Article pubs.acs.org/Langmuir
Effect of Environmental Humidity on Static Foam Stability Xueliang Li,† Stoyan I. Karakashev,‡ Geoffrey M. Evans,† and Paul Stevenson*,§ †
Centre for Advanced Particle Processing, University of Newcastle, Callaghan, NSW 2308, Australia Department of Physical Chemistry, Sofia University, 1 James Bourchier Avenue, 1164 Sofia, Bulgaria § Department of Chemical and Materials Engineering, University of Auckland, 20 Symonds Street, Auckland 1010, New Zealand ‡
ABSTRACT: The quality of foaming products (such as beer and shampoo) and the performance of industrial processes that harness foam (such as the froth flotation of minerals or the foam fractionation of proteins) depend upon foam stability. In this study, experiments are performed to study the effect of environmental humidity on the collapse of static foams. The dependency of the rate at which a foam collapses upon humidity is demonstrated, and we propose a hypothesis for bubble bursting due to Marangoni instability induced by nonuniform evaporation to help explain the dependency. This hypothesis is supported by direct experimental observations of the bursting process of isolated bubbles by high speed video recording and the thinning of isolated foam films under different values of humidity and temperature by microinterferometric methods.
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INTRODUCTION The high specific gas−liquid surface area of foams is exploited in many industrial separation processes such as foam fractionation1 and froth flotation.2 Although typically these applications are reliant upon a tenacious foam, once the foam has been extracted from the column it needs to be collapsed so that an enriched solution can be produced and the objective substances can be recovered. It is also evident that the mineral grade and recovery achieved in a flotation operation is dependent upon froth stability.3 Excess foaming may also be undesirable, for instance, in a fermentation tank where it can be detrimental to the process, but can be destroyed by using an antifoaming agent. However, the use of antifoam to cause collapse is not always feasible in foam fractionation, especially when external reflux4,5 is applied. In addition to these industrial applications, one’s experience with a variety of products such as beer and shampoo is dependent upon foam stability. Thus, foam stability is of fundamental interest to both industrial processes and in the design of consumer products. Several methods are available for characterizing the stability of foam. For relatively stable static foams, the most frequently used method is that developed by Ross and Miles.6 In this method, the foam is generated by pouring a known amount of the foaming liquid from a reservoir onto a known volume of the same solution in a receiving tube of a certain height. The initial height of the foam thus generated is used to characterize the © 2012 American Chemical Society
foaming ability of the solution, and the remaining foam height at some later time is used to characterize foam stability. Because the amount of energy available for foam generation depends on the mass and elevation of the liquid in the reservoir, the Ross− Miles method is dependent on the dimensions of the apparatus, and results are only comparable when the tests are performed on identical devices under the same conditions. It is for this reason that there are various standards (e.g., ISO 696:1975, GB/T7162-94 (P.R.C.)) where the dimensions of the Ross− Miles apparatus are defined. For less stable foams, Bikerman’s foam stability test7 is commonly adopted. In this method, a gas is continuously sparged into the foaming solution and, simultaneously, the foam collapses at its free surface. When the rate of foam collapse equals the rate of generation of fresh foam, an equilibrium foam height is attained. The equilibrium foam height divided by the superficial gas velocity is used as a measurement of foam stability. Unlike the Ross−Miles method, the foam stability defined by Bikerman was believed to be an intrinsic property of the foaming liquid and therefore independent of the apparatus used and the amount of solution employed in the measurement.8−11 Received: October 29, 2011 Revised: January 25, 2012 Published: February 3, 2012 4060
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the work of Yiantsios and Higgins,18 who demonstrated that instabilities can develop in liquid films with initially uniform thickness by the mechanism of the Marangoni effect: As the film thins due to evaporation, an initially random thickness perturbation leads to surfactant concentration and, hence, a surface tension perturbation. Thus, a Marangoni stress is formed at the surface of the film, which pulls liquid from the low surface tension region toward the high surface tension region. This in turn drives the instability and enhances uneven film drying.18 An analogy between these theories and foam stability observations has not yet been drawn. In the present study, an attempt is made to make such a connection, and to explain the experimental observation that the collapse of static foams is also dependent on environmental humidity. It will be experimentally shown that the conventional foam decay mechanisms, which require the bubbles to reach a critical film thickness via drainage8−11 or to lose their entire liquid inventory via uniform evaporation,16 are ineffective. A hypothesis that the Marangoni instability induced by nonuniform evaporation is proposed as a contributing mechanism to foam film rupture. It must be pointed out that the current study is focused on practical implications of the effect of evaporation on foam stability, rather than the mechanism of the instability of isolated thin liquid films.
