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Comparison between generations of foams and single vertical films – single and mixed surfactant systems† Laurie Saulnier,a Julia Boos,b Cosima Stubenrauchb and Emmanuelle Rio*a The purpose of this article is to compare experiments carried out with single vertical foam films and with foams. We focus on the generation of films and foams and measure (i) the quantity of water entrained and (ii) the stability of the systems. The surfactants we used are C12E6, b-C12G2 and their 1 : 1 mixture because those systems are very well characterised in the literature and are known to stabilise foams with very different properties. We show that the quantity of water uptake in foams and single vertical films scales in the same way with the velocity of generation. However, the different surfactant solutions have different foamabilities, whereas the films they stabilise have exactly the same thickness. Moreover, the foamability of a C12E6 solution is much lower than that of a b-C12G2 solution or of a solution of the 1 : 1 mixture. This is due to the rapid rupture of the C12E6 foam films during foam generation. Surprisingly, the isolated films have exactly the same lifetime for all the surfactant solutions. We conclude that, though drawing a correlation between films and foams is tempting, the results obtained do not allow correlating
Received 11th February 2014 Accepted 1st April 2014
of film and foam stability during the generation process. The only difference we observed between the single films stabilised by the different solutions is the stability of their respective black films. We thus
DOI: 10.1039/c4sm00326h
suggest that the stability of black films during foam generation plays an important role which should be
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explored further in future work.
1. Introduction The control of the foamability of a solution, i.e. its ability to generate a foam, is of utmost importance for many applications.1 Everyone knows that the choice of the physico-chemical system chosen to stabilise the foam is central in this control. Unfortunately, we still do not understand how the structure and the nature of the surfactant inuence its ability to generate foams. However, we need this information to understand the big picture, which, in turn, will enable us to tailor-make foam properties. The mechanical properties of the interface (dynamic surface tension, interfacial viscosity and elasticity)2 are good candidates to establish a link between the molecular and the macroscopic scales. These parameters are believed to control the velocity of drainage in foams (reviewed in ref. 3). They also impact the resistance of the lms to rupture and thus the foam coalescence (reviewed in ref. 4 and 5). These ndings led to dozens of studies showing a correlation between the surface rheology of
a Laboratoire de Physique des Solides, UMR 8502, Universit´e Paris-Sud, Bˆ atiment 510, 91405 Orsay Cedex, France. E-mail: [email protected]; Tel: +33-1-69-15-69-60 b Universit¨ at Stuttgart, Institut f¨ ur Physikalische Chemie, Pfaffenwaldring 55, 70569 Stuttgart, Germany
† Electronic supplementary 10.1039/c4sm00326h
information
5280 | Soft Matter, 2014, 10, 5280–5288
(ESI)
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solutions and the foamability and stability of foams made with these solutions. However, drawing general conclusions has not been possible up until now. The problem to be solved is very complicated because of the interplay between the different length scales: single molecules adsorbed at the liquid/air interface, foam lms separating bubbles, channels (so-called Plateau borders) through which the liquid ows, and foam bubbles encapsulating the dispersed gas phase. To simplify the problem, researchers oen try to benet from this multiscale structure of the foam by studying simpler objects like lms,6,7 bubbles8 or single Plateau borders9 to better understand the mechanisms acting in a foam. An attempt to simplify the problem by focusing on the dynamics of isolated lms in order to explain foam stability has been made very recently.10,11 In these articles, the authors explore the stability of a vertical foam lm by pulling a frame out of a surfactant solution. The stability is investigated during the generation of the lm, i.e. under dynamic conditions. The idea behind this work is that generating a vertical foam lm mimics well the generation of a foam by bubbling gas into a surfactant solution. Under certain conditions, the lm indeed ruptures during its generation just like foam lms do during the generation of the foam (for example, during topological events (T1)12). It is the purpose of the present article to look for a correlation between the experiments at the scale of the lm and at the scale of the foam.
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Concerning the systems, we focussed on two non-ionic surfactants, namely n-dodecyl-b-D-maltoside (b-C12G2), hexaethyleneglycol monododecyl ether (C12E6) and their 1 : 1 mixture.13–16 These surfactants are indeed very well characterised in the literature and are known to give rise to very different foams (Fig. 1). Although both sugar-based (CnGm) and oligoethylene oxide-based (CiEj) surfactants are typical examples of non-ionic surfactants with similar chain lengths, they indeed behave quite differently due to their different molecular structures. The different head group exibilities and the different hydration behaviour lead to different properties, which have been addressed in the studies quoted above and in references therein. Nevertheless, most interfacial properties such as surface viscoelasticity or dynamic surface tension16 are remarkably close to each other for the two surfactants and their 1 : 1 mixture. So the explanation of the very different behaviour of the foams stabilised by the respective surfactants remains a challenge. It was only recently that systematic investigations on the properties of mixtures of C12E6 and b-C12G2 were carried out.13–19 The focus was on mixtures with a xed molar ratio of 1 : 1 which in the following is referred to as “1 : 1 mixture”. These studies revealed that in most of the cases the 1 : 1 mixture behaves very much like the pure C12E6 (see e.g. Table 1 in ref. 17). However, in a very recent systematic foam study18 we could show that – other than what is stated in ref. 16 and 17 – the situation for foams does not follow this “rule of thumb”. The main results of our previous work on foam generation with the surfactants mentioned above indeed show that foams
Soft Matter
stabilised by the mixture or by b-C12G2 are much easier to generate than those stabilised by C12E6. This is a very surprising observation since, as mentioned above, all the interfacial properties of the two surfactants and of their mixture are very similar. In particular, the dynamic surface tension has been shown to be at the origin of different foamability22 or of differences in the generation of emulsions.23 The fact that we observe different foamabilities with similar dynamic surface tensions shows that other parameters should be investigated. As we will show later on, the present study allows the exploration of the importance of the surface elasticity measured in situ in the isolated lm. In the study at hand we investigate the generation of single vertical foam lms stabilised by the single surfactants and the surfactant mixture and compare the results with the generation of the respective foams. For this purpose, we compare (a) the quantity of liquid entrained during foam and lm generation, and (b) the lm lifetime with the foam stability during generation. Concerning lm rupture, we only present and discuss the measurements for those cases where the lm ruptured during its generation. We show that - the quantity of liquid entrained during foam and lm generation scales in the same way with the velocity of generation. - there is no correlation between the lm stability and the foamability of a given solution. - the only difference observed between the lms generated from the different surfactant solutions is the maximal length of the black lm that can be observed during an experiment.
Fig. 1 Comparison of the stability of 2D foams (collection of bubbles squeezed between two glass plates) stabilised by C12E6 or b-C12G2, respectively. The time evolution of both foams shows a lot more coalescence events in the foams stabilised by C12E6. Image courtesy Maha Hammouda and Wiebke Drenckhan.
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2.
