Journal of Colloid and Interface Science 333 (2009) 619–627

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Journal of Colloid and Interface Science

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Properties of aqueous foams stabilized by dodecyltrimethylammonium bromide

Enda Carey a,∗, Cosima Stubenrauch a,b

a University College Dublin, School of Chemical and Bioprocess Engineering, Belfield, Dublin 4, Irelandb Centre for Synthesis and Chemical Biology, SFI-Strategic Research Cluster in Solar Energy Conversion, University College Dublin, Belfield, Dublin 4, Ireland

a r t i c l e i n f o a b s t r a c t

Article history:Received 22 November 2008Accepted 10 February 2009Available online 21 February 2009

Keywords:Dodecyltrimethylammonium bromide(C12TAB)FoamabilityFoam stabilityRoss–Miles methodWinding methodFoamScan

Foamability, foam stability and the liquid volume of aqueous foams stabilized by dodecyltrimethylam-monium bromide (C12TAB) are studied. The foams are generated with a sparging method at different gasflow rates and surfactant concentrations. It is found that at concentrations c � cmc drainage dominatesfoam destruction while at c < cmc additional processes lead to a dramatic decrease in foam stability.Qualitatively similar results are obtained with the Ross–Miles (pouring) method and the winding (shak-ing) method, respectively. Increasing the gas flow rate of the sparging method at a fixed surfactantconcentration, one observes a decrease in the time required for the production of 60 ml foam, whilethe liquid volume of the generated foam increases. On the other hand, an increase of the surfactant con-centration at a fixed gas flow rate leads to an increase in the required foaming time with a plateau atc � cmc, while the liquid volume of the generated foam decreases. Finally, the influence of small im-purities is also tested and it is found that small amounts of impurities (“as received sample”) lead to asignificant increase of both the foamability and the stability of foams stabilized by C12TAB. The obtainedresults are discussed in terms of the different processes leading to foam destruction and a comparisonbetween the three different methods is made. Whenever possible and feasible, the correlation betweensingle surfaces, single foam films and foams is addressed.

© 2009 Elsevier Inc. All rights reserved.

1. Introduction

Foam is a disperse system consisting of gas bubbles sepa-rated by liquid layers which are generally stabilized by surfactants.Foams are widely used in industrial applications and everydayproducts such as cleaning agents, beverages, fire-fighting and flota-tion. Various surfactants are used to produce and stabilize aque-ous foams. Characterization of foaming properties of surfactantsolutions generally involves the investigation of both foamabilityand foam stability [1,2]. Foamability is a measure for the foam-generating power of a surfactant solution while foam stability isa measure for the time foams resist destruction. However, foamproperties are not yet predictable, which reflects the lack of gen-eral understanding.

The foamability of a surfactant solution depends on the con-centration and the type of surfactant. Surfactant adsorption at thewater–air surface decreases the surface tension, which reduces theenergy required to produce the foam. Therefore foamability in-creases with increasing surfactant concentration and often a max-imum is reached at concentrations c � cmc, i.e. the foamabilitybecomes relatively constant at concentrations above the cmc [1].

* Corresponding author. Fax: +353 1 716 1177.E-mail address: enda.carey@ucd.ie (E. Carey).

0021-9797/$ – see front matter © 2009 Elsevier Inc. All rights reserved.doi:10.1016/j.jcis.2009.02.038

However, foamability depends on both the adsorbed amount ofsurfactant and the rate of transport of the surfactant to the water–air surface. In the case of surfactants with very low cmc-valuesthe transport of the surfactant to the surface is not fast enough toreach a densely packed monolayer even at c > cmc. In other words,the foamability then continues to increase at concentrations abovethe cmc until the transport rate allows the formation of a denselypacked layer in the foam generation process [3,4].

The stability (i.e. the lifetime) of a foam is limited by thedrainage of the liquid, by Ostwald ripening of the bubbles and bybubble coalescence [5]. Therefore one can control the foam stabil-ity to a certain extent by increasing or decreasing the rate of theseprocesses. Foam stability also requires an interfacial film with suf-ficient cohesion to impact elasticity and mechanical strength tothe liquid lamellae enclosing the gas in the foam. In general asthe length of the hydrophobic group increases, the foam stabil-ity increases due to the increasing interchain cohesion. However,there is a balance: too short a chain may lead to insufficient co-hesiveness, whereas too long a chain leads to too much rigidity ofthe interfacial film and eventually to the insolubility of the sur-factant [2]. It is for this reason that common foaming surfactantshave a hydrophobic chain of C12–C14, which, in turn, allows for abalance between surface activity and solubility.

The study at hand is about properties of foams stabilized by thecationic surfactant dodecyltrimethylammonium bromide (C12TAB).

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To date studies have been performed with foam films of C12TAB[6] along with a recent study on foam films of C12TAB/β-C12G2mixtures [7] where β-C12G2 is the non-ionic surfactant dodecyl-β-D-maltoside. The correlation between the properties of single foamfilms and foams, focusing on the influence of the chain lengthand of impurities, has also been studied [8]. However, the latterstudy is restricted to the cmc of C12TAB and foams are not stud-ied under gravity but under pressure with the foam pressure droptechnique, FPDT [9]. The current study aims at complementing pre-vious work. For that purpose a much broader concentration rangewas investigated. Moreover, various foaming methods (Ross–Miles,winding, and FoamScan methods) were used to study the proper-ties of foams stabilized by C12TAB.

