Bubble Behavior and Surface Liquid Film Characteristics of Air Bubbles Crossing the Oil–Water Interface

Abstract

The interaction of bubbles with phase interfaces is an important phenomenon in science and industry. In this paper, the variation in bubble behavior and the characteristics of surface liquid film formation and shedding at the oil–water interface are investigated using bubble visualization high-speed photography and numerical simulation. The results show that the bubble rise trajectories can be divided into three different sets when the bubbles rise in a system composed of two mutually incompatible liquids, and the bubble shapes are more stable in white oil compared to water. During the passage of the bubble across the oil–water interface, the water phase is entrained to form a liquid film covering the bubble. We found that the change in the bubble liquid film and the collapse process of the water column are closely related to the bubble size. The trends of Eotvos (Eo) numbers for bubbles of different diameters in the oil–water coexistence system are approximately the same, with the Eo numbers of larger bubbles being much larger than those corresponding to smaller bubbles, from the beginning to the end. After crossing the oil–water interface, the Eo number of larger-diameter bubbles keeps fluctuating over a long distance before finally stabilizing. The Eo number of small-diameter bubbles remains essentially stable after crossing the oil–water interface.

1. Introduction

Gas–liquid multiphase flow is widely found in many industrial processes and practical applications, especially in energy engineering, such as in the electric power, coal, metallurgy, petroleum, and chemical industries [1,2]. For example, in distillation towers in the chemical industry, the gas phase rises in the form of bubbles moving through the liquid phase, and the bubbles’ movement process is closely related to the efficiency of the tower [3,4]. Gas–liquid multiphase flows are often characterized by nonlinearity, instability, and nonuniformity. The shape changes, interactions, and phase interface behavior of gas bubbles in different liquids have attracted extensive attention in the industry and academia [5,6]. For rising bubbles in liquids, their shape, size, rising velocity, and movement path are determined by a combination of factors, among which the physical properties of the liquid are particularly important [7,8]. In engineering applications, such as oil and gas extraction processes, there are cases where multiple liquids coexist, involving noticeable fluid interface phenomena. Therefore, in-depth studies of gas–liquid multiphase flow and the interfacial behavior of bubbles in the case of the coexistence of different liquids are of great significance in understanding the behavior of bubbles moving at multiphase interfaces and their interaction mechanisms [9,10].

In recent years, more and more researchers have utilized numerical methods to study bubble dynamics and have carried out a large number of numerical simulations and theoretical studies on the phenomenon of single bubbles rising in liquids due to buoyancy forces, and their results are essentially in agreement with the available experimental data [11,12,13,14,15,16,17]. However, in industrial applications, bubbles often exist in two kinds of phase interfaces, a gas–liquid interface, such as the interface between air and water, and a liquid–liquid interface consisting of two mutually incompatible liquids, such as the interface between water and oil [18,19]. The two different interfaces have different effects on the behavior of bubbles, and the possibility of bubble rupture is high when bubbles are close to the gas–liquid interface [20,21]. Bubble rupture leads to a transient change in the surface liquid film, which is related to factors such as the physical properties of the liquid and the geometry of the bubble [22,23].

Mao et al. experimentally investigated the transient bubble behavior at the water–oil interface and demonstrated that larger initial bubbles are one of the reasons for the early detachment of the water film [24]. When the bubble crosses the liquid–liquid interface, the surface of the bubble will be covered by the former liquid, which changes the stressed surface of the bubble from the gas surface to a liquid film, and the shape and motion behavior of the bubble will be changed [25,26]. Li et al. used experiments to investigate the traversal of bubbles from brine to various liquids and found that the size of the bubbles changed with the physical properties of the different liquids [27]. Emery et al. used a high-speed camera to study the localized flow state of bubbles at the liquid–liquid interface [17]. Bonhomme et al. investigated the bubble behavior of ascending bubbles as they traversed the liquid–liquid interface, observing that the bubbles entrained the lower liquid during the crossing of the interface and gradually elongated to form a liquid column [28]. In addition, Singh et al. investigated the bubble rebound behavior at the liquid–liquid interface and found that the bubble rebound was related to the velocity of bubble motion at the interface and the interfacial tension between the liquids [29].

From previous studies, it can be seen that, although there have been some studies on bubbles at two-phase interfaces, this research is still not adequately developed [30,31]. The experimental work on the bubble behavior and surface liquid film properties at the liquid–liquid interfaces where bubbles are immiscible is still not sufficient [32,33]. This study further explains the transient behavior of gas bubbles near the liquid–liquid interface and provides additional data support for related studies in this field. With the rapid development of computers, it has made computational fluid dynamics (CFD) an important alternative to simulate gas–liquid two-phase flow [34,35].

