Langmuir 1993,9, 1668-1677
1668
Mechanisms of Aqueous Foam Stability in the Presence of Emulsified Non-Aqueous-Phase Liquids: Structure and Stability of the Pseudoemulsion Film Lloyd Lobo+and Darsh T . Wasan’ Department of Chemical Engineering, Illinois Institute of Technology, Chicago, Illinois 60616 Received January 20,1993 The influence of the emulsified oil drops on the stability of an aqueous foaming system is investigated at the thin film level. In the first part of the paper we evaluate the theories that use the classical entering and spreading coefficients to predict the effect of oil drops on foam stability. A differential interference microscope was used to observe the configuration of oil drops at the air-water surface, which ia likened to the air-water surface of foam lamellae. The microscopic observations show that the entering and spreading coefficients cannot consistently predict the configuration of the oil at the air-water surface and, consequently, cannot predict the effect of oil on foam stability. The reason for this inconsistency is that the classical theories do not account for the role of the pseudoemulsion f i ,which is formed between an air-water surface and the surface of an oil drop which is approaching it. It is the Stability of this film that determines the configuration of the oil drop, as it was earlier suggested by Wasan and Nikolov (refs 10 and 11). In the second part of the paper, we use reflected light interference microscopy to observe the drainage and stability of the pseudoemulsion film. We observed, for the first time, that the f i thins in discrete steps, which is indicative of the presence of an ordered micellar structure within the film, and this structure was found to enhance the film stability. The f i excess energy, which is determined from the f i contact angles, is used to quantitatively characterize €he stability of the f i . The contact angles of the curved, asymmetric pseudoemulsion f i were measured by wing interference microscopy in conjunction with the Laplace equations for the film meniscuses. The f i excess energy calculations show that the equilibriumfilm thickness increaseswith increasing micellar concentrationaswell as with decreasing oil drop size or film area. The effect of these two parametera on the f i stability is explained due to the formation of the ordered micellar structure (i.e.,micellar layering) within the pseudoemuleion film.
Introduction Oil dispersed in a foaming system is encountered in several applications; foam mobility control processes in enhanced oil recovery @OR) applications, food foams, and antifoamers are a few examples. It has been found that, in some cases, the oil acts as a foam stabilizer (food foams),l whereas, in other cases, it acts as a foam destabilizer (antifoamers). When studying the &.ability of three-phase foams (aqueous foams containing oil), it is important to identify the system variables that could play a role in the foamstability. In many practical applications it is fairly common to employ surfactants at several times their critical micelle concentration (cmc), and in these circumstancesthe oil can exist in two forms: (i) solubilized within the micelles and (ii)as macroemulsions or oil drops. In these micellar systems the amount of solubilized oil is generally small (about 0.2-0.5 w t 5% 1, and is usually very minor compared to the amount of macroemulsions. However, it is important to realize that the two oil confiiation types (solubilizedlemulsified)can have very different effects on the foam stability. In an earlier paper,2 we have discussed the effect of solubilized oil on foam stability. It was found that the presence of solubilized oil inhibited the formation of an ordered micellar structure within the foam films which, according to Nikolov et al.,3 enhances the foam film stability. Thus, solubilized oil is always detrimental to
* To whom correspondence should be addreseed.
t Presently with Photographic Research Labe, Eaetman Kodak
Co., Rochester, NY 14660. (1) German,J.B.InFoodEmuLsionsandFoams: TheoryandPractice; Wan, P. J., Ed.; AIChE Symposium Series 277; American Institute of Chemical Engineers: New York, 1990; p 62. (2) Lobo,L.A.;Nikolov,A.D.;Wasan,D. T.J. DispersionSci.Technol. 1989, 10, 143. (3) Nikolov, A. D.; Wasan, D. T. J. Colloid Interface Sci. 1989,133, 1.
foam stability. We had also shown2 that the effect of macroemulsions on foam stability should be considered independently of the effect of solubilized oil. In this study, we investigated the interactions of the oil drops with the foaming system, in order to elucidate the mechanism of aqueous foam stability in the presence of oil drops. The results of our findings are also compared with someof the prevalentclassicaltheorieson this subject. When the oil is dispersed into the foaming system, the drops are initially present in the foam lamellae as well as within the Plateau borders of the foam films. The most widely accepted mechanism for foam stability in the presence of oil is that the oil drops, dispersed within the foam films, spread on the air-water surfaces of the foam films and, due to a variety of reasons (discussed below), enhance the film rupture and decrease the foam stability. The interactions of the oil drops with the foam film are characterized by the degree of oil spreading and the final configuration of the oil drop at the air-water surface. have defied two Robinson and Woods,4 as well as ROSS,~ coefficients-an entering coefficient, E, and a spreading coefficient, S-that can be used to predict the oil drop configuration at the air-water surfaces and to quantify the degree of spreading. These are given by where u is the interfacial tension and the subscripts 0, w, and a refer to oil, water, and air, respectively. The entering coefficient, E, represents the decrease in the free energy that occurs when an oil drop, which is within a solution (see Figure la), ‘enters” or forms a lens at the airwater surface as shown in Figure lb. The spreading coefficient, S, represents, quantitatively, the (4) Robinson,J. V.;Woods, W. W. J. SOC.Chem. Znd. 1948,67,361. (6)Ross, S. J. Phys. Colloid Chem. 1950, 54, 429.
0743-7463/93/2409-1668$04.00/00 1993 American Chemical Society
Mechanism of Aqueous Foam Stability a
Langmuir, Vol. 9, No. 7, 1993 1669 elr
air
pseudoemulsion film
water
I?X
@-oil
b
Figure 3. Thin film of the continuous phase separatingan oil drop from an air-water surface.
C
oil film /
+
Figum 1. Configuratioasof the drops aspredicted by the classical theory: (a)oil drop within the solution,(b) oil lens,and (c) spread oil at the surface.
