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The effect of particle size on the rising behavior of particle-laden bubbles Peipei Wang, Jan J. Cilliers, Stephen Johan Neethling, and Pablo R. Brito-Parada Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b04112 • Publication Date (Web): 20 Feb 2019 Downloaded from http://pubs.acs.org on February 27, 2019

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The effect of particle size on the rising behavior of particle-laden bubbles Peipei Wang*, Jan J. Cilliers, Stephen J. Neethling and Pablo R. Brito-Parada* Advanced Mineral Processing Research Group, Department of Earth Science and Engineering, Imperial College London, London SW7 2AZ, United Kingdom

ABSTRACT: The rising behavior of bubbles, initially half and fully coated with glass beads of various sizes, was investigated. The bubble velocity, aspect ratio and oscillation periods were determined using high-speed photography and image analysis. In addition, the acting forces, drag modification factor and modified drag coefficient were calculated and interpreted. Results show that the aspect ratio oscillation of the rising bubbles is similar, irrespective of the attached particle size. As the particle size is increased, the rising bubbles have a lower velocity and aspect ratio amplitude, with the time from release to each aspect ratio peak increasing. Higher particle coverage is shown to decrease the bubble velocity and dampen the oscillations, reducing the number of aspect ratio peaks observed. The highest rise velocities correspond to the lowest aspect ratios and vice versa, while a constant aspect ratio yields a constant rise velocity, independent of the particle size. Force analysis shows that the particle drag modification factor increases with increased particle size and is greatest for fully laden bubbles. The modified drag coefficient of particle-laden bubbles increases with particle size, although it decreases with Reynolds number independent of the particle size. The drag force exerted by the particles plays a more dominant role in decreasing

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bubble velocities as particle size increases. The results and interpretation produced a quantitative description of the behavior of rising particle-laden bubbles and the development of correlations will enhance the modelling of industrial applications.

Keywords: Particle size; Rising bubble; Velocity; Aspect ratio; Modified drag coefficient

 INTRODUCTION The behavior of rising air bubbles is a critical factor in determining the efficiency of a wide range of industrial applications such as gas-liquid reactors in the petrochemical industry1 and froth flotation for plastic recycling2, microalgae harvest3 as well as de-inking in the paper industry4. Froth flotation is also one of the most widely used methods in mineral processing5,6, and relies on the collection of hydrophobic particles by bubbles. More specifically, bubbles rise through a slurry of water and a mix of valuable and non-valuable mineral particles, known as the pulp phase; target mineral particles are selectively captured by bubbles, forming bubble-particle aggregates that reach the top of the pulp phase and form a mineral-rich froth which then overflows the flotation tank. The hydrodynamic conditions that the bubble-particle aggregates encounter in the pulp phase play a critical role in the process. However, investigations into the behavior of bubble-particle aggregates (particle-laden bubbles) have been limited due to the opaque and highly dynamic environment in the pulp phase. The behavior of rising bubbles has been studied using capillaries to generate the bubbles, in order to allow a good control of bubble size, and employing high speed photography to accurately track the aspect ratio (shape) and velocities of individual bubbles5. The change in bubble shape and velocity has been reported in many studies, which have focused on the influence of inorganic


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salts7,8, frothers9–11, ionic liquids12, bubble size13,14 as well as colloidal particles15. Recent studies suggest a unique relationship between bubble shape and rise velocity8,9,14. More specifically, bubbles with higher aspect ratio experience higher rise velocity while more spherical bubbles rise at a lower velocity. Buoyancy and drag forces dominate the behavior of a single bubble in a liquid column. The bubble rises due to buoyancy force but its shape and velocity depend on the balance of other forces produced by surface tension, inertia, and viscosity16. The bubble shape, which plays a key role in bubble dynamics17, is determined by the physical properties of the fluid, the bubble size and its velocity. The aspect ratio and the drag coefficient (a dimensionless quantity that is used to quantify the drag force) are two fundamental parameters for predicting the velocity of a rising bubble and thus for modeling bubbly flows17,18. Different models have been proposed for the prediction of these parameters, e.g. correlations combining Weber number with Eötvös number and Weber number with Reynolds number have been shown to satisfactorily predict aspect ratios19, whereas a correlation that combines Reynolds number, Eötvös number and Weber number has been proposed to calculate the fluctuation of drag coefficient20. Studies on rising bubbles have focused mainly on two-phase liquid-gas systems. In the cases where three-phase systems have been considered, e.g. bubble-particle aggregates motion, the focus has been either on the collision of the bubble-particle aggregates with a gas-liquid interface21 or on the detachment of particles from bubbles in a turbulent vortex22–24. Other research at the particle-bubble scale has considered different aspects of particle-stabilized bubbles25, such as coalescence26,27, but has only dealt with bubbles that are fixed to a capillary. It is only recently that further progress has been made concerning the rising behavior of bubbles coated with a controlled level of particles28 exploring how particles attached to the surface of bubbles not only induce an


