Advances in Colloid and Interface Science 205 (2014) 74–86

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Unusually stable liquid foams Emmanuelle Rio, Wiebke Drenckhan, Anniina Salonen, Dominique Langevin ⁎ Laboratoire de Physique des Solides, Université Paris-Sud 11, UMR CNRS 8502, Bâtiment 510, 91405 Orsay Cedex, France

a r t i c l e

i n f o

Available online 30 October 2013 Keywords: Stable foams Foam coarsening Foam drainage Foam coalescence

a b s t r a c t Obtaining stable liquid foams is an important issue in view of their numerous applications. In some of these, the liquid foam in itself is of interest, in others, the liquid foam acts as a precursor for the generation of solid foam. In this short review, we will make a survey of the existing results in the area. This will include foams stabilised by surfactants, proteins and particles. The origin of the stability is related to the slowing down of coarsening, drainage or coalescence, and eventually to their arrest. The three effects are frequently coupled and in many cases, they act simultaneously and enhance one another. Drainage can be arrested if the liquid of the foam either gels or solidifies. Coalescence is slowed down by gelified foam films, and it can be arrested if the films become very thick and/or rigid. These mechanisms are thus qualitatively easy to identify, but they are less easy to model in order to obtain quantitative predictions. The slowing down of coarsening requests either very thick or small films, and its arrest was observed in cases where the surface compression modulus was large. The detail of the mechanisms at play remains unclear. © 2013 Elsevier B.V. All rights reserved.

Contents

1. 2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . Fundamental mechanisms which control foam stability . . . . . 2.1. Evaporation . . . . . . . . . . . . . . . . . . . . . . 2.2. Coarsening . . . . . . . . . . . . . . . . . . . . . . 2.3. Foam drainage . . . . . . . . . . . . . . . . . . . . 2.4. Coalescence . . . . . . . . . . . . . . . . . . . . . . 3. Coarsening in very stable foams . . . . . . . . . . . . . . . . 3.1. Particle foams . . . . . . . . . . . . . . . . . . . . . 3.2. Mixtures of oppositely charged amphiphiles and particles . 3.3. Surfactant foams . . . . . . . . . . . . . . . . . . . 3.4. Protein foams . . . . . . . . . . . . . . . . . . . . . 4. Drainage of very stable foams . . . . . . . . . . . . . . . . . 4.1. Foams containing hydrophilic particles . . . . . . . . . 4.2. Surfactant foams . . . . . . . . . . . . . . . . . . . 4.3. Foamed emulsions or “foamulsions” . . . . . . . . . . . 5. Film rupture in very stable foams . . . . . . . . . . . . . . . 5.1. Films stabilised by mixture of oppositely charged surfactants 5.2. Particle foams . . . . . . . . . . . . . . . . . . . . . 5.3. Protein films . . . . . . . . . . . . . . . . . . . . . 6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction Foams are dispersions of gas in liquid or solid matrices [1,2]. In order to generate the foam, some energy is needed to create bubble surfaces. ⁎ Corresponding author. 0001-8686/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cis.2013.10.023

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This energy is the product of the surface tension γ and of the area created A, and is orders of magnitude larger than thermal energies. Furthermore, it is not minimised, and as a consequence, foams are thermodynamically unstable. However, metastable configurations can be produced, in which each bubble takes a shape having minimal area for the given configuration: spheres for isolated bubbles, polyhedra like the well-known

