Royal Society Publishing

The effects of surfactant on the multiscale structure of bubbly flows

Shu Takagi, Toshiyuki Ogasawara, Yoichiro Matsumoto

Abstract

It is well known that a bubble in contaminated water rises much slower than one in purified water, and the rising velocity in a contaminated system can be less than half that in a purified system. This phenomenon is explained by the so-called Marangoni effect caused by surfactant adsorption on the bubble surface. In other words, while a bubble is rising, there exists a surface concentration distribution of surfactant along the bubble surface because the adsorbed surfactant is swept off from the front part and accumulates in the rear part by advection. Owing to this surfactant accumulation in the rear part, a variation of surface tension appears along the surface and this causes a tangential shear stress on the bubble surface. This shear stress results in the decrease in the rising velocity of the bubble in contaminated liquid. More interestingly, this Marangoni effect influences not only the bubble's rising velocity but also its lateral migration in the presence of mean shear. Together, these influences cause a drastic change of the whole bubbly flow structures. In this paper, we discuss some experimental results related to this drastic change in bubbly flow structure. We show that bubble clustering phenomena are observed in an upward bubbly channel flow under certain conditions of surfactant concentrations. This cluster disappears with an increase in the concentration. We explain this phenomenon by reference to the lift force acting on a bubble in aqueous surfactant solutions. It is shown that the shear-induced lift force acting on a contaminated bubble of 1 mm size can be much smaller than that on a clean bubble.

Keywords:

1. Introduction

Bubbly flows are encountered in many industrial processes such as the flows in chemical reactors, aeration tanks and heat exchangers. Recently, the use of bubbly flows for reducing the drag experienced by ships has attracted much attention. Owing to the widespread occurrence and application of these flows, a considerable number of investigations on their turbulent structure have been carried out over the past three decades. However, due to the complicated multiscale structure of bubbly flows, researchers are often left puzzled by experimental results that give totally different conclusions despite similar experimental conditions. The early studies on the measurement of bubbly flows were conducted by Serizawa et al. (1975) and Theofanous & Sullivan (1982), in which local measurements of turbulent flow structure in a pipe were made using a hot-film anemometer and laser Doppler anemometer, respectively. Following these studies, Wang et al. (1987), Lance & Bataille (1991), Serizawa et al. (1991) and Liu & Bankoff (1993a,b) provided experimental information about the local void fraction profile and its dependence on bubble size and bubble-induced turbulence. Although there is wide scattering of the experimental data, these studies give the same qualitative description: the wall peak void fraction distribution in the case of low gas flow rate in upward bubbly flows. One of the reasons for the scattering of the data is due to the presence of impurities in water, especially surfactants. It is well known that a small amount of surfactant can drastically change bubble behaviour. For example, coalescence hardly occurs in the presence of surfactants. Another well-known surfactant effect is the reduction of rising velocity: a bubble in contaminated water rises much slower than one in purified water (Clift et al. 1978). This phenomenon is explained by the Marangoni effect, as follows. A surface concentration distribution exists along the bubble surface, because the surfactant is swept off the front part and accumulates in the rear part as the bubble rises. Owing to this surfactant accumulation in the rear part, a variation of surface tension along the surface is developed and this causes a tangential shear stress on the bubble surface. This is known as the Marangoni effect due to the presence of surfactant. This shear stress results in the decrease in the rising velocity of a bubble in contaminated water. In many cases, the bubble surface becomes sufficiently contaminated and a nearly no-slip surface is attained. The rising speed of the contaminated bubble goes until the same drag coefficient as a rigid particle is reached. Thus, it is often regarded that a fully contaminated bubble behaves like a rigid particle in water. This phenomenological explanation was first given by Frumkin & Levich (1947). A considerable number of studies have been conducted on this subject (Duineveld 1994; Cuenot et al. 1997; Takemura & Yabe 1999; Liao & McLaughlin 2000; Ybert & di Meglio 2000; Sugiyama et al. 2001; Zhang & Finch 2001; Takagi et al. 2003; Takemura 2005). A comprehensive review of the previous studies up to 1996 is given in Cuenot et al. (1997), following which more studies have been done both experimentally and numerically. Takemura & Yabe (1999) conducted experiments for the dissolution process of carbon dioxide gas bubbles with the effect of contaminant taken into account. They also conducted numerical simulations using a stagnant cap model, which assumes a no-slip surface beyond a given cap angle, and in so doing obtained good agreement between experimental and numerical results. Ybert & di Meglio (2000) also conducted both experiments and simulations using the stagnant cap model and obtained good agreement for the concentration dependence of alcohol species. Zhang & Finch (2001) conducted an experiment for the unsteady motion of a contaminated rising bubble. They reported that the transient distance to reach the steady state can be of the order of a few metres under the low concentration condition of Triton X-100 solution.

