Oil droplet movement and micro-flow characteristics during interaction process between gas bubble and oil droplet in flotation

Shenglin Yan, Yan Zhang, Chong Peng, Xiaoyong Yang, Yuan Huang, Zhishan Bai,*, Xiao Xu

1 State Environmental Protection Key Laboratory of Environmental Risk Assessment and Control on Chemical Process, School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, China

2 Sinopec Dalian Research Institute of Petroleum and Petrochemicals, Dalian 116041, China

3 Institute of Environmental Pollution and Health, School of Environmental and Chemical Engineering, Shanghai University, Shanghai 200444, China

Keywords:Flotation Oil droplet-gas bubble interaction Approach process Hydrodynamics

ABSTRACT Flotation is an efficient pre-treatment technology for oily water.In this work, the interaction process between the moving oil droplet and the gas bubble was studied by high-speed camera and Bassset-Boussinesq-Oseen(BBO)theoretical model,and the experimental and simulation results of the oil droplet trajectory were compared.Moreover,the micro-particle image velocimetry system was utilized to observe the flow inside and outside of the moving oil droplet.The results show that the BBO model with the mobile bubble’s surface can reflect the velocity change trend of the oil droplet during the interaction process between the moving oil droplet and the gas bubble, but there are some significant differences between the experimental and simulation results.While the oil droplet is moving on the bubble’s surface,the velocity of the area near the contact point of oil droplet-gas bubble is less than that of the other areas inside the oil droplet.Meanwhile,the flow of water above the oil drop is more biased towards the gas bubble.

1.Introduction

In the industrial production process (e.g., the petroleum exploitation and refining, textile, and food processing industries),a large amount of oily water needs to be treated.In order to protect human health and the ecological environment, the discharge of oily water is strictly monitored[1,2].Some regions and institutions have formulated strict discharge standards [3].For example, the Oslo-Paris Convention (OSPAR) stipulates that the oil content of discharged wastewater is less than 30 mg·L-1[4].To meet the discharge standards,wastewater needs to be treated before discharge.In order to reduce production costs and improve production efficiency, we should avoid using additives and expensive process steps in the wastewater treatment process [5].Flotation is a wastewater treatment method that meets the requirements and has the characteristics of rapid treatment of large amount of oily wastewater [6].In the water treatment process, the attachment between the gas bubble and the oil droplet forms an aggregate.The large density difference between the aggregate and the water can drive the aggregate to rise to the top of the water [7,8].

In the flotation process,the oil droplet-gas bubble aggregate in the form of oil film wrapping the bubble is the most stable[8].The formation of a stable aggregate between the oil droplet and the gas bubble generally goes through five stages: approach stage, film drainage stage, spread stage, oscillation stage, and equilibrium stage [9].After the collision event between the oil droplet and the gas bubble, the oil droplets and the gas bubble enter into the film drainage stage.In previous studies, it was pointed out that the drainage time in the drainage stage is a characteristic parameter,which determines the flotation efficiency[10-13].If the sliding time of the oil droplet on the bubble surface is greater than the drainage time,the oil droplet can cover the bubble to form oil film[8,14,15].However, the five stages during the attachment process of oil droplet-gas bubble are not independent of each other, but are progressive.The attachment process of oil droplet-gas bubble begins when the oil droplet approaches the gas bubble.The closeness between particles and bubbles is achieved through collisions[16].In flotation equipment, the approach process is very complicated and depends on the dynamics of bubbles and particles in turbulent flow [17-19].During the flotation process, the appearance of bubbles will change the local turbulent kinetics and form micro-turbulence [20].Micro turbulence controls bubble-droplet collision and detachment [21].The limit of the approaching process is determined by the area between the long-range hydrodynamic and interfacial force [15,16].Many researchers studied the interaction between bubbles and particles,and use predictive particle trajectories to calculate collision efficiency [22-25].Those studies pointed out that the velocity of the water flow passing the gas bubble is very important for calculating the particle trajectory.At present,the Basset-Boussinesq-Oseen(BBO)model is usually employed to predict the trajectory of particles in bubble-particle system [14,15,26].The BBO model takes into account the fact that the contact process between bubbles and particles is affected by a variety of interaction forces, including fluid dynamics, gravity, surface forces and capillary.Dealing with the flow velocity of the bubble surface,BBO usually defines the bubble surface as a mobile or immobile surface.Firouziet al.pointed out that the simplified model of bubble surface cannot fully reflect the flow characteristics of the bubble surface [27].Meanwhile,the flow of water can also affect the particle trajectory.Understanding and controlling the interaction between the oil droplet and the gas bubble is very important for successfully attaching oil droplets to gas bubbles.At present, there are few studies on velocity changes of the oil droplet and the flow regimes inside and around oil droplet in the approaching stage and movement on the gas bubble during the interaction between the oil droplet and the gas bubble.