Numerical simulations allow for rapid changes in test conditions compared to experiments, thus accelerating the optimization process for new research questions or different physical phenomena [36,37]. Due to the characteristics of the volume-of-fluid (VOF) model with interface-tracking algorithms, the model has been widely used in the study of bubble motion behavior and related mass transfer processes [38,39]. CFD simulations are significantly more cost-effective, flexible, and reproducible, provide more detailed flow field data, are capable of handling complex flow conditions and multiphase flows, and are time-efficient and safe compared to traditional experimental methods. CFD enables rapid performance prediction and optimization in the design phase and reduces the risk and resource consumption of actual experiments through virtual prototype testing. The advantages of CFD are more apparent when complex or extreme physical conditions need to be analyzed. Thus, CFD plays an irreplaceable role in improving engineering efficiency and innovation, although experimental validation is still an indispensable step in some critical areas.

There have been studies related to the passage of bubbles through liquid–liquid interfaces. Dietrich et al. investigated the dynamic behavior of liquid–liquid interfaces during bubble ascent using a particle image velocity (PIV) system. The effects of bubble size and liquid-phase viscosity on the retention time, liquid column length at the bubble tail, bubble velocity, and velocity field were investigated to improve the understanding of processes such as emulsification, mass transfer, and chemical reactions [15]. Singh et al. numerically simulated the phenomenon of a single bubble crossing the interface between two immiscible and stationary liquids using the VOF method. The relationships of bubble retention time and retention height with bubble size and physical properties were investigated, the corresponding correlation equations were proposed, and the key parameters affecting bubble behavior were revealed. This study deepens the understanding of the dynamic behavior of liquid–liquid interfaces [16]. Emery et al. used high-speed imaging to study the dynamic processes at the liquid–liquid interface when a single bubble or bubble flow passes through. The flow patterns associated with each flow type were captured and categorized, and four flow modes were identified for the passage of a single bubble, while six modes were determined for the passage of a bubble stream. A foundation for relevant engineering applications and further scientific research was thus provided [17].

In this paper, a combination of bubble visualization high-speed photography experiments and numerical simulation techniques was used to systematically study the bubble behavior and changes in surface liquid film properties at the interface of water and industrial white oil. Nozzles of different diameters were used to generate bubbles of different initial diameters, and high-speed photography was used to collect instantaneous bubble images. The formation and shedding of the liquid film on the bubble surface were investigated at the oil–water interface, and the trajectories of the bubbles were plotted during their ascent and crossing of the oil–water interface. We compared several published studies in related fields, and the conclusions obtained will further explain the transient behavior of bubbles near the liquid–liquid interface and provide more data support for related studies in this field.

2. Experimental and Numerical Calculation Scheme of Air Bubbles Crossing the Oil–Water Interface

2.1. Experimental Systems and Solutions

The layout of the entire experimental system is shown in Figure 1. The rectangular tank was made of a high-definition acrylic plate with dimensions of 150 mm × 150 mm × 400 mm, and two liquid media—deionized water and different types of industrial white oil—were used for the experiment. The viscosities, surface tension coefficients, and interfacial tension coefficients of the different liquids were measured using a viscometer and a surface tension meter, and their physical parameters at 21 °C are shown in

Table 1. Physical properties of water and different types of white oil at 21 °C.

Liquid	ρ (kg m−3)	μ (kg m−1s−1)	σ (N m−1)
Water	0.998 × 103	1.01 × 10−3	7.28 × 10−2
5# White oil	0.819 × 103	5.13 × 10−3	3.55 × 10−2
15# White oil	0.832 × 103	16.42 × 10−3	3.32 × 10−2
32# White oil	0.841 × 103	34.23 × 10−3	3.16 × 10−2

. The interfacial tension between water and white oil was 0.0376 N/m, and interfacial tension largely determines bubbles’ state near the liquid–liquid interface [40]. The tank size was large enough relative to the bubbles to eliminate the effect of the tank walls on the bubbles. The adjustable air volume of the single-channel air pump and parallel nozzles fixed at the bottom of the tank periodically generated bubbles. During the experiment, by adjusting the flow rate of the air pump, we ensured that the wake of bubbles would not affect the movement of subsequent bubbles. The initial bubble size could be adjusted by replacing the nozzle with others of different diameters.

First of all, three different types of industrial white oil were selected for the experiment. Although the physical properties of the three white oils were slightly different, the change observed in the liquid film after the bubbles passed through the oil–water interface was essentially the same. Therefore, the following sections analyze only one type of white oil.

During the experimental process, the water tank was injected with water and white oil, and, due to the density difference between the two, they did not mix. Instead, after being left for a period of time, the two liquids produced a clear stratification. The outlet diameters of the experimental nozzles were 2, 3, 4, 6, and 7 mm, and the structural parameters of the nozzles were the same, except for the different outlet diameters. According to the experimental needs, the light source comprised flicker-free light-emitting diode (LED) lights placed on the back side of the tank and supplemented with a diffusion plate to produce a more uniform backlight. A high-resolution cross-frame charge-coupled device (CCD) camera (TSI 4MP) was utilized to photograph the moving bubbles. The CCD camera had a resolution of 2048 × 2048 and a frame rate of 1000 FPS.