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additional drag force, but also dampen the bubble shape dynamics, both of which influence the bubble velocity. Yet the influence of particle size on the rising behavior of particle-laden bubbles has not been studied. The aim of this research is to explore the effect of particle size on the behavior of rising bubbleparticle aggregates. A better understanding of the hydrodynamics in these systems has important implications for processes such as froth flotation, where particle sizes play a key role in determining performance29. In this paper, a recently developed model28 is applied to calculate the effect exerted by particles of different size classes, more specifically, the modification drag factor of particles and the modified drag coefficient of particle-laden bubbles are calculated and analyzed. In addition, the oscillation periods of the bubbles as they rise are analyzed and the relative forces on the bubbles and particles are calculated. The findings provide a valuable insight into the behavior of particle-laden bubbles and can be used to inform the modelling of pulp phase flotation phenomena and other relevant processes that rely on particle-laden bubbles.

 EXPERIMENTAL DETAILS Materials Five sizes of spherical soda lime glass beads particles were supplied by SiLi Sigmund Lindner GmbH (Germany), with a mass density of 2.5 g/cm3. Myristyltrimethylammonium bromide (TTAB) of analytical grade was obtained from Sigma-Aldrich Chemical Co. (UK) and used as collector. The Sauter-mean diameter, 𝑑32, as well as 𝑑50 and 𝑑90 were determined using a Malvern Mastersizer 3000. Details are provided in Table S1 in the Supporting Information. The sample size distribution and cumulative volume fractions are shown in Figure 1a and Figure 1b, respectively.


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All of the samples used are in a narrow size distribution range. The experiments were performed at a temperature of 20 °C under natural pH condition.

(a)

(b)

Figure 1. (a) Particle size distribution and (b) cumulative volume fractions of the samples used in the experiments. The legends correspond to: Size 1 𝑑90=64 𝜇m, Size 2 𝑑90=91 𝜇m, Size 3 𝑑90=124 𝜇m, Size 4 𝑑90=156 𝜇m, Size 5 𝑑90=266 𝜇m.

Setup Detailed information of the experimental setup is given elsewhere28, and only a brief description is provided here. Figure 2a shows the schematic of the experimental rig. The experimental rig, placed on a vibration isolated table, allowed for continuous bubble generation and precise control of the air injection from a micro-syringe pump into a capillary (outer diameter of 1.27 mm and inner diameter of 0.84 mm). A clear visualization of the bubbles was achieved by using the camera/LED light source setup shown as a top view in Figure 2b. Bubble behavior was recorded using a high-speed video camera at a speed of 1000 frames per second. For a close-up view of the capillary pinned bubbles, a Canon EOS 600D camera was set perpendicular to the high speed


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camera. Images of the capillary pinned bubbles after they were coated with particles were also recorded for the calculation of particle coverage.

(a)

(b) Figure 2. Schematic of the experimental setup, showing (a) the equipment and (b) a top view of the cameras and LED light source arrangement.