Figure 2. Mechanism of foam rupture in the presence of oil.
driving force for the oil to spread on the surface and is also derived from the decreasein the free energy resulting from the oil spreading at the surface. Ross5 has proposed a mechanism, based on the oil spreading phenomenon, by which the oil drops rupture the foam films. The schematicof this mechanism is shown in Figure 2 and is summarized as follows: The oil drop initially within the film (Figure 2a) will enter one of the film surfaces if E > 0 (Figure 2b). Due to foam film thinning, the second film surface comes into contact with the oil drop and the oil enters this surface and bridges the film (Figure 2c). Robinson and Woods4have suggested that the formation of the oil bridge is sufficient to rupture the foam film (Figure 2d). Ross,however, postulates that, in order for the rupture to occur, the oil bridge must also spread as a duplex film on either side of the original film, thereby driving out the original aqueous film liquid and leaving a thin oil film which is not stable and easily ruptured. According to this theory, the antifoaming efficiency of the oil drops increases with the value of the spreadingcoefficient. Other mechanismsproposed on this subject are basically variations of the spreading theory. The spreading theory has been experimentally tested and many different investigators have found exceptions to the rule. Ross,himself, has found no direct relationship between the degree of antifoaming by the oil and the magnitude of the spreading coefficient, although he does find a 1:l relation between the sign of the spreading coefficient and the effect of the oil on the foam stability (positive values of S result in decreased foam stability).
Ross and Mcbain6found systems which were good antifoamersbut had negativespreadingcoefficients. Robineon and Woods+ in comparing different spreading oils, found that there is no correlation between the spreading coefficient and the degree of foam inhibition. Tsuge et al.7 have found systems in which the oil spreads but does not inhibit foaming. Kuhlman8suggested that the definition of the spreading coefficient should be modified by taking into account the geometry of the oil drops and the foam bubbles, but he still does not obtain a correlation between the spreading coefficient and foam stability. Garrettg suggests that the dynamic values of the interfacial and surface tensions should be used when determining the entering and spreadingcoefficients,but it is not clear what rates of surface/interfacial expansion should be used. Thus, the classical spreading theory is not consistent with many experimental findings. The main flaw in this approach is that it does not take into account the presence of a film (see Figure 3) that is formed between the oil drop and the air-water surface. Wasan et al.'OJ1 were the first to point out that this film, which they called the "pseudoemulsion film", can exhibit, in the presence of Surfaceactive substances, a stability similar to that of foam and emulsionf h . Unless this pseudoemulsion film ruptures, the oil drop cannot enter the &water surface, irrespective of the value of the entering coefficient. An analogy of the classical theories, regarding the concept of entering and spreading coefficients,can be drawn to both the foam and emulsion systems. In these systems, the interfacial and surface tensions are usually positive, implying that the systems should coalesce in order to decrease their free energy. However,the stability of these systemsis derived from the stability of the films of the continuous phase that prevent the disperse phase from coalescing. In order for the disperse phase to coalesce, an energy barrier, associated with the drainage and rupture of these films, has to be overcome. The importance of the pseudoemulsion film was f i t identified by Wasan and co-workerslOJ1in studies with enhanced oil recovery type foams,where they showed that the foam stability in the presence of emulsified oil is (6) Ross, S.; McBain, J. W. Ind. Eng. Chem. 1944, 36,670.
(7) Teuge,H.; Uehida,J.; Hibino, S. J. Colloid InterfaceSei. 1984,100,
176.
(8) Kuhlman, M. I. Paper presented at the SPE/DOE Enhanced Oil Recovery Symposium, Tulsa, OK,1988; SPE/DOE No. 17356. (9) Garrett, P. R.; Moore, P. R.; Ward, D. Foam and Dynamic Surface Properties of Micellar Anionic Surfactant. Paper presented a t the 8th Symposium on Surfactanta in Solution, Gainesville, FL, June 1990. (10)Wasan, D. T.; Nikolov, A. D.; Huang, D. D.; Edwards, D. A. In Surfactant Eased Mobility Control; Smith, D. H., American Chemical Society: Washington, DC, 1988; p 136.
(ll)Nikolov,AD.;Wasan,D.T.;Huang,D.W.;Edwards,D.A.Paper
presentedatthe 61st Annual Technical Conferenceof SPE, New Orleane, 1986; SPE No. 15443.
1670 Langmuir, Vol. 9, No. 7, 1993
controlled by the stability of the pseudoemulsion film. Later, Manlowe and Radke12also showed that the pseudoemulsion film stability controls the stability of single foam lamellae within porous media. The latter have suggested that the stability of the pseudoemulsion film is kinetic in nature. However, in many system and especially at high surfadant concentrations, the pseudoemulsionfilm can reach a thermodynamically metastable state. In studies with foam films, Nikolov e t ale3have shown that, at high micellar concentrations, the formation of an ordered ilm increased its stability due to the structure within the f structural contributionsto the micellar interactions. This structure was also found to stop the thinning process of the film. In the present study, we discuss the validity of the classical theories by qualitatively studying the pseudoemulsion film stability of different systems. Further, for one of the systems, we have investigated the role of micellar structuring on the stabilityof the pseudoemulaion films by (i) studying the film drainage characteristics and (ii) measuring the thermodynamic properties of the films, such as the contact angles and the excess film energies.
Lobo and Wasan
I
plastic shield
air
oil droD
glass cuvette
\
surfactant
solution
\
water
Figure 4. Schematic of the glass cell used for the microscopic studies.