2.2. Numerical Calculation Scheme

2.2.1. Governing Equations and Solution Method

In the numerical model, the entire computational domain uses a set of control equations that take into account the variation in surface tension and physical properties. Assuming that the fluid motion is governed by the incompressible Navier–Stokes equations and the continuity equations, the VOF surface tracking model can be used to determine the location of interfaces between multiple immiscible fluids [41,42]. In this model, the fluids share a momentum equation, and the volume fraction of each fluid is traced inside each grid, with the gas and liquid phases following the continuity and momentum equations as shown in Equations (1) and (2), respectively.

$$\nabla \cdot \mathbf{u}=0$$

(1)

$${\displaystyle \frac{\partial (\rho \mathbf{u})}{\partial t}}+\nabla \cdot (\rho uu)=-\nabla p+\nabla \cdot [\mu (\nabla u+\nabla u^T)]+\rho g+F_s$$

(2)

where u is the velocity vector, ρ is the density, p is the pressure, μ is the viscosity, and F_S represents the surface tension source term. This is achieved using the continuous surface force (CSF) model [43,44]. This model converts the surface tension into a volume force acting on the interface based on the scattering theorem. F_s disappears from the interface, suggesting that it has a finite-volume region of influence rather than acting only on the sharp interface. The resulting surface tension source term in the momentum equation is shown in Equation (3), where σ is the surface tension, α is the phase volume fraction, phase 1 is water, and phase 2 is air.

$$F_s=\sigma {\displaystyle \frac{\rho \kappa \nabla \alpha }{0.5({\rho }_1+{\rho }_2)}}$$

(3)

The VOF method is capable of both steady-state and transient calculations, with each grid cell hosting a variable phase volume fraction. The sum of volume fractions for each phase within a grid cell amounted to 1. Therefore, the calculated multiphase flow was assumed to be gas–liquid, with the volume fraction of the liquid phase denoted as α_l and the volume fraction of the gas phase denoted as α_g. Three scenarios could be identified: α_g = 0 indicated the absence of a gas phase in the grid; α_g = 1 implied that the grid was filled with the gas phase; and 0 < α_g < 1 indicated that there was a mixture of gasses and liquids in the grid. The gas–liquid interface was tracked by solving the continuity equation for the gas volume fraction, and the liquid volume fraction was calculated according to constraint equations, as shown in Equations (4) and (5), respectively:

$${\displaystyle \frac{\partial {\alpha }_g}{\partial t}}+\nabla \cdot \left(\overrightarrow{u}{\alpha }_g\right)=0$$

(4)

$${\alpha }_l+{\alpha }_g=1$$

(5)

A pressure-based non-stationary implicit solver was chosen to solve the equations. The volume fraction-related parameters were calculated using an explicit formula with the Courant number set to 0.25. The Courant number is a dimensionless number that is very important in computational fluid dynamics to measure the stability and convergence of numerical solutions. It is defined by the relationship between time and space steps [43]. It is calculated as follows:

$$CourantNumber={\displaystyle \frac{u\Delta t}{\Delta x}}$$

(6)

where u is the flow rate, ∆t is the time step, and ∆x is the grid size. The Courant number regulates the stability and convergence of the computation, and, if convergence is desired, there must be a Courant number below a certain critical value [14]. The momentum equation was discretized using the second-order upwind method, and the pressure was interpolated using the PRESTO! method. The coupling method of pressure and velocity used the PISO algorithm.

2.2.2. Determination of the Calculation Basin and Initial Boundary Conditions

In this study, the fluent VOF multiphase flow model was mainly used to calculate the behavior of bubbles with different initial diameters when they crossed the oil–water interface and the bubble motion path. To this end, a high-speed camera was used to collect instantaneous bubble images, and the focus of this study was on the formation and shedding of the liquid film on the bubble surface at the oil–water interface, not on the three-dimensional path of the bubble movement. Corresponding to the bubble experiments (where the bubbles were photographed from the front), the axisymmetric physical model was simplified to a two-dimensional rectangular computational domain. There are some differences between using 2D simulations compared to 3D simulations, but these differences have little effect on the analysis of the final results, which can be approximated as a cross-section of the 3D results. Therefore, the physical model was simplified to a two-dimensional rectangular computational domain with a size of 150 mm × 400 mm, as shown in Figure 2. In our study, the origin of the coordinate system was chosen to be the lower left corner of Figure 2. The initial bubble was placed at the bottom of the computational flow field, its upward behavior driven by buoyancy, and the liquid was initially assumed to be at rest during the simulation. The sides and bottom of the computational domain were set to no-slip wall boundary conditions, the top was set as a pressure outlet with water return only, and the effect of gravity was considered throughout the simulation.