Methodology Two grams of glass beads particles, 250 mL deionized water and TTAB with a final concentration of 1 × 10-6 M were added to a transparent chamber, where they were conditioned with a magnetic stirrer for 15 min. After the particles settled down, a bubble of 2.8-2.9 mm in diameter was generated in the capillary. For tests with uncoated bubbles, the bubble was then released after a continuous air injection at a rate of 0.72 mL h-1. On the other hand, for the study


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of coated bubbles, the stirrer was turned on and the time was adjusted according to the experimental conditions desired, i.e. to achieve bubble coating to the required particle coverage fraction. This allowed the investigation of particle coverage with time for the different particle sizes. To release the coated bubbles, the same air injection rate (0.72 mL h-1) was used. It is worth noting that in this work we refer to capillary pinned bubbles as those that were generated in the capillary and coated with particles, which become rising bubbles (diameter of 3.23.6 mm) once detached from the capillary. For the experiments of rising bubbles, the bubbles in the capillary were initially half or fully coated. Photos of the capillary pinned bubble were taken before and after achieving particle attachment. Once the bubble was released, its motion was recorded over a distance of 30 mm from the tip of the capillary. The comparison of the influence of particles on the bubble velocity and shape change was carried out for the initial time period when the angle (θ) between the bubble’s minor axis and its moving direction was lower than 10°, normally during the first 80 ms. Each experiment was carried out in triplicate. The surface area of the capillary pinned bubbles coated with particles, i.e. particle coverage, was calculated using Matlab, by fitting the pendant drop equation model30 to the edge points of half of the bubbles. Dividing the particle coverage by the surface area of the released bubble yields the actual percentage of the surface area of the released bubble that is covered by particles. During the rising process in the experiments conducted, the detachment of particles was negligible. It is important to note that once a bubble is released from the capillary, its surface area becomes larger, so the percentage of particle coverage of the rising bubble is lower than the one for the capillary pinned bubble. To determine the velocity and aspect ratio of the bubbles, videos of the rising bubbles were processed using ImageJ to obtain the bubbles position and dimensions. The aspect


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ratio (𝐴𝑅), a parameter that reflects the dynamic behavior of rising bubbles, was calculated as the ratio between the bubble diameter perpendicular to its moving direction and the one parallel to it. The velocity of the rising bubble (𝑢) was calculated from the vertical central position of the bubble over two consecutive frames. The tip of the needle was also photographed and used as a reference length to calculate the magnification of the optical system. Further details can be found in our previous study28.

 RESULTS AND DISCUSSION Particle coverage as a function of time in the attachment experiments The flotation rate of hydrophobic particles is determined by the interactions between particles and bubbles, i.e. the collision-attachment efficiency, which is highly dependent on particle size31,32 The experimental setup in this work allowed us to study the influence of particle size on the speed at which particles attached to the capillary pinned bubbles. An example of the change in particle coverage on bubbles at different times, for the sample of size 𝑑90=156 𝜇m, is shown in Figure 3. As can be seen, the coverage increased from 9.0 mm2 after 10 s to 23 mm2 (fully coated) at 97 s.


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Figure 3. Particle coverage on capillary pinned bubbles as a function of time for particles of size 𝑑90=156 𝜇m. The data is shown with 95% confidence intervals.

Table 1 presents the average time that was required to achieve a fully coated bubble for each of the particle size classes investigated. In general, a decrease in attachment speed with particle size is observed, with the coarsest particle class requiring substantially more times for full surface coverage.

Table 1. Average time needed for the bubbles to be fully coated with particles (95% confidence interval included). Particle

Size 1

Size 2

Size 3

Size 4

Size 5

Average time/s

29.9±4.3

59.8±4.1

93.3±8.7

97.1±8.6

>600

Bubbles


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The influence of particle size on rising bubbles As can be observed from Figure 4a, the aspect ratio oscillations of rising bubbles, half coated with particles of different sizes, followed a similar trend, with both a lag observed in the time at which the periodic peaks occur and aspect ratio values decreasing with increasing size of the particles covering the bubbles. The temporal evolution of the velocity of the rising particle-laden bubbles (half coated) is shown in Figure 4b. Similar to what it is observed for aspect ratio, velocities oscillated and exhibited a lag in local maxima with increasing particle size, which is particularly clear at earlier times. In general, velocity magnitudes also decreased with increased particulate size. Interestingly, from Figure 4a and Figure 4b, it can be seen that the periodic peaks in velocity coincided with local minima in aspect ratio.

