Adsorption and Coalescence in Mixed-Surfactant Systems: AirâWater

Ind. Eng. Chem. Res. 2010, 49, 1711–1724

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Adsorption and Coalescence in Mixed-Surfactant Systems: Air-Water Interface G. Suryanarayana and Pallab Ghosh* Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati - 781039, Assam, India

Mixtures of ionic and nonionic surfactants have a wide range of industrial and household applications. The properties of the monolayer formed by such systems at the air-water interface depend on the interactions between the surfactants. The presence of salt influences the interactions between the surfactants in the monolayer as well as in the micelle. In this work, these interactions in the presence and absence of a 1:1 salt were studied using nonideal solution theory. An anionic surfactant, a cationic surfactant, and a nonionic surfactant were used. The stability of foams was significantly affected by the interactions between the surfactants. To study this effect, the coalescence of air bubbles in the mixed-surfactant systems was studied and compared with that in the corresponding single-surfactant systems. The effect of salt on the coalescence time was also studied. The results were analyzed using the film drainage and stochastic theories of coalescence. Seven film drainage models were employed to predict the coalescence time, and the values predicted by these models were compared with the experimental data. The parameters of the stochastic model were analyzed based on the properties of the systems. Introduction Bubbles in aqueous solutions have been the subject of numerous studies. This is due to the fact that bubbles play a very important role, sometimes inconspicuously, in many industrial and biological processes. Often, the presence of gas bubbles is useful (e.g., heavy-metal ions can be efficiently removed from wastewater stream using gas bubbles). However, at times the presence of bubbles can be undesirable (e.g., the presence of gas bubbles affects the quality of the finished products in photographic and paper applications). The understanding of bubble growth, stability, and coalescence is crucial in many of these processes. Thus, a sound understanding of bubbles in aqueous solutions is essential not only from a fundamental viewpoint but also from an economic perspective. The adsorption of surfactants at the air-water interface is a very important factor in determining the stability of foams. Surfactant molecules adsorb at the air-water interface and prevent rupture of the thin liquid film trapped between the bubbles. This prevents the coalescence of the bubbles. Some of the common occurrences of foams are in environment and meteorology (e.g., polluted river foams and foam in the oceans), foods (e.g., champagne, soda and beer heads), geology, agriculture and soil science (e.g., fumigants and insecticide blankets), materials science (e.g., foam fractionation), biology and medicine (e.g., contraceptive and gastrointestinal foams, gas aphrons), petroleum production and mineral processing (e.g., refinery foams, mineral flotation froth and fire-extinguishing foam), and home and personal-care products (e.g., shampoos). In most practical applications, a mixture of surfactants, rather than a single surfactant, is used. In some cases, this is involuntary, because commercial surfactants are mixtures of surface-active materials as a result of the inhomogeneous raw materials used in their manufacture. In many cases, different types of surfactants are purposely mixed to improve the properties of the final product. When different types of surfactants are purposely mixed, what is usually sought is synergism (the opposite effect is known as antagonism or negative synergism). Synergism is the condition in which the properties * To whom correspondence should be addressed. E-mail: pallabg@ iitg.ernet.in. Tel.: +91.361.2582253. Fax: +91.361.2690762.

of the surfactant mixture are better than those attainable with the individual surfactants by themselves. For example, a longchain amine oxide is often added to a formulation based on an anionic surfactant because the foaming properties of the mixture are better than those of either surfactant by itself. Synergism can be quantified in various ways. For example, synergism exists when a mixture of two surfactants at its critical micelle concentration (CMC) reaches a lower surface tension value than that attained at the CMC of either individual surfactant. We refer to this type of synergism as type I synergism. Another type of synergism is manifested when a given surface tension can be attained at a total mixed-surfactant concentration lower than the concentration required of either surfactant by itself (type II synergism). Finally, type III synergism refers to the situation in which the CMC of any mixture of two surfactants is smaller than that of either individual surfactant. The criteria to be fulfilled for these three types of synergism to be exhibited have been described by Rosen.1 Inorganic salts play a very important role in the adsorption of ionic surfactants.2,3 Sometimes, the salt is inherently present in the system, and sometimes, it is added by the user to enhance the desired effect of the surfactant. Salts can markedly alter the adsorption characteristics of surfactants. Salts containing divalent and trivalent ions (e.g., MgCl2 and AlCl3) are more effective in enhancing the surface tension reduction efficiency of ionic surfactants than salts containing monovalent ions (e.g., NaCl). Enhanced electrostatic screening in the double layer and decreased repulsion between the surfactant ions have been suggested as likely reasons for this behavior.4 Apart from the ionic strength of the solution, the effect of binding of the counterions is also very important.3 The synergism in ionic-ionic and ionic-nonionic surfactant mixtures is strongly influenced by the presence of electrolytes.5 The coalescence of air bubbles is greatly influenced by the types and concentrations of surfactant and salt present in solution.2,3,6,7 In aqueous solutions, the main factors that determine the coalescence time are the surface excess concentration of the surfactant and the repulsive surface forces such as the electrostatic double-layer, hydration, and steric forces. The electrostatic double-layer repulsive force is quite sensitive to the concentration of salt in the solution. With increasing

10.1021/ie9012216  2010 American Chemical Society Published on Web 01/07/2010

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Ind. Eng. Chem. Res., Vol. 49, No. 4, 2010

concentration of salt, the surface excess concentration increases, whereas the electrostatic double-layer repulsion between the two air-water interfaces decreases. At low salt concentrations, the effect of the former phenomenon dominates over the latter, and the coalescence time of bubbles increases with increasing salt concentration. On the other hand, at high salt concentrations, the reduction in electrostatic double-layer repulsion becomes a significant factor, which causes rapid coalescence of the bubbles. For some surfactants (e.g., quaternary ammonium halides), the aqueous film is very stable even at high salt concentrations.8-10 The repulsive hydration force is believed to prevent the bubbles from coalescing in solutions of such surfactants. Only a few studies have reported the effects of inorganic salts on the synergism in binary mixtures of ionic and nonionic surfactants. On the other hand, hardly any work has been reported in the literature on the coalescence of bubbles in mixedsurfactant systems. Based on these observations, the present study had two major objectives. The first objective was to study synergism and the effect of an inorganic salt on it in binary mixtures of surfactants. An anionic surfactant (i.e., sodium dodecyl sulfate), a cationic surfactant (i.e., cetyltrimethylammonium bromide), and a nonionic surfactant (i.e., Tween 20) were used in the present study. The interaction parameters in the monolayer and in the mixed micelle were determined, and the conditions for synergism were evaluated. The second objective was to study the coalescence of air bubbles at a flat air-water interface in these surfactant solutions. The coalescence time distributions were fitted using the stochastic model developed by Ghosh and Juvekar.11 The significance of the model parameters was analyzed. The mean values of the coalescence time distributions were compared with the values predicted by seven film drainage models given by Slattery.12 General Theory Interactions in the Mixed-Surfactant Monolayer and in the Micelle. Theoretical investigations of the interactions between surfactants in the monolayers and micelles formed by mixed surfactants have been performed since the early 1980s. Rosen and Hua13 developed a procedure based on nonideal solution theory for the quantitative estimation of the interactions between two different surfactant molecules in a mixed-surfactant system. Let us consider a mixture of two surfactants, designated by the subscripts 1 and 2. The mole fraction of surfactant 1 in the mixed monolayer (x1) can be calculated by solving the equation x12 ln (1 - x1) ln 2

( ) [ ] C1

x1C01 C2

)1

(1)