Experimental Section b
Materialand Solutions. Two surfactantswere used in these studies-anionic and nonionic. The nonionic surfactant is an ethoxylated alcohol supplied by Shell Development Co. with a product name of C1215 AE30.'The surfactant molecule has a 12-15 carbon atom chain with an average of 30 ethoxy group per surfactant molecule. The average molecular weight of the monomer is 1530,and the micellar aggregationnumber obtained from light scatteringmeasurementsis 46. The concentration of the surfactant used in these studies was 4 wt % which was 1300 times the critical micelle concentration. The anionic surfactant was d u m dodecyl benzenesulfonate with a commercial name of Siponate DS10-which was supplied by Rhone Poulenc Inc. The concentrationused was 4 wt % ,which is severalt i " higher than the critical micelle concentration (cmc = 0.042%). n-Octane, n-decane, n-dodecane, hexadecane, and benzene were used as the oils. They were obtained from Fisher and were reagent grade. The surfactant solutions were equilibrated with the oils for 10-14 days to allow for complete solubilization,and the surfactant solutions were then separated from the oils by wing a separatoryfunnel. All the experimentswere made using the respective, equilibrated solutions. Interfacialand SurfaceTension. A Krw tensiometerwas used to measure the interfacial and surface tensions with a platinum Wilhelmy plate. These measurementa were used to calculate the entering and spreading coefficients. A spinning drop tensiometer was used to measure the interfacial tension when the vlaues were below 3 dynlcm. PseudoemulsionFilm Observations. We used an Aus Jena Epival Interphako microscope in order to determine the configuration of the oil at the h a t e r surface. This microscope is capable of viewing objects in transmitted light as well as in reflected light. The microscope is also equipped with a Max Bender interferometer, which splits the original beam of the image into two beams of different optical paths which, when recombined,give a shearing-typedifferentialinterferencepattem; this can be used to measure the curvature of s u r f a ~ e s . ~The ~J~ glass cell used for these studies is shown,schematically,in Figure 4. It consists of two concentricglass cylinders fused at one end to an optical glass plate. The surfactant solution is placed in the inner cylinder, and clean water (3-mm depth) is placed in the outer cylinder. A small oil drop (0.3-O.Ekmmdiameter)is i n j d , with a 0.25-pL Hamilton syringe, below the &water surface of the surfactant solution in the inner glass cylinder. By viewing the drop in both transmitted and in reflected light, as well as by
using the differential interference (DI) technique, it is possible to determine the confiiation of the oil drop at the air-water surface. The surfactant solutionwas protected from the outside environment by a plastic shield which fitted on the objective. The shield ale0 provided a saturated vapor environment around the &water surface of the surfactant solution. The two possible configurations of the oil drop are shown in ilm is stable, Figure 5. In confiiation a, the pseudoemulsion f andintransmittadlight( l i g h t s o ~ b e l o w t h e d r o p ) , i t i s ~ b l e to o b e e ~ ethe circumference of the drop whereas, in reflected light, only the circumference of the film is visible. The radius of the film (rc)is considerablysmaller thanthe radius of the drop (R)is this configuration. Confiiation b is an oil lens which ia formed after the oil drop has entered the akvater surface. In this confiiguration, both refleded and transmitted light microscopies revealed the circumference of the lens. Another way to differentiate between the two confiiations ia by observing the differentialinterferencepa" of the drop in reflected light. The photomicrograph of the differentialinterferencepattern of the pseudoemulsion film, for the 4 wt 9% C1215 AEso-octane system, is shown in Figure 6. It is similar to the differential interference pattem, obse~edby Nikolov et aL:6 of a foam f h formed by a floating air bubble. Mingins and NikoloP have studied oil lenses using the DI technique, and the differential pattem they obtained is quite different from that shown in Figure 6. From the differential interference pattern it is poeeible to conclude that the confiiation of the drop is similar to the one seen in Figure 5a. From Figure 6 it is also seen that the thin pseudoemulsion film appears bright, as opposed to the thin foam and emulsion f i i , which are black. The reason for this difference can be explained by the electromagnetic wave theory of light. Light rays which are incident on the fiilm reflect from the two surfacea of the film, and these reflected light rays interfere optically. When light rays of wavelength A are incident on a thin (zerothickneee) foam or emulsion film, they encounter, alternately, an optically dense and opticallyrare medium (the order depends on the type of emulsion). As a result, the two reflected rays from each of the
(12) Manlowe, D. J.; Radke, C. J. SPE Reeervoir Eng. 1990, 5, 496. (13) Beyer, H. Jenaer Rundsch. 1971,16,82. (14)Nikolov, A. D.; Dimitrov, A. 5.; Kralcheveky, P. A. Opt. Acta 1986, 33.
(16) Nilrolov, A. D.;Kralcheveky,I. B.;Ivanov,I. B. J. ColloidZnterface Sci. 1986,112, 122. (16) Mingins, J.; Nikolov, A. D. Ann. Unio. Sofia (Fac. Chim.) (in Bulgarian) 1981, 76, 3.
P Figure 6. Possible confiiations of the oil depending on the pseudoemulsion film stability: (a) stable pseudoemulsion film and (b) unstable pseudoemulsion film.
Mechanisms of Aqueous Foam Stability
Langmuir, Vol. 9, No. 7, 1993 1671 Table I. Entering and Spreading Coefficients
NaDBS-hexedecane NaDBS-decane NaDBS-dodecane NaDBS-benzene C1215AESO-octane C1215 AE30-dodecane
Figure 6. Photomicrograph of the differential interference pattern of the pseudoemulsion film (4w t % C1215 AE30 and octane).
filmsurfacesdiffer by a path length of X/2. This is the condition for the destructive interference of light, which is why the thin foam and emulsion filmsappear black in reflected light. On the other hand, light rays incident from the air side of a pseudoemulsion film encounter an optically denser medium at both the film surfaces (air to water and water to oil). Thus, both the reflected rays are shiftedby A/2, and the path differencebetween the two reflected rays is A. This is the conditionfor constructive interference, which is why the pseudoemulsion film appears bright. In order to study the effect of drop size on the film stability, a new drop was created each time and the size of the oil drop was controlled by the syringe. Once the pseudoemulsion film was formed and stopped thinning, the system was allowed to stand, undisturbed,for 15min, to allowfor saturationof the environment above the air-water surface and also for complete surfactant adsorption. After this, the microscope stage is gently tapped, so that the oil drop detaches and submerges below the surface. In this way, a new film is formed when the drop rises again, and usingthe reflectedlight mode, it is possible to observethe drainage characteristics of the film. The new film is left undisturbed for 30 min to allow the film to reach equilibrium, after which photomicrographsof the oil drop are taken in transmitted light, in reflected light, and with the use of the interferometer. These photographs are used to measure the common and differential interferencepatterns as well as the drop diameter. The common interference pattern is formed by the interference of the light raysrefleded from the wedge which is bound by the filmmeniscus and bubble surfacenear the three-phasecontactline. The pattern appears as concentriccircles which are similar to Newton rings. The distances between the interference patterns are measured, from the photomicrographs, by using an x-y translator (least count of 1pm) which is mounted on a goniometric microscope.
