/L) respectively; i.e., the difference in D 32 between the two random concentration curves appeared to increase with increasing suction capacity. For a fixed energy input (feeding pressure P = 0.10 MPa), the energy allocated to the unit air was reduced as the amount of suction capacity increased; therefore, the ability of energy to disperse the unit air was diminished.

Effect of sampling location on bubble size
D32 as a function of sampling location at P = 0.10 MPa and q = 0.5 L/min is shown in Figure 12. D32 almost linearly increased with the height of the sampling location for each MIBC concentration; Figure 11. D 32 as a function of suction capacity (q).

Effect of Sampling Location on Bubble Size
D 32 as a function of sampling location at P = 0.10 MPa and q = 0.5 L/min is shown in Figure 12. D 32 almost linearly increased with the height of the sampling location for each MIBC concentration; furthermore, the difference between two adjacent curves also increased. A higher concentration resulted in a smaller slope, which represents smaller variations in bubble size. During the ascending process of the bubble in the flotation cell, the hydrostatic pressure and concentration of frothers play an important role in the BSD; however, the hydrostatic pressure has little effect on the bubble size in the range of sampling height due to the difference in hydrostatic pressure between the top and the bottom of the slurry being very small, the study [34] had found that there was almost no variation on the bubble size during the rising process of single bubble at each concentration, however, the D 32 of the bubble group increased with the increase of sampling height, and a higher frother concentration resulted in a smaller increases. Hence, here, the frother concentration played a major role in BSD compared to the height of the sampling location. A coalescence phenomenon between bubbles affected the bubble size when the frother concentration was lower than the critical coalescence concentration; therefore, the bubble size changed significantly. When the concentration reached the critical coalescence concentration, there was almost no coalescence between bubbles due to the increase of the frother concentration on the bubble surface; hence, the bubble size change was not obvious. furthermore, the difference between two adjacent curves also increased. A higher concentration resulted in a smaller slope, which represents smaller variations in bubble size. During the ascending process of the bubble in the flotation cell, the hydrostatic pressure and concentration of frothers play an important role in the BSD; however, the hydrostatic pressure has little effect on the bubble size in the range of sampling height due to the difference in hydrostatic pressure between the top and the bottom of the slurry being very small, the study [34] had found that there was almost no variation on the bubble size during the rising process of single bubble at each concentration, however, the D32 of the bubble group increased with the increase of sampling height, and a higher frother concentration resulted in a smaller increases. Hence, here, the frother concentration played a major role in BSD compared to the height of the sampling location. A coalescence phenomenon between bubbles affected the bubble size when the frother concentration was lower than the critical coalescence concentration; therefore, the bubble size changed significantly. When the concentration reached the critical coalescence concentration, there was almost no coalescence between bubbles due to the increase of the frother concentration on the bubble surface; hence, the bubble size change was not obvious.  Table 6 represents the fitting function of different curves for different frother concentrations. The slopes for each concentration have the following order: 0.02060 (0.096 mmol/L) > 0.0087 (0.111 mmol/L) > 0.00476 (0.127 mmol/L); this implies that the slope of the fitting equation decreases as the concentration increases. The variation in bubble size, where the concentration was larger than 0.111 mmol/L, became less; almost no coalescence happened during the rising of the bubbles in the flotation cell. Hence, the slopes of the fitting equation given in Table 6 indirectly represent the probability of bubble coalescence, i.e., higher concentrations resulted in smaller slopes, indicating a smaller probability of coalescence among bubbles.

Conclusions
In this study, a new jet-stirring coupling flotation device was designed. It was found that due to the arrangement of double cosine self-aspirated nozzles in a non-submerged manner, a large amount of air was sucked into the flotation cell, which met the requirements of flotation in terms of the suction capacity. D32 decreased with an increasing MIBC concentration until the concentration reached the CCC, above which the bubble size stabilized at approximately 0.31 mm, which was smaller than the bubble size produced by the conventional flotation machine. Higher MIBC concentrations led to the  Table 6 represents the fitting function of different curves for different frother concentrations. The slopes for each concentration have the following order: 0.02060 (0.096 mmol/L) > 0.0087 (0.111 mmol/L) > 0.00476 (0.127 mmol/L); this implies that the slope of the fitting equation decreases as the concentration increases. The variation in bubble size, where the concentration was larger than 0.111 mmol/L, became less; almost no coalescence happened during the rising of the bubbles in the flotation cell. Hence, the slopes of the fitting equation given in Table 6 indirectly represent the probability of bubble coalescence, i.e., higher concentrations resulted in smaller slopes, indicating a smaller probability of coalescence among bubbles.

Conclusions
In this study, a new jet-stirring coupling flotation device was designed. It was found that due to the arrangement of double cosine self-aspirated nozzles in a non-submerged manner, a large amount of air was sucked into the flotation cell, which met the requirements of flotation in terms of the suction capacity. D 32 decreased with an increasing MIBC concentration until the concentration reached the CCC, above which the bubble size stabilized at approximately 0.31 mm, which was smaller than the bubble size produced by the conventional flotation machine. Higher MIBC concentrations led to the formation of a large number of small-sized bubbles. Moreover, D 32 decreased with the increasing feeding pressure; conversely, it increased with suction capacity and sampling location height, independent of the frother concentration. As stated above, bubbles suitable for froth flotation were generated by the jet-stirring coupling flotation device, verifying the efficacy of the overall structural design of the device.
In this study, all the bubble tests of the jet-stirring coupling flotation device were carried out in the presence of the frother. It is well known that the agent used in the froth flotation also includes a collector. However, the BSD tests were not studied under the interaction of the two agents. Therefore, the shape characteristic test of the bubble will be carried out under the action of the collector and frother in future work.