This work is about the study of the flow regimes inside and around the oil droplet during the interaction process.In this paper,the BBO theoretical model was employed to predict the trajectory of the oil droplet during the interaction process in the oil droplet--gas bubble system.The applicability of the theoretical model was evaluated through comparing the trajectory of the oil droplet predicted by the BBO model with that observed by experiment.Meanwhile, we employed the micro-particle image velocimetry (PIV)system to investigate the flow regimes inside and around the oil droplet during the interaction process.The evolution of twodimensional velocity field with time revealed the flow characteristics inside and around the oil droplet during the interaction process.

2.Methodology

2.1.Experiment method

2.1.1.Trajectory recording system

In order to study the interaction process of oil droplets-bubbles in a quiescent deionized water medium,we designed a high-speed recording experimental system to record the interaction process of oil droplets-gas bubble.Fig.1(a) is the schematic of trajectory recording system.The shape of the needle was L-shaped, and the outer diameter was 1.66 mm.During the experiment, the tip of the needle was horizontal.The length of the horizontal needle was approximately 2 cm, which ensured that the vertical portion of the needle was away from the focal plane of the lens and reduced interference with the experimental recording pictures.Fig.1(b) is the schematic of the oil droplet generation device.The piston in the syringe was pushed by high-pressure air to squeeze the oil phase into droplets.The duration of the oil droplets was controlled by the release time of high-pressure air.The pressure control valve controlled the release time of high-pressure air.In the present experiment, the release time was set as 0.6 s.The oil droplet generation device was fixed to the six degrees of freedom micro-platform, by which a micrometer adjustment was installed to ensure that the center planes of the oil droplet and bubble was on the same plane.

In the present experiment,the trajectory of the oil droplet in the interaction process was recorded by a high-speed digital video camera (FASTCAM SA-X2, Photron, Japan) coupled with a microscope lens (5×M Plan APO, EO, USA), with a recording speed of 1000 frames per second and a resolution of 1024×1024 pixels.The recorded images were magnified by the microscope assembly achieving 5×optical magnification with a depth of field of 180 μm.The material of the gas bubble was made of dry air, and the material of the oil droplet was the isooctane of 97% analytical reagent.The physical parameters of isooctane can be found in Yanet al.’s article [9].Bubble diameter of 2.38 mm was studied.The room temperature was approximately 20°C during the experiment.

2.1.2.Micro-PIV measurement system

Fig.1. Schematics of (a) the trajectory recording experiment system, (b) the oil droplet generated device, (c) the micro-PIV measurement system.

The 2D PIV measurement system was employed to investigate the evolution of velocity field inside and around the oil droplet.Fig.1(c) is the schematic of the 2D Micro-PIV measurement system.As shown in Fig.1(c),the micro-PIV experimental system consisted of a glass tank, a continuous laser device (MGL-N-532A,Cnilaser, China), a 45-degree Powell lens, a microscope lens (5×M Plan APO,EO,USA),and a high-speed digital video camera(FASTCAM SA-X2,Photron,Japan).To study the flow regimes inside and around the oil droplet during the interaction process,independent PIV experiments were carried out on oil droplet and water,respectively.The Rhodamine B fluorescent microspheres with a diameter of 0.76 μm and a density of 1050 kg·m-3were added to the oil droplet and water as tracing particles, respectively.The laser of 532 nm (beam size: 1.5 mm) emitted by the laser device passed through a Powell lenses of 45° and became a laser sheet with a thickness of approximately 1 mm.The fluorescent microspheres were excited by the laser, and the lights with a wavelength of 580 nm were emitted.The movements of the fluorescent microsphere were recorded by the high-speed digital video camera,with a recording speed of 5000 frames per second and a resolution of 1024×1024 pixels.The continuous sequence pictures taken by the high-speed camera were processed by MATLAB PIVlab 2.31[28]to obtain the velocity vector diagram inside and around the oil droplet.The time interval between two adjacent images was set as 0.05 ms in MATLAB PIVlab.A double pass algorithm was used for speed correction.The initial window size of 64×64 pixels was reduced to 32×32 pixels, and the window overlap rate was 50%.