In both the Bikerman foam stability test and the Ross and Miles method, the foam stability is characterized by the height of the foam layer, rather than other microscopic properties such as the thickness of foam films. It is this simplicity that has made these two methods popular and well-adopted in various industries such as mining, brewing, and detergent manufacturing. While it is true that the foam stability measured by these two methods is intrinsically related to the physicochemical properties of the foaming solution, there are many external factors, such as temperature or pressure changes and mechanical vibrations, which may directly or indirectly affect the results of such tests. The effects of some of these factors have been taken into consideration. For example, thermostatic jackets are sometimes used to control the temperature in the test apparatus.6 However, there are other factors, such as the effect of environmental humidity, which has been overlooked, but is the subject of this study. Feitosa and Durian12 mentioned that in their nonoverflowing pneumatic foam experiments (similar to the Bikerman foam stability test), the cause of bubble bursting at the surface of the foam “appeared to be evaporation”, although no systematic treatment of the problem was carried out. We systematically studied the dependency of the Bikerman foam stability upon the gradient of humidity in the space (which we refer to as the “freeboard”) above foams stabilized by SDS solutions of various concentrations, and we described the implications of this effect on foam stability measurements.13 However, recent publications indicate that the influence of environmental humidity on the foam stability is still being largely overlooked. For example, in a recent review3 of the significance of froth stability in mineral flotation, the effect of humidity was not considered. In an experimental study on the stability of individual soap films, it was also shown that the lifetime of soap films in a closed container is much longer (up to 60 days) than if they were exposed or partly exposed to ambient air (0−2 days).14 While we recognize that planar soap films are dissimilar to bubbles at the free surface of foam in that there is no pressure difference across a planar film, we maintain our postulate that evaporation may have contributed to the differences. Wang et al.15 found that, when subjected to reduced pressure, foam stability decreased significantly. This observation could possibly be explained by noting that reduced pressure promotes evaporation, although other factors may also have played a role. The neglect of the effect of humidity is common to theoretical treatments of foam stability, because conventional foam stability theories8−11 propose that foam films burst stochastically upon reaching a critical thickness, where the film thickness is a monotonic function of the film age. Therefore, the thicker is the film, the longer it can survive because it has more liquid to drain and vice versa. Because the rate of film thinning due to drainage is typically much greater than that due to liquid loss caused by evaporation, drainage was considered the sole reason for foam collapse. Even when the effect of evaporation was occasionally considered, it was based on a similar liquid inventory argument. For example, Exerowa and Kruglyakov16 postulated that the lifetime of a foam film was determined by the initial film thickness, h0 (m), and the rate of evaporation, q (m/s), by the simple relationship t = h0/q, where the foam film was assumed to evaporate evenly across its surface. There are theoretical studies showing that instabilities can develop in evaporating thin liquid films laid on a solid substrate that is heated.17−19 Of particular interest to the current study is
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EXPERIMENTAL METHODS
Static Foam Stability Test. The foam stability experiments employed in this study are simple: Identical foams (in terms of bubble size, initial foam height, and initial liquid fraction) are created in a tube, and their collapse under controlled environmental humidity and temperature is observed. Because neither the Ross−Miles apparatus nor the Bikerman foam stability test allows for the precise control of humidity and fundamental properties of the foam such as bubble size and liquid fraction, we designed an apparatus and procedure that not only allowed for humidity control at the top of the tube, but also produced foams with well-defined bubble size and liquid fraction. The apparatus is shown schematically in Figure 1. A 150 mL glass beaker
Figure 1. Schematic of the humidity-controlled foam stability apparatus. was used to contain the foaming solution, which was 0.5 g/L CTAB (cetyltrimethylammonium bromide, Roche (China) Ltd., analytical grade (A.R.)) in distilled water. CTAB was specifically chosen as Hutzler et al.11 suggested that it is less stable than SDS (sodium dodecyl sulfate), 4061