The Ross–Miles method (pouring method) is the oldest stan-dardized method dating back to 1941 [10]. A test solution is pouredfrom a fixed height through a calibrated orifice into a pool of thesame solution and the generated foam volume is measured. Thismethod is often used as a standard test to measure foamabilityespecially of formulations in the industrial sector. The Ross–Milesmethod is restricted to the study of dry foams as it produces quiteairy foam [11,12]. The winding method (shaking method) involvesinverting a cylinder which contains the sample solution a fixednumber of times at the same rotating rate. In both the Ross–Milesand the winding methods the height of the generated foam is mea-sured over a period of time which allows for foamability and foamstability determination. Finally, the FoamScan was used with whichthe foam is generated by sparging gas at a fixed flow rate througha porous disc which is located at the bottom of the foam column.The dispersity of the generated foam depends on the pore size ofthe disc, the flow rate of the gas, the type of gas, and the proper-ties of the foaming solution (surface concentration, surface tension,viscosity, etc.) [13]. The FoamScan (sparging method) uses imageanalyses and conductivity measurements to determine foam andliquid volume of the generated foam.

It is well known that a quantitative comparison of the com-mon methods used to determine foam properties is impossible aseach of these methods has different measuring conditions and pa-rameters to characterize the foam [5,8,13]. However, a qualitativecomparison should be possible if the same surfactant solutions arestudied. In an attempt to study foam properties on the one handand to compare different foaming methods on the other hand wecarried out systematic measurements with C12TAB solutions.

2. Experimental

2.1. Materials

The cationic dodecyltrimethylammonium bromide C12TAB (pu-rity >98% AT) was purchased from Fluka and purified by re-crystallizing it three times with pure acetone to which traces ofethanol were added. The cmc of C12TAB in aqueous solution is1.5×10−2 M [14]. Acetone (p.a.) and ethanol (p.a.) were purchasedfrom Aldrich. The solutions were prepared with Milli-Q® water. Allglassware was cleaned with deconex® from Borer Chemie (as re-placement for chromic sulphuric acid) and rinsed thoroughly withwater before use.

2.2. Ross–Miles and winding methods

2.2.1. Ross–Miles methodIn this method, 200 ml of the surfactant solution was taken in a

pipette of specified dimensions with an orifice of internal diameter(i.d.) 0.0029 m and length 0.010 m. The solution in the pipette wasallowed to fall from a height of 0.90 m on to 50 ml of the samesolution present in a cylindrical vessel (i.d. 0.05 m) surrounded bya water jacket. All measurements were performed at 22 ◦C. The

foam height in the receiver was measured immediately after thelast drop of the solution fell from the foam pipette. The type andamount of generated foam depends on the height of pouring, thevolume of liquid poured, the initial volume of liquid on which itis poured, and the construction of the experimental apparatus. Thefoam produced is not homogeneously dispersed but has a coarserfoam upper layer, which is less stable than the bulk foam [15].

2.2.2. Winding methodThe foam winding method has been designed and set up by

AkzoNobel, Stenungsund, Sweden. A fixed amount of surfactantsolution (100 ml in the present case) is poured into a 500 ml mea-suring glass cylinder. The glass cylinder has a diameter of 55 mmand a height of 375 mm. A stopper is placed onto the cylinderwhich is then rotated 40 times per minute (40 rpm) around its ra-dial axis. Measurements start after the foam has been generated,i.e. t = 0 is the time when rotation stops. The height of the pro-duced foam is measured in mm at certain time intervals to allowfor the determination of the foamability of the surfactant solutionand the stability of the generated foam. Foam heights can be de-termined with an accuracy of ±5%. Note that the maximum foamheight is 280 mm, i.e. that foam heights around this value indicatethat the cylinder is filled and not necessarily that no more foamcan be produced.

2.3. FoamScan

The FoamScan is a commercially available instrument (I.T. Con-cept), with which foamability (amount of foam generated during acertain time), foam stability (decay of foam volume as a functionof time), and foam drainage (change of liquid volume in the foamas a function of time) can be measured [16]. Foam is generated ina glass column (36 mm in diameter) by sparging N2 gas through afixed volume (20 ml) of the surfactant solution via a porous glassdisc (pore size 14–60 μm and thickness 3 mm). The N2 spargingrate, i.e. the gas flow rate, was set and adjusted to different ratesvarying from 5 to 100 ml min−1 to find out the optimum exper-imental conditions. The gas flow stopped automatically when thesystem had reached the preset foam volume (60 ml).

A gas flow rate of 20 ml min−1 turned out to be a good choiceand was thus used for most of the measurements. The initial max-imum foam volume was again set to 60 ml. It has to be mentionedthat the foam volume was always between 60 and 65 ml althoughthe FoamScan was set to terminate foam generation once 60 ml areformed. The only reasonable explanation is mechanical limitationsof the equipment (measuring foam volume and stopping the airflow is obviously no instantaneous process). The foam volumes, i.e.the amount of generated foam as well as the subsequent foam de-cay, are monitored by images of the column, which are constantlyrecorded by a CCD camera throughout the experiment. As a re-sult one obtains the foam volume as a function of time. Note thatt = 0 is defined as the time when foam generation via N2 sparg-ing starts, while for the foam winding and the Ross–Miles methodt = 0 was the time when foam generation stops. All measurementswere performed at 22 ◦C.

Measurements were carried out a minimum of two times (seeFig. 1 for reproducibility). Fig. 1 shows the data which can be ob-tained with the FoamScan for a gas flow rate of 80 ml min−1 anda surfactant concentration of 2 cmc. Seen are the time depen-dence of the foam volume V foam (Fig. 1 (top)), of the liquid inthe cell V liquid,cell and in the foam V liquid,foam (Fig. 1 (middle)) aswell as the time dependence of the change in the liquid volume�V liquid,foam (Fig. 1 (bottom)). Note that t = 0 is not the same forthe different sets of data. For V foam and V liquid, t = 0 is the timewhen the foaming process starts, while for �V liquid,foam, t = 0 isthe time at which the gas input is stopped.