Validity of the Classical Theories The microscopic technique was used to determine the oil drop configuration for the systems listed above. The predictions of the classical theories can be obtained by measuring the interfacial and surface tensions of the equilibrated solutions and oils and then calculating the entering and spreading coefficients. In this way, it is possible to check the validity of the classical theories. Table I shows the measured values of the interfacial and surface tensions as well as the calculated values of the entering and spreading coefficients. It is seen that, for all but one of the system (NaDBS + benzene), the entering and spreading coefficients are positive. According to the
31.1 28.2 28.2 27.3 43.5 43.5
26.6 23.2 25.4 28.2 21.3 25.4
0.09 0.06 0.09 0.02 10.2 9.4
4.6 5.1 2.9 -0.88 32.4 27.5
4.4 6.0 2.7 -0.92 12.0 8.7
classical theories, the oil drop in these systems should have entered and spread at the air-water surface. Using the microscopic technique described above, it was found that the pseudoemulsion films in all these systems were stable, even after they stopped draining, which prevented the oil drops from entering the air-water surface. The configuration of the oil drops in these cases is shown in Figures 3 and 5a. Thus, the classical theories do not predict the behavior of the oil drop at the air-water surface. The reason for this, as mentioned earlier, is that the decrease in the surface energies can be used only as a necessary but not as a sufficient condition to predict the behavior of the oil drop at the air-water surface. It is clearly evident that an additionalfactor, i.e., the pseudoemulsionf i i stability, should be taken into account. The stability of the pseudoemulsion film can be kinetic or thermodynamic in nature. The kinetic stability of a film is governed by the film drainage characteristics, and this aspect of stability has been analyzed by Manlowe and Radke.12 They used the Reynolds equation, which is valid for rigid or immobile film surfaces, to describe the film drainage rates. They also accounted for the disjoining pressure II,by using the DLVO model, which is valid for ionic surfactants. In the systems investigated in our present study, the pseudoemulsion films stopped draining and remained in a stable configuration for over 1h. This implies that the stability is thermodynamic in nature. In the subsequent section, the thermodynamic properties of the stable film are calculated, with the objective of characterizing the film stability. Thermodynamic Stability of the Pseudoemulsion Film Among the systems listed in Table I, the one with the highest spreading coefficientwas the C1215AESO-octane system. According to the classical theories, the foams of this system should be destabilized by the oil, by the highest degree. This was also one of the systems common to those studied in our previous p a p e r ~ , ~where J ~ we found that the effect of oil drops is to stabilize the foams-a result contradictory to the predictions of the classical theories. For this reason, this system was selected by us for the studies on the thermodynamic stability of the pseudoemulsion film. Two concentrations of the surfactant were used for this part of the study-4 and 1wt % Figure 7 shows the configuration of the oil drop at the air-water surface with the respective geometrical parameters that are used in the analysis below. At equilibrium,the excess pressure in the film,Pf, equals the disjoining pressure, n,
.
The above equation is an approximate one. In the case of symmetric systems (when the two tensions are equal), (17) Koczo, K.;Lobo, L. A.; Wasan, D.T.J. Colloid Interfuce Sci. 1992,150,492.
Lobo and Wasan
1672 Langmuir, Vol. 9,No. 7, 1993
and cy2 is the angle made by the h a t e r m e n k of the film. At equilibrium, the film tension is given by (ya/w+ yo/w),where Y ~ and / yOlw ~ are the tensions of each of the film surfaces given by
--
= uo/w cos "1; Yalw q w cos a2 The film excess energy, -W, is given by Yo/w
-W =
-Y
(6)
- r,/d = uo/w(l- cos q)+
~ /+ ~ (ua/w )
-
ua/w(l cos cy2) (6)
Figure 7. Geometrical parameters of the oil drop at the ai^
water surface.
The main oddity of the pseudoemulsion film is that it is an asymmetrical type of film; Le., it has two different phaeee on either side of the film, unlike foam or emulsion films. Consequently,the contact anglesof the asymmetric films, cy1 and a2, are not equal. On the other hand, foam or emulsionfilms, which are symmetrical,have equal angles which simplifies the measurement technique. For symmetrical films,the film excess energy is given by
,e, air
-=---------
water
---
-.,ah
- w =2@(1-c08((rh/2))
Figure 8. Definition of the contact angles for an asymmetric
fii.