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Experimental section
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2.1. Materials The non-ionic sugar surfactant n-dodecyl-b-D-maltoside (bC12G2) was purchased from Glycon and the non-ionic surfactant hexaethyleneglycol monododecyl ether (C12E6) was purchased from Sigma. Both surfactants were used as received. The solutions were prepared with double distilled water at room temperature (21 1 C). To ensure cleanliness all glassware was immersed in Deconex 22 LIQ-x (purchased from Borer Chemie AG) for 12 hours and rinsed ten times with tap water and ten times with ultrapure water (puried with a Millipore system). In order to compare the results obtained with the two surfactants, we used the same relative concentrations, namely three times their respective critical micellar concentration (cmc) (Table 1). Surface tensions (Table 1) were measured by a porous plate impregnation method (the Wilhemy plate method using a porous paper instead of the platinum plate to ensure cleanliness). We used the values of water for the refractive indices (nD20 ¼ 1.33) and viscosities (h ¼ 1.0 mPa s) of the solutions since at these low concentrations both surfactants do change neither the refractive index nor the viscosity of the solution. 2.2. Film generation A vertical foam lm is generated by pulling a frame out of 15 mL of a surfactant solution (see Fig. 2). The rectangular stainless steel frame is 4 cm long and 1.5 cm wide. At the beginning of the experiment, the frame is immersed in the solution so that the liquid meniscus reaches the top of the frame. A translation stage (Newport UTS 150CC) starts driving down the glass cell containing the solution. A motion controller (Newport SMC100CC) controls the entrainment speed V in the range between 0.01 and 15 mm s1 1 mm s1. In order to have controlled boundary conditions, the frame is gridded with shing lines (100 mm in diameter). The time t ¼ 0 s is dened as the time at which the horizontal shing line leaves the surfactant solution. The subject of the study at hand is the lm formed in between the two vertical shing lines which are separated by 1.3 cm. To ensure cleanliness, the glass container is cleaned just as the glassware (see the previous paragraph). The frame and shing lines are rinsed with ultrapure water until no lm is formed when the frame is pulled out of the water bath ensuring that no more surfactants are present. The shing lines are replaced by new ones when changing the surfactant. 2.3. Thickness measurement To measure the thickness we use a polychromatic light and a spectrometer. An optical ber allows the transmission of the Table 1 Surface tension values g of the surfactant solutions at 3 cmc and the respective cmc values
Surfactant
C12E6
b-C12G2
b-C12G2 : C12E6 ¼ 1 : 1
g at 3 cmc/mN m1 cmc/mol L1
32 7 105 (ref. 21)
35 1.5 104 (ref. 21)
32 1 104 (ref. 20)
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Fig. 2 Schematic drawing of the experimental set-up. The solution bath translates down at speed V. The film is formed in the frame during translation. Seven optical fibers (one for enlightening and six for collecting the reflected light) coupled with a spectrometer allow instantaneous and local thickness measurements of the film formed between the fishing lines.
light perpendicular to the lm and a lens allows focusing the beam on the lm surface to obtain a spot with a diameter of around 200 mm. The intensity of the reected light I is collected by 6 optical bers surrounding the rst one (IDIL, QR200-7-UVBX). A spectrometer (USB 400 Ocean Optics) extracts the spectrum I/I0 where I0 is the incident intensity. The reected intensity is given, in a two-wave approximation, by I 4pnh ¼ A sin ; I0 l
(1)
where l is the wavelength, n the refractive index and A the amplitude. We use the commercial soware Nanocalc to t the spectrum and extract the local lm thickness h. The accuracy is very good since only the period of the signals depends on h and the soware allows tting the period even in the presence of experimental inaccuracies (for example if the amplitude depends slightly on the wavelength because of a non-perfect calibration). The error for the thickness is estimated to be around 20 nm. To measure the thickness of the black lms we use the same polychromatic light and spectrometer. We measure the ratio I/I0 for three different wavelengths and then use the Scheludko renormalisation24 to deduce the lm thickness. We check (i) that the thickness is smaller than l/4 and (ii) that the thicknesses deduced from the three different wavelengths are identical 2 nm. 2.4. Rupture detection and lifetime measurement The frame is supported by a force transducer (HBM, 5 g) which allows the measurement of the stress exercised by the lm on
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the frame. When the lm breaks there is a sudden jump in the measured stress which allows the detection of the lm rupture. The lifetime s of the lm is dened as the time elapsed between t ¼ 0 s and the rupture of the lm. This method also allows the calculation of the total length of the lm llm ¼ Vs when it ruptures.
3.
Results and discussion
As stated in the Introduction, we will rst focus on the quantity of water entrained while generating foams and lms. We will show that a similar mechanism could act in lms and foams. We will then compare the lm lifetime with the foamability, i.e. with the foam stability during generation, of the different solutions. Finally, we will look at the formation of black lms prior to rupture. 3.1. Water uptake during lm and foam generation 3.1.1 Water uptake by the lm. For vertical foam lms it has been shown10 that the lm consists of three zones. (i) The zone at the bottom has a well-dened thickness, whose value depends on the capillary number Ca ¼ hV/g, with h and g being the solution's viscosity and surface tension, respectively, while V is the velocity at which the lm is generated. This zone can be observed at the bottom of the lm shown in Fig. 3 (homogeneous pink color). (ii) Above this zone a thinning zone develops (see Fig. 3) due to gravity drainage and expands as a function of time. The presence of interference fringes is the signature of a thickness variation. (iii) Just before lm rupture, a black zone appears at the top of the lm (see Fig. 3). A hole will nucleate in this area and the lm will burst almost instantaneously. To determine the water uptake, we concentrated our measurements in the bottom zone of homogeneous thickness. We measured the thickness h at the bottom zone of the foam lm (called the Frankel zone in Fig. 3) as a function of the entrainment velocity for aqueous solutions of C12E6, b-C12G2, and the 1 : 1 mixture at 3 cmc. Fig. 4 shows on a log–log plot the thickness normalised by the capillary length
Fig. 4 Thickness of the Frankel zone normalized by the capillary length k1 plotted versus the capillary number Ca of vertical foam films stabilised by b-C12G2, C12E6 and their 1 : 1 mixture at c ¼ 3 cmc. The error bar is of the size of the symbols.
k1 ¼
rffiffiffiffiffi g rg
and plotted versus the capillary number Ca ¼ hV/g, where r and h stand for the liquid density and viscosity, respectively, and g is the gravitational constant. Since this gure only shows the normalised, i.e. dimensionless, data, we plotted the real values of h as a function of the capillary number (see ESI†). This is to keep in mind that the initial thickness is around 1 mm, i.e. the lms are too thick for the disjoining pressure to have an effect. At small capillary numbers, the thickness is given by the socalled Frankel law (black line in Fig. 4). This law takes into account the fact that the viscous forces tend to thicken the lm and that they are balanced by the capillary suction in the meniscus, which, in turn, tends to thin the lm. The gravity turns out to be negligible25 for capillary numbers smaller than 103, as observed in our experiments. This balance leads to a thickness25 h ¼ 1.89k1Ca2/3.
Fig. 3 Photo of the vertical foam film stabilised by b-C12G2 at c ¼ 3 cmc generated with V ¼ 1.5 mm s1 in the z-direction. The film is divided into three zones, namely the “thinning zone” (heterogeneous thickness) with interference fringes, the “Frankel zone” (homogeneous thickness) at the bottom and the black zone on top.