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Fig. 1. FoamScan results for two separate experimental runs. Variation of foam vol-ume V foam (top) and liquid volume V liquid,foam (middle) in the foam as a function oftime for C12TAB foams generated at 2 cmc and a gas flow rate of 80 ml min−1. Thefoaming process starts at t = 0 and ends once a foam volume of 60 ml is generated.(Bottom) The change in liquid volume �V liquid,foam for the same C12TAB foams as afunction of time after termination of sparging, i.e. t = 0 is now the time at whichthe gas input is stopped. Note that the x-axes have a different scale compared tothat of Figs. 2, 4, 5, and 6 to better see the evolution of the data at the beginningof the process.

Throughout this study the term “drainage rate” will be usedextensively in order to describe the properties of foams stabilizedby C12TAB. The drainage rate is simply the loss of liquid in thefoam in a given period of time (�V liquid,foam/�t). In other words,it is the slope of the V liquid,foam(t)-curve after the foaming processis terminated as depicted in Fig. 1 (middle). The “foaming rate”, onthe other hand, can be described as the increase in foam volumein a given period of time (�V foam/�t) and is thus the slope ofthe respective V foam(t)-curve measured before sparging stops (i.e.during the foaming process) as depicted in Fig. 1 (top).

For the sake of completeness we would like to explain whybubble sizes of the generated foams could not be measured withthe FoamScan. Bubble sizes could not be determined because thefoam images obtained via the software only differed in the degreeof darkness (see Fig. 9 in [17]). Moreover, bubbles produced via aporous disc are too small to be distinguishable with the naked eye.Thus a more sophisticated method than just counting the numberof bubbles over a certain distance would be needed to determinethe size of the bubbles produced with the FoamScan, which wasbehind the scope of the present study.

3. Results and discussion

The present study is about properties of foams stabilized byaqueous solutions of the cationic surfactant dodecyltrimethylam-monium bromide (C12TAB). Various surfactant concentrations wereinvestigated and three different foaming methods were used. How-ever, the focus is on the measurements carried out with the sparg-ing (FoamScan) method as it allowed us to measure simultane-ously foamability, foam stability, and the liquid volume of thefoam. Note that the information on the liquid volume cannot beextracted from the pouring (Ross–Miles) and the shaking (wind-ing) methods, respectively. Moreover, with the sparging methodfoams can be generated at different gas flow rates, which provideadditional information especially on foamability. In the followingthe results obtained with the sparging method for different gasflow rates (Section 3.1), different surfactant concentrations (Sec-tion 3.2), and different degrees of surfactant purity (Section 3.3)will be presented and discussed. Moreover, the stability of C12TABfoams generated with different foaming methods will be quanti-tatively compared (Section 3.4). Finally, correlations between theproperties of single surfaces, single foam films, and foams will bedrawn to better understand the properties of the studied foams(Section 3.5).

3.1. Influence of gas flow rate

Systematic foaming experiments using the commercially avail-able FoamScan have been carried out to study the properties offoams stabilized by the cationic surfactant C12TAB. Studying a foamusually involves two stages. (1) Foamability: Initially gas is spargedthrough the surfactant solution and the sparging process is termi-nated once a specific foam volume (60 ml in our case) is reached.(2) Foam stability: After the termination of the sparging processthe time evolution of the produced foam is monitored over a pe-riod of time. Both the foamability and the foam stability are eval-uated by measuring the change in foam volume as a function oftime. However, the main advantage of the FoamScan is its abilityto measure simultaneously the liquid volume in the foam whichallows us to extract additional information on the processes thatdestroy the foam.

Fig. 2 (top) shows the variation of the foam volume V foam withtime for foams generated at a C12TAB concentration of 2.0 cmc andvarious gas flow rates (5, 20, 40, 60, 80 and 100 ml min−1) for apreset foam volume of V foam = 60 ml. Although the runs are setto terminate the foam generation when a foam volume of 60 mlis obtained, a slight overshoot was often observed which was thelarger the higher the gas flow rate (see Section 2.3 for furtherdetails). Looking at Fig. 2 (top) one sees that the time to reachthe preset foam volume value of 60 ml decreases with increas-ing gas flow rate. This trend is more clearly seen in Fig. 3 wherethe time required to generate a foam volume of 60 ml is plot-ted for various gas flow rates (data are taken from Fig. 2 (top)).A deeper look at low gas flow rates reveals that the time requiredreaching the specified foam volume of 60 ml increases dramati-cally with decreasing flow rate. This demonstrates that the foam

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Fig. 2. (Top) Variation of foam volume V foam and (middle) liquid volume V liquid,foamin the foam as a function of time for C12TAB foams generated at 2 cmc and variousgas flow rates (5, 20, 40, 60, 80 and 100 ml min−1). The foaming process starts att = 0 and ends once a foaming volume of 60 ml is generated. (Bottom) The changein liquid volume �V liquid,foam for the same C12TAB foams as a function of time aftertermination of sparging (i.e. t = 0 is the time at which the gas input is stopped) forthe various gas flow rates applied. The initial liquid volume of the generated foamV liquid,max is given in the legend.

is not very stable and collapses partially during the foam gener-ation process. The longer the foam generation process the morepronounced foam destruction. On the other hand, at high gas flowrates significant shear forces act on the foam, which may also leadto foam destruction during foam generation. Thus an intermediateflow rate needs to be found if one wants to separate foamabilityfrom foam stability as good as possible. In the study at hand weused gas flow rates of 20 ml min−1 (Section 3.2) and 60 ml min−1

(Section 3.3), respectively. Note that no lower or upper limit of thegas flow rates were determined as this would have been too timeconsuming (flow rate scans need to be carried out for each con-centration) and as this was not the focus of this study.