E. Rio et al. / Advances in Colloid and Interface Science 205 (2014) 74–86

tetrakaidecahedron proposed by Kelvin, for small liquid volume fractions. Foams being metastable, they require the use of stabilising agents, which are generally surfactant molecules (Fig. 1), but polymers, proteins or particles can also be used. The stabilisers' role is to slow down the different mechanisms of foam ageing: drainage, coalescence and coarsening. Liquid foams drain rapidly under the influence of gravity until the liquid volume fraction ϕ reaches values less than a few percent. The foams evolve slowly afterwards due to gas transfer between bubbles (coarsening) and rupture of the films separating the bubbles (coalescence), until they fully disappear typically a few hours later. Industrial applications necessitate larger liquid (or solid) volume fractions (frequently around 50%). To stabilise such wet foams, the continuous phase needs to be either solid or, at least gelified. If the continuous phase of the foam is a gel or a solid, it is melted to allow the production of the foam and re-gelified or solidified before drainage takes place. The continuous phase may also be liquid and contain polymerisation precursors allowing to gelify or solidify the foam immediately after production. Among the numerous applications of foams, let us mention the solid foams, made with polymers, silica, metals, etc. They are widely used for catalysis, thermal and sound insulation, scaffolds for drug delivery and tissue engineering, manufacture of light containers and seating furniture, and to obtain light and resistant materials (metallic foams in car and space industries for instance) [3]. Solid food foams include bread, cakes, and meringue among others. They are prepared in the liquid state, frequently by in situ gas generation so their control necessitates understanding the stability of liquid foams. Foams made with liquids are mostly aqueous foams. Organic liquids lead to more unstable foams which are mainly studied with view of how to avoid them, because they can be damaging (in motor oils for instance). Aqueous foams are widely used, in detergency, food, cosmetics, fire-fighting (as barriers to oxygen), oil recovery (to exert pressure on the trapped oil), flotation of minerals (bubbles behaving as carriers). Many aqueous foams are stabilised by surfactants. Exceptions include food foams which are commonly stabilised by proteins. In view of these numerous applications, obtaining stable foams is an important issue. It was reported earlier that unusually stable liquid foams could be made using lamellar liquid crystal dispersions [4] and more recently using particles [5]. In this short review, we will make a survey of a number of existing results in the area and discuss the different sources of enhanced foam stability. At the outset of this article (Section 2) we will provide a brief overview of the different mechanisms involved in the destabilisation

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of foams. We will then describe different types of aqueous foams which are outstandingly stable (over months) and will be called ultra-stable, together with long-lived foams (stable over weeks), and examine in each case if coarsening, drainage and/or coalescence are slowed down or stopped (Sections 3–5). Examples will include foams stabilised with surfactants, protein and particles. Aqueous foams can also be stabilised by polymers provided surfactants are added. However, only limited results were reported [6], and they will not be discussed here. 2. Fundamental mechanisms which control foam stability 2.1. Evaporation When left to open air, foams can be destroyed because of liquid evaporation. The surface monolayers can affect evaporation rates, and it is known that very compact monolayers such as those made from fatty alcohols can significantly reduce water evaporation [7]. A recent paper investigates this problem in detail [8]. In the following, we will not address this issue, since in most of the reported studies care has been taken to prevent evaporation. 2.2. Coarsening Coarsening involves the transport of gas between bubbles of different sizes, leading to the growth of the average bubble radius R with time t: R ~ t1/2 [1,2]. Coarsening has the same origin than the phenomenon of Ostwald ripening in dilute dispersions, where the gas diffuses from the smaller to the larger bubbles due to difference in Laplace pressure. In the latter situation however, R ~ t1/3. The law R ~ t1/2 arises from the fact that in foams, the gas mainly diffuses trough the thin films between bubbles for which the diffusion path is the smallest. The characteristic coarsening time can be estimated as: t coars ¼

R2 Deff f ðϕÞh

ð1Þ

where R is the average bubble radius, Deff an effective diffusion coefficient, f(ϕ) the fraction of total area A of the bubble covered by thin films (A ~ 14 R2 for the tetrakaidecahedron of Kelvin, independent of ϕ) and h the film thickness [9]. Let us also mention that the nature of the gas used for foaming plays a crucial role through the parameter Deff: gases soluble in water such as CO2

film

Plateau border

node Fig. 1. Aqueous foam stabilised by surfactants with polyhedral bubbles. Liquid film between bubbles (top right) covered by surfactant monolayers and Plateau border junction (bottom right). Surfactant molecules are represented by a circle (polar head), in contact with water, and a hydrophobic chain, in contact with air. The surfactant is also solubilized in water and present in the bulk liquid.