2.2.Theoretical

In the flotation system, during the interaction process, it is assumed that the oil droplets are still moving in a sphere.Fig.2 is the schematic of the oil droplet-gas bubble interaction process.Due to the density difference between the oil droplet and the water, the buoyancy drives the oil droplet to rise and approach the bubble.According to the quartz particle-gas bubble flotation system, the oil droplet is also subjected to the viscous stress of the water and the resistance of the liquid volume decelerating with the oil droplet motion.The motion of oil-droplet under buoyancy force through quiescent fluid can model BBO equation [14,15,26]described as:where v is the oil droplet velocity;mois the oil droplet mass;mfis the mass of liquid displaced by the oil droplet;μ is the viscosity of liquid;Rois the oil droplet radius;gis the acceleration of gravity;andtis the moving time.The term on the left side of BBO (Eq.(1)) represents the resultant force of the oil droplet, the first term on the right side is referred to as the viscous stress of the water,and the second term as the resistance of the liquid volume decelerating with the oil droplet motion.The last term on the right side presents the buoyancy force, as the main force driving the oil droplet to approach to gas bubble.

Fig.2. Illustration of the oil droplet-gas bubble interaction.R0 is the radius of the oil droplet,Rb is the radius of the gas bubble,Rc is the radius of grazing trajectory,and θ is the azimuth angle.

By substituting formoandmfin terms of theRoand the oil and fluid densities,ρoand ρf, and defining the Stokes velocity,vs, and the viscous relaxation time,τ, Eq.(1) can be simplified as

In order to ensure the stability of solving the BBO equation and anticipating the need to describe the flow around the spherical bubble, the Eq.(2) can be transformed into polar coordinatesr,θ( ), whererrepresents the distance of the oil droplet center to the gas bubble center, and θ is the polar angle.The BBO equation in the polar coordinate system is written as:

The above equation does not include the expression that the trajectory of the oil drop could deviate from the bubble surface.Therefore, it is necessary to add correction factors to the Eq.(5)to reflect the effect of the bubble on the oil droplet trajectory.Nguyen and Schulze [15]proposed a short-range hydrodynamic resistance function to correct Eqs.(5a) and (5b).After correction,the Eq.(5) can be written as:

wheref1andf2is the radial and tangential correction factors,respectively.During the particle moving on the bubble surface,two limit cases can be defined in the bubble surface, which are immobile and fully mobile, respectively.For the immobile bubble surface, the correction factors for tangential and radial are defined as follows:

For the fully mobile bubble surface, the correction factors for tangential and radial are defined as follows:

Here,H=r-Rb-Ro, represents the closest distance between the oil droplet and the gas bubble surfaces.

3.Results and Discussion

3.1.The interaction process

This system provides the possibility for us to directly observe the interaction process between the oil droplet and the gas bubble in the flotation system.Fig.3 shows the interaction process between the oil droplet and the gas bubble.During the oil droplet moving on the surface of the gas bubble, there are two consequences, fall off and coalescence.In the particle-bubble flotation system, after the rupture event of the liquid film, the three-phase contact line is formed, then the particle slides to the bottom of the bubble [14].Compared with the process of the bubble capturing the particle, during the coalescence process, the interfaces of the oil droplet and the gas bubble are greatly deformed, and then the oil droplet covers the surface of the bubble to form an oil film.The obvious interface deformation makes it easier to determine the time,at which the film ruptures and the spread stage starts.In the present experiment system, the oil droplet moves on the bubble surface driven by buoyancy force, which to a certain extent can reflect the characteristics of the interaction process of the oil droplets and the gas bubble in the oil droplet-gas bubble flotation system.However, this article is to study the interaction between the oil droplet and the gas bubble in the case of where the film is not ruptured, and the coalescence process of the oil droplets and the gas bubble will be studied in subsequent work.

3.2.Oil droplet movement behavior

Fig.3. The interaction process of the group of oil droplet and the gas bubble:(a)the oil droplet falls off from the surface of the bubble,(b)the oil droplets and the gas bubble coalesce into the aggregate, and the period of t is 3 ms.