(a)


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(b) Figure 4. (a) Aspect ratio and (b) velocity of rising bubbles (half coated) as a function of particle size.

The aspect ratio and velocity data from experiments in which the bubbles were fully coated can be seen in Figure 5a and Figure 5b, respectively. Similar to what was observed for half coated bubbles, there is a lag in the oscillations and a reduction in both aspect ratio and velocity values with increasing particle size. It is noticed, however, that the aspect ratio for fully coated bubbles stopped oscillating at 50 ms, with only relatively small changes after that point. The higher level of particle coverage also resulted in a reduction in the maximum values researched for both aspect ratio and velocity. From Figure 5, we can deduce that bubble velocity is constant when the aspect ratio is constant, irrespective of the attached particle size.


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(a)

(b) Figure 5. (a) Aspect ratio and (b) velocity of rising bubbles (fully coated) as a function of particle size.

Oscillation period To analyze the effect of particles on the aspect ratio change, the theoretically derived oscillation period (𝑇) of a rising uncoated bubble of radius 1.60 mm (𝑅) was calculated using equation33,34 (1) and the calculation results were compared to the experimental data of particle-laden bubbles.


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𝑇 = 2𝜋

∆𝜌𝑅3 , 6𝛾

(1)

where the density difference of water and gas ∆𝜌 is 1000 kg/m3, and the surface tension of the gasliquid interface 𝛾 is 74 mN. The measured oscillation periods of the aspect ratio of particle-laden bubbles are about 0.020 s, which are in excellent agreement with the calculated value of 0.019 s. The capillary force causes the small oscillation in aspect ratio while the overall aspect ratio change is determined by hydrodynamic forces. This implies that the high frequency oscillations observed in Figure 4 and Figure 5 are therefore capillary oscillations rather than hydrodynamic oscillations. Moreover, since capillary forces are related to surface tension, it can be concluded that the apparent surface tension of the bubbles is not significantly influenced by the particles attached to their surfaces. The hydrodynamic forces thus play a major role in the phenomena observed and need to be analyzed in detail. The times when periodic aspect ratio peaks occur for rising particle-laden bubbles, both half and fully coated, are shown in Figure 6a and Figure 6b, respectively. The bubble aspect ratio peaks were delayed when the bubble was coated with coarser particles. The number of aspect ratio peaks decreased with higher particle coverage, indicating a more strongly dampened bubble oscillation.


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(a)

(b) Figure 6. Times when aspect ratio peaks occur for rising bubbles (a) half coated and (b) fully coated.

Drag modification factors analysis In this study, the surface tension of the liquid is nearly that of pure water, due to the low concentration of TTAB used. The diameter of the bubbles, produced from the same capillary, can be roughly predicted using equation (2)35, 36:


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𝑑=

3

6𝐷𝛾 , 𝑔∆𝜌

(2)

where 𝑑 is the bubble equivalent diameter, 𝐷 is the capillary inner diameter and 𝑔 is the gravitational acceleration (9.8 m/s2). The calculated bubble diameter is 3.36 mm, which is in good agreement with the experimental results. Full details of the diameter of rising bubbles are provided in Table S2 and Table S3 in the Supporting Information. It should be noted that the diameter is calculated from the particle-bubble aggregate, which is slightly larger if coarser particles (or more particles) were attached to the bubble surface. Unlike a rigid particle, the shape of a rising bubble deforms from spherical to ellipsoidal. Moreover, their shape can be subject to dynamical changes such as periodic oscillations37. Based on our previous calculation model, the rise velocity of particle-laden bubbles is mainly influenced by the hydrodynamic forces, which can be expressed as: 𝑑𝑢 1 (𝐹 + 𝐹𝐵𝑝 ― 𝐹𝐷 ― 𝐹𝐷𝑝 ― 𝑚𝑝𝑔) , = 𝑑𝑡 𝑚𝑝 + 𝑚 ∗ 𝐵

