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Rupture of Wetting Films Caused by Nanobubbles Klaus Werner Sto¨ckelhuber,*,†,‡ Boryan Radoev,†,§ Andreas Wenger,† and Hans Joachim Schulze† Max-Planck-Research Group for Colloids and Surfaces at the Institute of Ceramics, Glass and Construction Materials at the TU Bergakademie Freiberg, Chemnitzer Strasse 40, D-09599 Freiberg, Germany, Institute of Polymer Research Dresden, Hohe Strasse 6, D-01067 Dresden, Germany, and University of Sofia, Department of Physical Chemistry, 1126 Sofia, Bulgaria Received August 14, 2003. In Final Form: October 28, 2003 It is now widely accepted that nanometer sized bubbles, attached at a hydrophobic silica surface, can cause rupture of aqueous wetting films due to the so-called nucleation mechanism. But the knowledge of the existence of such nanobubbles does not give an answer to how the subprocesses of this rupture mechanism operate. The aim of this paper is to describe the steps of the rupture process in detail: (1) During drainage of the wetting film, the apex of the largest nanobubble comes to a distance from the wetting film surface, where surface forces are acting. (2) An aqueous “foam film” in nanoscale size is formed between the bubble and the wetting film surface; in this foam film different Derjaguin-Landau-Verwey-Overbeek (DLVO) forces are acting than in the surrounding wetting film. In the investigated system, hydrophobized silica/ water/air, all DLVO forces in the wetting film are repulsive, whereas in the foam film the van der Waals force becomes attractive. (3) The surface forces over and around the apex of the nanobubble lead to a deformation of the film surfaces, which causes an additional capillary pressure in the foam film. An analysis of the pressure balance in the system shows that this additional capillary pressure can destabilize the foam film and leads to rupture of the foam film. (4) If the newly formed hole in the wetting film has a sufficient diameter, the whole wetting film is destabilized and the solid becomes dewetted. Experimental data of rupture thickness and lifetime of wetting films of pure electrolyte and surfactant solutions show that the stabilization of the foam film by surfactants has a crucial effect on the stability of the wetting film.
Introduction The rupture of the thin liquid film dividing two particles (solid particles, gas bubbles, or liquid droplets) is a crucial step in many coagulation processes of scientific and industrial relevance. For instance, the rupture of a thin liquid film between a gas bubble and a solid particle is one of the elementary steps of the flotation process.1 Two possible rupture mechanisms of the thin liquid film are possible: the capillary wave mechanism (also called spinodal dewetting) and the so-called nucleation mechanism. Both of these mechanisms exist; we could prove the occurrence of both in differently prepared samples of the system silica/water/gas.2 A necessary precondition for the occurrence of the capillary wave mechanism is the existence of attractive interaction forces between the solid surface and the gas bubble. We realized this in previous works2 by recharging the silica surface due to adsorption of multivalent ions, which leads to an attractive electrostatic interaction in the film. Without this treatment, all DLVO forces (van der Waals and electrostatic forces) in the silica/water/air system are repulsive and the wetting films are stable. If the solid surface is hydrophobized, the film ruptures, although there * Corresponding author. E-mail:
[email protected]. † Max-Planck-Research Group for Colloids and Surfaces at the Institute of Ceramics, Glass and Construction Materials at the TU Bergakademie Freiberg. ‡ Institute of Polymer Research Dresden. § University of Sofia. (1) Schulze, H. J. Physico-Chemical Elementary Processes in Flotation; Elsevier: Amsterdam, 1984. (2) Schulze, H. J.; Sto¨ckelhuber, K. W.; Wenger, A. Colloids Surf., A 2001, 192, 61-72.