the disjoiningpressure of a curved film is half the capillary pressure (equal to 2ulR). For plane parallel films, the excess film pressure, Pf,equals the capillary pressure. The disjoining pressure arises due to the interactions between the film surfaces, and the stable film represents an energy barrier for the oil drop to enter the air-water surface. The total energy barrier of the film, from its formation to its rupture at the critical thickness h,,, is given by
AE = Jmh-n dh
(3)
This represents the total work done in order for the film to drain from its formation to its rupture. The necessary condition for the oil drop to form a lens is for the oil drop to overcome the energy barrier given in eq 3. When the pseudoemulsion film stops thinning and reaches an equilibrium state at a thickness h, larger than the critical thickness h,,, the part of the energy barrier, bE, that is overcomeis given by the negative of the specificinteraction energy of the film, -W,
-W = Jmhhn dh
(4)
The specific interaction energy of the film is equivalent to the energy of the film in exces~of the energy of the two free film surfaceswhich are not interactingwith each other. Henceforth, we shall refer to this energy as the film excess energy. Thus, the film excess energy, of a film having a thickness h, is, in a thermodynamic sense, a measure of the stability of the pseudoemulsion film. In order to determine the film excess energy, it is necessaryto measure the contact angles of the film. Figure 8 shows a plane parallel pseudoemulsion film with the contact angles a1and (r2. It is important to point out that the plane parallel configuration of the pseudoemulsion film is not realistic because these types of films are usually curved (see Figure 7). However, Figure 8 is introduced to illustrate the definitions of the contact angle and the differentiating features of the pseudoemuleion film. The angle a1 is made by the oil-water meniscus of the film,
(7)
where u is the surface tension for both the meniscuses of the symmetricalfilm. The above equation holds true for a curved film only if the effect of the line tension is neglected. In this treatment we assume the effect of the line tension to be negligible, which is reasonable, since the size of the drops is larger than 100 pm and the film radii are of the order of 30pm. Thus, the value of the totalfilm contact angle, (rh (see Figure 81, is sufficient to determine the film excess energy, of symmetric films. The angle a h is easily determined (and fairly accurately) using purely optical techniques such as those of Princen and Frankells and Schel~dko.'~ In the case of asymmetric films, the independent determination of angles cy1 and cy2 cunnot be made from purely optical measurements. Additional information of the exact shapes of the two meniscuses around the threephase contact line is needed. A technique which we had developedm earlier, for foam films, is ideally suited for asymmetricfilms. In this technique,the Laplace equations for the drop/bubble surface and the meniscus are integrated to obtain the shapes of the two surfaces. The Laplace equations are used in conjunction with the information obtained from the common interference fringes (Newton rings) that are observed in the threephase contact region, to obtain the exact profiles of the drop surfaceand the meniscus and, subsequently,the three phase contact angles, 4, and $, (shown in Figure 7). Meaeumment of the Contact Angles. Figure 9 shows a detailed section of the three-phase contact region of the drop. In this case, the contact angles are defined for a film having a finite thickness, unlike the treatment in ref 20 where the angles are determined for films of zero thickness. The three main angles are qC,4, and 6. The angles a1 and a2 are related to the former angles by a1 = dc-6
=w,
(8) Determination of the Angles & and rLC. The angles $c and 4, are determined from the common interference pattern (Newton rings) using the procedure described in ref 20 with slight modifications. Figure 9 shows the definitions of the angles at the three-phase contact region of a film with a finite thickness, h. The technique in ref 20 extrapolates the film meniscuses till they meet (point a2
(18)Princen, H.M.;Frankel, S . J. Colloid Interface Sci. 1971,36,386. (19) Scheludko, A. Adu. Colloid Interjace Sci. 1967, I, 391. (20) Lobo, L. A.;Nikolov, A. D.; Dimitrov, A. S.; Kralcheveky, P.A.; Wasan, D.T.Langmuir 1990,6,996.
Langmuir, Vol. 9, No. 7,1993 1673
Mechanisms of Aqueous Foam Stability
d2
-=-tanom d.2
...
* .
water
(11)
om is the angle made by the normal to the meniscus and the vertical. The other variables remain the same as before except that they relate to the properties of the air-water phases rather than the oil-water phases. At point A the contact angles 42 and $2 are determined using the followingtwo equations: The first equation was derived by Kralchevsky et al.22where they obtained an asymptotic solution for the Laplace equation for the meniscus (eq 11).
=. . ..
I
.water
Figure 9. Three-phase contact region of the pseudoemulsion film.
A), and the contact angles &' and #: are defined for a film of zero thickness (point A). The film excess energy can be obtained from either of the two sets of contact angles bY
where 11 is the disjoining pressure and h is the film thickness. Again, the above equations are valid only if the effect of the line tension is neglected. [It is important to mention that the extrapolation procedure may not always result in the intersection of the two meniscuses, and this would occur if W became positive. In that case, the contact angles cannot be defined. In our systems, however, the extrapolation procedure resulted in the intersectionof the two meniscuses.] In Figure 9, the actual boundary of the thick film is at point B, and the measurement technique in ref 20 extrapolates the drop surface and the meniscus by integrating the Laplace equations up to A (zero thickness). The Laplace equation for the drop surface is given by21
where ye = 1.781 072 418 is Euler's number, h, is defined in Figure 7, and r: is the radius of the film after it is extrapolated to zero thickness. The above equation is a truncated form of their asymptoticsolution,and from their error analysis it is seen that it is sufficientlyaccurate for determiningthe contact angles. The second equation was originally proposed by P r i n ~ e nand ~ ~modified by Kralchevsky et aL2* This equation is obtained from the condition of the constancy of pressure at all pointa of the horizontal planes situated in the bulk aqueous and air phases. The hol'izontal planes selected are the one just abovethe film (situated in the bulk air phase) and the one just below the apex of the drop (situated in the bulk aqueousphase). The pressure drop acrossthese two planes along the axis of the bubble ( x = 0) is given by
is the density of the oil phase and Rf is the radius of curvature of the film. The definitions for the notations in the above equation are shown in Figure 7,and the prime refers to the film of zero thickness. The pressure drop acrossthe sametwo horizontal planes, taken at r = OD, is given by pail
(14) hp, -(zc - h,)p,gg - (h, + Rf - (R: - re1211/2 )p,& By equating the two pressure drops, a modified version of Princen's equation is obtained for asymmetric f h sin $: = where R and 2 are dimensionless variables of X and 2 (2 = X/Rb;2 = Z/Rb)and O d is the angle made by the tangent to the drop surface and the horizontal (measured counter clockwise from the horizontal), fld = (Apd)gRb2/ud,where h p d is the differencein the density between the oil and the aqueous phase, Ud is the interfacial tension between the drop phase (=uoIw)and the aqueous phase, and Rb is the radius of curvature of the bottom of the drop. The value of Rb can be calculated from the equatorial radius of the drop, R, using the equation derived by Kralchevsky et aL2' R is directly measured using transmitted light microscopy. The Laplace equation for the meniscus is given by dsino, -=-d2
-sin" R
fflm
(21) Hartland,5.;Hartley, R. Axisymmetric Fluid-Liquid Interfaces; Elsevier Science Publishing Co.: New York, 1976.
[g( 3 + (z, - h,)Ap,g + Rb
where Ape/, is the density difference between the oil and air phases. The values of &', &',h,, and zc can be determined from the integration of the Laplaceequations and by successive approximations between eqs 12 and 15,using exactly the same calculation procedure described in ref 20 (the only difference is that eq 10 in ref 20 should be substituted by eq 15derived above). The value of Rt, in eq 15,is obtained from the differential interference pattem, as discwed later in this paper. (2!2) Kralchevsky,P.A.;Ivanov,I. B.;Nikolov,A. I>. J. Colloidlnterface Sci. 1986, 112, 108. (23) Princen, H.M.J. Colloid Interface Sci. 1968, 18, 178. (24) Kralcheveky,P.A.:Nikolov.A.D.:Ivanov,I.B.J. ColloidInterfoce Sci. 1986, 112, 132.