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give less stable foams than less soluble ones such as N2, because CO2 transport across water films is faster. The stability of CO2 foams can be improved by adding small amounts of nitrogen: since the gas composition in each bubble cannot change (otherwise, the chemical potential would vary locally), the gas diffusion process is slowed down [10]. As in the case of evaporation, the diffusion of gas molecules through thin films is affected by the presence of surfactant monolayers. However, it is not yet clear whether the monolayer contribution is always significant as compared to the film liquid contribution [11]. The presence of the monolayer can have another, potentially more important influence on the coarsening process due to its mechanical properties. It was shown in numerical simulations by van Vliet and coworkers that Ostwald ripening in emulsions can be slowed down by increasing the compression elastic modulus E of the monolayer [12]. This was verified recently experimentally in surfactant-stabilised emulsions [13]. When the compression elastic modulus E reaches the value E = γ/ 2, the simulations show that Ostwald ripening stops as predicted earlier by Gibbs [14]. The Gibbs argument holds for a single bubble and makes use of the derivative of the Laplace pressure P with respect to the bubble radius R. For an isolated bubble covered by layers with a compression elastic modulus E, one has
 2γ d dP 2γ 2 dγ 2 R ¼− 2 þ ¼ ¼ ð2E−γ Þ dR dR R dR R2 R ¼ R2 dγ with the area of the bubble, A = 4πR2. If E b γ/2, since E ¼ A dγ dA dR the pressure inside the bubble increases when its radius decreases, which leads to a self-accelerated dissolution of the bubble, and to its complete disappearance. If, on the contrary, E N γ/2, the pressure inside the bubble decreases upon decrease of bubble radius. The dissolution of the bubble therefore slows down and eventually stops when the Laplace pressure approaches zero. In this case the bubble will distort and adopt faceted shapes: this has been observed both experimentally and in simulations on bubbles covered by particle monolayers [15,16]. Note that in their simulations, van Vliet and co-workers assume a constant surface elastic modulus E, which might not be the case in practice, as the surface layers become increasingly compressed (or expanded). Coarsening of foams is a much more complex issue: foams are assemblies of close packed bubbles and coarsening depends on the number of faces of the bubbles rather than on their size [17]. A slowing down of coarsening with increasing compression modulus was observed recently, but attributed to the influence of the local structure of the surfactant monolayers covering the film surface changing the film permeability to gases [18]. In practice, the condition E = γ/2 is never reached by surfactants: coarsening is a slow process, and surfactant can desorb and adsorb freely, so the resistance to compression (and expansion) of the layer at the bubble surfaces vanishes in the long-time limit. Protein-stabilised bubbles injected below the air–water surface also shrink and disappear [19]. This is at first sight in contradiction with the model presented previously, because protein layers can have very large compression moduli, well above γ/2 and the layers exchange little with bulk (proteins are frequently irreversibly adsorbed). However, these layers can slowly collapse upon increasing compaction, forming multilayers. The arrest of coarsening seems to request both a high surface elastic modulus and a resistance to collapse. Particle layers are irreversibly adsorbed; they resist collapse and buckle, possibly a reason why particle foams do not coarsen (Fig. 2) [20]. A special class of proteins, hydrophobins, share this property with particle layers and also inhibit foam coarsening [21]. The foam resistance to coarsening is therefore certainly linked to the surface compression modulus. However, going beyond the simple Gibbs argument, or even the simulations for an ensemble of spherical bubbles, is a very difficult task that deserves further investigations.