2.2.3. Mesh Size Independence

The mesh size independence test examines the effect of a grid on the computational results and achieves a balance between computational accuracy and computational cost by selecting a suitable grid size. Usually, the grid independence test is used to select one or two variables that are more representative of the simulation in numerical computation and compare the computational results with different grid sizes to see how the computational result error changes as the grid size becomes progressively finer, in order to determine the optimal grid. Three sets of grid solutions with different sizes were used in the numerical calculations, and, thus, the effect of the grid on the computational results needed to be examined. Considering the small size of the flow field calculation area and the need to accurately calculate the flow field conditions during bubble deformation and the change in flow pattern inside the bubble, the sizes of the three grids were set to small values. Using three different grid sizes—Scheme I, 0.6 mm × 0.6 mm; Scheme II, 0.5 mm × 0.5 mm; and Scheme III, 0.4 mm × 0.4 mm—simulations of the rising process of individual bubbles in water were performed to check the dependence of the simulation results on the grid resolution.

The initial shape of the bubble was set to be spherical with an initial diameter of 3 mm. A grid independence check was performed on the rise velocity and aspect ratio of the bubbles during rising. All three grid solutions yielded satisfactory numerical results in terms of grid size and number. The rate of bubble rise was consistent with the expected value and force balance of a spherical bubble. The formula for the bubble aspect ratio is as follows:

$$A_r={\displaystyle \frac{d_v}{d_h}}$$

(7)

where d_v is the vertical projection length of the bubble, and d_h is the horizontal projection length of the bubble. The calculation results of the three grids are shown in Figure 3. For the bubble rise rate, the results of the calculations for grid 3 and 2 were almost identical in general terms. The results of grids 1 and 2 showed a deviation between 0.15 s and 0.3 s, and the deviation reached its maximum at 0.275 s. The results of grids 1 and 2 showed the largest deviation, which was between 0.25 s and 0.3 s. For the aspect ratio of the bubbles, the three groups of grids were almost the same before 0.2 s. After 0.2 s, the calculations for grid 1 were significantly lower than the other two sets of grids, and the calculations for grids 2 and 3 were much closer. The total number for grid 1 was 176,589, for grid 2, it was 256,356, and, for grid 3, it was 395,664. After combining the calculation results of the bubbles’ rising velocity and aspect ratio for the three grids, to reduce the calculation cost, grid 2 was finally selected. The time step was set to 1.0 × 10⁻⁵ s, and the residual of velocity and continuity less than 1.0 × 10⁻⁵ was considered convergence.

2.2.4. Computational Model Validation

The validation of the computational model was carried out by comparing the computational and experimental results. In this study, the initial shape of the bubbles was spherical, so the best comparison condition in the experiments was to make the bubbles take on a spherical shape once removed from the injection device. High-speed photography was used to record the bubbles’ motion in the experimental case, and the aspect ratios of individual 3 mm diameter bubbles were compared.

Table 2. Comparison of experimental and numerically calculated values of bubble aspect ratio.

Time	25 ms	50 ms	75 ms	100 ms	125 ms
Experiment	0.843	0.854	0.742	0.635	0.572
Numerical Calculation	0.932	0.827	0.716	0.615	0.534
Relative Error (%)	10.6	3.2	3.5	3.1	6.6

shows the comparison between the experimental bubble aspect ratios and the numerically calculated values. From the results, it can be seen that the maximum error of both was 10.6% at 25 ms, and the relative error varied from 3.1% to 6.6% when comparing the results of 50 ms, 75 ms, 100 ms, and 125 ms, respectively. The relative errors were within reasonable limits except at 25 ms, when the relative error was 10.6%. In order to eliminate the occasionality which exists in the experimental process, several repeated experiments were carried out, and the results showed that the bubble shape obtained by numerical computation was essentially consistent with the experimentally captured image, and the motion behavior of the bubble in the process of rising was also fundamentally consistent with the experiment. In summary, the calculation method used in this paper has good accuracy.

In order to avoid the non-stationarity and occasionality of the experimental results, caused by various disturbing factors during experiments, 50 experiments were carried out under each working condition to ensure the reproducibility of the obtained results. In the description and analysis of the subsequent sections, only the recurrent experimental results are presented. As a pre-experiment, air was injected into water and white oil, in that order, and Figure 4a shows the morphology of the bubbles generated by injecting the gas into water at the moment of detachment from nozzle outlets of different sizes. As a comparison, Figure 4b shows the morphology of the bubbles at the moment of detachment from the nozzle in white oil. Bubble size and distribution are complex characteristics that are influenced by several factors. Nozzle diameter, flow rate, liquid properties, and hydrostatic pressure all work together to determine the final size and distribution of bubbles. Specifically, the nozzle diameter affects the initial size of the bubbles, the flow rate determines the rate and number of bubbles generated, liquid properties such as viscosity and surface tension affect the stability and shape of the bubbles, and hydrostatic pressure affects the expansion and bursting of the bubbles.

In the process of rising, the bubble deforms under the interaction of multiple forces, resulting in different shapes. The equivalent diameter of bubbles is denoted by D_e. In the experiment, the collected images were two-dimensional projection images. In this context, the diameter of a circle that has the same area as the projected area of the bubble is defined as the equivalent diameter of the bubble.

$$D_e=\sqrt{{\displaystyle \frac{4A}{\pi }}}$$

(8)

where A represents the projected area of the bubble, which corresponds to all the pixels within the contour of the bubble in the image.