Lobo and Wasan
1674 Langmuir, Vol. 9,No. 7, 1993 film edge a
b
\
I
1st thickness transition
Figure 10. Thinning pseudoemulsion f i i (a) thick film with dimple, (b) film undergoing stratification, two thickness transitions, and (c) enhanced image of a film undergoing stratification. The film has three discrete thicknesses resulting from the first two transitions.
The radius of curvature of the film, r:, at zero thickness cannot be directly measured from the photomicrographs, when the film has a finite thickness. Thus, the measurement procedure in ref 20 uses the radii of the Newton rings in order to obtain r,'. The Newton rings are formed due to optical interference of the reflected light rays in the region immediately adjacent to the perimeter of the film. By using the equations that satisfy the conditions of optical interference,we obtained information about the variation in the distances between the drop surface and the top meniscus, in this region. The value of r,' is used as a variable, in an iteration procedure which minimizes the square of errors between the distances (between the film menisci) obtained by the integration procedure and the distances obtained from the common interference pattern. For our experimentalmeasurements we used the maxima and minima in the optical interference pattern, such that we could determine the radii of seven Newton rings, which were subsequently used in the minimization procedure. The experimentalvalue of the vertical distance, de, between the film meniscuses, at the point of constructive or destructive interference (ie., along the circumference of the bright or dark Newton rings), is given by de = kX/ 4N,where k = 0, 1,2,3, ...,k increases away from the film perimeter with k = even numbers representing the constructive and k = odd numbers representing the destructive interference patterns. The details of this procedure are also given in ref 20. In order to determine the film excess energy, -W, we need to determine the values of the contact angles, 4, and $, for the film of finite thickness, i.e., at point B. The radius of contact of the film, r,, at point B, can be measured from the photomicrographs with a fair degree of accuracy (=tl pm). In order to compute the angles at point B, the meniscus and the drop surfaces are extended from point A (whose location is determined from the minimization procedure) to point B, by integratingthe respective Laplace equations of the two surfaces. The anglesO d and O m (from eqs 10and 11)of the surfacesat point B are used to obtain $c and 4 c (4, = - Wd; $c Om)* Determination of 8. The angle 8 -is obtained by measuringthe curvatureof the f i i R f ,from the differential interference pattern, seen in Figure 6. By measuring the distances between the parallel stripes in Figure 6, Rf is determined using the following equation, proposed by Nikolov et al.:15
where lk = kX/4, k is the order of interference of the streak (k = 1,2,3, ...,k increases away from the central streak),
X is the wavelength of incident light, d is the shearing distance of the image which depends on the settings on the microscope, and x k is the distance of the kth streak from the central streak (position of zero order of interference). Further details of this measurement technique are given in ref 15. The value of Rf, obtained using the above equation, can be used in eq 15. The angle 8 is calculated by
sin 8 = rJRf Once the vlaues of $, $, and 8 are determined, the angles a1 and cy2 are obtained from eq 8, and subsequently, the film excess energy, -W, is determined using eq 6. Results Film Drainage Observations. The drainage characteristics of the pseudoemulsion film were observed, in reflected light, by submerging the oil drop and allowing it to rise as described in the Experimental Section. The drainage characteristics for the solution of the higher surfactant concentration (4 wt %) are as follows: As the rising oil drop reached the surface, a thick, nonuniform film (with a dimple) was initially formed as seen in Figure loa. The film drained, continuouslyand rapidly, to form a parallel film without the dimple. After the film passed the last minimum in the intensity of reflected light (which correspondsto film thickness h = X / 4 N = 104nm; N is the refractiveindex of the solution),the film stopped thinning momentarily. After this, a spot of brighter intensity appeared at one edge of the film. The spot represented a portion of the film having a smaller thickness than the rest of the film. The distinct borders of the spot indicated that there is a sharp thickness transition within the film. The spot expanded, indicating that the film changed its thickness by a discrete jump. Three such thickness transitionswere observed (eachtime to a lower thickness), after which the film stopped thinning, and the final thickness of the bright film was approximated to about 20 nm. The thickness transitions are shown in Figure lob, where the upper right side of the film is in the state before transitions begin (approximately 8&100 nm). As one traverses from the right to the left of the film, the film thickness decreases sharply in three stages, and the brightest portion of the film representsthe thinnest section of the film. The photograph shows only the first two transitions; the third could not be captured photographically. Figure 1Oc shows a section of a film which is undergoing stratification. The image is enhanced with an image analyzer, to sharpen the contrast between the transitions. Again, these are the first two transitions. For the solution containing 1wt % surfactant, only one such
Mechanism of Aqueous Foam Stability
Langmuir, Vol. 9, No. 7, l S 3 1676
........... ............ V' ......... ............ ............ ...........
1.00 1
ordered structure
-4
mice"eS
YI
0.0.
~~
4
0.50
7
,0.00 (
~
wbs C1215 AE30 1 wbs C1215 AE30
200
100
300
400
Drop Radiue (microne)
Figure 13. Variation of Figure 11. Schematic of the model for stepwise f i b thinning due to the formation of colloid crystal structure.