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which we had previously used.13 The concentration of 0.5 g/L was used because there are literature data showing that at this concentration the equilibrium surface tension of a CTAB solution is the least sensitive to temperature changes.20 A glass tube with an internal diameter of 12 mm and a length of 145 mm was inserted into the beaker to support the foam. The beaker was placed on a lab jack so the vertical position of the beaker relative to the foam tube could be adjusted. This arrangement enabled manipulation of the foam/liquid interface in the foam tube independently of the foam height and the overall length of the tube. To minimize the possible effect of mechanical disturbance caused by air flow, the foam tube was placed in a large chamber (200 mm tall with an internal diameter of 90 mm) made of transparent acrylic glass (Perspex/ Plexiglas), the relative humidity inside which was controlled. The bottom of the chamber was fully open, while the top of it was covered by a lid with an air vent in the center of the lid to dampen possible pressure disturbances. Compressed air dried by a laboratory air drying unit (W.A. Hammond Drierite, U.S.) was passed into the chamber through a pipe. Note that the dry air was not blown toward the foam tube to avoid mechanical disturbance caused by the air flow. A precision humidity/ temperature meter (HT-3009, Lutron Electronic) was placed inside the chamber with the sensor at 2 cm above the top of the foam tube. By adjusting the flow rate of dry air, the relative humidity in the chamber was able to be controlled within ±1%. A needle with an internal diameter of 0.26 mm was connected to a syringe pump (TJP-3A/W0109-1B, Longer Precision Pump Co., Ltd., China) to make bubbles at 3 mL/min volumetric flow rate of prehumidified air. The diameter of the bubbles generated by the current apparatus was approximately 0.62 mm, and this diameter was constant between runs. The foam was allowed to overflow the foam tube for about 10 min to ensure that the foam exhibited the same liquid fraction for each experiment. Excess foam generated during the 10 min was wiped off from the top of the tube, and then the foam started to collapse. The collapse process was tracked by a computercontrolled camera, which took photographs of the foam at intervals of 20 s. The foam height was then measured from the images using the Optimas 6.5 software (Media Cybernetics, Silver Spring, MD). This arrangement, coupled with the special foam generation procedure as described above, ensured that the foams in each run were identical with respect to foam height, bubble size, and initial liquid fraction. Bursting of an Isolated Bubble. One particular experimental difficulty in the search for the mechanisms of bubble bursting is that the actual bursting event occurs in a very short period of time. In this study, the bursting of isolated bubbles stabilized by the same 0.5 g/L aqueous CTAB solution as used in the foam stability tests was captured using a high-speed video camera (Olympus iSpeed HG) mounted to an optical goniometer (DataPhysics OCA 15 EC, Germany). The electronic dosing unit of the goniometer was used to produce bubbles with a defined volume (8.0 μL). When the high speed video was recorded, a high intensity light source has to be used to illuminate the bubble due to the short exposure time; otherwise, the images will be too dark. The light source was placed to the left of the bubble. As a consequence of this illumination, evaporation from the left hemisphere of the bubble was promoted. It is recognized that the illumination could possibly increase the temperature of the liquid film of the bubble, which, in turn, could affect the properties of the gas−liquid interface. Therefore, the effect of temperature and evaporation on the dynamic surface tension of the foaming solution was also investigated using the goniometer, as described below. Effect of Temperature and Evaporation on the Dynamic Surface Tension. Although in the foam stability test the temperature was the same when the relative humidity was changed, there could possibly be a temperature elevation in the single bubble bursting experiments due to the illumination. Therefore, the effects of temperature and evaporation on the dynamic surface tension of the surfactant solution were studied. Because significant temperature elevation was unlikely to occur due to the latent heat of evaporation, the small projected area, and the short lifetime of the bubbles (typically 7−8 s), a temperature range from 19 °C (temperature of the surfactant solution in the bubble bursting experiments) to 30 °C was tested.