(1 - x1)C02

where C10 and C20 are the solution-phase concentrations of pure surfactants 1 and 2, respectively, and C1 and C2 are the corresponding solution-phase concentrations of these surfactants in their mixture, required to produce a given value of surface tension. The molecular interaction parameter (βσ), which is a measure of the deviation of the mixture from ideality and indicates molecular interactions between surfactants 1 and 2 at the aqueous solution-air interface, is given by

( )

ln βσ )

C1

x1C01

(2)

(1 - x1)2

In deriving eqs 1 and 2, the ratios of the activity coefficients of the surfactants in the mixture and in pure form in the solution have been assumed to be unity. This assumption is justified for the present work because the concentrations of the surfactants in the solutions were very small ( ln

C0,CMC C0,M 1 2 C0,CMC C0,M 2 1

Table 1. Film Drainage Models for the Coalescence Time of Bubbles equation for coalescence time tc1 ) 1.07

)|

(6)

where C10,CMC and C20,CMC are the concentrations of surfactants 1 and 2, respectively, required to yield a surface tension equal to that of a mixture of the two surfactants at its CMC. These quantities are determined by extrapolation of surface tension versus concentration profiles of the pure surfactants as described by Rosen.1 Coalescence of Air Bubbles at a Flat Air-Water Interface. Two theories for the coalescence of bubbles have been proposed in the literature: film drainage theory12,17,18 and stochastic theory.11,19-21 Almost all works reported in the literature until 2002 used the film drainage theory. A review of most of these works has been presented by Chaudhari and Hofmann.18 Slattery12 presented seven film drainage models for the prediction of coalescence times in surfactant systems. These models are listed in Table 1. They correlate the coalescence time (tc) with the physical properties of the system such as the density difference between the liquid and the gas (∆F), the surface tension (γ) and viscosity of the solution phase (µ), and the radius of the bubble (a). The equations presented in Table 1 were developed for the buoyancy-driven coalescence of a bubble at a flat gas-liquid interface. Several assumptions were made in their development, as follows. The two interfaces bounding the draining liquid film were assumed to be axisymmetric. The deformation of the flat interface was assumed to be small. The bubble was assumed to be small such that the Bond number (≡ ∆Fga2/γ) was much smaller than unity. Thus, the deformation of the bubble was assumed to be negligible. The Reynolds lubrication approximation was applied. It was assumed that the surfactant molecules adsorbed at the air-water interface such that the resulting interfacial tension gradients were sufficiently large and the tangential components of the velocity were zero. The effects of mass transfer were neglected. The film liquid was assumed to Newtonian. All inertial effects were neglected. The effects of the electrostatic double layer and other repulsive forces in the thin film (such as hydration or polymeric steric forces) were neglected. Nonetheless, the van der Waals

µa3.4(∆Fg)0.6 γ1.2B0.4

tc2 ) 0.705

based on the model of Chen et al.22

µa3.4(∆Fg)0.6 γ1.2B0.4

tc3 ) 1.046

tc4 ) 0.37

µa4.5∆Fg γ1.5B0.5

Mackay and Mason23

µa4.5∆Fg γ1.5B0.5

tc5 ) 5.202

(5)

and

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µa1.75 γ B

0.75 0.25

tc6 ) 0.79

µa4.06(∆Fg)0.84 γ1.38B0.46

tc7 ) 0.44

µa4.06(∆Fg)0.84 γ1.38B0.46

Hodgson and Woods24

Slattery12

attraction between the fluid surfaces was taken into account. An interesting aspect of these models is that they predict widely different values of coalescence time even for the same system. Some works on film drainage theory have suggested that the surface shear and dilatational viscosities play an important role in the coalescence process.17 However, these models do not give explicit expressions for coalescence time that can be used to compare the experimental data with the values predicted by these models. Jeelani and Hartland25 presented a film drainage model incorporating the effect of the surface tension gradient. However, there is hardly any method by which the value of the surface tension gradient can be predicted. Moreover, the values calculated from the coalescence time data by such models indicate that the values of the surface tension gradient can vary over a wide range. Therefore, although this model gives an explicit expression for coalescence time, it cannot be used to predict coalescence times. Nikolov and Wasan26 proposed that the thermodynamic stability of the thin liquid film determines the coalescence time. According to this theory, the thin liquid film ruptures because of the growth of instabilities that are caused by thermal fluctuations or mechanical perturbations. A film can rupture if a hole is spontaneously formed by the fluctuations in the film. The activation energy required to form such a hole is ∼γhc2, where γ is the surface tension and hc is the critical film thickness. The value of hc is usually greater than 10 nm.27,28 Thus, the quantity γhc2 is generally greater than the thermal energy kT (where k is the Boltzmann constant and T is the temperature). Therefore, this mechanism cannot explain the rupture of the film caused by the formation of a hole. Vrij and Overbeek29 suggested that the fluctuations can corrugate a deformable interface and that, in certain cases, the van der Waals force can be strong enough to cause thermodynamic instability in the film.

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Figure 1. Illustration of the surface diffusion process during the resting of an air bubble at a flat air-water interface. The figure shows the regions on the air-water interface where the surfactant concentration is depleted and the regions where the surfactant molecules are concentrated. The radius of the barrier ring is Rb, and the thickness of the thin aqueous film at the barrier ring is hr.

They developed an equation for the critical film thickness, which is given by26,28,29 hc ) 0.267

(

afAH2 6πγ∆p

)

1/7

(7) F(τR) )

where af is the area of the film, AH is the Hamaker constant, and ∆p is the excess pressure in the film. The mean time of film rupture is then given by τ¯ ) 96π2µγhc5 /AH2

dimple can flatten to some extent with time. Because the thickness of the film is at a minimum at the barrier ring, the repulsion between the bubble and the flat interface is largest in this region. When the bubble strikes the flat interface with a high velocity, it undergoes an up-and-down motion along with the interface, which is the characteristic of an underdamped system.11 The bubble comes to a rest position after the up-and-down motion ceases. The surfactant molecules diffuse back toward the center of the film driven by a concentration gradient, as depicted in Figure 1. This reduces the concentration of surfactant at the barrier ring, which leads to a reduction in the repulsive force. When the repulsion diminishes, the bubble comes closer to the interface. At a certain point of separation, the thickness of the thin film at the barrier ring becomes very small, and the film becomes unstable. At this point, the van der Waals attraction between the two surfaces exceeds the repulsive force, resulting in coalescence. From this description, it is apparent that coalescence is likely to occur at the barrier ring, which has been supported experimentally.24,31 Based on this physical description of the coalescence process, the following expression for cumulative distribution of coalescence time was developed by Ghosh and Juvekar11

(8)

where µ is the viscosity of the film liquid. Equation 8 indicates a dramatic dependence of mean rupture time on the critical film thickness. It also indicates that a film should rupture very rapidly when its thickness becomes less than ∼50 nm. It has been observed experimentally that the coalescence times of bubbles and drops do not have a single value even under identical experimental conditions (i.e., same size of bubbles and constant temperature), but that a wide distribution is omnipresent.6,11,21,30 To explain this finding and to explain some other observations that cannot be explained by film drainage theory (e.g., the effects of surfactants and salts on coalescence time), the stochastic model of coalescence was proposed by Ghosh and Juvekar.11 In this theory, the variation in coalescence time is attributed to the variation in the surface excess concentration of the surfactant at the air-liquid interface. The distribution of surface excess concentration was assumed to be Gaussian. The variation in surface excess is mainly caused by the hydrodynamic fluctuations in the region of contact where the bubble strikes the flat interface with a high velocity. This theory is concerned with the surfactant distribution in the thin liquid film trapped between the bubble and the interface. When the bubble approaches the interface with a high velocity, the thin liquid film trapped between the bubble and the interface drains rapidly. During the drainage of the film, the surfactant molecules, which were adsorbed on the two air-water interfaces, are swept toward the rim of the film, known as the barrier ring (see Figure 1). The stress can be so large that the surfactant molecules are likely to form a liquid-condensed (LC) phase. Ionic surfactants exert electrostatic repulsion between the surfaces, and nonionic surfactants exert a steric repulsive force that repels the bubble from the flat interface. During the approach of the bubble, a dimple forms in the film such that the thickness of the film is a maximum at the center and a minimum at the periphery. The