1.00 -4 wt% C1215 AE30 ww. 1 wt% C1215 AE30
0.00 100
200 300 Drop Radiur (microns)
400
Figure 12. Variation of a1 with drop size.
transition was observed, with the final thickness being approximately the same as that of the film formed from the 4 w t 9% solution. The stepwise film thinning, observed here, is similar to the stratification phenomenon studied by Nikolov et al. (formicellar system^).^ Accordingto the model of Nikolov et al.,%the three step transitions that we observed suggest that an ordered structure of micelles, which initially contains three layers of micelles, is formed within the film. The stepwise thinning was due to the layer-by-layer expulsion of the micelles from the film. Figure 11 schematicallyshows a section of a film which thins in such a stepwise manner. Nikolov et al.= also observed three thickness transitions, for thinning foam films stabilized by the same surfactant, used in this study,at approximately the same concentration (4 w t % ). They found that, upon decreasing the micellar concentration, the colloid crystallike structure was less developed and the total number of thicknesstransitions decreased. The fiidings of this study are consistent with their observations. Measurement of Film Properties. After it stopped thinning, the thermodynamic properties of the pseudoemulsion film were measured, and for each concentration, three different drop sizes were studied. The contact angles a1 and a2 were determined using the calculation procedure described above. The variation of a1 and a2, with the drop size, is shown in Figures 12 and 13, respectively. It is seen that both a1 and a2 increase with an increase in the film or drop size (the film radius, rc, is (26) Nikolov, A. D.; Kralcheveky, P. A.; Ivanov, I. B.; Wasan,D. T. J. Colloid Interface Sei. 1989,133,13. (26) Nikolov, A. D.;Wpan, D. T.;Kralchevsky, P. A.; Ivanov, I. B. In Ordering and Organization in Ionic Solutiona, Proceedinp of Yamada Conferenca XIX, he, N., Sogami, I., Eds.; World Scientific Publishing Co.: Singapore, 1988; p 302.
CYZ with
drop size.
+
related to the drop size, R,as rc2 = (2/3)R44&[(~m Ud)/UmUd]). It is also seen that, at the same film size, the contact angle increases with the decreese in the micellar concentration. The contact angle increases when it gets thinner, due to the larger interaction between the film surfaces. The results in Figures 12 and 13 indicate that the films are thinner when the micellar concentration ie lower, or when the drop size is larger. Effect of Micellar Concentration. Nikolov et d.*3 found that with the increasein micellar concentration the ordering started at an earlier stage of the film thinning process. They also found that, when the initial number of layers is large, the films could stop t b h g while there are still some layers within the film. The reaaon for this can be explained by their model;% the micellar ordering offera an additional componentof the disjoining preamre, which they termed the structural component, Thus, as the number of Iayers increases,thisstructural component also increases, and at some point, the disjoining pressure counterbalances the excesa film pressure at even lnrger film thicknesses. Their results can qualitatively explain thefindingsof thisstudy, which showsthat the equilibrium films are thicker at higher micellar concentrations. Effect of Film Size. Kralchevsky et al." p r o w a mechanism for the formation and expansion of the spota, which represents the transitions, from one thickness to the next. The colloid crystal structure is postulated to have a number of defeds or vacancies in it, and the concentration (number per unit volume) of vacanciee increases with the decrease in the micellar concentration. Since the structure is formed in the liquid fikn, theae vacancies are in a dynamicconditiondue to the movement of the micelles within the structure, and consequently, the vacanciesare said to 'diffuse" (itis actuallythemicelles that diffuse). According to their model, a spot is formed, in the f b , by the diffusing vacancies condensing (or meeting) at one point. They showed that, in order for thia spot to expand and the thickness transition to occur,the total number of vacancies should be greater thana critical value. At a given micellar concentration,the total number of vacancies is proportional to the size of the film, and thus, if the thickness transition is to occur, the size of the film should be greater than a critical value. If the film size is below this value, the thickness transition will not occur and the film will remain in equilibrium a t ita thicker state. Nikolov et al.= showed, experimentally,that, at a constant micellar concentration in the bulk, as the size of the film was decreased it stopped t h h i n g at a higher (27) Krqlchevaky, P. A.; Nikolov, A. D.; Wasan,D. T.; Ivauov, I. B. Langmir lWH), 6,1180. (28) Nikolov,A. D.;Wasan,D. T. Surface ForceBalancefor F h with Fluid Interfacee. Paper presented at the Artnd Meeting of AI-, Chicago, 1m.
Lobo and Wasan
1676 Langmuir, Vol. 9, Nu. 7, 1993 0'015
1
-4
WM
n+n 1 wt%
C1215 AE30 C1215 AE30
1
-0.010
F 7 0.005
s
.
.
0
0
1
0.000
100.0
200.0 300.0 400.0 Radiue of drop (microne)
Figure 14. Variation of the excess film energy with drop size.
equilibrium thickness with an increasing number of micellar layers remaining inside the stable film. The results of Figures 12and 13showthat, at the same micellar concentrations, the smaller sized films have a smaller contact angle, implying thicker films, which is also consistent with their findings. Film Excess Energy. The contact angles obtained were used to calculate the film excess energy according to eq 6, which is plotted in Figure 14. This f i e shows, qualitatively, the same trend as the contact angle measurements. The small value of the film excess energy, which implies a thicker film,decreaseswith the increasing micellar concentrationas well as with decreasingfilm area. NikoIov et al.25 have made theoretical estimates of the film excess energy, for anionic surfactant system, when there are different numbers of layers in the film. They found that every stage of the film (i.e., film with three layers, two layers, etc.) represents a metastable state and a thickness transition occurswhen the system moves from one metastable state to the next. They calculatedan excess energy associated with each of these metastable states taking into account the film surface interactions as well as the structural component of the disjoining pressure that arises due the ordered micellar structure. Thus, when the thicknessof the film pasees through severaltransitions, the total excess energy is given by the sum of the excess energy for each of those metastable states. If the film stops thinning before all the micellar layers are expelled, some of the metastable states will be missing and the total excess energy of the film will be less than that if the film had thinned completely. Thus,it is seen that when the area of the film is decreased, the f i i excess energy is lower, and this indicates that the smaller films have not thinned completely because some part of the micellar structure still remains in the stable films. A similar argument can be drawn for the effect of micellar concentration, although the total number of layers in the initial structure may be smaller. In the case when we have micellar structuring, the film excess energy is given by
S,:"n,,
dh + ... (18)