The effect of temperature on the dynamic surface tension was measured by the pendant bubble method21 where a bubble was immersed in the CTAB solution and evaporation eliminated. The temperature of the solution could be directly controlled by placing the glass cell holding the solution in the temperature and humidity control unit (TFC-100, DataPhysics, Germany) of the goniometer. The effect of evaporation on the dynamic surface tension was examined by the pendant drop method at a constant temperature of 22 ± 1 °C and two different values of relative humidity, 45% and 100%. Unlike the pendant bubble method, the pendant drop method created a drop of the surfactant solution at the tip of a needle. A detailed discussion of the pendant drop method and the pendant bubble method can be found elsewhere.21 Again, the needle was suspended in the glass chamber of the TFC-100 unit, which enabled temperature and humidity control. Film Thinning under Saturated and Unsaturated Vapor Conditions. It is noted that, although one can infer gas−liquid interfacial properties from the dynamic surface tension measurements as described above, neither the pendant drop method nor the pendant bubble method can measure any property of thin liquid films. Even in the pendant bubble method, the bubble is different from a bubble in a foam because the former consists of only one gas−liquid interface and it is submerged in liquid, while the latter consists of two gas−liquid interfaces on both sides of the thin liquid film. The question arises as to whether temperature and evaporation have any impact on the stability of thin liquid films? The microinterferometric method was exploited to investigate the transient behavior of planar thin foam films under saturated (RH = 100%) and unsaturated (RH = 40%) air at 20 and 30 °C. The foam film was also stabilized by 0.5 g/L CTAB. A full description of the experimental apparatus was previously reported16,22 and is not repeated here. Briefly, the experimental setup (see Figure 2) consists of a glass cell, with
Figure 2. Interferometric apparatus used for thin liquid films in saturated vapors. an inner diameter of 3.4 mm, for producing horizontal foam films. First, a droplet of surfactant solution was formed inside the film holder. The amount of liquid was then regulated by a gastight microsyringe connected to the film holder through a glass capillary. Finally, a microscopic film was formed between the apexes of the double-concave meniscus by pumping out the liquid from the drop. A metallurgical inverted microscope was used for illuminating and observing the film and the interference fringes (the Newton rings) in reflected light (wavelength = 546 nm). The interferograms were processed using “Image J” software,23 delivering the pixel signal from a given small area of the film as a function of the time, thus producing temporal interferograms, which were then used for further calculation of the film thickness versus time. Two variants of the experimental configurations were employed. In the first one (see Figure 2), the glass cell was closed with some surfactant solution placed at the bottom. The relative humidity of the air inside the cell approached 100% in this case. In the second configuration, the glass cell was open, allowing the foam film to evaporate 4062
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into ambient air of approximately 40% relative humidity. Rigorous humidity control within the measuring cell was not attempted due to the complexity arising from the small size of the cell.
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humidity of the air in the chamber was controlled at 50%, and the collapsed foam height as a function of foam age is plotted in Figure 4. It can be seen that the rate of foam collapse was
RESULTS AND DISCUSSION
Stability of Static Foams under Different Humidity. Figure 3 shows the collapsed foam height as a function of foam
Figure 4. Collapsed foam height versus foam age two different initial freeboard heights (0.5 g/L CTAB, RH = 50%). The bubble size, the initial foam height, and the initial liquid fraction were all identical in both cases. Figure 3. Collapsed foam height versus foam age at two different relative humidities (0.5 g/L CTAB solution, initial freeboard height = 0 mm). The bubble size, the initial foam height, and initial liquid fraction were all identical in both cases.
significantly reduced as compared to when the initial freeboard height was 0 mm. Note that the total foam heights were the same in both cases, so if there were any capillary effects, they should be the same for both cases so the differences should not be caused by capillary effects. Instead, we believe that it was because the humidity gradient was reduced when the freeboard height was increased (see Appendix I), which depressed evaporation. The different rates of collapse should have little to do with drainage-induced film thinning because in both cases the foam had the same age and the same drainage time. Static Foam Stability in the Absence of Evaporation. The above experiments clearly showed that the rate at which the foam collapses is strongly affected by evaporation. The question immediately arises as to what the stability of a foam is in the absence of evaporation? To test this, two identical tubes of foam were generated, but the top of one of the tubes was sealed (thereby completely prohibiting evaporation) and the other one was open to the atmosphere (which allowed for evaporation), as shown in the left panel of Figure 5. In the open tube, there could also be gas diffusion from the top layer bubbles to the ambient air, which could accelerate bubble size disproportion24,25 and destabilize the foam.21,22 However, as will be discussed immediately below, bubble size disproportion or foam coarsening does not necessarily lead to the collapse of a foam layer. After 5 h, the foam in the open tube had completely collapsed, while the foam in the sealed tube remained at the same height (right panel of Figure 5), although due to interbubble gas diffusion26,27 the foam coarsened and the liquid fraction had diminished significantly due to drainage. The resultant thin liquid films were almost planar and exhibited great stability, indicating that film thinning and coarsening did not necessarily lead to bubble bursting or the collapse of a foam layer. Therefore, previous foam stability models that were solely based on foam drainage are incomplete. The corollary is that any foam stability test that involves the measurement of foam height but without humidity control is not rigorous. The Bursting of an Isolated Bubble Due to Nonuniform Evaporation. Thus far, it has been experimentally confirmed that the humidity gradient in the freeboard of a foam