The pre-experiment carried out to obtain the equivalent diameter of the bubble at the instant of its separation from the nozzle is shown in

Table 3. Initial equivalent bubble diameter.

Nozzle diameter (mm)	2	4	6
Water	2.65	4.75	6.97
White oil	2.14	4.17	6.15

. The results of the pre-experiment show that the equivalent diameter of the bubble increased with the increase in the diameter of the nozzle outlet, and this phenomenon occurred in different liquid media. When the nozzle outlet diameter was the same, the bubbles generated in water were larger in terms of their overall height and width than those released in white oil, and this pattern was confirmed with different nozzle sizes.

3. Results and Discussion

3.1. Bubble Rise Trajectory

Before the experiments of bubbles crossing the oil–water interface, the bubble rise trajectories in water and white oil were obtained via pre-experiments for comparison purposes. By collecting the instantaneous images of bubbles at different moments during the bubble rise process, the bubble rise trajectories under different working conditions were plotted, as shown in Figure 5a,b, when a 2 mm diameter nozzle was used. As shown in Figure 5a, when the bubbles entered the water after detaching from the nozzle, they first moved in a straight line upward after the bubble deformation step and interacted with the surrounding flow field, at which point, lateral fluctuations increased, showing a zigzag upward trajectory. By rotating the high-speed camera around the nozzle at different angles, zigzag bubble trajectories were captured in all cases. The bubbles’ shape while moving upward showed variable characteristics: when the bubble first exited the nozzle, after detachment, it quickly transformed from a spherical shape into a flat ellipsoid and then, due to the surface oscillation effect, it showed a variety of shapes, such as a ball-cap shape and a mushroom shape. As shown in Figure 5b, the bubble trajectory in white oil was a straight line, and the shape of the bubbles was mostly spherical and ellipsoidal after detaching from the nozzle, essentially remaining unchanged while rising to the surface. Due to the differences in physical properties (viscosity, density, and surface tension) between water and white oil, the movement paths of the bubbles in water and white oil were different.

As shown in Figure 5c, the rising trajectories of the bubbles in the system composed of two mutually incompatible liquids behaved differently in the regions above and below the liquid–liquid interface. The rising trajectories of bubbles below the interface and the changes in bubble morphology were similar to those observed in water. As the bubbles approached the oil–water interface, the force state acting on the bubble changed, resulting in a shape and a trajectory which were significantly different from those seen in water. When the bubbles crossed the oil–water interface, the denser liquid attached itself to the surface of the bubbles in the form of a thin, liquid film. As the bubbles continued to rise, a small portion of the water wrapped around their surface began to fall, and the remaining water wrapped the bubbles completely, forming a closed liquid film, the constraint of which caused the bubbles to appear as approximate spheres.

Taking the instant of bubble detachment from the nozzle as the initial moment, Figure 6 shows the correspondence between the vertical height of a 2 mm diameter bubble and the time, providing a reference for determining the time span required for the bubble to reach different stages of its movement towards the surface. The three lines in the graph correspond to the three cases shown in Figure 5. For the bubbles in water or white oil alone, the slope of the curve does not change much throughout the process. The viscosity of white oil is greater than that of water, so the rise of bubbles in white oil is relatively slow. The height of the oil–water interface is 100 mm, and, in the case of the coexistence of the two liquids, the bubbles have to overcome interface resistance when passing through the oil–water interface, which leads to a slower rising speed and an increase in the time span taken passing through the interface. When the water film on the surface of the bubble is completely detached, resulting in an increase in the bubble’s rising rate, the slope of the curve is almost the same as in white oil.

The comparison of the rising behavior of 4mm bubbles with equivalent diameter and vertical height in water, white oil, and water and white oil is shown in Figure 7. The height of the oil–water interface is 100 mm. The shape of the bubbles changed during their upward movement, and the diameter of the bubbles fluctuated with their relative height. In water alone, the shape of the bubbles varied during their climb, so the equivalent diameter fluctuated considerably. In white oil alone, the shape of the bubble remained essentially unchanged after leaving the nozzle, and the equivalent diameter of the bubble rapidly decreased to a stable value. In the case of the coexistence of two immiscible liquids, the variation profile of bubbles with equivalent diameters was approximately the same as that seen in water alone prior to the bubbles making contact with the oil–water interface. As the bubbles gradually crossed the oil–water interface, the oil–water interface tension exerted a drag on the bubbles, decreasing the magnitude of fluctuations in the diameter of equivalent bubbles. Subsequently, the water film began to collapse and gradually fall off, and, when the bubbles were completely detached from the water film, the diameters of equivalent bubbles fluctuated slightly and then converged to a stable value. The comparison showed that the final diameter of equivalent bubbles under the coexistence of oil and water liquids was larger than in the case of white oil.