Fig.4. Observed oil droplet trajectories around a bubble, colored by the instantaneous velocity.

Fig.4 shows the trajectories of the oil droplets generated at eight different horizontal positions close to the bubble,and the trajectories are colored by the instantaneous velocity.From Fig.4, it can be found that when the initialRc/Rbis greater than 1, the oil droplets deviate from the gas bubble, without obviously interaction with the gas bubble.They are not significantly affected by the bubble during the floating process.Instead, the oil droplets maintain a certain acceleration movement under the action of buoyant force.When the initialRc/Rbis less than 1,the oil droplets are obviously affected by the gas bubble.While the oil droplet is approaching the gas bubble, the liquid between the oil droplet and the gas bubble is gradually discharged.The barrier effect of the bubbles makes the speed of the oil droplets significantly decrease.After the event of contact,due to the liquid film between the oil droplet and the gas bubble,this is not a real contact,the oil droplet continues to move on the surface of the gas bubble.During this process, the oil droplet has a significant acceleration process,then it reaches a peak of instantaneous velocity near the equator of the gas bubble,and it finally falls off the surface of the gas bubble.The above process of interaction between oil droplets and bubbles is similar to the interaction process of quartz particles and the gas bubble[14].This phenomenon may be caused by the fluidity of the bubble surface.

In order to study the interaction between the oil droplet and the gas bubble, the numerical calculation is utilized to predict the movement trajectory of oil droplets with the two types of bubble surface.The predicted trajectories are compared with the observed movement trajectories.For more convenience, we discuss the movement process of No.4 and No.5 oil droplet on the bubble surface.Fig.5 compares the predicted trajectories of the oil droplet with the experimentally observed results.It can be found from Fig.5 that during the interaction process, the predicted velocity of the oil droplet with both mobile and immobile bubble surface decreases with the distance between the oil drop and the gas bubble.But, there is a significant difference between the prediction with immobile bubble surface and the prediction with the mobile bubble surface and the experimental results.

Fig.5. Comparison of observed trajectory and velocity with prediction:(a)No.4 oil droplet, (b) No.5 oil droplet.In the figure, the result of experiment observed is on the left;the result of BBO model predicted with fully mobile bubble surface is at the center; and the result of BBO model predicted with immobile bubble surface is on the right.The diameters of oil droplets and bubbles are 0.52 and 2.38 mm,respectively.

The velocity curves of No.4 and No.5 oil droplets as a function of azimuth angle is plotted in Fig.6.In Fig.6, we can observe the azimuth angle at which the oil droplet contact and fall off the gas bubble.When the oil droplet contacts the bubble,the velocity of the oil droplet reaches the minimum.When the oil droplet falls off the gas bubble, the velocity of the oil droplet reaches the maximum value.This is because the oil droplet has been accelerating during the movement on the bubble surface.Comparing the contact azimuth angles of the results of each group, the experimental value of No.4 oil drop is basically consistent with the predicted value with the mobile bubble surface, and the experimental result of No.5 oil drop is 4.7% less than the predicted result with the mobile bubble surface.Comparing the fall off azimuth angles of the results of each group,the experimental value of No.4 oil drop is 120°, which is 5.2%higher than the predicted value (114°) with the mobile bubble surface, and the experimental value of No.5 oil drop is 116°,which is 5.5% higher than the predicted value (110°) with the mobile bubble surface.The predictions with the mobile bubble surface are in good agreement with the experimental results in terms of contact and fall off azimuth angles, but there is still a large difference between the predictions of the maximum velocity and the experimental results.For the No.4 oil droplet, the predicted maximum velocity with the mobile bubble surface is 40.6 mm·s-1, which is 31.7% higher than the experimental result.For the No.5 oil droplet, the predicted maximum velocity with the mobile bubble surface is 43 mm·s-1, which is 21% higher than the experimental result.It can be seen from Fig.6 that the prediction results with the immobile surface have the opposite trend to the experimental results, and the difference is large.It can be concluded that in the interaction process of the oil drop and the gas bubble, the type of bubble surface is between mobile and immobile, and the trend is similar to that of the mobile bubble surface.The BBO equation with mobile bubble surface does not introduce the complex flow regimes outside the gas bubble,so there is still a certain difference between the predicted and the experimental results.At present, the micro-hydrodynamic correction factors of the bubble and the partial mobile theory of the bubble surface are lacking.For researchers who are committed to the development of flotation kinetic model, the determination of these influencing factors will be a major challenge[27].