[{ [

1 1 erf 2 SΓ√2

PΓ ∞

(1 +

]}

-1

∑e

-λi2τR

)

i)1

+ erf

]

( ) 1 SΓ√2

(9)

In deriving eq 9, the curvature in the film (due to the presence of the dimple) and the nonuniformity in its thickness were ignored for simplicity. In eq 9, erf(x) represents the error function and λi represent the zeros of the Bessel function of first kind and order one (J1). τR is the dimensionless coalescence time, defined as τR ) t/tj, where jt is the characteristic diffusion time, which is given by jt )

Rb2 DΓ

(10)

The characteristic diffusion time is usually much longer than the coalescence time because coalescence occurs long before the entire surfactant buildup at the barrier ring is depleted to the initial uniform concentration. DΓ is the mean surface diffusivity of the surfactant molecules. Agrawal and Neuman32 presented the values of surface diffusivity for many surfactants at various states of the monolayer (e.g., gaseous, liquid-expanded, and liquid-condensed states). The radius of the barrier ring, Rb, can be estimated from the equation given by Princen33 Rb ) 2a2

∆Fg 3γ

(11)

where a is the radius of the bubble, ∆F is the density difference between the liquid and gas phases, g is the acceleration due to gravity, and γ is the surface tension. This equation was derived considering the buoyancy-induced deformation of a bubble on a flat deformable air-water interface. During the period in which the bubble rests at the interface, the barrier ring could expand or shrink. However, the stochastic model of Ghosh and Juvekar11 does not take into account this possibility. Therefore, Rb remains constant with time. PΓ is the dimensionless coalescence threshold, which is given by


PΓ )

Γm a ) RΓ¯ (wbfrR)Γ¯

∆Fgγ 3

(12)

where Γm represents the minimum value of surfactant concentration j is the at the barrier ring required to prevent coalescence and Γ mean value of the surface excess distribution in the film. R represents the fraction of surfactant molecules that remain at the barrier ring after the bubble strikes the flat interface; wb is the width of the barrier ring; and fr is the repulsive force generated by one mole of the adsorbed surfactant molecules, which depends on the type of surfactant used and can be affected by the presence of salt in the solution if the surfactant is ionic. Equation 12 was derived by a simple force balance as explained below. Consider a bubble pressed to the air-water interface by buoyancy as shown in Figure 1. It is evident that the bubble is pressed by the force (4πa3/3)∆Fg. This force is balanced by the repulsive force exerted by the surfactant molecules, which acts along the barrier ring. Therefore, the minimum repulsive force required at the barrier ring to prevent coalescence is equal to Γmfr(2πRb)wb. Therefore, at the point of coalescence Γm fr(2πRb)wb ) (4πa3 /3)∆Fg

(13)

Substituting Rb from eq 11 and using the definition of PΓ ≡ j ), eq 12 is obtained. Γm/(RΓ To achieve a finite coalescence time, RΓ should be less than Γm. As RΓ f Γm, τR f ∞. This means that bubbles for which RΓ g Γm will never coalesce. The reason is that, if the bubble rests at the interface for infinite time, then the quantity of surfactant that was initially concentrated at the barrier ring will spread uniformly over the entire film and the concentration of the surfactant will be RΓ everywhere, including the barrier ring. Therefore, for all finite times, the concentration at the barrier ring Γ(Rb) will be greater than RΓ. Thus, RΓ g Γm implies that Γ(Rb) will be greater than Γm at all times. Hence, those bubbles for which this condition is satisfied will never coalesce. Such a situation can arise in the case of very small bubbles and also when water-soluble polymeric surfactants are present. Therefore, for finite coalescence times, the value of PΓ must be greater than unity. In eq 9, SΓ is the normalized standard deviation in surface excess, which is defined as SΓ )

σΓ Γ¯

(14)

The value of SΓ usually lies between 0.1 and 0.5, depending on the breadth of the distribution. Therefore, this model has two unknown parameters, PΓ and SΓ, that can be obtained by fitting eq 9 to the experimental coalescence time distributions. The variation of PΓ with the physical properties of the system can be explained from eq 12. The fit of the stochastic model to the experimental distributions of coalescence time of bubbles has been good.2,3,6,7,19-21 The variation of the dimensionless coalescence threshold (PΓ) with bubble size, surface tension, surface excess concentration, and surface forces was explained in these works semiquantitatively. Experimental Section Materials Used. The anionic surfactant sodium dodecyl sulfate (SDS, C12H25SO4Na) was obtained from Sigma-Aldrich (Bangalore, India). It had >99% purity. The cationic surfactant cetyltrimethylammonium bromide (CTAB, C19H42NBr) was obtained from Merck (Darmstadt, Germany). It had >99% purity.

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Tween 20 (polyoxyethylene sorbitanmonolaurate, C58H114O26) having >99% purity was obtained from Merck (Mumbai, India). Sodium chloride was obtained from Merck (Mumbai, India). It had 99.5% purity. All of the surfactants and the salt were used as received from their manufacturers. The water used in this study was purified with a Millipore water purification system. Its conductivity was 1 × 10-5 S/m, and the surface tension was 72.5 mN/m (298 K). Experimental Conditions. All experiments on surface tension measurements and coalescence were carried out in an airconditioned room where the temperature was maintained at 298 K. The variation of temperature in the room was within 0.5 K. Neither surface tension nor coalescence time was found to be affected by this small fluctuation in temperature. Measurement of Surface Tension. Surface tension was measured using a computer-controlled tensiometer [Kru¨ss (Hamburg, Germany), model K100, precision ) 0.01 mN/m]. The Wilhelmy plate method was used to measure surface tension. The sample vessels and the plate were methodically cleaned before each measurement, following the equipment manufacturer’s instructions, with chromic acid, acetone, and Millipore water. The platinum plate was burned to red-hot conditions in the blue flame of a Bunsen burner. The sample vessel was moved with a very low speed (∼200 µm/s) during the measurements. The entire range of surfactant concentration under study was divided into several intervals. This enabled us to detect subtle changes in surface tension accurately. The surfactant solutions were prepared by dissolving the surfactant in water and subsequently diluting the stock solutions. The values of surface tension measured by the procedure mentioned above were highly accurate and reproducible. Study of Coalescence of Bubbles at the Air-Water Interface. The bubble coalescence time was studied in a specially designed coalescence cell made of glass (manufactured by Schott Duran, Mainz, Germany). The diameter of the cell was 10 cm. The details of this cell were described by Giribabu et al.2 The vessel had a hole on its wall near the bottom where a Teflon-coated rubber septum was fixed. Air bubbles were formed by a syringe inserted through the septum. Because the surface tension was kept constant by appropriately choosing the surfactant and salt concentrations, the size of the bubbles remained constant. The bubbles were released 5 cm away from the flat air-water interface. After the bubble struck the flat air-water interface, an up-and-down motion similar to that reported by Ghosh and Juvekar11 was observed. The time during which a bubble rested on the flat air-water interface (i.e., the coalescence time) was measured by a digital video camera [Sony (Tokyo, Japan), model DCR-HC32E, optical zoom ) 20×]. It had a timer with a resolution of 0.1 s fitted with it. The time count began as soon as the bubble struck the flat air-water interface. In some cases, especially at low surfactant and salt concentrations, some bubbles coalesced as soon as they struck the interface, which we call instantaneous coalescence. After a bubble coalesced, the next bubble was released after the visible disturbances at the flat interface had subsided. Coalescence times of 100 bubbles were studied in each experiment. The size of each bubble was determined by image analysis. Photographs of the near-spherical bubble were taken when it was about to be released from the tip of the syringe. The radius of the bubble corresponds to its spherical shape. Results and Discussion Adsorption at the Air-Water Interface. The adsorption of surfactants at the air-water interface was studied based on