To gain further insight into the foam properties the liquid vol-ume of the foams V liquid,foam was measured. It should be noted

Fig. 3. Time t required to generate 60 ml of foam and maximum liquid volume inthe foam V liquid,max measured after the termination of sparging as a function of theflow rate for 2.0 cmc C12TAB using the FoamScan.

that V liquid,foam is the overall liquid volume in the total foam andnot the liquid volume (e.g. liquid fraction) at a specific height ofthe foam column. Fig. 2 (middle) shows V liquid,foam and Fig. 2 (bot-tom) the corresponding change in the liquid volume �V liquid,foamas a function of time. In the former case t = 0 is the time at whichfoam generation starts, while in the latter case t = 0 is the timeat which foam generation is terminated. Looking at the data af-ter the foam has been generated one sees that the drainage rate isthe higher the higher the gas flow rate with which the foam hasbeen generated. This observation can be explained by the fact thatthe initial liquid volume of the foam V liquid,max is the higher thehigher the gas flow rate.1 A higher liquid volume in the foam isexpected to lead to a larger drainage rate for the same surfactantsolution and similar experimental conditions. The substantial in-crease in liquid volume with increasing gas flow rate is depicted inFig. 3. Comparing the data presented in Fig. 2 with those shown inFig. 3 one clearly sees the correlation between foam volume, initialliquid volume, and drainage. For instance at gas flow rates of 40and 60 ml min−1, respectively, almost identical V liquid,max valueswere obtained (Fig. 3) which results in identical drainage curves(Fig. 2 (middle and bottom)). As the corresponding V foam(t)-curvesare also identical (Fig. 2 (top)) one can conclude that foam destruc-tion is dominated by drainage. Another example of the relationbetween foam volume, initial liquid volume, and drainage is re-flected in the results obtained at 20 and 40 ml min−1. In this casethe foam generated at 40 ml min−1 has a higher V liquid,max, which,in turn, leads to a higher drainage rate and a faster decrease ofV foam compared to that generated at 20 ml min−1. In conclusionone can say that the gas flow rate allows one to control the liq-uid volume of the foam: the higher the gas flow rate the largeris V liquid,max until a limit is reached, i.e. the foam cannot take upany more liquid. As the decrease of V foam is the faster the largerV liquid,max one can further conclude that the destruction of foamsstabilized by a C12TAB solution at 2 cmc is dominated by drainage.In other words, foam stability is to a certain extend controllablevia the liquid volume of the foam.

3.2. Influence of surfactant concentration

After having studied foam properties as a function of the gasflow rate at a fixed surfactant concentration we were interestedin the influence of the surfactant concentration on the foam prop-

1 Foams generated at different flow rates most likely have different structures dueto different liquid volumes and bubbles sizes.

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erties. Thus we studied properties of foams generated at differentC12TAB concentrations and a fixed gas flow rate of 20 ml min−1.The results are shown in Fig. 4. The time required to generate afoam volume of 60 ml is concentration independent at c � cmcwith foaming times of ∼150 s, while for c < cmc a slightly longerfoaming time of ∼160 s was observed in agreement with otherfoam studies. As already mentioned in the introduction, whetherthe foamability becomes constant at the cmc depends upon bothsurfactant transport and minimum bubble lifetimes in the foam,the latter depending upon the foam generation method. A roughestimate of the time required for equilibrium to be obtained be-tween the adsorption at the air–water surface of a bubble and thebulk solution is the diffusion relaxation time.2 In the study at handthe time to reach adsorption equilibrium is ∼10−4 s without eventaking into account any reduction due to the effects of convec-tion. As the lifetime of the bubbles is in the order of secondsand thus orders of magnitudes larger than the diffusion relax-ation time, it can be assumed that equilibrium between the bulksolution and the surfaces of the bubbles is reached both belowand above the cmc. As in the study at hand a surfactant with ahigh cmc is used it is not surprising that the foamability becomesrelatively constant at c � cmc for all three foaming methods. How-ever, a clear reduction in the foamability is seen for c = 0.5 cmc,which is due to the low surface concentration rather than to anytransport effects.

Similar foaming rates are obtained for the various concentra-tions. The slope of the initial part of the V foam(t)-curve containsinformation on the foam generation process. A straight line is ob-tained for the foaming period of all solutions (Fig. 4 (top)) whichindicates a stable build-up process with foam destruction pro-cesses (i.e. drainage, Ostwald ripening, coalescence) not acting onthe same time scale as foam generation. Looking at the evolutionof the V foam(t)-curve after the foam has been generated one seessimilar foam stabilities for concentrations c � cmc, while the foamgenerated at 0.5 cmc is much less stable. Unfortunately there isno direct correlation between surfactant concentration and foamstability [18]. However, the observation made for the foams is inline with single foam film studies where it was also found that thefoam film stability increases with surfactant concentration reach-ing a maximum at concentrations c � cmc. To be more preciseit was found that a single foam film can be stabilized with aC12TAB solution at c = cmc, while no film could be stabilized atc = 0.5 cmc [7]. We will come back to the relation between foamand foam film properties in Section 3.5.