is no attractive interaction in the film. To find an explanation for this behavior, a number of authors have postulated a “long-range hydrophobic force”, but in the past years it turned out more and more that the reason for the rupture is most probably the occurrence of nanoscaled bubbles adhered to the solid surface. The rupture mechanism in this case can be regarded as a nucleation process (see i.e. the review article3). Recently, a number of papers have been published that give clear evidence for the existence of such nanobubbles by means of IR spectroscopy,4 force measurements,5-7 and imagegiving methods such as tapping-mode atomic force microscopy.8-10 During drainage of the wetting film, the apex of the largest nanobubble comes to a distance from the wetting film surface, where surface forces are acting. This leads to the formation of a local foam film (between the nanobubbles and the film/gas interface) which is only metastable in contrast to the surrounding wetting film. After the rupture of the foam film, a hole with threephase contact in place of the nanobubble is formed. If the (3) Ralston, J.; Fornasiero, D.; Mishchuk, N. Colloids Surf., A 2001, 192, 39-51. (4) Gong, W.; Stearnes, J.; Fornasiero, D.; Hayes, R.; Ralston, J. Phys. Chem. Chem. Phys. 1999, 2799-2803. (5) Mahnke, J.; Stearns, J.; Ralston, J. Phys. Chem. Chem. Phys. 1999, 1, 2793. (6) Ishida, N.; Sakamoto, M.; Miyahara, M.; Higashitani, K. Langmuir 2000, 16, 5681-5687. (7) Tyrell, J. W. G.; Attard, P. Langmuir 2002, 18, 160-167. (8) Ishida, N.; Sakamoto, M.; Miyahara, M.; Higashitani, K. J. Colloid Interface Sci. 2002, 253, 112-116. (9) Tyrell, J. W. G.; Attard, P. Phys. Rev. Lett. 2001, 87, 176104. (10) Lou, S.; Gao, J.; Xiao, X.; Li, X.; Li, G.; Zhang, Y.; Li, M.; Sun, J.; Hu, J. Chin. Phys. 2001, 10, 108-110.
10.1021/la0354887 CCC: $27.50 © 2004 American Chemical Society Published on Web 11/26/2003
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Figure 1. (a) Wetting film with gas bubbles adhered to the solid substrate. For a large film thickness hw, where no rupture occurs, bubbles play no role in film behavior. (b) Beginning of interactions between a nanobubble and the surface of the wetting film. Film rupture occurs at a film thickness on the order of the biggest bubble height (hw ) hrupture ≈ hb).
Figure 2. Sketch of a foam film surrounded by a wetting film. Geometric parameters: hw, wetting (nondeformed) film thickness; hb, bubble height; hf, foam film thickness (the film between the bubble cap and the deformed upper film surface); Rf, curvature radius of the deformed film surface. Pressures acting in the foam and in the wetting films: pf and pw, fluid pressures in the foam film and in the wetting film, respectively; Π, disjoining pressures; pσ, capillary pressure; pg, gas pressure.
hole has a sufficient size,2,11 the three-phase contact line expands, which finally leads to the dewetting of the solid surface. The aim of this paper is to give a description of the detailed rupture process caused by nanobubbles adhering to the solid surface and to show how one can affect this process by addition of surfactants to the film-building fluid.
pressure of nanobubbles!), and pg is the gas pressure in the adjacent gas phase. Equation 1 is applied separately on the foam film region, where the film surface is more or less deformed, and on the wetting film far from the bubble, where the film surface is flat (Figure 2). After eliminating the gas pressure pg, balance 1 leads to
Modeling and Pressure Balance
pf + Πf(hf) - pσ ) pw + Πw(hw)
A model of our system is given in Figure 1. It presents a sketch of a wetting film with gas bubbles (nanometer scaled) adhered to the solid substrate. For thick films (film thickness hw much greater than bubble height hb, Figure 1a), bubbles play no role in film behavior. At a film thickness on the order of the bubble height, interaction forces begin to act between the film surface and the biggest nanobubble. The strongest interaction takes place in the thinnest part between the bubble cap and the film interface (hf), where, as shown below, film rupture occurs. There are different reports about the coverage degree of the solid with bubbles in the literature, beginning from solitary bubbles6,8 to a nearly complete coverage.7,9 As shown below, for both extreme cases our approach is valid for the largest bubble in the wetting film that is responsible for starting the rupture process. In this section, the mechanical balance of “fluid surfacebubble” interactions and the condition of film instability is formulated. As seen from Figure 2, the interaction between the film surface and the bubble occurs at the thinnest part of the film, where a “foam film” is formed, surrounded by the wetting film. The behavior of this foam film plays a crucial role in the wetting film stability. Force analysis is based on a pressure balance, which for fluid film interfaces can be written in the form (see for instance ref 12)
p + Π - p σ ) pg
(1)
where p is the film pressure, Π is the disjoining pressure, pσ is the capillary pressure caused by the deformed fluid film interface (not to be confused with the capillary (11) Sharma, A.; Ruckenstein, E. J. Colloid Interface Sci. 1990, 137, 433. (12) de Feijter, J. A. In Thin Liquid Films; Ivanov, I. B., Ed.; Surfactant Science Series, Vol. 29; Marcel Dekker: New York, 1988; Chapter 1.