2.3. Foam drainage Bubbles with sizes larger than a few microns rise quickly due to gravity and the liquid is collected at the bottom of the created foam: this is the phenomenon of drainage (Fig.3). When the liquid volume fraction of the foam falls below about 30%, the bubbles are no longer spherical, they distort into polyhedra, the flattened regions being the liquid films. Drainage of foams was extensively studied [1,22,23]. The liquid flows through the interstitial spaces between bubbles, which are composed of thin films, Plateau borders (PBs) made of connections of three films and junctions or nodes made of connections of four PBs (Fig. 1). When drainage continues, the films separating the bubbles thin and eventually break. The characteristic time of drainage is given by [22,23]: t drain ¼

Hη KρgR2 ϕα

ð2Þ

where H is the foam height, R the average bubble radius, ρ the liquid density, η its viscosity, g the acceleration of gravity, K a dimensionless permeability constant of order 10−2 and α an exponent between 0.5 and 1; K and α depend on the mobility of the surface layers protecting the bubbles, which depends itself not only on the compression modulus E but also on the surface shear viscosity [23]. 2.4. Coalescence When drainage has been completed, and the equilibrium liquid volume fraction profile ϕ(z) reached [24], the films between bubbles have become thin and they can then rupture, leading to bubble coalescence. The first point to be taken into account is the surface coverage of the bubbles, which should be sufficient to resist coalescence. Considering that the bubbles have the shape of a tetrakaidecahedron (Kelvin cell) and using the known calculations of bubble volumes [25], the surface concentration of the particles can be estimated as Γ = 11.31 Cl ϕ/[26.8(1-ϕ)], where C is the surfactant(/protein/particle) concentration and l is the length of the Plateau borders (l ~ 0.72 R, R being the radius of a sphere having the same volume than the bubble; all Plateau borders have the same length in a Kelvin cell). This expression is not very different when one assumes spherical bubble geometry: Γ = C R ϕ/[3 (1-ϕ)]. Studies of monolayers have shown that the saturation surface concentration Γ is of the order of 1 mg/m2 for surfactants, 2–3 mg/m2 for proteins and 50 mg/m2 for 10 nm radius particles. Taking the example of foams made by turbulent mixing [26], the bubble size is about 100 μm for surfactants, 50 μm for proteins and 25 μm for particles. Taking equal volumes of air and liquid during the mixing process (ϕ = 0.5) leads to minimum concentrations of 3 · 10− 3 wt.% for

50 μm

Fig. 2. Optical microscopy picture of a bubble in a foam stabilised with particles. The bubble surface is corrugated, suggesting a resistance to shrinkage. After [20].

E. Rio et al. / Advances in Colloid and Interface Science 205 (2014) 74–86

surfactants, 2 · 10−2 wt.% for proteins and around 1 wt.% for particles. Despite the fact that particles are very good stabilisers, they have therefore to be added in significant amounts to produce stable foams. So far, very little is understood about the main mechanisms of film rupture. Some authors report that coalescence in foams occurs once the bubbles have reached a critical size [27] as in emulsions [28], once the liquid fraction has reached a critical value [29] or when the applied pressure or the capillary pressure reaches a critical value [30]. Even if these mechanisms are very different, it is difficult to distinguish experimentally between them since capillary pressure, liquid fraction and bubble size are linked as in the case of emulsions [31]. The different behaviours observed in the literature might also be due to different flow conditions and accordingly to different coalescence processes. More details on this complex issue can be found in Ref. [32]. We will not discuss here the corresponding mechanisms, since very stable foams usually have thick gelified or solid foam films, for which film rupture mechanisms are different. In the case of particles, an issue is the possible rupture of the films promoted by the particles. Whether a particle acts as antifoam or not depends in particular on the interfacial tensions between the three phases (air, water, particle). One generally introduces various coefficients (such as the entry coefficient En and the bridging coefficient Br) to describe the particle antifoam potential [33,34]. These coefficients En and Br are defined as follows: En ¼ γaw þ γpw −γap 2