Fig. 4 (middle) illustrates how the liquid volume of the gener-ated foams changes as a function of time for the various surfactantconcentrations. As was the case for varying the gas flow rate dif-ferent values are obtained for V liquid,max (liquid volume in theproduced foam at the time of termination of sparging). Althoughthe differences in V liquid,max are not very pronounced a trend isclearly seen, namely that V liquid,max decreases with increasing sur-factant concentration. A possible explanation is the slightly longerfoaming time at lower concentrations (∼160 s for c = 0.5 cmccompared to ∼150 s for c � cmc) during which more water canbe transferred into the foam. Note that Beneventi et al. [20] mea-sured the liquid volume in the foam as a function of the bubblingtime for different surfactant concentrations. A maximum was ob-served for all solutions indicating the presence of two differentfoam generation phases, namely the undisturbed transfer of wa-

2 τD ≈ (1/D)(Γ /cbulk)2 where τD is the diffusion relaxation time, D is the dif-

fusion coefficient, Γ the surface concentration and cbulk the bulk surfactant con-centration [19]. With D = 5 × 10−10 m2 s−1, Γ = 3.2 × 10−6 mol m−2 (0.5 cmc)and Γ = 3.9 × 10−6 mol m−2 (1.0 cmc) [7,14], cbulk = 7.5 × 10−3 M (0.5 cmc) and1.5 × 10−2 M (1.0 cmc) one obtains diffusion relaxation times of τD ≈ 3.6 × 10−4 s(0.5 cmc) and 1.4 × 10−4 s (1.0 cmc), respectively.

Fig. 4. (Top) Variation of foam volume V foam and (middle) liquid volume V liquid,foamin the foam as a function of time for various concentrations (0.5, 1.0, 2.0 and5.0 cmc) of C12TAB. 60 ml of foam was generated at a flow rate of 20 ml min−1.(Bottom) The change in liquid volume �V liquid,foam for the same C12TAB foams asa function of time after termination of sparging (i.e. t = 0 is the time at which thegas input is stopped). The initial liquid volume of the generated foam V liquid,max isgiven in the legend.

ter into the foam followed by a second phase, which starts whengravitational drainage becomes dominant. The maximum is shiftedtoward higher bubbling times with increasing surfactant concen-tration (see Fig. 11 in [20] but note that both the x-label and thefigure caption are wrong; the x-label has to be “bubbling time” andin the figure caption “bubbling time 180s” has to be deleted). Com-paring these results with ours one can argue that at a bubblingrate of 20 ml min−1 the maximum liquid volume is not reached(in agreement with Fig. 2) so that the water content indeed in-creases linearly with the bubbling time, which is reflected in theconstant foaming rate seen in Fig. 4 (top).

Comparing finally the drainage rate (slope of V liquid,foam(t)-curve in Fig. 4 (middle) after foam generation has been stopped)and the total loss of liquid volume �V liquid,foam(t) (Fig. 4 (bottom))with the decrease in foam volume V foam (Fig. 4 (top)) one gets

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additional information about the dominating foam destruction pro-cess. As can be seen the drainage rate slightly decreases as the sur-factant concentration increases up to a concentration of 2.0 cmc,which is directly correlated with the decrease in V liquid,foam asdiscussed above. However, major differences in the drainage rateswere not observed. For example, in the first 200 s after foam gen-eration the loss of liquid volume �V liquid,foam is roughly the samefor all solutions, which is not the case for the corresponding de-crease in foam volume. Thus the much faster decay observed forV foam at the lowest surfactant concentration cannot be caused bydrainage but has to be attributed to bubble coalescence and Ost-wald ripening.

In conclusion no significant difference in the drainage behavior(Fig. 4 (middle)) is observed and thus the different foam stabilities(Fig. 4 (top)) is attributed to a more pronounced Ostwald ripen-ing and coalescence for the foams generated with a solution of0.5 cmc compared to c � 1.0 cmc. The argument that bubble coa-lescence plays an important role is supported by the properties ofthe corresponding single foam films which are stable at c � cmcbut cannot be stabilized at all at c < cmc (see Section 3.5). Ost-wald ripening is expected to also play a major role if the foam isinhomogeneous, i.e. if the foam has a broad bubble size distribu-tion. Unfortunately, Ostwald ripening could not be studied as theFoamScan does not provide any information on the bubble sizedistribution (see Section 2.3 for details). Ongoing work involvesthe use of a foam conductivity apparatus (FCA) [21]. This methodinvolves blowing gas through a thin nozzle into the surfactant so-lution which allows not only for the production of monodispersefoams but also for the determination of bubble sizes. We expectthat these results will shed further light on the role of Ostwaldripening, which is required to distinguish between the three majorfoam destruction processes.

3.3. Influence of surfactant purity

The foaming properties of surfactant solutions can be modifieddramatically by the presence or addition of other organic com-pounds, which either increase or decrease foamability and foamstability, respectively. Unfortunately, general rules cannot be givenas the influence of the additive not only depends on the natureof the additive but also on its interaction with the main surfac-tant. In a lot of cases, impurities originate from by-products ofthe synthesis and thus the commercially available (“as received”)and the corresponding purified surfactant behave differently. Itgoes without saying that understanding the influence of impuri-ties on surfactant properties is beneficial from both a theoreticaland practical point of view. However, systematic studies are rare.We know of four studies only where the properties of foam filmsstabilized with unpurified (“as received”) and purified surfactants,respectively, were investigated more or less systematically [6,22–24] and of one systematic study on properties of foams stabilizedwith unpurified and purified surfactants [8]. The latter study alsocontains surface tension isotherms of the unpurified and the pu-rified (threefold recrystallized) surfactants according to which aminimum is only observed for the unpurified surfactant. In or-der to complete these two studies on alkyltrimethylammoniumbromides [6,8] we investigated foaming properties of surfactant so-lutions that either contained purified (threefold recrystallized) orunpurified (“as received”) C12TAB. In both cases foams were gener-ated with the sparging method (FoamScan) at a fixed gas flow rateof 60 ml min−1 and at c = 0.5 cmc. The resulting foam and liquidvolumes are presented in Fig. 5.