(2)
where pf and Πf(hf) are the fluid and disjoining pressure of the (curved) foam film and pw and Πw(hw) are the fluid and disjoining pressure of the (flat) wetting film (see Figure 2). Note that Πf and Πw differ not only because of the different local thicknesses hf and hw but also because of different surface potentials Ψ and different van der Waals constants AvdW in the foam and in the wetting film, respectively (for more about Πf and Πw, see Figure 3a,b). At equilibrium pf ) pw and eq 2 turns into
∆Π ) pσ
(2′)
with ∆Π t Πf(hf) - Πw(hw). For an estimation of pσ at the top of the profile, one can use the Laplace equation pσ ) 2σ/Rf, where Rf denotes the local curvature radius. Rewritten for the foam film, balance 2′ now takes the form
∆Π )
2σ Rf
(3)
Figure 3a presents Π(h) isotherms of aqueous KCl electrolyte solution (cel ) 10-3 mol/L), and Figure 3b presents the same isotherms but with sodium dodecyl sulfate (SDS) added as surfactant (cSDS ) 10-5 mol/L; cel ) 2 × 10-3 mol/L KCl). The higher electrolyte concentration was chosen to counterbalance the higher surface potential of the fluid surface with surfactant, so we could reach the same equilibrium thickness of wetting films in both cases. According to our model, the presence of foam films is crucial for the stability of the surrounding wetting film. On the other hand, the stabilizing role of surfactants on foam films is well-known. From this viewpoint, it was interesting to look for similar stabilization effects of surfactants on wetting films. SDS was chosen as a very well studied surfactant.
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Sto¨ ckelhuber et al. Table 1. Parameters at the Instability Point of Wetting Films without (see Figure 3a) and with Added Surfactant (see Figure 3b) parameters
without surfactant (Figure 3a)
with surfactant (Figure 3b)
∆Πmax ) Πf(hf)max - 4400 - 250 ) 4150 55250 - 250 ) 55000 Πw(heq) [Pa] Rf(crit) [nm] (see 35000 2230 eq 3) hf [nm] 9.5 4.7
Figure 3. Disjoining pressures (resultant) Π ()Πel + ΠvdW) versus film thickness h of the foam film and of the wetting film (note the different scaling of the Π axis). van der Waals constants: foam film, (AvdW)f ) 3 × 10-20 J; wetting film, (AvdW)w ) -3 × 10-20 J (ref 15). Electrochemical parameters: (a) Without surfactant (csurf ) 0); electrolyte concentration cel ) 10-3 mol/L KCl; surface potential at the liquid-gas interface ψg ) -35 mV; surface potential at the solid-liquid interface ψs ) -30 mV (ref 16). (b) With surfactant (SDS) csurf ) 10-5 mol/L; electrolyte concentration cel ) 2 × 10-3 M KCl; surface potential at the liquid-gas interface ψg ) -83 mV (ref 17); surface potential at the solid-liquid interface ψs ) -30 mV.