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(2)
(3)
In other words, the higher the entrainment velocity, the thicker is the resulting foam lm. The thickness is thus proportional to Ca2/3 and does not depend on the surfactant used. As can be seen in Fig. 4 and as has already been observed in many studies,10,26–28 the Frankel law only describes the lm behaviour at small capillary numbers. At high velocities the Frankel model does not anymore describe the data accurately. In recent works29,30 it was proposed that the leveling off of the thickness is due to a lack of rigidity of the interfaces. The Frankel model indeed makes the hypothesis that the interfaces can be considered as rigid, i.e. that the liquid velocity is zero at the liquid/air interface. This seems to hold true for low capillary
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numbers but it turns out that at high capillary numbers, the interfacial slip velocity between the liquid and the gas is not zero. This is due to the nite elastic modulus of the interface which controls the gradient in the surfactant concentration and thus in the surface tension. At small capillary numbers this gradient is always large enough to fulll the requirements for Frankel's law whatever the elastic modulus. In the papers quoted above, it is demonstrated that the thickness is expected to level off at high capillary numbers at a thickness equal to E/g with E being the surface dilational elasticity. Here, E is an apparent dilational surface elasticity which takes into account the effect of the extension rate and the connement. The characteristic adsorption time depends very little on the surfactant used16 and is of the order of 10 seconds. This time is large compared to the time spent by the surfactants in the dynamic meniscus (where all the hydrodynamics happens and the lm thickness is set). The dynamic meniscus is indeed around 40 mm long and the typical velocity is 1 mm s1 so that the relevant characteristic time is 40 ms. Adsorption is obviously an important feature and must contribute to the value of the effective surface elasticity. In the same time, the lms are thin: if we compare the total amount of surfactants in the lm (ch with c being the concentration of surfactants) to the amount of surfactants at the interface (G, the surface concentration) we nd a value close to 1 so the volume is depleted and the effective value of E also takes this effect into account. Surprisingly, it turns out that a constant value is sufficient to describe the data obtained at different capillary numbers.30 Thus, the apparent dilational surface elasticity E describes well the dynamics of the surfactants in the soap lm. The superposition of the data obtained from the three solutions (Fig. 4) then suggests that this effective elasticity is very similar in the three solutions which is in agreement with previous work where surface elasticities at concentrations above the cmc of b-C12G2 and C12E6 have been measured or extrapolated.6,19 To conclude one can say that the initial thickness of freshly generated foam lms as well as the dependence of this thickness on the capillary number is the same for all three systems because the effective surface dilational elasticity measured in situ is the same. 3.1.2 Water uptake by the foam. To compare the results obtained on lms with foam experiments, we went back to our previous study on foams.18 In this work we performed foaming experiments by bubbling N2 into the surfactant solution at a controlled ow rate. The foams are stabilised by the same surfactants used in the study at hand but at slightly higher concentrations (10 cmc instead of 3 cmc). Note that in a previous study a similar change in the concentration did not modify the power law for soap lms10 which justies our comparison. In each foam we measured the initial liquid fraction 30. For the paper at hand, we calculated gas velocities from the gas ow rates (velocity ¼ ow rate divided by the crosssection of the cell) and plotted the maximum liquid content versus the gas velocity (see Fig. 5). Let us consider that a bubble entering the foam entrains a liquid layer whose thickness is xed by the same mechanism as
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Fig. 5 Maximum liquid fraction 30 of foams stabilised by b-C12G2, C12E6 and their 1 : 1 mixture as a function of the gas velocity v at c ¼ 10 cmc. The gas velocity is the velocity of the gas that is used to generate the foam. The power law resembles almost eqn (3). Data are taken from ref. 18.
the thickness of a lm pulled out of a solution. In this case the liquid fraction 30 should scale like the entrained layer, i.e. like Ca2/3 (see eqn (3)). Fig. 5 shows that 30 indeed scales with the velocity with a power law around 0.6 in very good agreement with the respective foam lms (see Fig. 4). Note that there is no quantitative correlation between the velocity of lm formation and the gas velocity in foaming experiments. A foam is formed by the rising bubbles, the velocities of which do not equal the gas velocity. Strictly speaking it is the velocity of lm formation and the velocity of the rising gas bubbles that need to be compared. However, there is a linear relationship between the gas velocity and the velocity of the rising bubbles which justies plotting the liquid fraction versus the gas velocity if one is only interested in the respective power law. A closer look reveals that the water uptake of foams stabilised by C12E6 is slightly larger than that of foams stabilised by b-C12G2 while that of the mixture is between the two pure compounds. These differences are due to the fact that the foamability is lowest for C12E6, i.e. it takes the longest time to produce a given amount of foam with C12E6. It results in wetter foams (we will come back to the foamability in Section 3.2.1) because foam lms rupture during foam generation: some bubbles are created and then burst, making the foam wetter. Comparing the different water contents of the foams with the lm data one sees that in single vertical foam lms the quantity of liquid entrained is the same whatever the stabilizing solution. The reason for this difference is the fact that the lm thickness is measured just aer its generation, while the water content of the foams is affected by the number of lms which burst during generation. Speculative as it may be, it is possible that the quantity of water uptake at the beginning of the foam generation process is similar or even the same for the three foam solutions. In any case, these details do not jeopardise the
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observation that the water uptake in lms and foams follows a very similar power law which suggests that water uptake may follow the same mechanism. This result was rather surprising since it is unclear how to dene the viscous forces and the capillary suction in a polydisperse foam. 3.2. Stability 3.2.1 Film stability during generation. We measured the total length of the lm before rupturing llm (Fig. 6 (top)) and the lifetime s (Fig. 6 (bottom)) for both surfactants and the 1 : 1 mixture as a function of the capillary number (lifetime and length are linked by the entrainment velocity). Note that it is only at small velocities that the lm ruptures during generation. In the following we will focus on these data to explore lm rupture under dynamical conditions and mimic the foam coalescence during generation. As can be seen in Fig. 6, the lm has a longer lifetime at small velocities whereas the lifetime is shorter at high velocities, i.e. when the thickness of the lm is larger. This is a surprising result which we discuss in another paper.11 The mechanism explaining this unexpected observation is that the lm breaks as soon as the weight of the lm is larger than the Marangoni forces holding the lm. These Marangoni forces are due to the installation of a surfactant gradient along the interface during the generation of the lm and set by hydrodynamics. A look on the data shows that the vertical foam lms of the three different systems have roughly the same length and lifetime before rupturing. 3.2.2 Foam stability during generation. To compare the results obtained on the lms with the foamability of the solutions, we use data published in one of our previous paper.18 We performed tests on each solution by bubbling N2 in the solution and by measuring the height of foam produced versus time. The result is plotted in Fig. 7. The main observation is that it takes more time to create a given volume (here 80 mL) of foam by bubbling in C12E6 (around 120 s) than in b-C12G2 (85 s) or in the 1 : 1 mixture (95 s). This observation is important since almost any liquid is expected to foam by bubbling fast enough in the
Fig. 7 Foam volume created versus time by bubbling N2 at a flow rate Q ¼ 50 mL min1 in a surfactant solution. The figure is taken from ref. 18 and redrawn.
solution. But the signicant difference measures the competition between bubbles creation and bubbles rupture. The time then measures the efficiency of bubbling and is the shortest if all the gas is incorporated in the foam. Since the experiment is quite fast (less than two minutes), coarsening is very unlikely to happen and thus gas that is not incorporated in the foam is very likely expelled due to coalescence, i.e. due to the rupture of lms between the gas bubbles. The coalescence events during foam generation may have many sources. There are a lot of bubbles encountering each other during formation and this can favour coalescence.31,32 Moreover, a lot of topological changes (T1) can be observed which are expected to also lead to coalescence events.12 These two scenarii are of particular interest for our study since it has been demonstrated12 that the lms obtained during the fusion of two bubbles or during a T1 event are formed via the exact same mechanism as the lms pulled out of a frame.