Not only single bubble behaviour itself but also this change of behaviour greatly affects the whole bubbly flow structure, and it is indeed this multiscale nature that makes the understanding of bubbly flow structure difficult. In our previous experiments on upward channel flow, bubbles show migration tendency towards the wall and form a crescent-like bubble cluster near the wall (So et al. 2002). The origin of this bubble migration is thought to be a shear-induced lift force. Recently, there have appeared some numerical approaches addressing the shear-induced lift force on a clean bubble and on a rigid sphere (Legendre & Magnaudet 1998; Kurose & Komori 1999; Bagchi & Balachandar 2002). A comparison of these studies shows that there is a large discrepancy between the case of the clean bubble and that of the rigid sphere. From this result, it is suggested that the contamination of water will influence bubble migration. In addition, Mazzitelli et al. (2003) indicated through numerical work that the effect of the lift force is crucial for the energy spectrum of microbubble-laden homogeneous and isotropic turbulence. Thus, the effect of the lift force is important also from the viewpoint of a modification of turbulence by microbubbles. In this paper, the motion of bubbles in upward turbulent channel flow is illustrated and a bubble clustering phenomenon near the wall is discussed. Furthermore, surfactant effect on the spatial distribution of the bubbles is discussed by changing the concentration and the species of surfactant.

2. Experimental set-up

The experimental apparatus for upward channel flow is shown in figure 1. The experiments were conducted in a vertical circulating water tunnel, which was operated in the upward direction (x-direction) in the test section that is located at a height of 1600 mm above the bubble injection point so that the distance to the test section is long enough for the void fraction profiles to be sufficiently developed for the bubbly flow and to be fully developed for the single-phase turbulent channel flow. The test section has a thickness of 2H=40 mm (y-direction) and a width of 400 mm (z-direction), giving an aspect ratio of 10. The large aspect ratio ensures that two-dimensional flow is attained in the central region of the channel. Note that the x-coordinate denotes the streamwise direction, y the perpendicular direction from the wall and z the spanwise direction. The bubbles were generated through 474 stainless steel pipes of 0.07 mm inner diameter. All the bubbles were removed from the flow by a bubble separator tank set atop the channel. A high-speed digital camera (Motion Pro 10000, Redlake MASD, Inc.) with 1280×1024 pixels and 8-bit resolution was used to capture the bubble behaviour. The movies were taken at 500 fps.

Figure 1

Schematic of the experimental apparatus for bubbly flow in a vertical channel.

The experimental conditions are shown in table 1. Since we have previously reported a parametric study on the dependence of Reynolds number and void fraction with a fixed 3-pentanol concentration (So et al. 2002), here we show the results for the dependence of surfactant concentration and species with a fixed bulk Reynolds number of 8200, where Reb=2UbH/ν with Ub representing the mean bulk velocity of the liquid phase. Two kinds of surfactant, 3-pentanol and Triton X-100, were used in this study to look into the dependence of surfactant adsorption/desorption kinetics. Triton X-100 has a much lower desorption rate constant, for which we can expect a larger Marangoni effect than with 3-pentanol. We set the bulk concentration of 3-pentanol from 21 to 168 ppm, and Triton X-100 at 2 ppm.

View this table:
Table 1

Experimental conditions of bubbly flow.