3.2. Transient Behavior and Liquid Film Properties of Bubbles Crossing the Oil–Water Interface

3.2.1. Transient Behavior and Liquid Film Characteristics of a 2 mm Diameter Bubble at the Oil–Water Interface

It can be found from the experiments that the geometrical features and kinematic properties of the bubbles were similar to those of their counterparts in a single-liquid medium when the bubbles were far away from the oil–water interface. When the bubbles were located near the oil–water interface, they showed noticeable differences. Bubble size can have an effect on changes in the surface water film. Therefore, the behavior of bubbles with different initial diameters near the oil–water interface is hereby further analyzed.

Figure 8 shows the liquid film change process of 2 mm diameter bubbles at the oil–water interface under the high-speed visualization experiment of bubble flow. As shown in Figure 8, when a bubble rises in water and gradually approaches the oil–water interface, the shape of the bubble changes greatly, and the bubble in the water appears ellipsoidal. When the bubble crosses the oil–water interface, the bubble gradually replaces the water film, and the shape of the bubble gradually returns to being spherical. With the increase in time, 15.7–17.8 ms, the blank area between the right part of the water film and the bubbles is larger than on the left side, and the bubbles have a tendency to move to the upper left. At 20.7–23.1 ms, the area to the left part of the water film gradually increases, and the bubble has a tendency to move to the upper right. The bubbles essentially remain spherical during the whole movement process, which is noticeably different from the change in the geometric characteristics of bubble movement in water. As the bubble moves upward, at 32.7–35.3 ms, the liquid film is symmetrical to the centerline of the bubble, and the neck of the liquid film narrows. The shape and velocity of the bubbles in water fluctuate during the process shown in Figure 8. The bubbles also show a similar situation at the oil–water interface, and the bubbles have a tendency to move in the horizontal direction. When the bubbles enter the white oil, the bubbles are constrained by the water film, reducing the trend of their lateral movement, rising in an approximately straight line.

Figure 9 shows the liquid film change process of a 2 mm diameter bubble at the oil–water interface under numerical simulation. When the bubble crosses the oil–water interface, the bubble gradually pushes up the water film. With the increase in time, as shown in Figure 9b,c, there is a change in the blank area between one side of the water film and the bubbles, and there is a tendency for the bubbles to move towards the deflection, which is in agreement with the results shown in the high-speed photography experiments. As the bubble crosses the oil–water interface, the bubble gradually pushes the water film upward. In this process, the interaction between the bubble and the water film significantly affects the shape and trajectory of the bubble, and the blank area in this region changes with time. This phenomenon is consistent in the results of both numerical simulations and high-speed photography experiments. The inhomogeneous distribution of fluid during the interaction between the bubbles and the liquid film may lead to the deflection of the bubbles, resulting in a lack of symmetry.

Figure 10 shows the collapse process of the water column below the 2 mm bubble during the bubble flow high-speed visualization experiment. Figure 11 shows the collapse process of the water column below the 2 mm bubble during the numerical simulation, and the comparison shows that the results obtained by numerical computation are essentially the same as the experimentally captured image, which confirms that the model used in numerical computation can achieve a more accurate calculation.

As the bubbles rise, the water column generated by the entrapment of the liquid film on the surface is elongated, and the oil–water interface is raised upward in the shape of an umbrella. After a period of time, a nuchal constriction point forms below the fluid film, and the lower end of the water column narrows. The break in the water column occurs between 42.7 and 45.7 ms, with rupture occurring at the point of neckdown. The water film on the surface of the bubble is completely separated from the water column below, and the water column then falls back toward the oil–water interface under the force of gravity. The numerical simulation results are consistent with the overall trends of the bubble high-speed photography experimental results. After the separation of the water column from the bubbles, the height of the bulge at the oil–water interface gradually decreases, and, due to the detachment of the water film on the surface leading to an increase in the rising rate of the bubbles, the shape of the bubbles changes from spherical to ellipsoidal, and they keep rising vertically in the white oil.

3.2.2. Transient Behavior and Liquid Film Characteristics of a 4 mm Diameter Bubble at the Oil–Water Interface

Figure 12 shows the liquid film change process of a 4 mm diameter bubble at the oil–water interface under the high-speed visualization experiment of bubble flow. When the bubble crosses the oil–water interface, the bubble is spherical in shape and pushes up the water film. With the increase in time, the blank area between the water film and the bubble gradually increases and is axisymmetric with respect to the bubble’s centerline. Compared to the 2 mm bubbles, the biggest difference is that the blank area between the water film and the bubbles does not appear asymmetric, and there is no tendency for the bubble movement path to be deflected, and the bubbles rise in a nearly straight line. When the bubbles continue to move upward, the water film changes, similarly to the 2 mm bubble, and the neck of the water film gradually becomes narrower. In addition, the initial size of the bubbles generated by the 4 mm diameter nozzle is larger, and the water film entrapment capacity is stronger. Comparing Figure 12 and Figure 11, it can be seen that the volume of water entrained by the 4 mm diameter bubbles is larger, and the upward raised umbrella area of the oil–water interface is larger.