The electrostatic and van der Waals components of Π(h) are computed by eqs 4 a,b:14
( ) kT ze
Πel(h) ) 20κ2 4
2
tanh
( ) ( )
zeΨ1 zeΨ2 tanh 4kT 4kT exp(-κh) (4a)
ΠvdW(h) ) -
AvdW 1 6π h3
(4b)
Expressions 4 for Πel and ΠvdW are valid both for wetting films as well as for foam films but with different surface potentials Ψ and van der Waals constants AvdW (see the captions of Figure 3a,b). As shown in Figure 3a,b, the disjoining pressure of the foam film (Πf) passes through a maximum, while Πw of the wetting film is a monotone positive (repulsive) function in the entire thickness interval. The maximum of Πf also causes a maximum of ∆Π (∆Πmax ) (Πf)max - Πw, see eq 5). During the drainage of the film, the curvature radius Rf continually gets smaller, with the nanobubble radius (13) Princen, H. M. In Surface and Colloid Science; Matievic´, E., Ed.; Wiley-Interscience: New York, 1969; Chapters II and III. (14) Vervey, E. J. W.; Overbeek, J. Th. G. Theory of Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948.
Rb as an ultimate limit. Evaluations below show that far before this limit is reached, the foam film becomes unstable. It ruptures, and a hole with a three-phase contact in place of a nanobubble is formed. In a previous paper,2 we pointed out conditions under which such a newly formed hole in the wetting film can lead to dewetting of the wetting solid surface or not. The mean parameters for opening or closing of the newly formed hole are the contact angle of the solid and the rupture thickness of the wetting film.11 A combination of terms with maximum (∆Π) and monotonic terms (pσ) in a balance (see eq 3) is a certain sign of emerging instability, which starts by reaching the maximum point ∆Πmax. To get a correct impression of the film parameters at the instability point, typical values are given in Table 1. Some explanations of the parameter values in Table 1 are as follows: All estimations are related to the apex point of the deformed film surface; the equilibrium disjoining pressure of the wetting film Πw(heq) is equal to the experimental gas pressure pg ) 250 Pa,2 which leads to an equilibrium thickness of 40 nm. (Πf)max and hf values are taken from the corresponding Πf(h) isotherms (see the caption of Figure 3). The curvature radii Rf(crit) are evaluated via eq 3 at (∆Π)max. The existence of a critical radius of curvature Rf(crit) of the film surface, corresponding to (∆Π)max, is maybe one of most important facts supporting our rupture mechanism of wetting films. Once the instability point (∆Π)max is achieved, any further thinning of the wetting film will lead to “piercing” the upper film surface by the biggest nanobubble. Note that smaller curvature radii than Rf(crit) could not arise, because ∆Π cannot counterbalance higher capillary pressures (see eqs 2′ and 3). The nanobubble height hb is another significant parameter of our system. As briefly mentioned in the Introduction, there are only few experimental data about nanobubble sizes reported in the literature and they lie all in the interval of 30-100 nm.6,8 Here we shall give some other additional considerations leading to similar conclusions about the order of nanobubble size values in wetting films. According to the present model, film rupture occurs after a maximum in disjoining pressure of the foam film is reached, that is, at Πf f Πf(max) (see Figure 2). The local film thickness at the apex of the foam film is hb + hf(Πmax ). Experimental data for rupture thickness are scattered from >100 nm down to the equilibrium thickness of the wetting film hw(eq) (see Figure 4). Due to the small critical thickness of the foam film hf(crit) and the small deformation of the film surface, which results from its high radius of curvature Rf(crit), it is reasonable that the critical thickness of the wetting film reflects the height of the largest nanobubble, which causes the rupture of the film. Influence of Surfactant As shown above, the addition of a small amount of surfactant changes the electrostatic force in the foam film
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Figure 4. Rupture thickness vs lifetime of wetting films of 10-3 mol/L KCl solution on hydrophobic silica with different degrees of hydrophobicity. Note that the time scale was set to 0 at a thickness of 87 nm (last interferometric minimum in the experimental measuring procedure); also, rupture takes place in thicker films up to 500 nm. The line shows the calculated draining behavior of the film by numerical solution of the Reynolds equation (ref 2); the dotted line marks the equilibrium thickness of the wetting film hw(eq).