Fig. 6 Length lfilm (left) and lifetime s (right) of the vertical films stabilised by b-C12G2, C12E6 and their 1 : 1 mixture just before rupture plotted versus the capillary number Ca at c ¼ 3 cmc.
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Finally, the main conclusion that can be drawn from Fig. 7 is that foams stabilised by C12E6 coalesce more than those stabilised by b-C12G2 or by the 1 : 1 mixture. To compare these results with those obtained for the lms we estimated the capillary number in this experiment. A ow rate of 50 mL min1 in a tube of cross-section 2.5 2.5 cm2 corresponds to a velocity of 1.3 mm s1, i.e. a capillary number around 4 105. At such a capillary number, all lm lifetimes are comparable within the error bar (Fig. 6). This indeed is not mirrored in the foam data where the lower foamability of foams stabilised by C12E6 can be attributed to a faster lm rupture (shorter lm lifetimes) during foam generation.
3.3. Visual observation of the black area In the last section we would like to enlarge on the only difference that we observed for single vertical foam lms generated from C12E6, b-C12G2 and their 1 : 1 mixture. What is different is the black lm formation at the top of the foam lm (see Fig. 8). As mentioned previously, the lm thins until a black area appears at the very top. A hole then nucleates in that area
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leading to an instantaneous rupture of the lm. We measured the length (expansion in the vertical direction) of the black area LBF just before rupture (see Fig. 8) and the lm thickness hc in the black area. In Fig. 9 (le) the different values of LBF and in Fig. 9 (right) the hc-values are plotted as a function of the capillary number. As can be seen in Fig. 9 neither the length of the black area nor the critical lm thickness depends on the capillary number. Comparing the results for the different surfactant solutions one sees that vertical lms stabilised by b-C12G2 have signicantly larger black areas as well as the thinnest critical lms. Please note that the values measured for C12E6 must be taken with caution. Since the black area is quite small for these lms the bre size (200 mm) is comparable to or larger than the black lm. Thus the thickness value is certainly an average on the black zone and the direct neighbourhood. Nevertheless, we can extract from Fig. 9 (right) that black spots are signicantly thicker for lms stabilised by C12E6. In conclusion one can say that the black lms formed in foam lms stabilised by C12E6 are thicker and shorter prior to rupture compared to those stabilised by b-C12G2 and the 1 : 1 mixture.
Fig. 8 Photo of a vertical foam film stabilised by C12E6 (left), b-C12G2 (middle) and the 1 : 1 mixture (right) pulled at a velocity V ¼ 1 mm s1. At the top of the film one can see the different dimensions of the black film LBF.
Fig. 9 Vertical length of black area LBF just before rupture (left) and critical film thickness hc (right) before rupture versus the capillary number Ca for films stabilised by b-C12G2, C12E6 and their 1 : 1 mixture at c ¼ 3 cmc.
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The total lifetime of the foam lm is the sum of the thinning time and of the lifetime of the black lm. The latter was found to be longer for lms stabilised by b-C12G2 than for those stabilised by C12E6 and their 1 : 1 mixture. However, this difference is not reected in the total lifetime, i.e. the lifetime of the black lm is small compared to the total lm lifetime (see Fig. 6).
4. Conclusion In this work we compare properties of single vertical foam lms and foams during their generation. Single vertical foam lms are generated by pulling a frame out of a surfactant solution, while foams are generated by bubbling N2 through the surfactant solution. We rst show that the water uptake in both foams and lms scales like Ca2/3 which is a clear indication that there may be a common mechanism behind water uptake. However, irrespective of the surfactant solution used to stabilise the lms, there is no variation in the quantity of water uptake. On the other hand, the corresponding surfactant solutions have different water uptakes. We discuss that these differences in the quantity of water uptake for the foams are not necessarily in disagreement with the idea that the same water uptake mechanism is at work in lms and foams. In foams, the solution of C12E6 is indeed less foamable because lms rupture during their generation. It makes the foams wetter whatever the initial water uptake by the foam. As regards the lifetime of the lms, it is clear that the different foamabilities are due to different lifetimes of the foam lms during generation. Comparing this observation with the lm data one sees that the different foam lm stabilities are not reected in the stability of the different single vertical lms although the timescales are comparable. An explanation for this result cannot be given yet. Another important observation we made is the leveling off of the thickness observed at high capillary numbers in the lm experiments. We discuss that generating single vertical lms in the way described in the paper at hand allows the measurement of the apparent dilational surface elasticity, i.e. the ability of the solution to create and sustain surface tension gradients at interfaces. Our results reveal that the surface elasticities of the different solutions are very close to each other. It is believed for foams that the surface elasticity plays a key role as regards their stability and thus the stability of the individual foam lms either during or aer generation. However, we found no experimental evidence for the correlation between the apparent surface elasticity on the one hand and the foam or lm stability during generation on the other. Speculative as it may be one could argue that the differences in the surface elasticities are simply not visible (not measurable) via the approach used in the paper at hand. Another explanation may be that other parameters (surface viscosity, surface elasticity at another frequency) impact the foamability. Finally, the only difference that we observed between the single vertical lms stabilised by the different surfactant solutions concerns the black lms. The lms stabilised by b-C12G2 or by the 1 : 1 mixture exhibit black lms of smaller thicknesses and larger length than the one stabilised by C12E6. This is
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correlated with foamability measurements and it is a reasonable hypothesis that the stability of black lms in dynamical situations should be explored to give insights on foamability. In conclusion one can say that nding a direct correlation between the behaviour of isolated foam lms and foams is tempting. However, the study at hand, which is the rst of its kind addressing the early stages of lm and foam formation, revealed that no correlation exists at these short timescales. The very different behaviour of foams stabilised by b-C12G2 and C12E6 remains a mystery.
Acknowledgements We thank D. Brunello for technical support with the experiment and F. Restagno, D. Langevin as well as W. Drenckhan for fruitful discussions. L. Saulnier and E. Rio are grateful to CNES and ESA for nancial support. The project has also been funded by the ANR program F2F.