(3)

where 𝑢 is the rise velocity; 𝑡 is the time frames; 𝑚𝑝 is the mass of particles (calculated from the particle coverage and with particles being regarded as a monolayer evenly distributed onto the bubble surface without any aggregation); 𝑚 ∗ is the added mass of the bubble, which is directly related to its aspect ratio value; 𝐹𝐵 is the buoyancy force on the bubble (particles excluded); FBp is the buoyancy force on the particles; FDp is the drag force on the particles and FD is the drag force on the bubble part which is given by the following equation:

2

𝐹𝐷 =

2

𝐶𝐷𝜌𝑢 𝜂B𝜋𝑑 𝐴𝑅 8cosθ

2 3

,


(4)

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where 𝐶𝐷 is the drag coefficient calculated from the Schiller-Naumann model38, which is related to the Reynolds number (Re); 𝜌 is the density of water; μ is the dynamic viscosity of the water; 𝜂𝐵 is the bubble drag modification factor, which is introduced to fit the calculated velocity to the experimental one, using least squares regression analysis; 𝐴𝑅 is the bubble aspect ratio and 𝜃 is the angle between the bubble’s minor axis and its moving direction. The drag force on the particles is expressed as:

𝐹𝐷𝑝 = 𝜂p𝐹𝐷,

(5)

where 𝜂𝑝 is the particle drag modification factor, reflecting the drag influence corresponding to different levels of particle coverage. The calculated velocity as a function of time was fitted to the experimental data, and least squares regression analysis was also used to obtain the particle drag modification factors. The modified drag coefficient 𝐶′𝐷 of the uncoated bubble is

𝐶′𝐷 = 𝐶𝐷𝜂𝐵 .

(6)

The modified drag coefficient of the particle-laden bubble 𝐶𝐷 ― 𝐵𝑝 is 𝐶𝐷 ― 𝐵𝑝 = 𝐶′𝐷(1 + 𝜂𝑝) .

(7)

A bubble attached to the capillary is deformed due to the forces on it, which affect its behavior when it is released. Immediately after detachment, the velocity oscillates for the first 10 ms, after which the velocity increases rapidly before further fluctuation. The first 10 ms were therefore not used for the calculations. For half coated bubbles, the bubble drag modification factor was 0.63, calculated from a released uncoated bubble with a diameter of 3.11 mm. For fully coated bubbles, the bubble drag modification factor was 0.65, which was calculated from a released bubble with a diameter of 3.31 mm. Detailed information about the covered area, particle-bubble aggregates


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diameter, percentage of particle coverage and average particles drag modification factor (𝜂𝑝) for rising bubbles which were initially half and fully coated are provided in Table S2 and Table S3, respectively in the Supporting Information. The particle drag modification factors are the average values from the experiments, with 95% confidence intervals, which are also shown in Figure 7.

Figure 7. The particle drag modification factors for rising particle-laden bubbles as a function of particle size. For initially half and fully coated bubbles, 95% confidence intervals are shown.

As can be seen from Figure 7, for half coated bubbles, the particle drag modification factors increased with an increase in particle size, rising from 0.53 to 1.45. For fully coated bubbles, the particle drag modification factors followed a similar trend, rising steadily from 1.31 to 1.98 as the particle size increased. Overall, a higher fraction of particle coverage induced a higher particle drag modification factor on rising particle-laden bubbles. This is in line with what is observed from Figure 4b and Figure 5b and that the rising bubble velocity decreased when more particles were attached to the bubbles.


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The modified drag coefficient and force analysis of particle-laden bubbles The modified drag coefficient of particle-laden bubbles with different particle size as a function of the Reynolds number are summarized in Figure 8. The modified drag coefficient of particleladen bubbles decreased with the increase in the Reynolds number, independently of particle size. When the particle size (d90) was increased from 64 𝜇m to 124 𝜇m, the modified drag coefficient showed only a minor increase. However when particle size (d90) was increased further to 156 𝜇m and subsequently to 266 𝜇m, the modified drag coefficient increased sharply. The reason is that when the particles are small, the mass force and drag force are mostly balanced by the buoyancy force. However, as the particle size increases, the mass force and drag forces, play a more dominant role in dampening the shape oscillations and decreasing the velocity of particle-laden bubbles. This modified drag coefficient is useful for predicting the behavior of rising bubble-particle aggregates in three-phase systems.