3. Results and discussion

Figure 2ad shows snapshots of bubbly channel flow at a bulk Reynolds number (Reb) of 8200 and superficial gas velocity (vg) of approximately 1.4 mm s−1 under different surfactant conditions. In these figures, the front view is a snapshot for the spanwise–streamwise plane (xz-plane), while the side view is that for the wallnormal–streamwise plane (xy-plane).

Figure 2

Photographs of upward bubbly flows in the vertical channel (Reb=8200, vg=1.4 mm s−1): (a) tap water (without surfactant), (b) 42 ppm 3-pentanol solution, (c) 168 ppm 3-pentanol solution and (d) 2 ppm Triton X-100 solution. Average bubble diameters are approximately 0.9 mm for the 3-pentanol solution and 1.0 mm for the Triton X-100 solution with standard deviations of 0.1 mm. (i) Front view and (ii) side view.

Figure 2a illustrates the situation without surfactant: a wide distribution of bubble size is apparent. This results from bubble coalescence: although bubbles were injected from the needles in a monodispersed way, some bubbles coalesced during the rising process leading to bubbles of larger size on arrival at the test section. The larger bubbles—distributed throughout the cross section of the channel—rise with a zigzag ‘leaping’ motion when against the vertical wall. It is observed that this kind of bubble leaping motion enhances the mixing of the fluid and seems to produce large fluctuations in the flow.

On the other hand, bubbly flows with surfactant solution, shown in figure 2bd, maintain a monodisperse size distribution of approximately 1 mm diameter, corresponding to what we observe near the bubble injection point. This result indicates the well-known fact that surfactants prevent the coalescence of bubbles. Figure 2bd illustrates the results for three different surfactant conditions: 42 ppm 3-pentanol solution, 168 ppm 3-pentanol solution and 2 ppm Triton X-100 solution. It is interesting to see that once even a small amount of surfactant is added, the whole aspect of the bubbly flow structure is drastically changed. And more interestingly, the bubbly flow structures are not the same in each case, although the bubble size distributions are nearly the same. As shown in figure 2b, the bubbles start showing a horizontal clustering and these clusters rise up along the wall without producing a large meandering motion in the spanwise direction. The size of this horizontal cluster is approximately 10–40 mm, which corresponds to a few hundreds of wall units of turbulent boundary layer. Hence, the size of the cluster is much larger than the well-known coherent vortical structure in turbulent boundary layers and this indicates that a drastic change of turbulent flow structure was given by the bubble clustering. A detailed discussion of the change of turbulent statistics is given in So et al. (2002). On the other hand, no cluster appears in the cases of 168 ppm 3-pentanol solution and 2 ppm Triton X-100 solution. Since the clustering occurred near the wall, the reason for the difference between the case of 42 ppm 3-pentanol and the other two cases is the number of bubbles rising near the wall. As shown in figure 2b(ii), there is an accumulation of bubbles near the wall for 42 ppm 3-pentanol solution, while bubbles are uniformly distributed across the channel in the cases of 168 ppm 3-pentanol solution and 2 ppm Triton X-100 solution as shown in figure 2c,d.

There are two well-known methods to prevent bubble coalescence. One is the addition of surfactant and the other is the addition of salt. Zenit et al. (2001) added salt to the liquid phase to avoid coalescence. In their study, in order to compare the experimental results with potential flow theories applied to bubble suspensions (Sangani & Didwania 1993; Smereka 1993; Spelt & Sangani 1998), they used salt which does not give Marangoni effects. They tried to capture the horizontal bubble clustering that was predicted by the theory. On the other hand, in the present experiment, bubbles are contaminated by surfactant. In this situation, the tangential stress at the gas–liquid interface resulting from the Marangoni effect is not negligible and the boundary condition on the bubble surface can be regarded as being in an intermediate state between rigid particle and clean bubble boundary conditions. It is also noted that, in our experiment, the liquid phase is an upward flow which has a strong shear near the wall. Taken together, these facts suggest that our experimental conditions are not suitable for the potential flow assumption. Therefore, there are differences between our experiment and that conducted by Zenit et al. (2001) and our experimental system should not be used for a comparison with potential flow theory. It should also be mentioned that our bubbles have a smaller rising velocity due to the Marangoni effect, and they end up with a more spherical shape even if the bubble size is nearly the same as that of a clean bubble.