References 1 P. Stevenson, Foam engineering: fundamentals and applications, Wiley.com, 2012. 2 L. M. C. Sagis, Dynamic properties of interfaces in so matter: Experiments and theory, Rev. Mod. Phys., 2011, 83(4), 1367–1403. 3 S. Cohen-Addad, R. H¨ ohler and O. Pitois, Flow in Foams and Flowing Foams, Annu. Rev. Fluid Mech., 2013, 45(1), 241. 4 E. Rio and D. Langevin, Coalescence in Foams and Emulsions, in Encyclopedia of Surface and Colloid Science, ed. P. Somasundaran, Taylor and Francis, 2012. 5 E. Rio and A.-L. Biance, Coalescence in liquid foams: mechanics or thermodynamics, 2014, in preparation. 6 C. Stubenrauch and R. Miller, Stability of foam lms and surface rheology: an oscillating bubble study at low frequencies, J. Phys. Chem. B, 2004, 108, 6412–6421. 7 K. Golemanov, N. D. Denkov, S. Tcholakova, M. Vethamuthu and A. Lips, Surfactant Mixtures for Control of Bubble Surface Mobility in Foam Studies, Langmuir, 2008, 24(18), 9956–9961. 8 S. Sett, S. Sinha-Ray and A. L. Yarin, Gravitational Drainage of Foam Films, Langmuir, 2013, 29, 4934–4947. 9 O. Pitois, C. Fritz and M. Vignes-Adler, Hydrodynamic resistance of a single foam channel, Colloids Surf., A, 2005, 261(1), 109–114. 10 L. Saulnier, F. Restagno, J. Delacotte, D. Langevin and E. Rio, What is the mechanism of soap lm entrainment?, Langmuir, 2011, 22, 13406–13409. 11 L. Saulnier, L. Champougny, F. Restagno, D. Langevin and E. Rio, A study of generation and rupture of soap lms, So Matter, 2014, 10, 2899. 12 A.-L. Biance, A. Delbos and O. Pitois, How Topological Rearrangements and Liquid Fraction Control Liquid Foam Stability, Phys. Rev. Lett., 2011, 106(6), 068301. 13 S. R. Patil, N. Buchavzov, E. Carey and C. Stubenrauch, Binary Mixtures of b-Dodecylmaltoside (b-C12G2) with Soft Matter, 2014, 10, 5280–5288 | 5287
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PAPER
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Comparison between generations of foams and single vertical films – single and mixed surfactant systems† Laurie Saulnier,a Julia Boos,b Cosima Stubenrauchb and Emmanuelle Rio*a The purpose of this article is to compare experiments carried out with single vertical foam films and with foams. We focus on the generation of films and foams and measure (i) the quantity of water entrained and (ii) the stability of the systems. The surfactants we used are C12E6, b-C12G2 and their 1 : 1 mixture because those systems are very well characterised in the literature and are known to stabilise foams with very different properties. We show that the quantity of water uptake in foams and single vertical films scales in the same way with the velocity of generation. However, the different surfactant solutions have different foamabilities, whereas the films they stabilise have exactly the same thickness. Moreover, the foamability of a C12E6 solution is much lower than that of a b-C12G2 solution or of a solution of the 1 : 1 mixture. This is due to the rapid rupture of the C12E6 foam films during foam generation. Surprisingly, the isolated films have exactly the same lifetime for all the surfactant solutions. We conclude that, though drawing a correlation between films and foams is tempting, the results obtained do not allow correlating
Received 11th February 2014 Accepted 1st April 2014
of film and foam stability during the generation process. The only difference we observed between the single films stabilised by the different solutions is the stability of their respective black films. We thus
DOI: 10.1039/c4sm00326h
suggest that the stability of black films during foam generation plays an important role which should be
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explored further in future work.
1. Introduction The control of the foamability of a solution, i.e. its ability to generate a foam, is of utmost importance for many applications.1 Everyone knows that the choice of the physico-chemical system chosen to stabilise the foam is central in this control. Unfortunately, we still do not understand how the structure and the nature of the surfactant inuence its ability to generate foams. However, we need this information to understand the big picture, which, in turn, will enable us to tailor-make foam properties. The mechanical properties of the interface (dynamic surface tension, interfacial viscosity and elasticity)2 are good candidates to establish a link between the molecular and the macroscopic scales. These parameters are believed to control the velocity of drainage in foams (reviewed in ref. 3). They also impact the resistance of the lms to rupture and thus the foam coalescence (reviewed in ref. 4 and 5). These ndings led to dozens of studies showing a correlation between the surface rheology of
a Laboratoire de Physique des Solides, UMR 8502, Universit´e Paris-Sud, Bˆ atiment 510, 91405 Orsay Cedex, France. E-mail: [email protected]; Tel: +33-1-69-15-69-60 b Universit¨ at Stuttgart, Institut f¨ ur Physikalische Chemie, Pfaffenwaldring 55, 70569 Stuttgart, Germany
† Electronic supplementary 10.1039/c4sm00326h
information
5280 | Soft Matter, 2014, 10, 5280–5288
(ESI)
available.
See
DOI:
solutions and the foamability and stability of foams made with these solutions. However, drawing general conclusions has not been possible up until now. The problem to be solved is very complicated because of the interplay between the different length scales: single molecules adsorbed at the liquid/air interface, foam lms separating bubbles, channels (so-called Plateau borders) through which the liquid ows, and foam bubbles encapsulating the dispersed gas phase. To simplify the problem, researchers oen try to benet from this multiscale structure of the foam by studying simpler objects like lms,6,7 bubbles8 or single Plateau borders9 to better understand the mechanisms acting in a foam. An attempt to simplify the problem by focusing on the dynamics of isolated lms in order to explain foam stability has been made very recently.10,11 In these articles, the authors explore the stability of a vertical foam lm by pulling a frame out of a surfactant solution. The stability is investigated during the generation of the lm, i.e. under dynamic conditions. The idea behind this work is that generating a vertical foam lm mimics well the generation of a foam by bubbling gas into a surfactant solution. Under certain conditions, the lm indeed ruptures during its generation just like foam lms do during the generation of the foam (for example, during topological events (T1)12). It is the purpose of the present article to look for a correlation between the experiments at the scale of the lm and at the scale of the foam.
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Concerning the systems, we focussed on two non-ionic surfactants, namely n-dodecyl-b-D-maltoside (b-C12G2), hexaethyleneglycol monododecyl ether (C12E6) and their 1 : 1 mixture.13–16 These surfactants are indeed very well characterised in the literature and are known to give rise to very different foams (Fig. 1). Although both sugar-based (CnGm) and oligoethylene oxide-based (CiEj) surfactants are typical examples of non-ionic surfactants with similar chain lengths, they indeed behave quite differently due to their different molecular structures. The different head group exibilities and the different hydration behaviour lead to different properties, which have been addressed in the studies quoted above and in references therein. Nevertheless, most interfacial properties such as surface viscoelasticity or dynamic surface tension16 are remarkably close to each other for the two surfactants and their 1 : 1 mixture. So the explanation of the very different behaviour of the foams stabilised by the respective surfactants remains a challenge. It was only recently that systematic investigations on the properties of mixtures of C12E6 and b-C12G2 were carried out.13–19 The focus was on mixtures with a xed molar ratio of 1 : 1 which in the following is referred to as “1 : 1 mixture”. These studies revealed that in most of the cases the 1 : 1 mixture behaves very much like the pure C12E6 (see e.g. Table 1 in ref. 17). However, in a very recent systematic foam study18 we could show that – other than what is stated in ref. 16 and 17 – the situation for foams does not follow this “rule of thumb”. The main results of our previous work on foam generation with the surfactants mentioned above indeed show that foams
Soft Matter
stabilised by the mixture or by b-C12G2 are much easier to generate than those stabilised by C12E6. This is a very surprising observation since, as mentioned above, all the interfacial properties of the two surfactants and of their mixture are very similar. In particular, the dynamic surface tension has been shown to be at the origin of different foamability22 or of differences in the generation of emulsions.23 The fact that we observe different foamabilities with similar dynamic surface tensions shows that other parameters should be investigated. As we will show later on, the present study allows the exploration of the importance of the surface elasticity measured in situ in the isolated lm. In the study at hand we investigate the generation of single vertical foam lms stabilised by the single surfactants and the surfactant mixture and compare the results with the generation of the respective foams. For this purpose, we compare (a) the quantity of liquid entrained during foam and lm generation, and (b) the lm lifetime with the foam stability during generation. Concerning lm rupture, we only present and discuss the measurements for those cases where the lm ruptured during its generation. We show that - the quantity of liquid entrained during foam and lm generation scales in the same way with the velocity of generation. - there is no correlation between the lm stability and the foamability of a given solution. - the only difference observed between the lms generated from the different surfactant solutions is the maximal length of the black lm that can be observed during an experiment.