As can be seen in Fig. 5 (top) the foamabilities of the two sam-ples are nearly the same, while the stability of the foam stabilizedwith the unpurified C12TAB is much greater compared to that sta-bilized with the purified C12TAB. Note that low concentrations of

Fig. 5. (Top) Variation of foam volume V foam and (middle) liquid volume V liquid,foamin the foam as a function of time for foams generated with purified and “as re-ceived” C12TAB. 60 ml of foam was generated at a concentration of 0.5 cmc anda flow rate of 60 ml min−1. (Bottom) The change in liquid volume �V liquid,foam forthe same C12TAB foams as a function of time after termination of sparging (i.e. t = 0is the time at which the gas input is stopped). The initial liquid volume of the gen-erated foam V liquid,max is given in the legend.

contaminants do not necessarily influence the foamability due tothe slow diffusion times but may well influence foam stability. Theobserved dramatic decrease in foam stability is in perfect agree-ment with results reported in [8] although the foams were studiedunder different experimental conditions. Firstly, foams were gener-ated from solutions with higher surfactant concentrations, namelywith c = 1.0 cmc, and secondly, foams were investigated at dif-ferent applied pressures. However, as in the present case it wasalso found that foams stabilized with the unpurified surfactant aremuch more stable than those stabilized with the purified. Comingback to the results of the present study a look at the liquid vol-umes (Fig. 5 (middle)) and the change in liquid volumes (Fig. 5(bottom)) reveals that the drainage rates of the two foams areroughly the same. Thus the same picture as in Section 3.2 emerges,namely that the different foam stabilities are not due to different

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drainage rates. At first sight we can argue as above, namely thatbubble coalescence and Ostwald ripening are not very pronouncedin the case of the unpurified sample, while they play an importantrole during the destruction of the foam stabilized with the puri-fied sample. This argument, however, is not quite correct as it hasbeen concluded in Section 3.2 that bubble coalescence and (mostlikely) Ostwald ripening start playing a role at c < cmc. Thus in thepresent case it is more reasonable to argue that purification leadsto an increase of both bubble coalescence and Ostwald ripening,which, in turn, decreases the foam stability as compared to the un-purified sample. A more pronounced bubble coalescence in case ofthe purified sample is again in agreement with results obtained forsingle foam films [6]. In contrast to the unstable foam films pro-duced from solutions of purified C12TAB, solutions of unpurifiedC12TAB (at cmc) as well as solutions of purified C12TAB (at cmc)to which small traces of dodecanol (C12OH) were added producedhighly stable foam films. This suggests that the impurity – whichis most likely dodecanol in the case of C12TAB – helps stabilizingfoam films of C12TAB which, in turn, leads to more stable foams.We will come back to this point in Section 3.5.

3.4. Comparison of different foaming methods

In order to compare properties of foams that have been gen-erated by different techniques we generated foams from C12TABsolutions using the standardized Ross–Miles (pouring), the home-built winding (shaking), and the commercially available FoamScan(sparging) methods. In all cases foams were produced at three sur-factant concentrations, namely 0.5 cmc, 1.0 cmc, and 2.0 cmc. Afterthe foams have been generated the evolution of the foam volumeV foam was followed as a function of time. The results obtained withthe three techniques are shown in Fig. 6.

As already mentioned in the introduction, a quantitative com-parison of foams generated with different techniques is usuallynot possible. However, comparing the results presented in Fig. 6one sees that qualitatively similar results are obtained. With allthree techniques it was found that at c < cmc foamability andfoam stability are quite low. However, the generated foam decaysvery fast. The situation changes completely at c � cmc where sta-ble foams could have been generated with all techniques. Anothercommon feature is the fact that the foamability and foam stabil-ity of foams generated at 1.0 cmc and 2.0 cmc, respectively, arethe same for each technique. However, comparing the results ob-tained with different techniques one sees that the foam volumesdecay differently. Foams generated with the winding method decaymuch more rapidly than those generated by the FoamScan and theRoss–Miles methods, respectively. Further comparison is unreason-able due to the following reasons. Firstly, the foams are producedwith different energy impacts. Secondly, the Ross–Miles and thewinding methods do not provide any information about the liquidvolume of the generated foams and thus a distinction between dif-ferent foam destruction processes is impossible. Finally, the threemethods lead to the production of structurally different types offoam. (a) The Ross–Miles method is notorious for the productionof quite dry foam, which explains the constant value of V foamfor c � cmc. (b) The winding method leads to a wide distribu-tion of bubbles sizes, which explains the non-linear, rapid decreaseof V foam even for c � cmc. (c) The FoamScan method producesreasonably monodisperse foams, which explains both the constantfoam generation and foam destruction rates.

3.5. Correlation between Foams, foam films, and surfaces

In order to learn more about the properties of foams, the prop-erties of the corresponding single foam films and single water–air surfaces are generally regarded as essential (reviewed in [13,

Fig. 6. Time dependence of foam volume for C12TAB at 0.5, 1.0 and 2.0 cmc mea-sured with the Ross–Miles (top), the winding (middle) and the FoamScan (bottom)methods, respectively. In all cases t = 0 is the time at which foam generation isstopped.