2

2

Br ¼ γaw þ γ pw −γ ap

ð3Þ

where γ refers to the different surface tensions and the indexes p, a and w stand respectively for the particle, air and the aqueous phase. The entry coefficient En is linked to the potential of the dispersed particles to penetrate into the air–water interface. It should be positive for the particle to act as antifoam. The bridging coefficient Br is linked to the ability of the particles to bridge the foam films. Positive values indicate potentially fast antifoam. The actual antifoam action also depends on an energy barrier for entering the gas–water interface, which appears to be the best measure of antifoam activity, i.e. how easily the droplets can enter the air/water interface, but which is not obvious to measure [35]. Particles that cannot enter the surface of films will be trapped in the Plateau borders and can act as foam stabilisers [36]. 3. Coarsening in very stable foams 3.1. Particle foams Excellent candidates to fight the foam destabilisation by coarsening are surface-active particles. Although the capability of particles to stabilise bubbles has been known for almost one hundred years, mainly in industrial domains such as flotation [37] and food processing [38], the fundamental understanding of the underlying mechanism preventing coarsening at the scale of individual bubbles or of entire foams is much more recent and still incomplete (see [20,39–41] and the references therein). An important point is the high adsorption energy of the particle at the air/water interface Eads = πa2γW(1-cos θ)2, with a being the particle radius, γW the surface tension of the air/water interface and θ the contact angle of the particle at the air/water interface measured through the water [42]. This energy is maximum for θ = 90°, and about 104kBT for a particle with a radius of 10 nm (kB being the Boltzmann constant, T the absolute temperature). This is three orders of magnitude higher than the adsorption energy for surfactants [43] and therefore leads to an irreversible attachment of the particles to the air/water interface, and to the formation of solid-like surface layers. Together with the resistance of the interfaces to collapse, this may prevent both coarsening and coalescence [15,43–46].

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Foams can be stabilised in practice by particles provided that they are not too hydrophilic, i.e. when the contact angle between particles and water is not too small. A number of studies were made using fumed silica nanoparticles of variable hydrophobicity, controlled by chemical coating with a short-chain silane reagent (dichlorodimethylsilane). Fig. 4 shows the aspect of the foams for different silanisation degrees together with the measured contact angles [47,48]. The maximum in foamability corresponds to a residual percentage of OH groups at the surface of the particles of around 35% SiOH, i.e. to a contact angle of 120°. This may seem high, but it should be stressed that θ was measured using pellets made of compacted particles, so the actual contact angle could be different. The foams prepared with particles possessing 32% and 42% SiOH were stable over years against coarsening and coalescence [44]. Similar results have been found with other types of particles, of varying shape, size and surface chemistry [45]. These particle-stabilised foams are however ultra-stable only if the particle concentration in the initial dispersion is large enough. It was reported, using multiple light scattering techniques (see in Fig. 5), that the stability of the foams produced by turbulent mixing with silica particle concentrations below 0.7 wt.% was limited, and comparable to that of the foam made with a standard surfactant such as sodium dodecyl sulfate (SDS) [46]. However when the particle concentration reaches the value of 0.7 wt.%, the stability becomes remarkable, with foams lasting for months. After a drainage period where the liquid drained is clear (as compared with the dispersions which are turbid), the foam evolves little with time. If initially after creation the bubble surfaces are not sufficiently covered by particles, upon coalescence, the surface to volume ratio of the created bubbles decreases, hence the eventually released particles could re-adsorb and the surface concentration of the particles increases. Coalescence should then proceed until the surface is sufficiently covered. This phenomenon was called limited coalescence [49] and was observed with emulsion stabilised by the same type of particles. For foams, as can be seen in Fig. 5, the bubble size never stops increasing with time, even when the concentration is above the stability limit. The limited coalescence has never been observed with the foams and the reason for this being not at all obvious. X-ray tomography of foams made by shaking revealed that some bubbles shrink, but that other bubbles become larger. This contradiction with the previous results could be due to (i) the fact that coarsening might only be arrested after some time, (ii) the fact that the bubbles could be less well covered than in foams made by turbulent mixing [50] or (iii) the fact that the DWS method only probes the averaged value of the bubble size. Visual observations after several months also revealed the presence of bubbles which are sometimes broken, but seemingly without having influenced their neighbours (Fig. 6) [20]. The fact that the large bubbles are frequently broken may perhaps be related to the fracture of particle monolayers seen upon expansion [51]. The role of particle concentration in foam stability can be rationalised by surface coverage (as explained in Section 2.4). Studies of particle mono-layers have shown that the maximum surface concentration is Γ = 50 mg m−2 [52] and measured bubble radii are of the order of 25 μm in the foams made by turbulent mixing; using Γ = C R ϕ/[3 (1-ϕ)]. Since usually comparable volumes of gas and liquid are mixed, we will use ϕ = 0.5 that leads to C ~ 0.7 wt.%, in good agreement with the observed behaviour. It was also checked that for C N 0.6 wt.%, the surface elastic compression modulus was larger than half the surface tension in surface layers adsorbed at the surface of the dispersions, in line with the Gibbs criteria exposed in Section 2.2 [53]. Note that 50 mg/m2 corresponds to an incomplete surface coverage by particles, which form rather a rigid percolated network at the surface [53]. This peculiar behaviour was also observed in particle stabilised emulsions [54]. It has to be noted that these foams are difficult to produce. The particles generally bear electrical charges and they create large adsorption barriers, much larger than ionic surfactants [41,46]. This means that