Fig. 1 Comparison of the stability of 2D foams (collection of bubbles squeezed between two glass plates) stabilised by C12E6 or b-C12G2, respectively. The time evolution of both foams shows a lot more coalescence events in the foams stabilised by C12E6. Image courtesy Maha Hammouda and Wiebke Drenckhan.
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2.
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Experimental section
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2.1. Materials The non-ionic sugar surfactant n-dodecyl-b-D-maltoside (bC12G2) was purchased from Glycon and the non-ionic surfactant hexaethyleneglycol monododecyl ether (C12E6) was purchased from Sigma. Both surfactants were used as received. The solutions were prepared with double distilled water at room temperature (21 1 C). To ensure cleanliness all glassware was immersed in Deconex 22 LIQ-x (purchased from Borer Chemie AG) for 12 hours and rinsed ten times with tap water and ten times with ultrapure water (puried with a Millipore system). In order to compare the results obtained with the two surfactants, we used the same relative concentrations, namely three times their respective critical micellar concentration (cmc) (Table 1). Surface tensions (Table 1) were measured by a porous plate impregnation method (the Wilhemy plate method using a porous paper instead of the platinum plate to ensure cleanliness). We used the values of water for the refractive indices (nD20 ¼ 1.33) and viscosities (h ¼ 1.0 mPa s) of the solutions since at these low concentrations both surfactants do change neither the refractive index nor the viscosity of the solution. 2.2. Film generation A vertical foam lm is generated by pulling a frame out of 15 mL of a surfactant solution (see Fig. 2). The rectangular stainless steel frame is 4 cm long and 1.5 cm wide. At the beginning of the experiment, the frame is immersed in the solution so that the liquid meniscus reaches the top of the frame. A translation stage (Newport UTS 150CC) starts driving down the glass cell containing the solution. A motion controller (Newport SMC100CC) controls the entrainment speed V in the range between 0.01 and 15 mm s1 1 mm s1. In order to have controlled boundary conditions, the frame is gridded with shing lines (100 mm in diameter). The time t ¼ 0 s is dened as the time at which the horizontal shing line leaves the surfactant solution. The subject of the study at hand is the lm formed in between the two vertical shing lines which are separated by 1.3 cm. To ensure cleanliness, the glass container is cleaned just as the glassware (see the previous paragraph). The frame and shing lines are rinsed with ultrapure water until no lm is formed when the frame is pulled out of the water bath ensuring that no more surfactants are present. The shing lines are replaced by new ones when changing the surfactant. 2.3. Thickness measurement To measure the thickness we use a polychromatic light and a spectrometer. An optical ber allows the transmission of the Table 1 Surface tension values g of the surfactant solutions at 3 cmc and the respective cmc values
Surfactant
C12E6
b-C12G2
b-C12G2 : C12E6 ¼ 1 : 1
g at 3 cmc/mN m1 cmc/mol L1
32 7 105 (ref. 21)
35 1.5 104 (ref. 21)
32 1 104 (ref. 20)
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Fig. 2 Schematic drawing of the experimental set-up. The solution bath translates down at speed V. The film is formed in the frame during translation. Seven optical fibers (one for enlightening and six for collecting the reflected light) coupled with a spectrometer allow instantaneous and local thickness measurements of the film formed between the fishing lines.
light perpendicular to the lm and a lens allows focusing the beam on the lm surface to obtain a spot with a diameter of around 200 mm. The intensity of the reected light I is collected by 6 optical bers surrounding the rst one (IDIL, QR200-7-UVBX). A spectrometer (USB 400 Ocean Optics) extracts the spectrum I/I0 where I0 is the incident intensity. The reected intensity is given, in a two-wave approximation, by I 4pnh ¼ A sin ; I0 l
(1)
where l is the wavelength, n the refractive index and A the amplitude. We use the commercial soware Nanocalc to t the spectrum and extract the local lm thickness h. The accuracy is very good since only the period of the signals depends on h and the soware allows tting the period even in the presence of experimental inaccuracies (for example if the amplitude depends slightly on the wavelength because of a non-perfect calibration). The error for the thickness is estimated to be around 20 nm. To measure the thickness of the black lms we use the same polychromatic light and spectrometer. We measure the ratio I/I0 for three different wavelengths and then use the Scheludko renormalisation24 to deduce the lm thickness. We check (i) that the thickness is smaller than l/4 and (ii) that the thicknesses deduced from the three different wavelengths are identical 2 nm. 2.4. Rupture detection and lifetime measurement The frame is supported by a force transducer (HBM, 5 g) which allows the measurement of the stress exercised by the lm on
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the frame. When the lm breaks there is a sudden jump in the measured stress which allows the detection of the lm rupture. The lifetime s of the lm is dened as the time elapsed between t ¼ 0 s and the rupture of the lm. This method also allows the calculation of the total length of the lm llm ¼ Vs when it ruptures.
3.
Results and discussion
As stated in the Introduction, we will rst focus on the quantity of water entrained while generating foams and lms. We will show that a similar mechanism could act in lms and foams. We will then compare the lm lifetime with the foamability, i.e. with the foam stability during generation, of the different solutions. Finally, we will look at the formation of black lms prior to rupture. 3.1. Water uptake during lm and foam generation 3.1.1 Water uptake by the lm. For vertical foam lms it has been shown10 that the lm consists of three zones. (i) The zone at the bottom has a well-dened thickness, whose value depends on the capillary number Ca ¼ hV/g, with h and g being the solution's viscosity and surface tension, respectively, while V is the velocity at which the lm is generated. This zone can be observed at the bottom of the lm shown in Fig. 3 (homogeneous pink color). (ii) Above this zone a thinning zone develops (see Fig. 3) due to gravity drainage and expands as a function of time. The presence of interference fringes is the signature of a thickness variation. (iii) Just before lm rupture, a black zone appears at the top of the lm (see Fig. 3). A hole will nucleate in this area and the lm will burst almost instantaneously. To determine the water uptake, we concentrated our measurements in the bottom zone of homogeneous thickness. We measured the thickness h at the bottom zone of the foam lm (called the Frankel zone in Fig. 3) as a function of the entrainment velocity for aqueous solutions of C12E6, b-C12G2, and the 1 : 1 mixture at 3 cmc. Fig. 4 shows on a log–log plot the thickness normalised by the capillary length
Fig. 4 Thickness of the Frankel zone normalized by the capillary length k1 plotted versus the capillary number Ca of vertical foam films stabilised by b-C12G2, C12E6 and their 1 : 1 mixture at c ¼ 3 cmc. The error bar is of the size of the symbols.
k1 ¼
rffiffiffiffiffi g rg
and plotted versus the capillary number Ca ¼ hV/g, where r and h stand for the liquid density and viscosity, respectively, and g is the gravitational constant. Since this gure only shows the normalised, i.e. dimensionless, data, we plotted the real values of h as a function of the capillary number (see ESI†). This is to keep in mind that the initial thickness is around 1 mm, i.e. the lms are too thick for the disjoining pressure to have an effect. At small capillary numbers, the thickness is given by the socalled Frankel law (black line in Fig. 4). This law takes into account the fact that the viscous forces tend to thicken the lm and that they are balanced by the capillary suction in the meniscus, which, in turn, tends to thin the lm. The gravity turns out to be negligible25 for capillary numbers smaller than 103, as observed in our experiments. This balance leads to a thickness25 h ¼ 1.89k1Ca2/3.