25–27]). Thus previous studies of foam films [6–8], static surfacetensions [6,14,28], dynamic surface tensions [28–30], and surfaceelasticities [29,31,32] of C12TAB solutions have been examined tobetter understand the foam properties of C12TAB solutions.

3.5.1. Correlation between foam and foam film propertiesIn the present study the foaming properties (both foamability

and foam stability) of aqueous C12TAB solutions are found to beindependent of the concentration for c � cmc, i.e. from 1.0 to 5.0cmc, while a significant reduction in foam stability is obtained atc < cmc (Section 3.2) which is in agreement with previous studiesof C12TAB single foam films [6,7]. In the foam film studies the dis-joining pressures, film thicknesses and film stabilities of C12TABfoam films were measured with the thin film pressure balance(TFPB). In both studies the formation of a foam film with a solu-tion of 0.5 cmc C12TAB was not possible, while at 1.0 cmc C12TAB

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a foam film could be stabilized and studied over a broad pressurerange (see [7] and Ref. [35] therein).

Apart from the concentration dependent foam stability the in-fluence of small amounts of impurities was studied. A dramaticdecrease in both foamability and foam stability was found when“as received” C12TAB was purified by three-fold recrystallizationand used for the foam studies (Section 3.3). Knowing that theimpurity is mainly dodecanol, one can deduce that it is the ad-sorption of the long-chain alcohol at the water–air surface that isresponsible for the increase in stability. That this is indeed the casewas demonstrated previously by adding small amounts of dode-canol to highly purified C12TAB. While foam films could not bestabilized with solutions of the purified C12TAB, the addition ofdodecanol lead to the formation of stable foam films, the stabilityof which resembles that of foam films stabilized by the unpuri-fied C12TAB [6]. In another systematic study the influence of smallimpurities on properties of foams stabilized by CnTAB surfactantswith n = 10, 12, 14, and 16 was investigated [8] and compared withthe results obtained for the respective single foam films [6]. Notethat in [8] foams were not studied under gravity but at a certainapplied pressure so that a study under gravity was indispensableto complement the previous one. The fact that foam studies carriedout under quite different conditions and studies of the correspond-ing single foam films lead to the same general results not onlyshows how reliable the results are but also illustrates the strongcorrelation between the properties of single foam films and foamsstabilized by aqueous CnTAB solutions. Whether or not this conclu-sion can also be drawn for foams and foam films stabilized withnon-ionic surfactants is still an open question as telling systematicstudies are missing.

3.5.2. Correlation between foam and surface propertiesDynamic interfacial properties such as dynamic surface ten-

sion and dilatational surface elasticity are considered to have asignificant contribution to the formation and stability of foamsand foam films [25,28,29,33,34]. A prerequisite for good foama-bility is the ability of the surfactant to lower the surface tensionin a short time when a new surface is created. In other words,foam formation requires enough surfactant to be transported asfast as possible to the rapidly expanding surface. Previous workshave shown that an increase in foamability appears to parallel thelowering of the dynamic surface tension but not the equilibriumsurface tension, which is almost constant in the same concentra-tion range [25]. This, however, cannot be considered as general ruleas it depends on the timescales of foam generation and surfac-tant diffusion whether foamability and dynamic surface tension arerelated. As already discussed in Section 3.2, the surfactant concen-trations used in the current C12TAB study lead to diffusion timesof ∼10−4 s. Thus we can claim that dynamic surface tension doesnot play a notable role in the case of both foamability and foamstability, simply because diffusion is much faster than foam gener-ation.

Apart from dynamic surface tensions, surface rheology is con-sidered to be another important player, especially when it comesto foam and foam film stability. Surfaces with high dilatationalelasticities resist disturbances and deformations and are generallybelieved to stabilize foams and foam films more effectively thansurfaces with low elasticities (reviewed e.g. in [28,34]). Althoughextended studies on foams, foam films, and surface rheology ofthe same system are rare, some authors indeed reported on clearcorrelation between surface elasticity and foam film stability [6,28,29,35], while to our knowledge there are only three studieswhere a clear correlation between surface elasticity and foam sta-bility were found [8,36,37]. One illustrative example is a previousstudy on the surface elasticities of alkyltrimethylammonium bro-mides which showed that the surface elasticity increases dramati-

cally from C12TAB to C14TAB, while the surface elasticity of C14TABwas found to be comparable to that of C16TAB [31]. Moreover it isargued [6] that the surface elasticity cannot only be increased byincreasing the chain length of the surfactant but also by adding along-chain alcohol. Both trends are in line with the observed in-crease in foam film stability [6] and foam stability [8], respectively,and clearly illustrate that there is a correlation between surfaceelasticity and foam (foam film) stability. Unfortunately, quantita-tive correlations have not been found yet.