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E. Rio et al. / Advances in Colloid and Interface Science 205 (2014) 74–86

Reduced height H* = R /l c2H

20

15

Average Bubble Radius 100 1000 326 50 180 900 253 464

10

μm μm μm μm μm μm μm μm

R

5

0 0,0

0,1

0,2

0,3

Liquid fraction φ Fig. 3. Draining foam (left): the top of the foam is dry and composed of polyhedral bubbles. The bottom of the foam, which is in contact with the liquid, is wet and contains spherical bubbles. Right: vertical profile of the equilibrium volume fraction ϕ(z) calculated (line) and measured (points) for a foam with different mean bubble radii R; H* is the reduced height pffiffiffiffiffiffiffiffiffiffiffi H R/l2c , lc ¼ γ=ρg being the capillary length. Adapted from [24].

getting the particles onto the interfaces is difficult, and the foams are even hard to produce by handshaking. Microfluidic techniques which have the advantage of producing monodisperse foams [55] are here inoperant. In situ hydrophobising methods have been devised to surmount this difficulty [56] (Section 3.2).

3.2. Mixtures of oppositely charged amphiphiles and particles The surface of hydrophilic particles can also be rendered partially hydrophobic by making use of the complexation with oppositely charged amphiphilic molecules [57–59]. Due to the ease of preparation

Fig. 4. Top: Photograph of vessels containing fumed silica particle dispersions for particles of different wettabilities. The dispersions were aerated and the photographs were taken two weeks after the creation of the foam. The primary silica particles are quasi-spherical, of 20–30 nm in diameter, and are aggregated into clusters of about 200 nm in diameter. Particles become more hydrophilic from left to right as the % SiOH content on particle surfaces (written above) increases; the mixtures change from water-in-air powders to air-in-water foams (with drained water) to aqueous dispersions. Data from [47]. Bottom: Advancing contact angle, θ, of pure water droplets on flat surfaces formed from fumed silica particles of different percentages of surface SiOR groups (SiOR% = 100 - SiOH%) [48].