age at two different values of relative humidity (RH), 50% and 65%, and a temperature of 22 ± 1 °C. The initial foam height was 10 cm, and less than 3 cm of the foam collapsed, which made the capillary effect insignificant (it might become more significant if the foam height further reduced). Experiments at each relative humidity were repeated three times, and the average results are shown, with error bars indicating the absolute range of deviations from the arithmetic mean. It can be seen that, when the environment was drier, the rate at which the foam collapsed was much higher than when the environment was more humid, because a lower relative humidity promoted evaporation. It can also be seen from Figure 3 that when the free surface of the foam fell further away from the top of the tube, that is, when the foam collapsed more and the freeboard height increased, the rate at which it collapsed decayed. To explain this phenomenon, some researchers have adopted the concept of the “half-life”3 (presumably by drawing an analogy to radioactive decay) as an indicator of froth or foam stability. However, the concept of decay is contrary to the conventional understanding that foam collapse is caused by film thinning. For example, at a foam age of 15 min, the foam films should be thinner than that at t = 0 due to drainage, so, if foam stability was dependent upon film thickness, which decreased by liquid drainage under gravity alone, by conventional drainage arguments the foam should be less stable. However, by considering the decay behavior, the foam superficially appears to be more stable rather than less. By invoking the evaporation argument, we propose that the reduction in foam collapse rate can be attributed to the fact that the humidity gradient (which is the driving force of evaporation) decreases as the freeboard height increases. To further test the effect of humidity gradient, the freeboard height was deliberately increased, so that at t = 0 the free surface of the foam was already 30 mm below the tip of the foam tube, but the actual height of the foam was maintained the same by adjusting the height of the lab jack (see Figure 1). The relative 4063
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evaporation is faster at the left-hand apex of the bubble. As the bubble loses water due to evaporation, the local surfactant concentration increases both in the bulk and at the interface, simply due to material balance. As the surface excess increases, the local surface tension decreases, while the surface tension in the less actively evaporating region remains at a relatively higher value. Therefore, a gradient of surface tension is formed, with a lower surface tension at the most actively evaporating region. The surface tension gradient pulls liquid away via the Marangoni effect from the already thinning region, which further decreases the local surface tension and increases the surface tension gradient, until the bubble bursts due to the pressure inside the bubble, as observed in Figure 6 by highspeed video recording. The above analysis is based on an isolated bubble, which is subjected to nonuniform evaporation. It remains to be explained why bubbles at the free surface of a foam experience nonuniform evaporation. We propose the following hypothesis to explain this. Without the illumination, a humidity gradient like that shown in the left panel of Figure 8 is expected for an isolated bubble. The contours are those of constant relative humidity, or “isohumes”. The evaporation should be uniform across the surface of the bubble. In the case of a foam column, a nearlinear global humidity gradient in the freeboard far from the free surface has been previously observed.13 However, at the scale of the bubbles at the very top of a foam layer, a humidity distribution as that schematically shown in the right panel of Figure 8 is expected. In the direction normal to the bubble surface, the humidity gradient is a maximum at the apex of the bubble and decreases as the position on the bubble surface falls away from the top. Because of this, the rate of evaporation is greater at the apex, and decreases with position away from the apex. As a consequence, a Marangoni flow, caused by this nonuniform evaporation, pulls liquid away from the bubble apex, which accelerates the bursting process. We stress that this distribution is conjecture, and we propose to conduct NMRI experiments in the future to test the humidity distribution near the free surface of a foam. The mechanism has analogy to the Marangoni drying process28−30 where liquid is withdrawn from the substrate to be dried due to a surface tension gradient, except that, in the case of Marangoni drying, surface tension gradient is induced by dissolving an organic vapor into water, rather than being induced by nonuniform evaporation as in this study. Although the Marangoni effect is a stabilizing factor for soap films against stretching or shearing, there is the possibility that it can also cause instability if it is induced by nonuniform evaporation. Effect of Temperature and Evaporation on the Dynamic Surface Tension. In the single bubble bursting experiments (but not in the foam stability experiments), a highintensity light source was used to create a nonuniform evaporation condition. It is pertinent to check if this could have also resulted in any temperature effects. However, it is difficult to measure the temperature distribution along the bubble surface due to the small bubble size and its short lifetime. It is more straightforward to check the relative significance of the effects of temperature difference and evaporation on the interfacial properties, which will be discussed below. The effect of temperature on the dynamic surface tension of the same solution as used in the foam stability and bubble bursting experiments was measured by the pendant bubble method, and the results are shown in Figure 9. When the temperature increased from 19 to 30 °C, a difference in dynamic
Figure 5. Foam stability tests with evaporation and in the absence of evaporation (0.5 g/L CTAB).
column plays an important role in determining the rate at which the foam collapses. Therefore, an explanation of the mechanism by which evaporation affects foam stability is now required. To do that, we first observed the bursting process of isolated bubbles using high-speed video recording. Figure 6
Figure 6. Bursting of a bubble captured at 8000 frames per second (0.5 g/L CTAB). The radius of the bubble was 1.22 mm. The ambient air temperature was 19 °C with a relative humidity of 43% during this specific session.