where is the disjoining pressure due to surface interactions (steric forces in the case of nonionic surfactants), avw is due to the van der Waals forces, and u, and u,,-1 are the structural components of the disjoining pressure where the subscripts refer to the number of micellar layers present in the f i between transitions in thickness, which are given by the limits of the respective
integrals. AB mentioned above, the transition from one thickness to the next is dependent on the film area. Consequently, the film excess energy w(h)is a function of not only the intensive propedies of the system (temperature and concentration) but also an extensive property (film area). This fact differentiates these f i (films stabilized by a micellar structure) from the films at surfactant concentrations below the cmc. In the latter case, the disjoining pressure isotherm is continuous with film thickness, as in the case predicted by the DLVO theory, and the film excess energy w(h), which is also continuous, is only a function of the intensive properties of the system. Thus, for our system, due to the fact that we have stratification, each point in Figure 14 is unique to a film of a given area and represents the energetics of the finalstate of the film. The points in Figure 14are not connected because we have not determined, in a continuous manner, how the film excess energy changes with a change in film area. For this reason also, we cannot use eq 18 to determine the structural components of the disjoining pressure, from the data in Figure 14. Table I1 shows the various measured and calculated properties of the pseudoemulsion film for the two concentrations tested. It is important to point out that when the f i area decreaseswith decreasingdrop size,the excess film pressure,Pf,increases simultaneowly. The increasing excessfilm pressure and the decreasing film area have two opposing effecta on the film drainage. The excess film pressure, Pf(given by eq 21, is the difference between the pressures in the film and the meniscus and represents the driving force for film drainage. At high excess film pressures, the driving force for film drainage is higher,29 which tends to drive the film to a lower equilibrium thickness. However, at the same time, as the film area decreases, the total number of vacancies in the colloid cryetal structure reduces-according to the model of Kralchevsky et aL2' Consequently, the expansion of the spotsin the film (or the transition to a lower film thickness) takes a longer time to occur. Additionally, as discueeed earlier, the thickness transition may not even occur below a critical film area, which will result in a higher value of the structural component of the disjoiningpressure. Thus, when the drop size (and the film size)is reduced, the effect of the increasing excess film pressure is to drive the film to a lower thickness,while the effect of an ordered micellar structure is to stop the films from thinning. The resulta in Table 11 show that the excess energy of the films is smaller for the smaller drops-indicating thicker films-which implies that the stabilizing effect of the micellar structuring overwhelms the effect of the excess film pressure. Summary It isshown that the classical understanding, whichuses the spreadingand enteringcoefficientswithoutaccounting for the presence of the pseudoemulsion f i , does not represent the complete physical picture of the behavior of oil drops in a foaming system. AB a result, it may not accurately predict the effect of oil on foam stability. Our previous studies2J7with the same surfactant-oil system (C1215 A E 3 h t a n e ) show that t h d oil drops do not destabilize the foam even though the entering and spreading coefficients are positive. In fact simple bottle tests showed that, upon the introduction of oil drops (17 vol %) to the system, the foam stability increased from 2.5 to over 10 h. The mechanism of foam stabilization by (29) Ivauov, I. B. Pure Appl. Chem. 1980,62, 1241.
Langmuir, Vol. 9, No. 7,1993 1677
Mechanism of Aqueous Foam Stability
Table 11. Propertier of the Pneudoemulrion Film for the C1216 AE3Octane Syrtem surfactant concn (wt %)
1.0 4.0
R (10' cm)
r, (10' cm)
film area (10' cm)
II = Pf(dyn/cm2)
ai (deg)
a2 (deg)
368.2 277.6 241.7 267.0 275.6 156.4
72.25 42.87 32.40 69.7 40.32 14.23
1.64 0.58 0.33 1.52 0.51
448.7 596.3 W.6 469.8 699.6 1056
2.38 2.13 1.68 1.85 1.45 1.37
0.45 0.46 0.37 0.34 0.3 0.31
0.064
the oil drops, in this system, is discussed in ref 17. Thus, for this particular system,the classicaltheories incorrectly predict the effect of oil on foam stability. While the surface energies are a useful measure of the tendency of the oil to destabilizea foam, they cannot, as seen fromthe qualitative observations of the pseudoemulsion f i i s , be used for absolute predictions because they fail to predict the configuration of the oil drop at the air-water surface. The reason for this, as mentioned earlier, is that while the entering and spreading coefficients are necessary conditions, they are not sufficient to predict the entering and spreadingof oil drops at the +water surfaces. In addition to the surfaceenergies, thestability of the pseudoemulsion film should also be considered since it is the main factor that determines if the oil drop can or cannot enter the ail-water surface. The f i i drainage studies with the C1215 AE30-0ctane system revealed, for the first time, the presence of an ordered structure of micelles in the pseudoemulsion film. The concentrations used in these studies were 300-1300 times greater than the critical micelle concentration. As a result the f i exhibited three layers of micelles at the higher concentration (4 wt %) and one layer at the lower concentration (1 wt %). When the pseudoemulsion films reach an equilibrium film thickness, they are said to be stable, and a relative measure of their stability is the value of the film excess energy. When the excess energy is small, the films are relatively thick and more stable, and when the excess energy is large, the films are relatively less stable. The
-w X 102 (erg/cm2)
1.01
0.84 0.53 0.6 0.39 0.36
f i i excess energy can be determined from the contact angle measurements. Due to the asymmetric nature of the pseudoemulsion film, the contact angle cannot be determined from pure optical measurements and, in addition to these, the exact shape of the f i meniscuses should be known. We have adopted the measurement technique describedin ref 20 to study the pseudoemulsion film properties. Thistechnique usesthe informationfrom common interferometry (Newton ring@ and differential interferometry in conjunction with the Laplace equation for the film meniscuges,in order to obtain the exact shape of the meniscuses and the contact angles. The values of the contact angle and the excess f i i energy were used to evaluatethe role of the micellar structuring in the stability of the pseudoemulsion film. We found that, due to the stabilization by micellar layering, the film stability was promoted by a higher micellar concentration. It was also found that smaller drops had a film with a lower excess energy and were, therefore, more stable. Thie result is consistent with the findingsof Nikolovet ale3Thus,when micelhr stabilization is operative, the relative stability of the pseudoemulsion film is higher for the small drop sizes.
Acknowledgment. This study was funded in part by grantsfrom Kraft GeneralFoods, Inc., the National Science
Foundation, and the Department of Energy. The authors gratefully acknowledge the assistance provided by Dr. A. D. Nikolov.