Figure 8. The modified drag coefficient of particle-laden bubbles with different size of particles as a function of the Reynolds number.

To further explore the influence of particle size on the motion of particle-laden bubbles, the forces exerted on the bubbles and particles were calculated and compared for the case of fully


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coated bubbles. These include the bubble drag force, the particle drag force, the bubble buoyancy force, and the difference between the particle buoyancy and gravity forces. The forces on the rising bubbles originally fully coated with finer particles (size 1) and coarser particles (size 5) are shown in Figure 9a and Figure 9b, respectively. As can be observed, the buoyancy force of the bubble was significantly larger than the other forces. Both the drag forces from the particles and the bubbles increased initially and remained constant thereafter. For the bubble coated with finer particles, the difference between the particle buoyancy and gravity forces was relatively small, and the particle drag force was only slightly higher than that of the bubble. For the bubble coated with coarser particles, the particle buoyancy and gravity force difference was larger than for finer particles. The drag force on the bubble was smaller when coated with coarser particles, mainly due to a more spherical bubble formed with coarser particles attached. The drag force from coarser particles was twice that exerted on the bubble, and also higher than that from finer particles. It can be concluded that particles decrease the bubble motion, not only due to the added mass force but more so due to the added drag force. When bubbles are coated with coarser particles, the particle drag force plays a more significant role in reducing the rising velocity of particle-laden bubbles.


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(a)

(b) Figure 9. Forces acting on rising particle-laden bubbles which are fully coated. (a) Particle size d90=64 𝜇m and (b) particle size d90=266 μm.

 CONCLUSIONS The behavior of rising particle-laden bubbles was investigated as a function of particle size. A series of experiments combined with theoretical analyses of forces acting on the bubbles were used


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to propose a drag modification factor. This drag modification factor allows for the quantification of the effect which particles of different sizes exert on the rising bubbles. A capillary placed in a transparent chamber was connected to a programmable micro-syringe pump, and this pump allowed the control of the air injected into the capillary, essential for the generation of repeatable bubbles. Results show that it takes more time for a capillary-pinned bubble to be fully coated with coarser particles. It was found that after the bubbles are released, and as they rise, their aspect ratio oscillations follow a similar trend regardless of the size of the attached particles. An increase in particle size, however, results in both a delay in the periodic peaks in aspect ratio and lower aspect ratio oscillation amplitudes. The increase in particle size also lowered the velocity of the rising bubbles. It is noted that all peak velocities correspond to valleys of aspect ratio, independent of the particle size. Another interesting finding is that for fully coated bubbles, their shape oscillation is more strongly dampened and presents fewer aspect ratio peaks than those half coated bubbles. A force analysis showed that the particle drag modification factor increases as either particle size or particle coverage increases. The modified drag coefficient, calculated from the particle drag modification factor, increases with particle size, although it decreases with Reynolds number independent of the particle size. The analysis also shows that as particle size increases, the particle drag force, plays a more dominant role in decreasing the velocity of particle-laden bubbles, rather than the bubble aspect ratio. This is the first study of the influence of particle size on the motion of particle-bubble aggregates. It can be used as an important contribution to the modeling of particle-laden bubble motion, such as in a flotation tank.


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 ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Details of characteristic particle diameters as well as detailed information on the covered area, particle-bubble aggregates diameter, percentage of particle coverage and average particles drag modification factor for rising bubbles. (PDF)

 AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] [email protected] Notes The authors declare no competing financial interest.

 ACKNOWLEDGMENTS The authors would like to thank IOM3 (The Institute of Materials, Minerals & Mining) for their financial support for the purchase of one of the high-speed cameras used in this work. Peipei Wang would like to thank the President’s PhD Scholarship from Imperial College London for financial assistance. Thanks are also due to Francisco Reyes for his contribution to the Matlab code.

 REFERENCES (1) Boyer, C.; Duquenne, A. M.; Wild, G. Measuring Techniques in Gas-Liquid and GasLiquid-Solid Reactors. Chem. Eng. Sci. 2002, 57, 3185–3215.