shows the bursting sequence at 8000 FPS (frames per second) of one bubble. It can be seen that the bubble started to burst from the left hemisphere, which was the illuminated side. It is clear that the bursting of the bubble could not have been caused by drainage; otherwise, the bubble would have started to burst from the top, where the film was the thinnest due to drainage. Note that the first frame in Figure 6 is not of the time the bubble is formed. Figure 6 represents the last 2.5 ms of the bubble’s lifetime only, while the bubbles normally last 7−8 s. This experiment was repeated several times (sometimes with even higher frame rate of 15 000 FPS, but lower image quality), and the results were the same. It can be seen from Figure 6 that at the time the bubble bursts, there is still a significant amount of liquid contained in the foam film. Therefore, the argument that the bubble bursts when it loses its entire liquid inventory16 is incorrect. The proposed mechanism of evaporation-induced bursting, or, more precisely, nonuniform evaporation-induced bursting, can be explained schematically as shown in Figure 7. As represented in this figure, an air bubble bounded by a thin liquid film containing a surfactant is placed in a humidity gradient where 4064
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Figure 7. Schematic of the Marangoni effect induced by nonuniform evaporation.
Figure 8. Schematic of the isohume plots around an isolated bubble (left) and at the freeboard of a foam column (right). Note that these are not experimental results or simulation results, but are hypotheses based on water vapor diffusion considerations.
surface tension of about 1 mN/m was engendered. This is a relatively small difference in comparison with the absolute value of the surface tension (∼39 mN/m). Similar observations are available in the literature where the equilibrium surface tension of CTAB solutions at different temperatures and concentrations was reported,20 and it has been shown the equilibrium surface tension of 0.5 g/L CTAB solution does not change significantly for a temperature from 10 to 90 °C. It has also been reported that the temperature has an insignificant effect on the disjoining pressure of liquid films stabilized by C14TAB.31 Figure 10 shows the evolution of drop volume and surface tension as a function of adsorption time at two different values of relative humidity as indicated in the legend. It can be seen that at RH = 100%, the drop volume is constant with time, while the surface tension decreases as adsorption proceeds. At RH = 45%, the drop volume decreases almost linearly with
Figure 9. Effect of temperature on the dynamic surface tension of 0.5 g/L CTAB (pendant bubble method). 4065
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Figure 11. Evolution of the thickness of planar foam films with the same radius of 28 μm in saturated or unsaturated air at 20 °C. Figure 10. Dynamic surface tension and drop volume at different relative humidities (pendant drop method, 0.5 g/L CTAB).
time, and the surface tension decreases slightly faster than in the case of RH = 100%. This can be explained by that at RH = 45%, the liquid evaporates so the drop loses water from the surface. At any time, the surfactant concentration is higher than when RH = 100%, resulting in a lower surface tension. As water evaporates from the surface, desorption of surfactant molecules from the interface may occur, and the rate of this depends on the adsorption/desorption kinetics. However, from material balance considerations, the surfactant concentration in the evaporating drop is always higher than when there is no evaporation. It should be noted that here we are measuring the dynamic surface tension of a droplet subjected to evaporation; the effect of evaporation on the dynamic surface tension of a gas bubble bounded by a thin liquid film should be more significant, because a bubble has a much smaller liquid inventory than a droplet. This can be shown by a simple calculation. If the amount of liquid lost due to evaporation is dV, the concentration increment in a droplet of radius r is dV/4/3πr3, while the concentration increment in a bubble of the same radius and a film thickness of h is dV/4πr2h, which is greater than the case of droplet by a factor of r/3h (about 103 if r = 1 mm and h = 0.3 μm). The above analysis indicates that, in the single bubble bursting experiments, the effect of temperature should be insignificant in comparison with the effect of evaporation. This is consistent with the foam collapse experiments, where all of the tests were carried out at the same temperature, yet a significant effect of humidity was observed. However, the dynamic surface tension measurements do not give any information about the effects of different rate of evaporation on thin liquid films. In the section below, experimental results of the effects of humidity on thin film thickness at two different temperatures are discussed. Effect of Humidity and Temperature on Film Thickness. The evolution of foam film thickness in contact with saturated or unsaturated air is shown in Figures 11 and 12, respectively. These experiments were carried out to simulate the different conditions on the left and right hemispheres of the bubble shown in Figure 7: On the left hemisphere, the evaporation rate is higher, while on the right hemisphere, the evaporation rate is lower. It can be seen in Figures 11 and 12 that at both temperatures, the films thinned faster when they were exposed to an ambient
Figure 12. Evolution of the thickness of planar foam films with the same radius of 36 μm in saturated or unsaturated air at 30 °C.