Fig. 3 Photo of the vertical foam film stabilised by b-C12G2 at c ¼ 3 cmc generated with V ¼ 1.5 mm s1 in the z-direction. The film is divided into three zones, namely the “thinning zone” (heterogeneous thickness) with interference fringes, the “Frankel zone” (homogeneous thickness) at the bottom and the black zone on top.
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(2)
(3)
In other words, the higher the entrainment velocity, the thicker is the resulting foam lm. The thickness is thus proportional to Ca2/3 and does not depend on the surfactant used. As can be seen in Fig. 4 and as has already been observed in many studies,10,26–28 the Frankel law only describes the lm behaviour at small capillary numbers. At high velocities the Frankel model does not anymore describe the data accurately. In recent works29,30 it was proposed that the leveling off of the thickness is due to a lack of rigidity of the interfaces. The Frankel model indeed makes the hypothesis that the interfaces can be considered as rigid, i.e. that the liquid velocity is zero at the liquid/air interface. This seems to hold true for low capillary
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numbers but it turns out that at high capillary numbers, the interfacial slip velocity between the liquid and the gas is not zero. This is due to the nite elastic modulus of the interface which controls the gradient in the surfactant concentration and thus in the surface tension. At small capillary numbers this gradient is always large enough to fulll the requirements for Frankel's law whatever the elastic modulus. In the papers quoted above, it is demonstrated that the thickness is expected to level off at high capillary numbers at a thickness equal to E/g with E being the surface dilational elasticity. Here, E is an apparent dilational surface elasticity which takes into account the effect of the extension rate and the connement. The characteristic adsorption time depends very little on the surfactant used16 and is of the order of 10 seconds. This time is large compared to the time spent by the surfactants in the dynamic meniscus (where all the hydrodynamics happens and the lm thickness is set). The dynamic meniscus is indeed around 40 mm long and the typical velocity is 1 mm s1 so that the relevant characteristic time is 40 ms. Adsorption is obviously an important feature and must contribute to the value of the effective surface elasticity. In the same time, the lms are thin: if we compare the total amount of surfactants in the lm (ch with c being the concentration of surfactants) to the amount of surfactants at the interface (G, the surface concentration) we nd a value close to 1 so the volume is depleted and the effective value of E also takes this effect into account. Surprisingly, it turns out that a constant value is sufficient to describe the data obtained at different capillary numbers.30 Thus, the apparent dilational surface elasticity E describes well the dynamics of the surfactants in the soap lm. The superposition of the data obtained from the three solutions (Fig. 4) then suggests that this effective elasticity is very similar in the three solutions which is in agreement with previous work where surface elasticities at concentrations above the cmc of b-C12G2 and C12E6 have been measured or extrapolated.6,19 To conclude one can say that the initial thickness of freshly generated foam lms as well as the dependence of this thickness on the capillary number is the same for all three systems because the effective surface dilational elasticity measured in situ is the same. 3.1.2 Water uptake by the foam. To compare the results obtained on lms with foam experiments, we went back to our previous study on foams.18 In this work we performed foaming experiments by bubbling N2 into the surfactant solution at a controlled ow rate. The foams are stabilised by the same surfactants used in the study at hand but at slightly higher concentrations (10 cmc instead of 3 cmc). Note that in a previous study a similar change in the concentration did not modify the power law for soap lms10 which justies our comparison. In each foam we measured the initial liquid fraction 30. For the paper at hand, we calculated gas velocities from the gas ow rates (velocity ¼ ow rate divided by the crosssection of the cell) and plotted the maximum liquid content versus the gas velocity (see Fig. 5). Let us consider that a bubble entering the foam entrains a liquid layer whose thickness is xed by the same mechanism as
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Fig. 5 Maximum liquid fraction 30 of foams stabilised by b-C12G2, C12E6 and their 1 : 1 mixture as a function of the gas velocity v at c ¼ 10 cmc. The gas velocity is the velocity of the gas that is used to generate the foam. The power law resembles almost eqn (3). Data are taken from ref. 18.
the thickness of a lm pulled out of a solution. In this case the liquid fraction 30 should scale like the entrained layer, i.e. like Ca2/3 (see eqn (3)). Fig. 5 shows that 30 indeed scales with the velocity with a power law around 0.6 in very good agreement with the respective foam lms (see Fig. 4). Note that there is no quantitative correlation between the velocity of lm formation and the gas velocity in foaming experiments. A foam is formed by the rising bubbles, the velocities of which do not equal the gas velocity. Strictly speaking it is the velocity of lm formation and the velocity of the rising gas bubbles that need to be compared. However, there is a linear relationship between the gas velocity and the velocity of the rising bubbles which justies plotting the liquid fraction versus the gas velocity if one is only interested in the respective power law. A closer look reveals that the water uptake of foams stabilised by C12E6 is slightly larger than that of foams stabilised by b-C12G2 while that of the mixture is between the two pure compounds. These differences are due to the fact that the foamability is lowest for C12E6, i.e. it takes the longest time to produce a given amount of foam with C12E6. It results in wetter foams (we will come back to the foamability in Section 3.2.1) because foam lms rupture during foam generation: some bubbles are created and then burst, making the foam wetter. Comparing the different water contents of the foams with the lm data one sees that in single vertical foam lms the quantity of liquid entrained is the same whatever the stabilizing solution. The reason for this difference is the fact that the lm thickness is measured just aer its generation, while the water content of the foams is affected by the number of lms which burst during generation. Speculative as it may be, it is possible that the quantity of water uptake at the beginning of the foam generation process is similar or even the same for the three foam solutions. In any case, these details do not jeopardise the
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observation that the water uptake in lms and foams follows a very similar power law which suggests that water uptake may follow the same mechanism. This result was rather surprising since it is unclear how to dene the viscous forces and the capillary suction in a polydisperse foam. 3.2. Stability 3.2.1 Film stability during generation. We measured the total length of the lm before rupturing llm (Fig. 6 (top)) and the lifetime s (Fig. 6 (bottom)) for both surfactants and the 1 : 1 mixture as a function of the capillary number (lifetime and length are linked by the entrainment velocity). Note that it is only at small velocities that the lm ruptures during generation. In the following we will focus on these data to explore lm rupture under dynamical conditions and mimic the foam coalescence during generation. As can be seen in Fig. 6, the lm has a longer lifetime at small velocities whereas the lifetime is shorter at high velocities, i.e. when the thickness of the lm is larger. This is a surprising result which we discuss in another paper.11 The mechanism explaining this unexpected observation is that the lm breaks as soon as the weight of the lm is larger than the Marangoni forces holding the lm. These Marangoni forces are due to the installation of a surfactant gradient along the interface during the generation of the lm and set by hydrodynamics. A look on the data shows that the vertical foam lms of the three different systems have roughly the same length and lifetime before rupturing. 3.2.2 Foam stability during generation. To compare the results obtained on the lms with the foamability of the solutions, we use data published in one of our previous paper.18 We performed tests on each solution by bubbling N2 in the solution and by measuring the height of foam produced versus time. The result is plotted in Fig. 7. The main observation is that it takes more time to create a given volume (here 80 mL) of foam by bubbling in C12E6 (around 120 s) than in b-C12G2 (85 s) or in the 1 : 1 mixture (95 s). This observation is important since almost any liquid is expected to foam by bubbling fast enough in the
Fig. 7 Foam volume created versus time by bubbling N2 at a flow rate Q ¼ 50 mL min1 in a surfactant solution. The figure is taken from ref. 18 and redrawn.