One more thing should be mentioned related to the work of Figueroa-Espinoza & Zenit (2005). They used a very thin channel and observed the horizontal clustering of bubbles. The salt was used to avoid bubble coalescence and keep a clean surface for the argument of potential theory. Although this experiment is not the same as our surfactant-contaminated one, the similarity between these experiments is the two-dimensional structure of rising bubbles. In the case of Figueroa-Espinoza & Zenit (2005), the thinness of the channel constrains the bubble motions in a plane, while in our experiment it is the lift force that sustains the two-dimensional structure near the wall. In both cases, these geometric constraints seem to be an important factor for the horizontal bubble clustering.

To investigate the dependence of bubble motion on surfactant conditions, we set up a simple experiment of a single bubble rising in quiescent water. A single bubble that had nearly the same size as those in the above experiment was generated and released in quiescent water. The apparatus for this experiment is shown in figure 3. This apparatus was originally used to analyse the behaviour of a single bubble in super purified water. The water flows through a cylindrical glass test section of diameter 64.5 mm, height 700 mm, which is surrounded by an acrylic rectangular parallelepiped tank. Surfactant is added to the test section by micro-syringe. A single bubble is generated through a glass capillary whose internal diameter is approximately 50 μm. By switching a magnetic valve off/on instantaneously, a slight pressure change is passed to the capillary edge and a single bubble can be released at the desired time. The advantage of this bubble generation method is that we can repeatedly obtain almost the same size bubble if the nozzle, hydraulic pressure, gas pressure and switching interval are configured appropriately. We keep the interval of bubble generation over 10 s in order to reduce the influence of the wake flow of the previous bubble. The bubble motion is captured by high-speed camera (Kodak SR-500) with a frame rate of 250 fps, a resolution of 512×480 pixels, and an exposure time of 0.2 ms. Because tap water was used in the bubbly channel flow experiments herein, all of the single bubble experiments were also conducted using the same tap water either with or without surfactant. Bubble diameters are in the range of 0.8–1.0 mm, and the bubble Reynolds number is based on the bubble diameter and the rising velocity. It is noted that the bubble Reynolds number depends on surfactant species and their concentrations, because the rising velocity is different due to the Marangoni effect even when the diameter is the same. The experimental uncertainty for the rising velocity is less than 1% and that for the bubble diameter less than 2%. These give an uncertainty for the drag coefficient of less than 4% and that for the Reynolds number of less than 3%.

Figure 3

Schematic of the experimental apparatus for a single bubble in quiescent water.

The experimental results are shown in figure 4. Although bubbles of 1 mm diameter in tap water are sometimes modelled to have the drag coefficient of a rigid sphere due to the presence of contaminants, it is noted that a bubble in tap water in the present experiment has nearly the same rising velocity as that in super purified water. With the addition of surfactant, the rising velocity changes. For 3-pentanol solution, the terminal velocity is gradually reduced with an increase in 3-pentanol concentration from 21 to 168 ppm. On the other hand, in the case of Triton X-100 solution, 2 ppm is enough to produce a rigid particle-like behaviour. These results indicate that a bubble in 42 ppm 3-pentanol solution shows ‘half-contaminated behaviour’, which is to say that the drag coefficient of an approximately 1 mm single rising bubble in a quiescent liquid takes an intermediate value between that of a clean bubble and that of a rigid sphere. On the other hand, the drag coefficients of a bubble in 168 ppm 3-pentanol solution and 2 ppm Triton X-100 solution show a value which is nearly the same as that of a rigid sphere. Numerical results by Takagi et al. (2003) corresponding to these experimental conditions also show that the surface velocity of a bubble in 42 ppm 3-pentanol solution still has a slip velocity, while that in Triton X-100 solution has a no-slip surface due to the strong Marangoni effect. The bubble size shown in figure 2 is approximately 0.9–1.0 mm and the corresponding Reynolds number is approximately from 100 to 300 depending on the level of contamination. The bubble keeps a nearly spherical shape in this parameter range as shown in figure 2. In this range of Reynolds number, there is a very interesting feature related to the lift force acting on a bubble and a particle in a linear shear flow. Figure 5 shows a comparison of the numerical results of Legendre & Magnaudet (1998) for a spherical bubble and Kurose & Komori (1999) and Bagchi & Balachander (2002) for a rigid sphere. Following Auton (1987), the lift coefficient in the figure is defined asEmbedded Image(3.1)where CL and ρ are the lift coefficient and the density at liquid phase, respectively. For a clean bubble, Legendre & Magnaudet (1998) showed that the lift coefficient asymptotically approaches CL=0.5 with an increase in Reynolds number, where CL=0.5 is the theoretical value for a sphere in a weakly rotational inviscid flow derived by Auton (1987). On the other hand, for the rigid sphere Kurose & Komori (1999) and Bagchi & Balachandar (2002) showed that CL decreases with an increase in Re, and CL takes a near-zero value at Re∼100. Beyond this value of Re, CL keeps decreasing slightly and takes a small negative value, which indicates that the lift force on a rigid sphere acts in the opposite direction of that on a clean bubble. Considering that the bubble Reynolds number for the current experiment is approximately from 100 to 300, we find a remarkable difference of the lift coefficient between the clean bubble and the rigid sphere in this Reynolds number range. Therefore, it is expected that the lift force may decrease drastically as the surface approaches the no-slip condition due to the Marangoni effect. These results suggest that half-contaminated bubbles feel a sufficient lift force which causes the lateral migration, although the fully contaminated bubbles cannot.