air of low relative humidity, although the effect of evaporation on the film thickness appeared to be slightly different at different temperatures. At 20 °C, the film in the unsaturated air thinned much faster initially, but soon reached an equilibrium thickness similar to that in the saturated case. However, at 30 °C, the initial thinning rates were similar in both saturated and unsaturated cases, but the equilibrium film thickness was much smaller when evaporation existed. This might be caused by the exchange of surfactant molecules between the surface and the bulk of the liquid film, and between the central area of the films and the meniscus far away from the film. Nevertheless, it is evident that at both temperatures, the relative humidity of the ambient air has significant effects on film thickness, which in turn affects the local surfactant concentration and surface tension. In the above experiments, the evaporation was expected to be uniform across the surface of the film, given the small size of the films (radii of films were 28−36 μm). The time required for the films to reach equilibrium thickness was comparable to the lifetime of isolated bubbles in the high-speed video experiments, but the films did not break. A difference in the lifetime of the films at the two different temperatures (the radius and the initial and equilibrium film thickness were also different) was not observed either. This indicates that uniform thinning caused by uniform evaporation does not necessarily lead to film breakage, which again refutes the mechanism proposed by Exerowa and Kruglyakov.16 Of course, there are other factors such as the absence of a pressure difference across the planar films. It is not our intention to investigate the stability of planar liquid films in this work. 4066
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Notes
CONCLUSIONS The rate of collapse of a static foam stabilized by a 0.5 g/L CTAB solution under controlled humidity is investigated. It is observed that the collapse of the foam is strongly dependent upon the humidity gradient in the space above the foam. This observation is consistent with previous studies on dynamic foams stabilized by SDS solutions of different concentrations.13 Experimental results also show that conventional foam decay models based solely on foam drainage8−11 or on uniform evaporation16 are incomplete and not always effective. A new mechanism based on the Marangoni effect induced by nonuniform evaporation of the foam film is proposed to explain the strong dependence of foam stability on environmental humidity has been proposed. The mechanism is supported by observations of the bursting of an isolated bubble subjected to nonuniform evaporation and by experimental investigations on the effects of temperature and evaporation on the dynamic surface tension of the surfactant solution and on the thinning of planar liquid films.
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The authors declare no competing financial interest.
ACKNOWLEDGMENTS
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REFERENCES
X.L., G.M.E., and P.S. thank the Australian Research Council for financial support from the Discovery Projects scheme under grant number DP0878979. They are grateful to Neil Broom and Woong Kim of the Department of Chemical and Material Engineering, University of Auckland, for their help with the high speed video recording. S.I.K. thanks the EC/“Marie Curie Actions” for financial support through the DEFFED − Project No. 230626/2009 and FP7 project BeyondEverest.
(1) Lemlich, R. Adsorptive bubble separation methods−Foam fractionation and allied techniques. Ind. Eng. Chem. 1968, 60, 16. (2) Wills, B. A.; Napier-Munn, T. Froth flotation. Wills’ Mineral Processing Technology, 7th ed.; Butterworth-Heinemann: Oxford, 2005. (3) Farrokhpay, S. The significance of froth stability in mineral flotation−A review. Adv. Colloid Interface Sci. 2011, 166, 1−7. (4) Lemlich, R.; Lavi, E. Foam fractionation with reflux. Science 1961, 134, 191. (5) Martin, P. J.; Dutton, H. M.; Winterburn, J. B.; Baker, S.; Russell, A. B. Foam fractionation with reflux. Chem. Eng. Sci. 2010, 65, 3825. (6) Ross, J.; Miles, G. An apparatus for comparison of foaming properties of soaps and detergents. J. Am. Oil Chem. Soc. 1941, 18, 99. (7) Bikerman, J. J. The unit of foaminess. Trans. Faraday Soc. 1938, 34, 634. (8) Neethling, S. J.; Cilliers, J. J. Predicting air recovery in flotation cells. Miner. Eng. 2008, 21, 937. (9) Neethling, S. J.; Lee, H. T.; Grassia, P. The growth, drainage and breakdown of foams. Colloids Surf., A 2005, 263, 184. (10) Grassia, P.; Neethling, S. J.; Cervantes, C.; Lee, H. T. The growth, drainage and bursting of foams. Colloids Surf., A 2006, 274, 110. (11) Hutzler, S.; Lösch, D.; Carey, E.; Weaire, D.; Hloucha, M.; Stubenrauch, C. Evaluation of a steady-state test of foam stability. Philos. Mag. 2011, 91, 537. (12) Feitosa, K.; Durian, D. J. Gas and liquid transport in steady-state aqueous foam. Eur. Phys. J. E 2008, 26, 309. (13) Li, X.; Shaw, R.; Stevenson, P. Effect of humidity on dynamic foam stability. Int. J. Miner. Process. 