solution. But the signicant difference measures the competition between bubbles creation and bubbles rupture. The time then measures the efficiency of bubbling and is the shortest if all the gas is incorporated in the foam. Since the experiment is quite fast (less than two minutes), coarsening is very unlikely to happen and thus gas that is not incorporated in the foam is very likely expelled due to coalescence, i.e. due to the rupture of lms between the gas bubbles. The coalescence events during foam generation may have many sources. There are a lot of bubbles encountering each other during formation and this can favour coalescence.31,32 Moreover, a lot of topological changes (T1) can be observed which are expected to also lead to coalescence events.12 These two scenarii are of particular interest for our study since it has been demonstrated12 that the lms obtained during the fusion of two bubbles or during a T1 event are formed via the exact same mechanism as the lms pulled out of a frame.
Fig. 6 Length lfilm (left) and lifetime s (right) of the vertical films stabilised by b-C12G2, C12E6 and their 1 : 1 mixture just before rupture plotted versus the capillary number Ca at c ¼ 3 cmc.
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Finally, the main conclusion that can be drawn from Fig. 7 is that foams stabilised by C12E6 coalesce more than those stabilised by b-C12G2 or by the 1 : 1 mixture. To compare these results with those obtained for the lms we estimated the capillary number in this experiment. A ow rate of 50 mL min1 in a tube of cross-section 2.5 2.5 cm2 corresponds to a velocity of 1.3 mm s1, i.e. a capillary number around 4 105. At such a capillary number, all lm lifetimes are comparable within the error bar (Fig. 6). This indeed is not mirrored in the foam data where the lower foamability of foams stabilised by C12E6 can be attributed to a faster lm rupture (shorter lm lifetimes) during foam generation.
3.3. Visual observation of the black area In the last section we would like to enlarge on the only difference that we observed for single vertical foam lms generated from C12E6, b-C12G2 and their 1 : 1 mixture. What is different is the black lm formation at the top of the foam lm (see Fig. 8). As mentioned previously, the lm thins until a black area appears at the very top. A hole then nucleates in that area
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leading to an instantaneous rupture of the lm. We measured the length (expansion in the vertical direction) of the black area LBF just before rupture (see Fig. 8) and the lm thickness hc in the black area. In Fig. 9 (le) the different values of LBF and in Fig. 9 (right) the hc-values are plotted as a function of the capillary number. As can be seen in Fig. 9 neither the length of the black area nor the critical lm thickness depends on the capillary number. Comparing the results for the different surfactant solutions one sees that vertical lms stabilised by b-C12G2 have signicantly larger black areas as well as the thinnest critical lms. Please note that the values measured for C12E6 must be taken with caution. Since the black area is quite small for these lms the bre size (200 mm) is comparable to or larger than the black lm. Thus the thickness value is certainly an average on the black zone and the direct neighbourhood. Nevertheless, we can extract from Fig. 9 (right) that black spots are signicantly thicker for lms stabilised by C12E6. In conclusion one can say that the black lms formed in foam lms stabilised by C12E6 are thicker and shorter prior to rupture compared to those stabilised by b-C12G2 and the 1 : 1 mixture.
Fig. 8 Photo of a vertical foam film stabilised by C12E6 (left), b-C12G2 (middle) and the 1 : 1 mixture (right) pulled at a velocity V ¼ 1 mm s1. At the top of the film one can see the different dimensions of the black film LBF.
Fig. 9 Vertical length of black area LBF just before rupture (left) and critical film thickness hc (right) before rupture versus the capillary number Ca for films stabilised by b-C12G2, C12E6 and their 1 : 1 mixture at c ¼ 3 cmc.
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The total lifetime of the foam lm is the sum of the thinning time and of the lifetime of the black lm. The latter was found to be longer for lms stabilised by b-C12G2 than for those stabilised by C12E6 and their 1 : 1 mixture. However, this difference is not reected in the total lifetime, i.e. the lifetime of the black lm is small compared to the total lm lifetime (see Fig. 6).
4. Conclusion In this work we compare properties of single vertical foam lms and foams during their generation. Single vertical foam lms are generated by pulling a frame out of a surfactant solution, while foams are generated by bubbling N2 through the surfactant solution. We rst show that the water uptake in both foams and lms scales like Ca2/3 which is a clear indication that there may be a common mechanism behind water uptake. However, irrespective of the surfactant solution used to stabilise the lms, there is no variation in the quantity of water uptake. On the other hand, the corresponding surfactant solutions have different water uptakes. We discuss that these differences in the quantity of water uptake for the foams are not necessarily in disagreement with the idea that the same water uptake mechanism is at work in lms and foams. In foams, the solution of C12E6 is indeed less foamable because lms rupture during their generation. It makes the foams wetter whatever the initial water uptake by the foam. As regards the lifetime of the lms, it is clear that the different foamabilities are due to different lifetimes of the foam lms during generation. Comparing this observation with the lm data one sees that the different foam lm stabilities are not reected in the stability of the different single vertical lms although the timescales are comparable. An explanation for this result cannot be given yet. Another important observation we made is the leveling off of the thickness observed at high capillary numbers in the lm experiments. We discuss that generating single vertical lms in the way described in the paper at hand allows the measurement of the apparent dilational surface elasticity, i.e. the ability of the solution to create and sustain surface tension gradients at interfaces. Our results reveal that the surface elasticities of the different solutions are very close to each other. It is believed for foams that the surface elasticity plays a key role as regards their stability and thus the stability of the individual foam lms either during or aer generation. However, we found no experimental evidence for the correlation between the apparent surface elasticity on the one hand and the foam or lm stability during generation on the other. Speculative as it may be one could argue that the differences in the surface elasticities are simply not visible (not measurable) via the approach used in the paper at hand. Another explanation may be that other parameters (surface viscosity, surface elasticity at another frequency) impact the foamability. Finally, the only difference that we observed between the single vertical lms stabilised by the different surfactant solutions concerns the black lms. The lms stabilised by b-C12G2 or by the 1 : 1 mixture exhibit black lms of smaller thicknesses and larger length than the one stabilised by C12E6. This is
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correlated with foamability measurements and it is a reasonable hypothesis that the stability of black lms in dynamical situations should be explored to give insights on foamability. In conclusion one can say that nding a direct correlation between the behaviour of isolated foam lms and foams is tempting. However, the study at hand, which is the rst of its kind addressing the early stages of lm and foam formation, revealed that no correlation exists at these short timescales. The very different behaviour of foams stabilised by b-C12G2 and C12E6 remains a mystery.
Acknowledgements We thank D. Brunello for technical support with the experiment and F. Restagno, D. Langevin as well as W. Drenckhan for fruitful discussions. L. Saulnier and E. Rio are grateful to CNES and ESA for nancial support. The project has also been funded by the ANR program F2F.
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