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Figure 2. Variation of the surface tension with the concentration of surfactant for SDS, CTAB, and Tween 20 in the absence of salt.

Figure 3. Variation of the surface tension with the concentration of surfactant for SDS, CTAB, and Tween 20 in the presence of 100 mol/m3 sodium chloride.

the surface tension versus surfactant concentration curves. In mixed-surfactant systems, the concentration of one surfactant was fixed. The interaction parameters for the monolayer and the micelle were determined from these surface tension profiles. The surface tension profiles of the aqueous solutions of the single surfactants are shown in Figure 2. It can be observed from this figure that the critical micelle concentrations of the surfactants used in the present study varied over a wide range (e.g., the CMCs of sodium dodecyl sulfate, cetyltrimethylammonium bromide, and Tween 20 are 8, 1, and 0.05 mol/m3, respectively). These results agree well with the results reported in the literature.2,19,34,35 The strong effects of inorganic salts on the surface tension profiles of aqueous solutions of ionic surfactants are welldocumented in the literature.1,2 The effects of salt on the surface tension profiles of single surfactants are shown in Figure 3. Surface tension was found to decrease significantly in 100 mol/ m3 NaCl solution. The CMCs also decreased significantly in the presence of NaCl. For example, the CMC of aqueous CTAB solution decreased to 0.07 mol/m3 at 100 mol/m3 concentration of NaCl. A similar large reduction in CMC was observed for SDS as well. These results agree well with the data reported in the literature.3,7,35 The effect of salt on the enhancement in surfactant adsorption (and hence reduction in surface tension) is mainly due to the reduction in the electrostatic double-layer repulsion between the charged headgroups of the surfactant molecules. This favors more adsorption of the surfactant molecules at the air-water interface. However, the effect of

Figure 4. Variation of the surface tension with the concentration of SDS at different concentrations of Tween 20, in the absence of sodium chloride.

salt on the nonionic surfactant Tween 20 was insignificant because of the absence of any significant electrostatic interaction. The surface tension profiles for the Tween 20-SDS binary mixed-surfactant system are shown in Figure 4. At a particular concentration of SDS, the surface tension decreased with increasing concentration of Tween 20. Apparently, this happened because of the increase in the total concentration of the surfactant in the solution. The value of surface tension at the CMC, γCMC, also decreased upon the addition of Tween 20. The value of γCMC for the binary mixture was found to be lower than the γCMC value of either SDS or Tween 20 (see Figure 2). Therefore, type I synergism was present in this mixed-surfactant system. The concentration of SDS at which γCMC was attained decreased with increasing concentration of Tween 20, which indicates an enhancement in adsorption and an increase in surface coverage. The interaction parameters are presented in Table 2. It can be observed from columns 9 and 10 in this table that the conditions for type I synergism (i.e., eqs 5 and 6) were satisfied. The values of βσ and βM did not change appreciably with the change in surfactant composition of the solution. The average values of βσ and βM were -3.94 and -1.98, respectively (based on 22 compositions studied). These values of the interaction parameters compare well with other mixed-surfactant systems composed of a nonionic surfactant and an anionic surfactant.1 The magnitude of βσ was larger than that of βM, which indicates that the interaction in the mixed monolayer was stronger than the interaction in the mixed micelle. Addition of salt had a very interesting effect on the surface tension profiles of the mixed-surfactant system, which are shown in Figure 5. The same set of concentrations of Tween 20 as in the absence of salt was used in these experiments. The CMCs were attained at much lower concentrations of SDS. As compared to the mixed-surfactant system without salt (see Figure 4), the values of γCMC were significantly lower. In addition, these values were lower than the γCMC values for the single-surfactant systems in the presence of salt (see Figure 3). Therefore, type I synergism was apparent in the presence of salt as well. The values of interaction parameters are presented in Table 2. The average values of βσ and βM were -4.9 and -2.1, respectively (based on 19 compositions studied). Therefore, it is evident that the value of βσ increased in the presence of NaCl in the solution. This finding corroborates the results reported by Rosen and Zhou.14 It has been suggested in the literature36 that the Na+ present in the aqueous solution forms a complex with the polyoxyethylene chain of Tween 20 in the form of an open crown ether and that this gives the nonionic surfactant a positive charge. Therefore, the positively charged unit can have a strong

Ind. Eng. Chem. Res., Vol. 49, No. 4, 2010 Table 2. Interaction Parameters for the Binary Mixed-Surfactant Systems binary surfactant system (with or without salt) Tween 20 (1) + SDS (2) Tween 20 (1) + SDS (2) + 100 mol/m3 NaCl Tween 20 (1) + CTAB (2) Tween 20 (1) + CTAB (2) + 100 mol/m3 NaCl CTAB (1) + SDS (2) CTAB (1) + SDS (2) + 100 mol/m3 NaCl

C1 (mol/m3) C2 (mol/m3) γ (mN/m) 0.010 0.010 0.005 0.005 0.100 0.015

0.98 0.06 0.24 0.02 0.65 0.05

39.0 39.0 38.5 38.5 37.0 37.5

x1

xM 1

βσ

βM

βσ - βM

0.54 0.59 0.42 0.43 0.50 0.58

0.40 0.40 0.26 0.23 0.40 0.44

-3.79 -4.46 -4.11 -3.83 -6.54 -5.32

-1.94 -1.87 -1.79 -1.41 -3.90 -2.35

-1.85 -2.59 -2.32 -2.42 -2.64 -2.97

(

ln

C0,CMC C0,M 1 2 C0,CMC C0,M 2 1

1717

)

0.61 0.28 0.01 -0.07 0.06 0.21

electrostatic attraction with the dodecyl sulfate anion. This effect increases the absolute value of βσ. The attractive interaction offsets the effect associated with the reduction in Debye length surrounding the headgroup of the surface-active C12H25SO4-, which tends to decrease the absolute value of βσ. The surface tension profiles in the Tween 20-CTAB mixedsurfactant system in the presence and absence of NaCl are presented in Figures 6 and 7, respectively. The effects of salt on surface tension and CMC were similar to that observed in the Tween 20-SDS system. The interaction parameters are presented in Table 2. In the absence of salt, the average values of βσ and βM were -4.06 and -1.95, respectively (based on 19 compositions studied). The corresponding values in the presence of 100 mol/m3 NaCl were -3.79 and -1.49, respectively (based on 18 compositions studied). Therefore, the interaction decreased in the presence of salt. Similar observation has been reported in the literature for the binary mixtures of cationic and polyoxyethylene nonionic surfactants.14 The reason for the

decrease in the attraction is the reduction of the Debye length with the increase in the ionic strength of the solution upon the addition of NaCl. Another factor that reduces the attraction is the repulsion between the cationic surfactant and the nonionic surfactant, which acquires a positive charge by complexation with Na+. The surface tension profiles for the CTAB-SDS mixedsurfactant system are presented in Figures 8 and 9 in the absence and presence of NaCl, respectively. From Figure 8, it can be observed that the CMC of the mixed-surfactant system containing 0.05 mol/m3 CTAB was ∼4 mol/m3 SDS, which decreased to 0.5 mol/m3 SDS when the CTAB concentration in the solution was increased to 0.4 mol/m3. The effect of salt on γCMC was spectacular in this system, and γCMC values as low as 30 mN/m were attained. The interaction parameters were larger in magnitude than those for the Tween 20-SDS and Tween 20-CTAB systems (Table 2). The average values of βσ and βM in the absence of salt were -6.4 and -3.9, respectively

Figure 5. Variation of the surface tension with the concentration of SDS at different concentrations of Tween 20, in the presence of 100 mol/m3 sodium chloride.