2010, 94, 14. (14) Tobin, S. T.; Meagher, A. J.; Bulfin, B.; Mobius, M.; Hutzler, S. A public study of the lifetime distribution of soap films. Am. J. Phys. 2011, 79, 819. (15) Wang, J.; Liu, G.; Wu, Z.; Zhang, L. Intensified effect of reduced pressure on the foam fractionation process of bovine serum albumin. Sep. Sci. Technol. 2010, 45, 2489. (16) Exerowa, D.; Kruglyakov, P. M. Foam and Foam Films: Theory, Experiment, Application; Marcel Dekker: New York, 1997. (17) Shklyaev, O. E.; Fried, E. Stability of an evaporating thin liquid film. J. Fluid Mech. 2007, 584, 157. (18) Yiantsios, S. G.; Higgins, B. G. A mechanism of Marangoni instability in evaporating thin liquid films due to soluble surfactant. Phys. Fluids 2010, 22. (19) Danov, K. D.; Alleborn, N.; Raszillier, H.; Durst, F. The stability of evaporating thin liquid films in the presence of surfactant 1. Lubrication approximation and linear analysis. Phys. Fluids 1998, 10, 131. (20) Tang, Y.; Du, B. Y.; Yang, J.; Zhang, Y. M. Temperature effects on surface activity and application in oxidation of toluene derivatives of CTAB-SDS with KMnO4. J. Chem. Sci. 2006, 118, 281. (21) Li, X.; Shaw, R.; Evans, G. M.; Stevenson, P. A simple numerical solution to the Ward-Tordai equation for the adsorption of non-ionic surfactants. Comput. Chem. Eng. 2010, 34, 146.
APPENDIX I
The Effect of Freeboard Height on Humidity Gradient
In a previous study,13 the humidity in the freeboard of a foam column was found to decrease nearly linearly from a high relative humidity (∼100%) at the free surface of the foam to a low relative humidity at the top of the column. Thus, there is a gradient of relative humidity in the freeboard of the column, and it is this gradient that is the driving force for evaporation. If the relative humidity at the top of the foam column is fixed (as in the foam collapse experiments in the present study), the humidity gradient decreases with an increase in the freeboard height, as shown schematically in Figure A1. In case of a
Figure A1. Effect of freeboard height on the humidity gradient.
collapsing foam, as the distance between the surface of the foam and the top of the tube increases, the humidity gradient decreases; therefore, the rate of evaporation decreases, and the foam appears to be more stable. If the freeboard is infinitely high, the humidity gradient will be zero, and the foam will behave like that shown in the tube on the extreme right of Figure 5.
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(22) Karakashev, S. I.; Grozev, N.; Díez, I.; Ras, R. H. A.; Tsekov, R. Rheology of silver nanocluster solutions under confinement. Colloids Surf., A 2011, 384, 570. (23) Image J; avaliable at http://rsbweb.nih.gov/ij/index.html. (24) Meinders, M. B. J.; Kloek, W.; van Vliet, T. Effect of surface elasticity on Ostwald ripening in emulsions. Langmuir 2001, 17, 3923. (25) Kloek, W.; van Vliet, T.; Meinders, M. Effect of bulk and interfacial rheological properties on bubble dissolution. J. Colloid Interface Sci. 2001, 237, 158. (26) Lemlich, R. Prediction of changes in bubble size distribution due to inter-bubble gas diffusion in foam. Ind. Eng. Chem. Fundam. 1978, 17, 89. (27) Stevenson, P. Inter-bubble gas diffusion in liquid foam. Curr. Opin. Colloid Interface Sci. 2010, 15, 374. (28) Matar, O. K.; Craster, R. V. Models for Marangoni drying. Phys. Fluids 2001, 13, 1869. (29) Thess, A.; Boos, W. A model for Marangoni drying. Phys. Fluids 1999, 11, 3852. (30) Leenaars, A. F. M.; Huethorst, J. A. M.; Oekel, J. J. v. Marangoni drying: A new extremely clean drying process. Langmuir 1990, 6, 1701. (31) Schulze-Schlarmann, J.; Buchavzov, N.; Stubenrauch, C. A disjoining pressure study of foam films stabilized by tetradecyl trimethyl ammonium bromide C14TAB. Soft Matter 2006, 2, 584.
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