(Figure 3b) and, as a consequence, the critical parameters for the rupture of the foam film (Table 1). The concentration of the used surfactant sodium dodecyl sulfate of 10-5 mol/L was chosen to get a maximum effect on the potential of the liquid gas surface ψg by a minimum of SDS addition.17 Electron spectroscopy for chemical analysis (ESCA) measurements of the solid surface after 1 h disposition of the SDS solution showed that no surfactant is adsorbed at the liquid/solid interface, so we can be sure that the potential of the solid surface remains unchanged. To compensate the influence of the higher potential of the liquid gas surface ψg on the equilibrium thickness of the wetting film hw(eq) due to the surfactant, the electrolyte content of the solution was increased to 2 × 10-3 mol/L KCl. Measurements of the dependency of rupture thickness of a wetting film on its lifetime (see Figure 4, for details see ref 2) give a dramatic increase in lifetime of wetting films with added surfactant (see Figure 5a-c). We consider the drastic increased lifetime of the wetting films with SDS as an effect of the enhanced electrostatic stabilization of the foam film between the nanobubble and the fluid surface of the wetting film. Table 1 shows that with added surfactant a 13 times higher capillary pressure has to be applied for the rupture of the wetting film as compared to that for a film from pure electrolyte solution. This energy barrier stabilizes the free foam film and also the complete wetting film, which leads to a prolongation of the lifetime up to “long time stability”. The influence of the hydrophobicity of the solid surface on the number and size of the adhering nanobubbles has not explored till now, but the trend seems clear: the more hydrophobic the surface, the bigger the number and the size of the adhering nanobubbles. Conclusions Nanobubbles in wetting films can be the cause of rupture of wetting films, especially when all acting surface forces are repulsive. An introduction of “long-range hydrophobic (15) Lyklema, J. Fundamentals of Interface and Colloid Science, Volume 1: Fundamentals; Academic Press: London 1991; Appendix 9. (16) Own measurements, streaming potential, unpublished. (17) Exerowa, D.; Kruglyakov, P. M. Foam and Foam Films. Theory, Experiment, Application; Elsevier: Amsterdam, 1998; p 138.
Figure 5. (a) Influence of surfactant on the lifetime and rupture of wetting films on hydrophobized silica with a contact angle θ ) 90°. The maximum lifetime without SDS is 3 s; addition of 10-5 M SDS increases the lifetime of the wetting film up to 300 s. The lines show the calculated drainage for the system without surfactant (solid line, 10-3 mol/L KCl) and with surfactant (dotted line, 2 × 10-3 mol/L KCl + 10-5 mol/L SDS). (b) Influence of surfactant on the lifetime and rupture of wetting films on hydrophobized silica with a contact angle θ ) 56°. The maximum lifetime without SDS is 42 s; after addition of 10-5 mol/L SDS, 43% of wetting films are long time stable. (c) Influence of surfactant on the lifetime and rupture of wetting films on hydrophobized silica with a contact angle θ ) 20°. The maximum lifetime without SDS is 56 s; after addition of 10-5 mol/L SDS, all wetting films are long time stable.
interaction forces” is neither necessary nor appropriate. Between the apex of the nanobubble and the gas/fluid interface, a nanosize foam film is generated during wetting film drainage. The repulsive electrostatic forces in this foam film can be counterbalanced by the capillary forces, as a result of the deformation of the film surface. Once the maximum of the DLVO isotherm (∆Π)max is reached, any
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further thinning of the wetting film will lead to rupture of the foam film. Hereby a hole with a three-phase contact line in place of the nanobubble is formed, which can spread and cause dewetting of the solid surface. Addition of a small amount of surfactant molecules stabilizes the nanosized foam film electrostatically; in this case, a higher capillary pressure due to a smaller radius of curvature of the deformation of the film surface is necessary for the film rupture. This effect is experimentally observable by a strongly increased lifetime of wetting films containing surfactants. The dramatically increased lifetime of wetting films due to surfactant addition is further
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evidence for the existence of nanobubbles in our system and for the rupture of a nano-foam-film as the causal process of the nucleation mechanism. Acknowledgment. The financial support of the German Research Council (DFG) special research area “Particle interaction” (SFB 285) is gratefully acknowledged. B.R. is grateful for the financial support of the Bulgarian National Science Foundation (Project X-826). The authors thank Emil Manev for useful discussions. LA0354887