Figure 7. Variation of the surface tension with the concentration of CTAB at different concentrations of Tween 20, in the presence of 100 mol/m3 sodium chloride.

Figure 6. Variation of the surface tension with the concentration of CTAB at different concentrations of Tween 20, in the absence of sodium chloride.

Figure 8. Variation of the surface tension with the concentration of SDS at different concentrations of CTAB, in the absence of sodium chloride.

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Figure 9. Variation of the surface tension with the concentration of SDS at different concentrations of CTAB, in the presence of 100 mol/m3 sodium chloride.

(based on 21 compositions studied), and the corresponding values in the presence of 100 mol/m3 NaCl were -5.2 and -2.3, respectively (based on 19 compositions studied). Similar observations have been reported in the literature for binary mixtures of cationic and anionic surfactants.5,37 The oppositely charged headgroups of the surfactants electrostatically attract, and the hydrocarbon chains attract by van der Waals and hydrophobic forces. The absolute values of the β parameters decrease in the presence of salt as a result of the weakened electrostatic attraction. Coalescence of Air Bubbles at a Flat Air-Water Interface. Coalescence of air bubbles was studied at a fixed value of surface tension (e.g., 50 mN/m). The compositions of the single and binary surfactant systems needed to attain this surface tension were determined from Figures 2-9. These compositions are presented in Table 3. Experiments were carried out at a fixed surface tension for two reasons. The first reason was that the variation in the size of the bubbles was negligible when the surface tension was kept constant, and the second reason was that the coalescence time, as per the film drainage models given in Table 1, is related to the surface tension as, tc ∝ γ-n, where n varies between 0.75 and 1.5. Therefore, as per these models, the coalescence times for the single- and mixedsurfactant systems should be the same at a given value of surface tension. Thus, the effects of the interfacial forces and the surface excess concentration of the surfactants on the coalescence of bubbles can be investigated by keeping the surface tension constant. A photograph of an air bubble resting at the air-water interface is shown in Figure 10. The characteristic diffusion time, jt, of the stochastic model was calculated from eq 10, and the radius of the barrier ring, Rb, was calculated from eq 11. The calculation of jt requires the mean value of the surface diffusivity of the surfactant molecules, DΓ. The value of DΓ, however, is approximate. From the results reported in the literature,32 it is evident that it depends significantly on the state of the monolayer (i.e., gaseous, liquidexpanded, or liquid-compressed states). In a multi-ion aqueous electrolytic solution, the speed of movement of an ion affects the movement of other ions for maintaining the electrical neutrality.38 The surface diffusion coefficient of the surfactant ions (e.g., C12H25SO4- and C19H42N+) in the surfactant mixture is likely to be influenced by the composition. However, the data necessary to compute this effect are hardly available. Therefore, in the present study, a value of DΓ ) 1 × 10-10 m2/s was used for both single-surfactant and binary-surfactant systems based on the values reported by Agrawal and Neuman.32 As pointed

out by Ghosh and Juvekar,11 the parameters jt and PΓ are dependent on each other. Therefore, a different choice of DΓ will lead to a different value of jt and, hence, of PΓ. However, it has been observed that the trends in the variation of PΓ with the properties of the systems (viz., surfactant and salt compositions) remain the same even if a different value of DΓ is chosen. Because the values of DΓ are approximate, the regression estimates of PΓ are also approximate. However, the choice of DΓ is practically immaterial because the stochastic model is used to study the trends in the variation of the model parameters with the system properties. The coalescence time distributions of air bubbles in the Tween 20-SDS system are shown in Figure 11. Coalescence time distributions in the single-surfactant systems are also shown in this figure for comparison of the effectiveness of the surfactants in stabilizing the thin liquid films. The surface tension was kept constant at 50 mN/m for this system. It can be observed from these distributions that SDS stabilized the bubbles much more effectively than Tween 20. The mean values of the distributions are presented in Table 4. Because the radius of the bubbles and the surface tension were kept constant, the difference in coalescence time, as per the stochastic theory, can be attributed to the differences in surface excess concentration (Γ) and interfacial repulsive force (fr) (see eq 12). An increase in both of these quantities leads to an increase in coalescence time. The surface excess concentrations, which were calculated from the Gibbs adsorption equation, are listed in Table 3. The Gibbs adsorption equations for the various surfactant systems are presented in Table 5. The surface excess concentrations reported in Table 5 represent the total values of Γ. The equations for Γ for the mixed-surfactant systems were derived following the approach of Sugihara et al.39 and Oida et al.40 The effect of NaCl was incorporated by adopting the approach of Prosser and Franses41 and Kumar et al.30 From Table 3, it can be observed that the value of Γ was higher for the Tween 20 system than for the SDS system. These values agree well with those reported in the literature.20,42 Therefore, the repulsive electrostatic doublelayer force between the air-water interfaces was the dominating factor behind the higher stability of the bubbles in the presence of SDS. The interesting aspect about the mixed-surfactant systems is that the coalescence times were significantly larger than the coalescence times in the Tween 20 system, but lower than the coalescence times in the SDS system. The coalescence times of bubbles in the system designated as set 1 in Figure 11 were lower than the coalescence times in the system designated as set 2. It can be observed from Table 3 that the concentration of SDS was higher in set 1 than in set 2. However, the concentration of Tween 20 was lower in set 1 than in set 2. The mole fraction of SDS in the monolayer at the air-water interface for the set 1 system was 0.6, and the same for the set 2 system was 0.5. The value of total surface excess concentration, Γ, however, was slightly higher in the set 2 system. The effect of electrostatic double-layer repulsion between the two approaching air-water interfaces due to the presence of SDS was rendered less effective in the presence of Tween 20 because of the attraction between the SDS and Tween 20 molecules in the monolayer. The resulting effect of these parameters was such that the coalescence times of the bubbles in the set 2 system were higher than the coalescence times in the set 1 system. The parameters of the stochastic model for the surfactant systems shown in Figure 11 are presented in Table 3. The dimensionless coalescence threshold (PΓ) is inversely proporj . The variations in fr and Γ j affect PΓ tional to the quantity frΓ accordingly. The value of PΓ for the Tween 20 system was


1719

Table 3. Parameters of the Stochastic Model system Tween 20 (1) + SDS (2)

a (mm) γ (mN/m) C10 (mol/m3) C20 (mol/m3) C1 (mol/m3) C2 (mol/m3) Γ × 106 (mol/m2) 1.1