Figure 4

Surfactant dependence on the drag coefficient CD as a function of bubble Reynolds number Re. Markers represent the present experimental results. The dashed line represents CD on a rigid sphere at finite Re (cf. Clift et al. 1978) and the solid line represents that on a clean bubble at finite Re from the numerical simulation by Mei et al. (1994). Open circles, pure water; filled diamonds, tap water; inverted triangles, 3-pentanol (21 ppm); pluses, 3-pentanol (63 ppm); open triangles, 3-pentanol (168 ppm); open squares, Triton X-100 (2 ppm).

Figure 5

Lift coefficients for spherical bubbles and rigid spheres in a linear shear flow at the dimensionless shear rate of Sr=0.2. The range between the dashed lines, 100<Re<300, corresponds to that of bubble Reynolds number in the present bubbly flow experiment. The solid line represents the theoretical value obtained by Auton (1987) for inviscid flow (CL=0.5). Open symbols represent the values from numerical simulations. Clean bubble: open circles (Legendre & Magnaudet 1998); rigid sphere (Kurose & Komori 1999): open squares, non-rotating (Bagchi & Balachandar 2002); triangles, torque free; inverted triangles, non-rotating.

Related to this observation, Fukuta et al. (2005) conducted numerical simulations based on the stagnant cap model to see the effect of surfactant on the lift force acting on a single bubble in a linear shear flow. They assumed an axisymmetric cap angle with a stress free condition imposed below this angle and a no-slip condition beyond it. They obtained the drag and lift for the stagnant cap bubble in a linear shear flow, their drag and lift coefficients being shown in figure 6. The results show that with a decrease in cap angle, CD increases and CL decreases. This decrease in the lift coefficient seems to be the main reason why the tendency of the lateral migration of bubbles towards the wall disappears with the stronger Marangoni effect. Furthermore, the figure indicates that CD increases from the value for a clean bubble (Legendre & Magnaudet 1998) to that for a rigid sphere (Mei 1993) with the decrease in cap angle. This gives the reduction of the rising speed of bubbles in surfactant solutions, which is confirmed by previous experimental studies (Zhang & Finch 2001; Takagi et al. 2003). By contrast, CL decreases away from the value for a clean bubble with the decrease in cap angle. Below the cap angle of 90°, the lift coefficient took a negative value, which means that the lift force acting on a bubble acts in the direction where the relative velocity becomes smaller. This negative lift force is also observed in the numerical studies for a rigid sphere by Kurose & Komori (1999) and Bagchi & Balachandar (2002). To analyse these changes of forces acting on bubbles, we plot in figure 6 the contributions of each stress component, the pressure distribution to the drag coefficient CDP, that to the lift coefficient CLP, the viscous stress to the drag coefficient CDV and that to the lift coefficient CLV. Note that CDP+CDV=CD and CLP+CLV=CL. For the drag force on bubbles shown in figure 6a, CDP and CDV contribute to CD in the same order of amplitude independent of cap angle and both components increase monotonically with a decrease in cap angle. Thus, both the pressure and viscous stress contributions become important to the drag force for any value of cap angle. On the other hand, for the lift force shown in figure 6b, CLP contributes much more significantly than CLV beyond a cap angle of 90°. This indicates that the lift force on a bubble is dominated by the inertia effect when the cap angle is larger. In the case of a clean bubble, Legendre & Magnaudet (1998) showed that CLP contributes to CL dominantly and the inertia effects affect significantly the lift force in the range of Re>50. For the viscous stress