Fig.6. Comparison of the instantaneous velocities of experimental and predicted:(a)No.4 oil droplet,(b)No.5 oil droplet.The diameters of oil droplets and bubbles are 0.52 and 2.38 mm, respectively.

Fig.7. The evolution of two-dimensional velocity field inside the oil drop in the focal plane during the interaction process.The diameters of the oil drop and the gas bubble are 1.08 and 2.38 mm, respectively.

Fig.8. Comparison of the instantaneous velocity near the droplet center and the bubble-oil droplet contact point with different azimuth angles.

3.3.Internal flow inside the oil droplet

To reveal the flow characteristic of the trajectory of the oil droplet during the interaction process,we used micro-PIV to study the change of the internal micro-flow inside the oil droplet during the movement.Fig.7 shows the micro-flow inside the droplet at six different azimuth angles during the interaction process.In the present experiment, the diameter of the bubble was controlled as 2.38 mm, and the diameter of the oil drop was controlled as 1.08 mm, so that the high-speed camera could observe the movement of the tracer particles inside the oil drop.At the azimuth angle of 10°, the oil droplet rises to approach the bubble at about 75 mm·s-1.When the oil droplet collides with the gas bubble at azimuth angle of 12°, due to the high impact velocity, the area near the contact point is squeezed, and a velocity component is produced on both sides of the contact point and deviates from the contact point.The velocity in the area near the contact point is significantly lower than that in other areas inside the oil droplet.During the moving process on the bubble surface,the corresponding azimuth angles are 45°and 90°,the velocity direction in the oil droplet is approximately perpendicular to the line of the contact point and the bubble center.The swirl flow is not found inside the oil droplet,it may indicate that the oil droplet does not roll during the movement on the bubble surface.This is consistent with the phenomenon observed by Nguyen and Evans[29],and Verrelliet al.[14].It shows that no matter whether the dispersed phase is oil droplets or solid particles, there is not a roll during movement on bubble surface.After the oil droplet falls off from the bubbles,the corresponding azimuth angles are 105° and 120°, the velocity inside the oil droplet decreases significantly.This is consistent with the result in section 3.2.

Also, it can be found from Fig.7(c) and (d) that the velocity of the area near the contact point of the oil droplet and the bubble is lower than the velocity of other areas inside the oil droplet, as shown by the green dotted line mark in Fig.7(c) and (d).Fig.8 shows the changing process of the instantaneous velocity near the droplet center and the bubble-oil droplet contact point with different azimuth angles.After a collision event, the thin film of water is trapped between the oil droplet and the gas bubble.During while the oil droplet is moving on the gas bubble surface, the velocity difference exists in the liquid film.Because the thickness of the liquid film is very thin, basically on nanometer scale, the flow in the liquid film has large shear stress.The large shear stress induces the velocity of the area near liquid film to be smaller than that in the other areas inside the oil droplet.

3.4.External flow around the oil droplet

Fig.9 shows external flow outside the droplet at six different azimuth angles during the interaction process.In the section, the diameters of the bubble and the oil droplet are the same as in section 3.3.At the azimuth angles of 10°(Fig.9(a))and 12°(Fig.9(b)),the bubble approaches the bubble with an approximately rectilinear motion, and the velocity field outside the oil droplet shows a simple flow structure:the fluid above the oil droplet flows upward.Due to the existence of the gas bubble,the fluid is divided into two streams,and they flow along both sides of the gas bubble.Since the oil droplet eccentrically collides with the gas bubble,the results do not show a symmetric flow structure.Meanwhile, the fluid in the outer region of the oil droplet flows downward to fill the wake of the oil droplet.A vortex flow structure is formed during the filling process, as shown by the red dotted line mark in Fig.9(b).Therefore,a strong diversion flow is formed during while the oil droplet is approaching the gas bubble.At the azimuth angles of 30°(Fig.9(c))and 45°(Fig.9(d)),the oil droplet is moving on the bubble surface.The peripheral fluid in the left region outside the oil droplet flows downward, and there is still a vortex flow structure on the left side of the oil droplet.Due to the existence of the gas bubble,the original down-flowing feature in the right region outside the oil droplet disappears.And, the vortex flow structure in the right region outside the oil droplet is also destroyed.When the oil droplet moves to the azimuth angle of 90°,the oil droplet begins to fall off the surface of the bubble.There is a gap area between the oil droplet and the bubble.At the azimuth angles of 120°, the vortex flow structure is observed again,as shown by the red dot-line mark in Fig.9(f).The above is the changing process of the micro-flow outside the oil droplet during the action of the oil droplet-bubble process.Before the oil droplet collides with the gas bubble, there are a pair of vortexes on the left and right regions outside the oil droplet, which is consistent with the result of Liu and Zheng’s study[30]about the bubble rising behavior.After the event of collision,the gas bubble changes the micro-flow structure outside the oil droplet,which is the validation of the assumptions used by Darabiet al.[20].