Figure 13 shows the collapse process of the water column below a 4 mm bubble under the bubble flow high-speed visualization experiment. The water column generated by the entrapment of the surface liquid film is elongated, and the oil–water interface is raised upward in the shape of an umbrella. As the bubble continues to rise, the lower end of the water column narrows, the necking point breaks, and the water film completely wraps around the bubble, separating completely from the water column below. The biggest difference compared to the 2 mm bubble is the tendency of the water column to move upward after collapse. At 20.5 ms, the bubble is not pierced by the jet, and spherical small droplets do not form inside the bubble. At 23.7 ms, the water column below the bubble forms a jet with an upward tendency, which passes through the bubble, enters its interior, and is transformed into small spherical water droplets. At 25.3 ms, the bubble becomes ellipsoidal, and the small water droplets inside break through the bubble and gradually separate completely from it.

Figure 14 shows the collapse process of the water column below the 4 mm bubble during the numerical simulation, and the results obtained from the numerical simulation are in good agreement with the experimental results of the high-speed visualization of bubble flow. The shedding of the surface water film leads to an increase in the bubble’s rising speed, and the bubble shape is changed to ellipsoidal by the force of the ambient flow field, continuing to rise vertically in the white oil. The water column is gradually stretched as the bubble rises, and the contact area between the two decreases.

3.2.3. Transient Behavior and Liquid Film Characteristics of a 6 mm Diameter Bubble at the Oil–Water Interface

Figure 15 illustrates the liquid film change process of a 6 mm diameter bubble at the oil–water interface under the bubble flow high-speed visualization experiment. Overall, the phenomenon is similar to that observed for the conditions of 4 mm diameter bubbles. However, there are still the following two differences. First, the initial size of the bubbles is large, which makes the bubbles always remain spherical while crossing the oil–water interface, and the shapes of the bubbles remain stable, indicating that large bubbles are more morphologically stable in the oil-phase environment after crossing the oil–water interface. Secondly, compared to the 2 mm and 4 mm diameter bubbles, the blank area between the water film and the bubble is cylindrical rather than umbrella-shaped at 0–6.8 ms, just after the bubble crosses the oil–water interface. The entrapment ability of the liquid is further enhanced during the passage of the large bubbles across the oil–water interface, and the blank area between the water film and the bubbles becomes larger and more axisymmetric with respect to the centerline of the bubbles compared to 4 mm diameter bubbles.

Figure 16 demonstrates the collapse process of the water column below a 6 mm bubble under the bubble flow high-speed visualization experiment. The biggest difference compared to the 4 mm bubble is the increase in the vertical distance between the bubble and the separated water column and the faster fallback of the height of the umbrella raised by the oil–water interface. The cause of this phenomenon is the greater buoyancy of large bubbles in the liquid, which causes them to rise faster. The relative speed of separation of the water column from the bubbles increases after the necking point breaks.

Figure 17 shows the collapse process of the water column below the 6 mm bubble during the numerical simulation, and the results obtained from the numerical simulation are in good agreement with the experimental results of the high-speed visualization of bubble flow. The water column below the bubble is elongated, and the oil–water interface is raised upward in the shape of an umbrella. At the same time, the lower end of the water column is narrowed, the neck constriction point is fractured, and the water film is completely wrapped around the bubble and completely separated from the water column below. The results of the study of bubbles of different sizes show that bubble size is the key factor affecting the transient behavior of bubbles and liquid film changes at the oil–water interface. Industrial white oils with different kinematic viscosities did not affect the transient behavior and liquid film change of bubbles at the oil–water interface, but only the rising speed of bubbles in white oil.

When the bubbles rise from the lower water section to the white oil, the running path of the bubbles with different diameters in the white oil is kept straight and pointed upward. White oil has a high viscosity, and the bubbles are affected by the fluid’s viscosity when they rise in it. The higher viscosity makes the resistance of the fluid to the bubbles increase during the movement process, which reduces the acceleration of the bubbles and makes their movement path more stable. In Figure 18, the velocity vector diagram of the surrounding flow field during the process of a bubble rising toward the surface is plotted, having been obtained from the numerical simulation.

3.3. Effect of Bubble Rising Rate and Bubble Size on Eo Number

3.3.1. Analysis of Bubble Rising Rate in the Oil–Water Coexisting Liquid Phase

We selected a 4 mm diameter bubble to analyze its movement speed in different liquid phases. As shown in Figure 19, the instantaneous position of the bubble was determined by high-speed visualization experiments, and the longitudinal rise velocity of the 4 mm diameter bubble was plotted as a function of the longitudinal coordinate. The change in the velocity of the bubble motion depended on the change in the overall force applied on the bubble, and the slope of the velocity curve indicated the change in the acceleration of the bubble. The experimental results show that, in water, the rising velocity of the bubble first increases after it is detached from the nozzle, and the velocity curve begins to fluctuate up and down after a height of 25 mm. The main reason for the velocity fluctuations is the frequent changes in the overall force applied on the bubble and the breaking of the symmetry of the wake. The liquid at the top of the bubble is in a relatively static state when no bubbles are passing through it, and the liquid at the bottom instantly creates a void and pressure difference in the area where the bubbles are passing through due to the rise of said bubbles. The surrounding liquid fills these voids, causing a large disturbance in the flow field which affects the bubble rising rate. When the height of the vertical coordinate exceeds 200 mm, the bubble rising rate stabilizes. In contrast, in white oil alone, the velocity of the bubbles increases rapidly after detaching from the nozzle, and the bubble velocity stabilizes when the height of the longitudinal coordinate exceeds 100 mm. The bubble stabilization velocities in only water and only white oil were about 0.22 and 0.18 m/s, respectively, and it is clear that the difference in liquid viscosity was the main influencing factor for the difference in bubble stabilization velocities.