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5

SDS surfactant

/

4

3

particles : 1 wt. % 0.1 wt. % 0.3 wt. % 0.5 wt. % 0.7 wt. %

2

1 101

102

103

104

105

106

foam age (s) Fig. 5. Normalised average bubble radius versus time for sodium dodecyl sulfate (SDS) and silica particle-stabilised foams, the latter made with different bulk particle concentrations (given), prepared via turbulent mixing. The particles surface possesses 34% SiOH. After [46].

and its applicability to very different types of particles and amphiphiles, the method is becoming popular for the generation of highly stable foams. It has also the advantage of being applicable to microfluidic devices, since the hydrophobisation of the particles is produced in situ [60]. Most available studies of these types of systems combine simple foaming experiments (shaking or mixing) with investigations of the bulk properties and simple surface tension measurements. A more recent study of the foaming properties of aqueous dispersions containing mixtures of hydrophilic silica nano-particles (Ludox) and a short-chain amphiphile (n-amylamine) combined standard handshaking methods, microfluidic techniques and surface rheology measurements [60]. The study showed that stable foams can be obtained at amine concentrations above approximately Ca* = 0.5 wt.%, independently of particle concentration, which appeared to be a critical concentration for cooperative association between particles and amine. In contrast to foams stabilised solely by nano-particles, these foams suffer from slow coarsening despite their high surface elastic modulus, due to gas exchange between bubbles. This is possibly due to the non-permanent nature of the association between the amphiphile and the particle and/or to the formation of multilayers of particles under compression. Ultra-stable foams for which coarsening is inhibited can only be produced at sufficiently high particle and amine concentrations (typically 10 and 3 wt.%, respectively) for which the dispersions also gel in the continuous phase of the foam. Similar results were found by Gonzenbach and

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Gauckler [57] who studied the same silica/amylamine system, using still larger particle concentrations (35 wt.%). They obtained foams stable against coarsening, coalescence and even drainage. Pictures of the foams made using microfluidic methods are shown in Fig. 7. For amine concentrations Ca between 0.5 and 1 wt.% but small particle concentration (Cp = 5 wt.%) limited coalescence is observed, leading to a range of different bubble shapes since the shape relaxation is arrested when the surface layers are sufficiently rigid [61]. Beyond this stage, foam destabilisation occurs via coarsening only. For higher particle and amine concentrations, the interfaces seem to be covered sufficiently so that coalescence is completely suppressed, giving rise to a perfectly monodisperse foam. However, after sufficiently long waiting times, these bubbles (and therefore the foams) disappear through coarsening. Upon further increase of Ca until Ca = 3 wt.%, both coalescence and coarsening are fully suppressed by bulk gelification for Cp = 10 wt.%. For Cp b 5 wt.%, the foam could not be produced using microfluidic methods. Handshaking methods were applied to produce foams with Cp = 1 wt.%. The behaviour observed is similar, except that the solutions do not gelify at large amine concentration, so the foams are never ultra-stable. Particle aggregation is important between 2.5 and 5 wt.%, causing a fast phase separation and suppressing the capability of the solution to foam. Close, but below Cp = 2.5 wt.%, particle aggregation occurs more slowly, which seems to be responsible for the enhanced foam stability. When Ca is larger than 5 wt.%, a bilayer is formed at the particle surface causing particle re-dispersion in bulk but making them again so strongly hydrophilic that solutions do not foam. Foams generated from silica particle/amine mixtures are therefore ultra-stable only when particle and surfactant concentrations are sufficiently high, and when the bulk phase is gelified, otherwise coarsening persists. Whether foams from particle/surfactant mixtures coarsen or not, seems to depend on the surfactant type used. For instance, foams made from mixed dispersions of Ludox silica particles and cetyl trimethyl ammonium bromide (CTAB) [62] show the same general behaviour as for the Ludox/amine system, whereas Ludox-dimethyl didecyl ammonium bromide mixed solutions could produce ultrastable foams, that do not coarsen even without bulk gelation [58]. Future research therefore needs to establish the conditions which a particle/surfactant mixture needs to fulfil in order to arrest coarsening. In particular, our guess that the concomitance of a high elastic surface modulus and a resistance to collapse is mandatory needs confirmation. 3.3. Surfactant foams The typically unstable nature of pure surfactant foams can be counteracted by exploiting synergies which arise in surfactant mixtures