The flow near the bubble surface at the azimuth angles of 90°is extracted for research.Fig.10 shows the velocity profiles along the straight-line of AB in Fig.9 when the oil droplet arrives at the azimuth angles of 10°, 12° and 45°.It can be found from the Fig.10 that the relative position of the velocity peak is less than 1, at the azimuth angle of 10°, the relative position is 0.67; at the azimuth angle of 12°, the corresponding relative position is 0.51,and, at the azimuth angle of 45°, the corresponding relative position is 0.86.This result shows that during the interaction process,the mainstream area of the flow formed by the oil droplet pushing the fluid near the water-air interface is biased towards the bubbles.Furthermore, the relative position of the velocity peak varies with the azimuth angle.The flow near the bubble surface is the multi-phase flow.At the water-air interface, there is not only a large density difference, but also a large difference in viscosity.The viscosity of air is less than that of water,so the effect of viscous shear stress of air at the interface is lower than that of water for the flow near the interface.Therefore, because of the viscosity difference, the mainstream area of the flow above the oil droplets is more inclined to the gas bubble.

Fig.9. The evolution of two-dimensional velocity field outside the oil drop in the focal plane during the interaction process.The diameters of the oil drop and the gas bubble are 1.08 and 2.38 mm, respectively.

During the oil droplet-gas bubble interaction process, the bubble will change the flow structure outside the oil droplet.Moreover, the flow near the bubble interface is also changeable.From the results of 2D PIV, the flow around the bubble is not a simple potential flow or Stokes flow, but a complex three-dimensional flow.If the bubble mobility factors can reflect the changing processes of the flow structure around the oil droplet and the microflow near the bubble interface, the BBO theoretical model with the mobility factors may accurately predict the movement trajectory of the oil droplet during interaction process.

4.Conclusions

In this work,the high-speed camera experiment system and the BBO theoretical model are employed to study the interaction between the oil droplet and the gas bubble, and micro-PIV is utilized to investigate the flow regimes inside and outside the oil droplet,revealing the flow characteristics of the oil droplets during the interaction process.

Fig.10. The velocity profile along the straight-line of AB in Fig.9 at the azimuth angle with the oil droplet located at different azimuth angle.H is the distance from the bubble surface with the azimuth angle of 90°,Uinit is the initial velocity of the oil drop.

(1)In the case of where the film is not ruptured,the interaction process between the oil droplet and the gas bubble can be divided into three stages: approaching, movement on the bubble surface,and falling off.The BBO model with mobile bubble model can reflect the motion tendency of the oil droplet during the interaction process.About regarding the maximum instantaneous velocity of oil droplets moving on the bubble surface, there is a large difference between the predicted value and the experimental value.

(2) During the movement of the oil droplet on the bubble surface, and in the case where the film is not ruptured, due to the strong viscous shear stress in the liquid film, the velocity in the area near the contact point of the oil droplet and the bubble is lower than that in the other areas inside the oil droplet.

(3) During the movement interaction process, due to the existence of the bubble,the vortex flow structure near the bubble disappears while the oil-droplet is moving around the bubble surface.Among the flows near the bubble interface, because the viscous shear stress of the air at the interface is lower than the shear stress of the water body,the mainstream area of the flow near the waterair interface above the oil droplet is more biased toward the bubble.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was supported by the National Natural Science Foundation of China (51578239) and the Education and Scientific Research Projects of Shanghai (17DZ1202802), for which the authors express their appreciation.