50.0

0.009 2.806

Tween 20 (1) + SDS (2) + NaCl

1.1

50.0

0.001 0.002

0.795 0.441

0.001 0.002

0.037 0.015

0.002 0.005

0.163 0.065

0.002 0.005

0.007 0.003

0.050 0.100

0.243 0.088

0.002 0.005

0.036 0.010

0.007 0.259

Tween 20 (1) + CTAB (2)

1.1

45.0

0.018 0.586

Tween 20 (1) + CTAB (2) + NaCl

1.1

45.0

0.015 0.026

CTAB (1) + SDS (2)

1.1

50.0

0.411 2.806

CTAB (1) + SDS (2) + NaCl

1.1

50.0

0.014 0.259

higher than that for the SDS system, which reflects the higher stabilization imparted to the bubbles by SDS as compared to Tween 20. In the mixed-surfactant systems, the value of PΓ was higher in the set 1 system than that in the set 2 system, which reflects a lower coalescence time for the former system. The value of PΓ is decided by the values of fr and Γ. The values of the normalized standard deviation, SΓ, were quite small in these systems as compared to the coalescence systems studied

Figure 10. Photograph (taken from the top) of an air bubble resting at a flat air-water interface.

Figure 11. Coalescence time distributions in the Tween 20 (1)-SDS (2) system in the absence of NaCl. Set 1 corresponds to a mixture of 0.001 mol/m3 Tween 20 and 0.795 mol/m3 SDS, and set 2 corresponds to a mixture of 0.002 mol/m3 Tween 20 and 0.441 mol/m3 SDS.

3.290 2.640 2.260 2.399 3.010 3.490 3.004 3.062 3.400 2.910 2.533 2.529 3.140 3.180 2.697 2.635 2.610 2.640 2.155 2.159 3.060 3.490 3.745 3.784

jt (s) 3830.1

PΓ

8.00 4.83 5.32 5.05 7.05 4.87 10.50 8.20 4255.7 7.10 5.19 6.57 6.90 6.90 5.38 8.25 8.73 3830.1 5.13 4.83 5.20 5.00 5.55 4.87 5.05 4.95

SΓ 0.155 0.052 0.079 0.070 0.145 0.052 0.120 0.140 0.100 0.056 0.130 0.100 0.120 0.060 0.081 0.080 0.063 0.052 0.075 0.065 0.068 0.052 0.060 0.060

earlier.6,7,19 This indicates a narrow distribution of the surface excess concentration Γ. The coalescence times predicted by the seven film drainage models are presented in Table 4. The mean values of the coalescence time distributions are also given in this table. All of the film drainage models except model 5 (for which the coalescence time is represented by t5c ) predicted coalescence times much higher than the experimental value. Furthermore, the predicted values are quite different from one another, even though they predict the same quantity. As pointed out by Bommaganti et al.,3 this can be attributed to the various assumptions made during the development of these models. The factors such as interfacial shear and dilatational viscosities, and repulsive disjoining pressure due to the presence of electrostatic double-layer and steric forces were ignored in these models. As evident from the results discussed above, the interaction between the surfactant molecules complicates these effects further. The coalescence time distributions in the presence of 100 mol/m3 NaCl at the same surface tension (i.e., 50 mN/m) showed a different trend. These distributions are shown in Figure 12. The amount of SDS necessary to stabilize the bubbles in the presence of salt was very small. Nonetheless, the coalescence time distribution in the SDS system was comparable to the distribution in the absence of salt. The electrostatic double-layer repulsion decreased in the presence of NaCl; however, the surface excess concentration increased considerably in the presence of the salt (see Table 3). The latter observation is corroborated by the results reported by Tajima.35 In the Tween 20 system, the coalescence time was slightly higher than that in the absence of salt, even at a lower concentration of the surfactant. This is likely due to the positive charge acquired by Tween 20 in the presence of NaCl. In the mixed-surfactant systems, the presence of salt reduced the coalescence times significantly such that the coalescence times were lower than the coalescence times either in the Tween 20 system or in the SDS system. This reduction in the values of coalescence time is probably due to the enhanced attraction between the two surfactants in the presence of NaCl. The parameters of the stochastic model for these coalescence time distributions are presented in Table 3. The values of PΓ for the single-surfactant systems were similar to the values of PΓ for the single-surfactant systems without NaCl. This reflects

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Table 4. Comparison of the Film Drainage Models with the Experimental Data for the Coalescence of Air Bubblesa C10 (mol/m3) C20 (mol/m3) C1 (mol/m3) C2 (mol/m3) tc1 (s)

system Tween 20 (1) + SDS (2)

0.009

133.7

tc2 (s)

tc3 (s)

tc4 (s)

tc5 (s) tc6 (s)

tc7 (s) tcexpt (s)

88.1 4452.2 1574.9

3.3

819.9 456.6

151.7 100.1 5214.4 1844.5

3.5

948.2 528.1

133.7

3.3

819.9 456.6

2.806 Tween 20 (1) + SDS (2) + NaCl

0.001 0.002

0.795 0.441

0.001 0.002

0.037 0.015

0.007 0.259

Tween 20 (1) + CTAB (2)

0.018 0.586

Tween 20 (1) +

0.002 0.005

0.163 0.065

0.002 0.005

0.007 0.003

0.015 0.026

CTAB (2) + NaCl CTAB (1) + SDS (2)

0.411 2.806


0.050 0.100

0.243 0.088

0.002 0.005

0.036 0.010

0.014 0.259

a

88.1 4452.2 1574.9

6.8 24.3 18.8 21.8 9.5 23.6 3.6 6.7 10.0 22.2 12.7 11.1 10.8 20.1 7.0 6.1 20.8 24.3 19.8 22.1 16.9 23.6 21.4 22.8

∆F ) 1000 kg/m3, µ ) 1 × 10-3 Pa s, g ) 9.8 m/s2, B ) 10-28 J m.

Table 5. Expressions for the Gibbs Adsorption Equation for the Various Single and Binary Surfactant Systems surfactant system

Γ

SDS or CTAB

-

1 dγ 2RT d ln Ct

Tween 20

-

1 dγ RT d ln Ct

Tween 20 (1) + SDS (2) [or Tween 20 (1) + CTAB (2)]

-

1 dγ (2 - x1)RT d ln Ct

CTAB (1) + SDS (2)

-

1 dγ 2RT d ln Ct

SDS + NaCl

-

dγ 1 RT d ln[Ct(Ct + Cs)]

CTAB + NaCl

-

dγ 1 RT d ln(CtCs)

Tween 20 + NaCl

-

1 dγ RT d ln Ct

Tween 20 (1) + SDS (2) + NaCl

-

dγ 1 RT d ln[Ct(Ct + Cs)] - x1 d ln(Ct + Cs)

Tween 20 (1) + CTAB (2) + NaCl

-

dγ 1 RT d ln(CtCs)


-

dγ 1 RT d ln[Ct(Ct + Cs)] - x1 d ln(Ct + Cs)

Figure 12. Coalescence time distributions in the Tween 20 (1)-SDS (2) system in the presence of 100 mol/m3 NaCl. Set 1 corresponds to a mixture of 0.001 mol/m3 Tween 20 and 0.037 mol/m3 SDS, and set 2 corresponds to a mixture of 0.002 mol/m3 Tween 20 and 0.015 mol/m3 SDS.