Page 22 of 28

Page 23 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(2)

Zhao, Y.; Li, Y.; Huang, J.; Liu, J.; Wang, W. Rebound and Attachment Involving Single Bubble and Particle in the Separation of Plastics by Froth Flotation. Sep. Purif. Technol. 2015, 144, 123–132.

(3)

Huang, Z.; Cheng, C.; Liu, Z.; Luo, W.; Zhong, H.; He, G.; Liang, C.; Li, L.; Deng, L.; Fu, W. Gemini Surfactant: A Novel Flotation Collector for Harvesting of Microalgae by Froth Flotation. Bioresour. Technol. 2019, 275, 421–424.

(4)

Shemi, A.; Hsieh, J. S. Electroflotation Combined with Flotation Deinking of Flexographic Newsprint. Ind. Eng. Chem. Res. 2010, 49, 2380–2387.

(5)

Wills, B. A.; Napier-Munn, T. J. Mineral Processing Technology; Elsevier Science & Technology, 2005.

(6)

Mesa, D.; Brito-Parada, P. R. Scale-up in Froth Flotation: A State-of-the-Art Review. Sep. Purif. Technol. 2019, 210, 950–962.

(7)

Maldonado, M.; Quinn, J. J.; Gomez, C. O.; Finch, J. A. An Experimental Study Examining the Relationship between Bubble Shape and Rise Velocity. Chem. Eng. Sci. 2013, 98, 7– 11.

(8)

Quinn, J. J.; Maldonado, M.; Gomez, C. O.; Finch, J. A. Experimental Study on the ShapeVelocity Relationship of an Ellipsoidal Bubble in Inorganic Salt Solutions. Miner. Eng. 2014, 55, 5–10.

(9)

Kracht, W.; Finch, J. A. Effect of Frother on Initial Bubble Shape and Velocity. Int. J. Miner. Process. 2010, 94, 115–120.

(10)

Tan, Y. H.; Finch, J. A. Frother Structure-Property Relationship: Effect of Alkyl Chain


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Length in Alcohols and Polyglycol Ethers on Bubble Rise Velocity. Miner. Eng. 2016, 95, 14–20. (11)

Tan, Y. H.; Zhang, W.; Finch, J. A. Frother Structure-Property Relationship: Effect of Polyethylene Glycols on Bubble Rise Velocity. Miner. Eng. 2018, 116, 56–61.

(12)

Dong, H.; Wang, X.; Liu, L.; Zhang, X.; Zhang, S. The Rise and Deformation of a Single Bubble in Ionic Liquids. Chem. Eng. Sci. 2010, 65, 3240–3248.

(13)

Manica, R.; Klaseboer, E.; Chan, D. Y. C. Force Balance Model for Bubble Rise, Impact, and Bounce from Solid Surfaces. Langmuir 2015, 31, 6763–6772.

(14)

Liu, L.; Yan, H.; Zhao, G.; Zhuang, J. Experimental Studies on the Terminal Velocity of Air Bubbles in Water and Glycerol Aqueous Solution. Exp. Therm. Fluid Sci. 2016, 78, 254–265.

(15)

Ata, S.; Ng, K. Y.; Law, E.; Lim, M. Influence of Particles on the Formation of Bubbles from a Submerged Capillary. Miner. Eng. 2014, 66–68, 47–53.

(16)

Talaia, M. A. R. Terminal Velocity of a Bubble Rise in a Liquid Column. Eng. Technol. 2007, 22, 264–268.

(17)

Ziegenhein, T.; Lucas, D. Observations on Bubble Shapes in Bubble Columns under Different Flow Conditions. Exp. Therm. Fluid Sci. 2017, 85, 248–256.

(18)

Li, H.; Liu, Z.; Chen, J.; Sun, B.; Guo, Y.; He, H. K. Correlation of Aspect Ratio and Drag Coefficient for Hydrate-Film-Covered Methane Bubbles in Water. Exp. Therm. Fluid Sci. 2017, 88, 554–565.