For bubbles rising under conditions of the coexistence of two liquids, oil and water, the bubble velocity profile can be divided into three stages, A, B and C, as shown by the red curve in Figure 19. It can be noticed that the velocity profile in stage A approximates the corresponding part of the velocity profile in the water, while the degree of fluctuation in the curve in stage C is approximated by the corresponding part of the velocity profile in white oil. Stage B corresponds to the process of formation and collapse of the water film of bubbles. As the bubbles gradually traverse the oil–water interface, the oil–water interfacial tension exerts resistance on the bubbles, and the minimum velocity value of the bubbles decreases to 0.02 m/s. Immediately after, the speed gradually increases from 0.02 m/s to 0.12 m/s, the stage of the water film shape changes significantly, the water column below the bubble in the vertical direction is gradually elongated, and the water column and contact area below the bubble decrease. Throughout this process, the shape of the bubbles changes, from initially spherical to ellipsoidal. At Y = 160 mm, the water film begins to collapse and gradually falls off. After some time, at Y = 185 mm, the water film is completely detached from the bubble. The resistance of the bubble suddenly decreases, and the rising velocity increases rapidly. Finally, the bubble’s rising velocity fluctuates briefly and then tends toward a stable value of about 0.17 m/s.

3.3.2. Analysis of the Effect of Bubble Size on Eo Number

The results of both experiments and numerical simulations of the high-speed visualization of bubble flow show that the shape of bubbles changes to some extent during their ascent. The shape change of the bubbles can be described by the dimensionless number Eo, which can be used to describe the shape of the bubble in the moving fluid and can be regarded as the ratio of buoyancy and surface tension, and its expression is as follows:

$$Eo={\displaystyle \frac{\Delta \rho g{L}^2}{\sigma }}$$

(9)

where Δρ is the density difference between the two phases, L is the horizontal bubble diameter, and σ is the surface tension.

Figure 20 demonstrates the trend of Eo numbers for bubbles of different diameters as they rise in the oil–water system. D denotes the nozzle diameter. As shown in Figure 20, the Eo numbers of bubbles generated with the 6 mm nozzle are much larger throughout than the corresponding Eo numbers of bubbles generated with 2 and 4 mm nozzles, and the larger bubbles are more buoyant in the liquid. The Eo numbers of bubbles with different diameters in the oil–water coexistence system have similar trends, all of which show oscillations first, followed by a rapid increase, and finally tend to stabilize. The Eo number becomes larger overall as the bubbles traverse from the de-watered water to the white oil.

The location of the oil–water interface is labeled in the figure, and when the bubbles traverse the oil–water interface, the bubble shape and surface tension change drastically, resulting in significant fluctuations in Eo. When D = 2 mm and D = 4 mm, the Eo number essentially remains stable after the bubble crosses the oil–water interface. Finally, a stable shape is reached in the case of D = 6 mm, and, after the bubble crosses the oil–water interface, the Eo number keeps fluctuating over a long distance, eventually stabilizing. The trend of the Eo number is consistent with the transient behaviors of the bubbles depicted in Figure 8, Figure 12 and Figure 15.

4. Conclusions

In this work, a combination of bubble high-speed photographic visualization experiments and numerical simulation techniques is used to systematically investigate the bubble behavior and changes in surface liquid film properties at the interface of water and industrial white oil. The conclusions obtained in this study will further explain the transient behavior of bubbles near the liquid–liquid interface and provide more data support for related studies in this field.

It was found that the bubble rising trajectories can be divided into three different phases when the bubbles move upward in a system composed of two mutually incompatible liquids, and the bubble shapes are more stable in white oil compared to water. During the passage of the bubble across the oil–water interface, the underlying liquid is entrained to form a liquid film covering the bubble. The bubble size is a key factor influencing the transient behavior of bubbles and liquid film changes at the oil–water interface. The Eo numbers of bubbles with different diameters in the oil–water coexistence system have similar trends, all of which show oscillations first, followed by a rapid increase, eventually stabilizing. The Eo numbers of larger bubbles are much larger than those corresponding to smaller bubbles from the beginning of their climb to the end. After crossing the oil–water interface, the Eo number of the larger-diameter bubbles keeps fluctuating over a long distance before finally stabilizing. The Eo number of small-diameter bubbles remains essentially stable after crossing the oil–water interface.