the fact that the coalescence times with and without NaCl were similar. The values of SΓ were also similar in the presence and absence of NaCl for the single-surfactant systems. Because the coalescence times decreased considerably in the mixed-surfactant systems in the presence of NaCl, the values of PΓ were considerably higher in these systems. The values of SΓ were slightly higher for the mixed-surfactant systems in the presence of NaCl, which indicates an increase in the nonuniformity of the surfactant composition at the air-water interface. A comparison of the predictions from seven film drainage models with the experimental values of coalescence time is shown in Table 4. Because the surface tension was maintained at 50 mN/m (i.e., at the same value as in the absence of salt), the coalescence times predicted by these models are the same as the coalescence times for the systems without salt. Note that the effect of salt on the modified Hamaker’s constant (B) was ignored in these film drainage models. The coalescence time distributions in the Tween 20-CTAB system are shown in Figure 13. The compositions were chosen in these experiments such that the surface tension was kept fixed


Figure 13. Coalescence time distributions in the Tween 20 (1)-CTAB (2) system in the absence of NaCl. Set 1 corresponds to a mixture of 0.002 mol/m3 Tween 20 and 0.163 mol/m3 CTAB, and set 2 corresponds to a mixture of 0.005 mol/m3 Tween 20 and 0.065 mol/m3 CTAB.

at 45 mN/m. The coalescence times were higher in the presence of the cationic surfactant CTAB and much lower in the presence of Tween 20. This supports the proposition that the electrostatic double-layer force is the main stabilizing factor for the bubbles. The coalescence times of the bubbles in the mixed-surfactant systems were much lower than the coalescence times in the CTAB system. The values of coalescence time were similar to those in the Tween 20 system. Therefore, the electrostatic repulsive force in the mixed-surfactant systems was largely reduced by the interaction among the surfactant molecules. The coalescence times in the set 1 system were slightly higher than the coalescence times in the set 2 system. The former system contains a higher amount of CTAB and a lower amount of Tween 20 than the latter system. It is likely that the hydration force provides additional stabilization in the presence of a higher amount of CTAB. The effect of hydration force is evident in the presence of 100 mol/m3 NaCl, where the electrostatic doublelayer repulsion greatly diminishes. The parameters of the stochastic model for the Tween 20-CTAB system are presented in Table 3, and the mean values of the coalescence time distributions are presented in Table 4. The values of PΓ for the single-surfactant systems indicate that the coalescence times were higher in the presence of CTAB than in the presence of Tween 20. The value of PΓ for the Tween 20 system was, in fact, lowered by the higher value of Γ for the surfactant. The values of PΓ for the mixed-surfactant systems reflect that the system designated as set 1 stabilized bubbles more than the system designated as set 2. Therefore, the coalescence times of the bubbles were higher in the former system. The surface excess concentrations for the mixedsurfactant systems were comparable. Therefore, it is evident that the repulsive hydration force stabilized the bubbles in the set 1 system, which lowered the value of PΓ. The values of SΓ for the single-surfactant systems were small and comparable to those for the Tween 20-SDS system. However, for the mixedsurfactant systems, the values of SΓ were slightly larger than the values for the Tween 20-SDS systems. This reflects higher heterogeneity in surfactant composition in the Tween 20-CTAB mixed systems. The effect of salt on coalescence time is shown in Figure 14. The high coalescence times in the CTAB system were achieved at a much lower surfactant concentration than in the system in the absence of salt. The reduction in electrostatic double-layer force was compensated by the increase in the surface excess concentration and the repulsive contribution from the hydration force.8 The coalescence time distributions in the mixed-surfactant systems were

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Figure 14. Coalescence time distributions in the Tween 20 (1)-CTAB (2) system in the presence of 100 mol/m3 NaCl. Set 1 corresponds to a mixture of 0.002 mol/m3 Tween 20 and 0.007 mol/m3 CTAB, and set 2 corresponds to a mixture of 0.005 mol/m3 Tween 20 and 0.003 mol/m3 CTAB.

significantly lower than the coalescence times in the singlesurfactant systems. This is similar to the behavior observed in the Tween 20-SDS system. The likely reason for the decrease in coalescence time is the reduction of the electrostatic double-layer repulsion in the presence of salt, which is not sufficiently compensated by the increase in the surface excess concentration. However, the coalescence times in the set 1 system (which contains a higher concentration of CTAB than the set 2 system) were slightly higher. This is likely due to the stabilization of the bubbles by the hydration force. The parameters of the stochastic model are presented in Table 3, and the mean values of coalescence time are presented in Table 4. It can be observed from Table 3 that the values of PΓ in the presence and absence of NaCl were similar in magnitude. This indicates that the coalescence times were similar in the presence and absence of NaCl. The values of PΓ for the mixedsurfactant systems were much higher than the corresponding values in the absence of NaCl. This reflects the fact that the coalescence times were significantly reduced in the presence of NaCl. The values of SΓ for the single-surfactant systems were similar in the presence and absence of NaCl. However, these values were slightly lower for the mixed-surfactant systems in the presence of NaCl, which indicates that the nonuniformity in the composition of surfactant at the air-water interface was reduced in the presence of NaCl. The coalescence time experiments in the CTAB-SDS systems were carried out at a surface tension of 50 mN/m. The coalescence time distributions in the absence of salt are shown in Figure 15. It can be observed from this figure that SDS stabilized the bubbles more effectively than CTAB. This is probably due to the steric repulsion between the CTAB molecules at the air-water interface, which makes them less effective in the stabilization of the bubbles. It can be observed from Figure 15 that the difference between the coalescence times for the single- and mixed-surfactant systems was small for this surfactant combination, which is evident from the mean values of the coalescence time distributions presented in Table 4. The coalescence times in the mixed-surfactant systems, however, were lower than the coalescence times in the SDS system. The attraction between the surfactant molecules reduces the effect of repulsive disjoining pressure (due to the electrostatic doublelayer) between the air-water interfaces. The parameters of the stochastic model are presented in Table 3. It can be observed from this table that the values of PΓ for the single-surfactant systems were similar. This indicates that

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Figure 15. Coalescence time distributions in the CTAB (1)-SDS (2) system in the absence of NaCl. Set 1 corresponds to a mixture of 0.05 mol/m3 CTAB and 0.243 mol/m3 SDS, and set 2 corresponds to a mixture of 0.1 mol/m3 CTAB and 0.088 mol/m3 SDS.

The parameters of the stochastic model for the CTAB-SDS system in the presence of NaCl (see Table 3) were similar in magnitude to those for the same surfactant system without NaCl. However, in the presence of salt, the difference between the values of PΓ for the single-surfactant systems increased, which reflects the fact that the effectiveness of SDS over CTAB was enhanced in the presence of NaCl. This is possibly due to the larger increase in the value of Γ for the SDS system in the presence of NaCl. The value of PΓ was the result of the two opposing effects: reduction in repulsive force fr and increase in the surface excess concentration Γ by the addition of salt. The mean values of the coalescence time distributions are compared with the values predicted by the seven film drainage models in Table 4. The values of PΓ for the mixed-surfactant systems were marginally reduced in the presence of NaCl, which indicates a small increase in the coalescence time in the presence of NaCl, which can also be observed from the mean values presented in Table 4. However, the interesting fact was that this increase was achieved at very small quantities of the surfactants. Conclusions

Figure 16. Coalescence time distributions in the CTAB (1)-SDS (2) system in the presence of 100 mol/m3 NaCl. Set 1 corresponds to a mixture of 0.002 mol/m3 CTAB and 0.036 mol/m3 SDS, and set 2 corresponds to a mixture of 0.005 mol/m3 CTAB and 0.01 mol/m3 SDS.