Page 24 of 28

Page 25 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(19)

Liu, L.; Yan, H.; Zhao, G. Experimental Studies on the Shape and Motion of Air Bubbles in Viscous Liquids. Exp. Therm. Fluid Sci. 2015, 62, 109–121.

(20)

Yan, X.; Jia, Y.; Wang, L.; Cao, Y. Drag Coefficient Fluctuation Prediction of a Single Bubble Rising in Water. Chem. Eng. J. 2017, 316, 553–562.

(21)

Ireland, P. M.; Jameson, G. J. Collision of a Rising Bubble–particle Aggregatewith a Gas– liquid Interface. Int. J. Miner. Process. 2014, 130, 1–7.

(22)

Wang, G.; Evans, G. M.; Jameson, G. J. Bubble – Particle Detachment in a Turbulent Vortex I : Experimental. Miner. Eng. 2016, 92, 196–207.

(23)

Wang, G.; Evans, G. M.; Jameson, G. J. Bubble-Particle Detachment in a Turbulent Vortex II—Computational Methods. Miner. Eng. 2017, 1102, 58–67.

(24)

Wang, G.; Evans, G. M.; Jameson, G. J. Bubble Movement in a Rotating Eddy: The Implications for Particle-Bubble Detachment. Chem. Eng. Sci. 2017, 161, 329–340.

(25)

Bournival, G.; Ata, S.; Wanless, E. J. The Roles of Particles in Multiphase Processes: Particles on Bubble Surfaces. Adv. Colloid Interface Sci. 2015, 225, 114–133.

(26)

Ata, S. Coalescence of Bubbles Covered by Particles. Langmuir 2008, 24, 6085–6091.

(27)

Bournival, G.; Ata, S.; Wanless, E. J. Behavior of Bubble Interfaces Stabilized by Particles of Different Densities. Langmuir 2016, 32, 6226–6238.

(28)

Wang, P.; Cilliers, J. J.; Neethling, S. J.; Brito-parada, P. R. The Behavior of Rising Bubbles Covered by Particles. Chem. Eng. J. 2019, 365, 111–120.

(29)

Muganda, S.; Zanin, M.; Grano, S. R. Influence of Particle Size and Contact Angle on the


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Flotation of Chalcopyrite in a Laboratory Batch Flotation Cell. Int. J. Miner. Process. 2011, 98, 150–162. (30)

Arashiro, E. Y.; Demarquette, N. R. Use of the Pendant Drop Method to Measure Interfacial Tension between Molten Polymers. Mater. Res. 1999, 2, 23–32.

(31)

Miettinen, T.; Ralston, J.; Fornasiero, D. The Limits of Fine Particle Flotation. Miner. Eng. 2010, 23, 420–437.

(32)

Ren, L. Y.; Zhang, Y. M.; Qin, W. Q.; Bao, S. X.; Wang, J. Collision and Attachment Behavior between Fine Cassiterite Particles and H2 Bubbles. Trans. Nonferrous Met. Soc. China. 2014, 24, 520–527.

(33)

Lord Rayleigh. On the Capillary Phenomena of Jets. Proc. R. Soc. London 1879, 29, 71– 97.

(34)

Nair, P.; Pöschel, T. Dynamic Capillary Phenomena Using Incompressible SPH. Chem. Eng. Sci. 2018, 176, 192–204.

(35)

Hemmati Chegeni, M.; Abdollahy, M.; Khalesi, M. R. Bubble Loading Measurement in a Continuous Flotation Column. Miner. Eng. 2016, 85, 49–54.

(36)

Yang, J.; Yu, K.; Zuo, Y. Y. Accuracy of Axisymmetric Drop Shape Analysis in Determining Surface and Interfacial Tensions. Langmuir 2017, 33, 8914–8923.

(37)

Clift, R.; Grace, J. R.; Weber, M. E. Bubbles, Drops, and Particles; Academic Press: New York, 1978.

(38)

Schiller, L.; Nauman, A. Über Die Grundlegenden Berechnungen Bei Der


Page 26 of 28

Page 27 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Schwerkraftaufbereitung. Zeitschrift Des Vereines Dtsch. Ingenieure 1933, 77, 318–320.


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