A difficulty may arise if one measures foam stability, foam filmstability, and surface elasticity as a function of the surfactant con-centration. For example, it was found for aqueous solutions ofC12TAB that stable foams and foam films can only be generatedat c � cmc. However, measuring surface elasticities as a functionof the surfactant concentration one may obtain a maximum. Theconcentration at which the maximum surface elasticity is mea-sured depends on the frequency and can either be below or abovethe cmc. As regards C12TAB the dilatational surface elasticity wasstudied from 0.05 cmc to 1.3 cmc at frequencies of 240 Hz and800 Hz using the excited capillary wave technique [31,32]. It wasfound that the surface elasticity runs through a maximum around0.1 cmc for 240 Hz [32], at 0.2 cmc for 800 Hz [31], and at 0.4 cmcfor the high frequency limit [32]. Thus the increase of foam andfoam film stability is observed in a concentration range in whichthe surface elasticity decreases so that one is tempted to say thatthere is no correlation between surface elasticity and foam (foamfilm) stability. However, with the excited capillary wave technique(and most other surface rheometers) the rheological properties ofa single water–air surface after having brought in equilibrium withthe bulk phase are studied. If one took this bulk phase and gener-ated a foam one would end up with a much lower bulk concentra-tion as surfactant is needed for creating surface.3 Thus informationabout the bulk or – much better – the surface concentration of thefoam films is needed to compare directly foam stability and sur-face elasticity. In addition the thickness of the foam films has to beknown for a sophisticated analysis as the surface elasticity may beinfluenced by interaction forces between the two monolayers. Toconclude one can say that quantitative correlations between foam(foam film) stability and surface elasticity have not been foundyet which is mainly due to the fact that in most studies the con-centration and frequency dependence of the surface elasticity isoverlooked. However, a quantitative comparison of systems stud-ied under similar experimental conditions leads to astonishinglyclear correlations as was discussed above [6,8,28,29,35–37].

4. Conclusions

The FoamScan was used to study the properties of aqueousfoams stabilized by dodecyltrimethylammonium bromide (C12TAB)at different gas flow rates and surfactant concentrations. Moreover,the influence of small impurities was studied. For concentrationsof c � cmc the foaming properties (both foamability and foam

3 A depletion of the bulk solution caused by the generation of new surface canbe neglected if cbulk � (Γ Abubbles)/V liquid where cbulk is bulk concentration of thefoaming solution, Γ the surface concentration, Abubbles the total surface area of thebubbles in the foam column and V liquid the volume of liquid in the foaming so-lution. It holds Abubbles = 4πr3

bubble × number of bubbles in foam with rbubble =250 μm (a value taken from literature where the same setup and porous disc alongwith similar flow rates was used [20]). To simplify this calculation spherical foambubbles are assumed with the number of bubbles = (V foam − V liquid,max)/V bubblewhere (V foam − V liquid,max) corresponds to 52.4 ml (0.5 cmc) and 50.2 ml (2.0 cmc).For the present study it holds cbulk = 7.5 × 10−3 M (0.5 cmc) and 3.0 × 10−2 M(2.0 cmc) [7,14], Γ = 3.2 × 10−6 mol m−2 (0.5 cmc) and 3.9 × 10−6 mol m−2

(2.0 cmc) [7,14], V liquid = 20 ml and one can calculate 7.5×10−3 M � 3.8×10−5 Mfor 0.5 cmc and 3.0 × 10−2 M � 4.7× 10−5 M for 2.0 cmc. Thus surfactant depletiondue to surface generation can be completely neglected in the study at hand.

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stability) of C12TAB are found to be independent of the concen-tration in a range of 1.0 to 5.0 cmc. A significant reduction in bothfoamability and foam stability is observed at c < cmc which is inagreement with previous studies of single foam films stabilized byC12TAB. Monitoring the time evolution of the foam volume V foamand of the liquid volume in the foam V liquid,foam allowed us to con-clude that the dominating process at c � cmc is drainage, while forconcentrations at c < cmc bubble coalescence plays an equally im-portant role. The latter conclusion is supported by the propertiesof single foam films which are stable at c � cmc but cannot bestabilized at all at c < cmc. Note that Ostwald ripening is expectedto also play a major role if the foam is inhomogeneous, i.e. if thefoam has a broad bubble size distribution. Unfortunately, Ostwaldripening could not be studied as the FoamScan does not provideany information on the bubble size distribution.

Another important result of the study at hand is the observa-tion that foamability and foam stability of foams stabilized withthe “as received” C12TAB are much higher compared to that ofthe purified C12TAB. This result is in perfect agreement with ob-servations made for single foam films and illustrates again thecorrelation between single foam films and foams: the more sta-ble the single foam film the lower the rate of bubble coalescence,which, in turn, results in both a higher foamability and foam sta-bility.

In addition to the FoamScan both the Ross–Miles and the wind-ing methods were used to examine the effect different foamingmethods have on the properties of the generated foam. Qualita-tively similar results were obtained with all three methods (pour-ing, shaking, sparging), namely foaming properties that are inde-pendent of the concentration at cmc � c � 2 cmc and a dramaticreduction in foamability and foam stability at c < cmc. Thus cheapand quick tests like the Ross–Miles and the winding methods canindeed be used for qualitatively measuring (“screening”) foama-bility and foam stability. However, for an understanding of themechanisms leading to foam generation and destruction, respec-tively, the liquid fraction and the bubble size (distribution) of thefoam need to be known [5,21,38].

Ongoing work involves the use of a foam conductivity appara-tus (FCA) [18], which consists of a foam column in which foamis produced and studied via conductivity measurements. The FCAallows for the accurate (as low as 10−5) determination of the liq-uid fraction at various heights throughout the foam column [39].In addition, the actual bubble size can be monitored during ex-perimental runs. With this information not only the correlationbetween bubble size and foam properties but also the role of Ost-wald ripening can be addressed.

Acknowledgments

E.C. would like to acknowledge UCD Ad Astra Research Schol-arship. We are grateful to Dr. Ingegärd Johansson, Akzo Nobel Sur-face Chemistry (Ross–Miles and winding methods), Stenungsund,

Sweden and to Prof. Per Claesson, KTH Chemistry/Surface Chem-istry (FoamScan), Stockholm, Sweden for allowing the use of theirequipment. Part of the work was funded by the European Com-munity’s Marie Curie Research Training Network “Self-Organisationunder Confinement (SOCON)”, contract number MRTN-CT-2004-512331.

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