the coalescence times in the presence of SDS and CTAB were close to each other, which can also be observed from Figure 15 and Table 4. In addition, the values of PΓ in the mixed-surfactant systems were also similar in magnitude, which indicates that the coalescence time distributions in the CTAB-SDS systems varied within a small range. In fact, the mean values of the four coalescence time distributions varied between 19.8 and 24.3 s (Table 4). A remarkable feature of these surfactant systems was that the values of SΓ were small, which reflects the fact that the fluctuations in surfactant composition at the air-water interface were small, which can be attributed to strong interactions among the surfactant molecules. The mean values of the coalescence time distributions are compared with the values predicted by the seven film drainage models in Table 4. In the presence of 100 mol/m3 NaCl, very small quantities of these ionic surfactants were sufficient to stabilize the bubbles, as is evident from the coalescence time distributions presented in Figure 16. SDS was more effective than CTAB in the presence of salt, as in the absence of salt. The coalescence times in the mixed-surfactant systems increased in the presence of salt as well. From Table 3, it can be observed that the surface excess concentrations increased significantly for ionic surfactant systems in the presence of the salt and that the effect was more significant for the mixed-surfactant systems. This provided stability to the bubbles even though the electrostatic doublelayer force decreased in the presence of the salt.

The adsorption of surfactants in binary mixtures at the air-water interface was studied in the present work. An anionic surfactant (i.e., SDS), a cationic surfactant (i.e., CTAB), and a nonionic surfactant (i.e., Tween 20) were used in these studies. The coalescence of air bubbles at a flat air-water interface was studied in the mixed-surfactant systems at a constant surface tension and bubble size. The effect of NaCl on adsorption and coalescence was investigated. The adsorption of surfactants was studied by measuring the surface tension of the aqueous solutions of the surfactants. The surface tension profiles in the mixed-surfactant systems were presented. The interactions between the surfactants in the monolayer and in the micelle were studied. The type I synergism was observed in all three binary mixtures of surfactants. The presence of NaCl augmented the attractive interaction between Tween 20 and SDS. This was attributed to the enhanced attraction between the negatively charged SDS molecules and the Tween 20 molecules, which acquired a positive charge by complexation with the sodium ions present in the aqueous solution. In the Tween 20-CTAB system, however, the addition of salt reduced the attraction between the surfactant molecules, mainly because of the reduction in the Debye length with the increase in the ionic strength of the solution. The interactions in binary mixtures of cationic and anionic surfactants were much stronger than those between ionic and nonionic surfactants. Addition of salt reduced the electrostatic attraction between the oppositely charged headgroups of the ionic surfactant molecules, which reduced the magnitudes of the interaction parameters in these systems. Coalescence of air bubbles was studied keeping the surface tension and the radius of the bubbles constant. It was observed that the ionic surfactants stabilized the bubbles much more strongly than the nonionic surfactant. The electrostatic doublelayer repulsion is the likely reason for this stabilization. The coalescence times in the mixed-surfactant systems of ionic and nonionic surfactants (e.g., SDS-Tween 20 or CTAB-Tween 20) were always lower than the coalescence times in the singleionic-surfactant systems (i.e., in SDS or CTAB). Therefore, although type I synergism was exhibited by the binary surfactant mixtures, the mixed-surfactant systems were less effective in stabilizing the bubbles. In the presence of salt, the coalescence times in the singleionic-surfactant systems were quite high, even at low surfactant


concentrations. The effect of salt on the coalescence time in the nonionic surfactant system was found to be small. Addition of salt reduced the coalescence times in the mixed ionic-nonionic surfactant systems significantly, rendering these surfactant mixtures quite ineffective for stabilizing the bubbles. However, in the mixed system of ionic surfactants, addition of salt increased the total surface excess concentration at the air-water interface, which stabilized the bubbles appreciably. Broad distributions of coalescence time were observed in all coalescence systems. The stochastic model fitted the distributions well. The variation of the dimensionless coalescence threshold with the composition of the system was explained in terms of the interfacial repulsive force and the surface excess concentration of the surfactants. The mean values of the coalescence time distributions experimentally obtained were quite different from the values predicted by seven film drainage models. These models predicted widely different values of coalescence time even for the same system. The possible limitations of these film drainage models were discussed. Acknowledgment The authors thank the Department of Science and Technology (Government of India) for the financial support of the work reported in this article. Nomenclature a ) radius of bubble (m) af ) area of the film (m2) AH ) Hamaker’s constant (J m) B ) modified Hamaker’s constant (J m) C1 ) solution-phase concentration of surfactant 1 in the mixture (mol/m3) 0 C1 ) solution-phase concentration of pure surfactant 1 (mol/m3) C10,CMC ) concentration of surfactant 1 that is required to yield a surface tension equal to that of a mixture of the two surfactants at its CMC (mol/m3) 0,M C1 ) CMC of surfactant 1 (mol/m3) CM 1 ) concentration of surfactant 1 in the mixture at its CMC (mol/ m3) C2 ) solution-phase concentration of surfactant 2 in the mixture (mol/m3) 0 C2 ) solution-phase concentration of pure surfactant 2 (mol/m3) C20,CMC ) concentration of surfactant 2 that is required to yield a surface tension equal to that of a mixture of the two surfactants at its CMC (mol/m3) 0,M C2 ) CMC of surfactant 2 (mol/m3) CM 2 ) concentration of surfactant 2 in the mixture at its CMC (mol/ m3) Cs ) concentration of salt (mol/m3) Ct ) total concentration of surfactant (mol/m3) DΓ ) mean surface diffusivity of the surfactant molecules (m2/s) fr ) repulsive force generated by one mole of surfactant at the barrier ring (N/mol) F(τR) ) cumulative probability distribution of coalescence time g ) acceleration due to gravity (m/s2) hc ) critical film thickness (m) hr ) thickness of the film at the barrier ring (m) k ) Boltzmann’s constant (J/K) PΓ ) dimensionless coalescence threshold Rb ) radius of the barrier ring (m) SΓ ) normalized standard deviation t ) time (s) tc ) coalescence time (s)

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jt ) characteristic diffusion time (s) T ) temperature (K) wb ) width of the barrier ring (m) x1 ) mole fraction of surfactant 1 in the mixed monolayer x1M ) mole fraction of surfactant 1 in the micelle Greek Letters R ) fraction of the total amount of surfactant at the air-water interface that remains at the barrier ring after the displacement of surfactant molecules to the barrier ring βM ) interaction parameter that measures the nature and extent of interactions between the two different surfactant molecules in the mixed micelle βσ ) interaction parameter that measures the nature and extent of interactions between the two different surfactant molecules in the mixed monolayer γ ) surface tension (N/m) γCMC ) surface tension at the CMC (N/m) Γ ) surface excess concentration of the surfactant (mol/m2) j ) mean value of the distribution of the surface excess concentraΓ tion, Γ (mol/m2) Γm ) minimum value of the surfactant concentration at the barrier ring required to prevent bubble coalescence (mol/m2) ∆p ) excess pressure in the film (Pa) ∆F ) difference in density between the two phases (kg/m3) λi ) roots of the Bessel function of the first kind and order 1 µ ) viscosity of the aqueous phase (Pa s) σΓ ) standard deviation in the distribution of Γ (mol/m2) jτ ) mean time of rupture of the films (s) τR ) dimensionless coalescence time

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ReceiVed for reView August 2, 2009 ReVised manuscript receiVed November 27, 2009 Accepted December 10, 2009 IE9012216

Adsorption and Coalescence in Mixed-Surfactant Systems: AirâWater

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