contribution to the lift force on a clean bubble, they illustrated that CLV takes a small negative value, and it contributes only a few per cent of CL at high Reynolds number. In contrast, for a contaminated bubble, CLP decreases while CLV does not change much with a decrease in cap angle. Below a cap angle of 90°, where the negative lift force acts on a contaminated bubble, CLP reaches almost zero and the viscous stress contribution CLV becomes dominant giving the negative value in their simulation condition. As is shown here, the lift force is greatly affected by the slip velocity of the gas–liquid interface. That is, as the free-slip condition approaches the no-slip condition by the addition of the surfactant, the lift force acting on the bubble decreases and approaches that on a rigid sphere which has a much smaller lift coefficient. This is the reason why the tendency of bubble migration weakens with the increase in concentration of 3-pentanol or Triton X-100 solution.

Figure 6

(a) Drag coefficient CD (rigid sphere (cf. Clift et al. 1978), clean bubble (Mei et al. 1994); filled circles, CD; open squares, CDP; open triangles, CDV) and (b) lift coefficient CL (clean bubble (Legendre & Magnaudet 1998), rigid sphere, non-rotating (Bagchi & Balachandar 2002); filled circles, CL; open squares, CLP; open triangles, CLV) for a stagnant cap bubble in simple shear flow at a bubble Reynolds number of Re=100 and dimensionless shear rate of Sr=0.2 (Fukuta et al. 2005).

4. Conclusion

The effect of surfactants on the multiscale structure of bubbly channel flows has been discussed in this paper. By adding a small amount of 3-pentanol or Triton X-100, small spherical bubbles of monodispersed size were obtained. This addition of the surfactant drastically changes the whole bubbly flow structure depending on the surfactant species and its concentration. As an example, it is shown that, under the condition of 42 ppm 3-pentanol solution, the bubbles tend to migrate towards the wall and they accumulated near the wall. These accumulated bubbles form horizontal bubble clusters of approximately 10–40 mm in size in the spanwise direction, having a thin crescent-like shape. The average cluster size is much larger than the well-known coherent vortical structure in turbulent boundary layers. This fact indicated a drastic modification of the turbulent flow structure. Interestingly, an increase in 3-pentanol concentration or a change of surfactant species to a small amount (2 ppm) of Triton X-100, which has a stronger Marangoni effect, further change the whole bubbly flow structures. Under these conditions, bubble clusters totally disappeared and the lateral migration of bubbles towards the wall was no longer observed. Numerical simulation for a contaminated bubble using a stagnant cap model suggests that there exists a drastic change of the lift force acting on an approximately 1 mm size bubble in a linear shear flow. This change of lift force gives a qualitative difference of the lateral migration of bubbles towards the wall, in which slightly contaminated bubbles can feel an Auton-type lift force and migrate towards the wall. This in turn causes the formation of bubble clusters near the wall. On the other hand, fully contaminated bubbles cannot feel the lift force and they disperse uniformly across the channel without forming bubble clusters.

As is shown here, a small amount of surfactant drastically affects the multiscale structure of bubbly flows. The presence of surfactants affects the small-scale behaviour of each bubble and then this change of bubble behaviour leads to a large-scale change of whole bubbly flow structures.

Footnotes

  • One contribution of 11 to a Theme Issue ‘New perspectives on dispersed multiphase flows’.

References

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