Fig. 6. (Left) Photograph of a silica particle-stabilised foam aged nine months. The foaming dispersion contained 0.6 wt.% silica (34% SiOH). The scale bar corresponds to 200 μm. (Right) Enlargement of the portion shown by the black square, showing a partially ruptured film between two bubbles. The intact portion appears rough, the ruptured part smooth, and the limit between the two (arrow) is irregularly shaped, as expected after the rupture of a fragile film.

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Fig. 7. Monodisperse foams obtained at various Ca and two particle concentrations, 5 and 10 wt.%. For Ca = 1 wt.%, limited coalescence is observed at Cp = 5 wt.% whilst almost no coalescence is noticed at Cp = 10 wt.%. In the last case, coarsening is still present. At higher amine concentration, coarsening is also stopped, accompanied with bulk gelation. All bubble sizes are around 500 μm. Data from [60].

[63,64]. For example, foams made with mixed solutions of myristic acid and cetyl trimethylammonium chloride (CTACl) were shown recently to be very stable [65,66]. The two surfactants have opposite charges and associate in the solutions in the form of vesicles [67]. These surfactant mixtures are sometimes called catanionic surfactants. The mixed monolayer which is formed by vesicle rupture at the air–water surface is extremely rigid and prevents further vesicle rupture by avoiding contact of the vesicles with air. Confocal fluorescence microscopy revealed the presence of layers of intact vesicles that are progressively creaming towards the mixed monolayer, giving rise to an extremely thick layer [68]. The mixed monolayer not only has a large compression modulus but behaves as an amorphous solid (glassy) with a finite shear elastic modulus and time and temperature dependent properties.

Fig. 8 shows a typical image sequence of foam generated from a 0.5 wt.% mixed solution by handshaking. The solutions show only reasonable foamability, but the foam stability is much better than for standard surfactant foams. Three features have been observed: complete absence of bubble coalescence, very slow gravity-driven drainage of liquid out of the foam and very slow coarsening. These foams then combine resistance to the three types of destabilisation mechanisms. Let us discuss the coarsening issue below (drainage and coalescence will be discussed respectively in Sections 4.2 and 5.1). The coarsening is much slower than that of standard surfactant foams. This could be due either to the very closely packed monolayers, which act as gas barriers, to the high elastic modulus E of the monolayer, which counteracts coarsening, or to the presence of closely packed

Fig. 8. Image sequence of a foam made with mixed solutions of myristic acid and CTACl (C = 0.5 wt.%) generated by handshaking. The foams do not coalesce, coarsen very slowly and maintain a significant amount of liquid in comparison to standard surfactant foams with the same structural properties. From [66].

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vesicles between the bubbles. It was observed that at long time scales, the average bubble size at the top of the foam increases more rapidly than in the remaining foam (without bubble coalescence). Closer analysis showed that this part of the foam is essentially free of vesicles, which must have drained. This leads to two conclusions. Even without vesicles, the coarsening is slowed down significantly, indicating an important role of the interfaces. The presence of vesicles seems to contribute additionally to the slowing down of coarsening, due to the thickening of films and film junctions, as in protein foams (discussed in Section 3.4). Foams made with other types of catanionic mixed solutions, hydroxyl stearic fatty acid and ethanol amine were found to be ultra-stable [69]. At the difference of the myristic acid–CTACl mixtures, they contain long tubes which form spontaneously and reversibly, and block Plateau borders (Fig. 9). The sizes of the foam films were found much smaller than for standard surfactant foam films, with a very thick meniscus full of tubes. According to Eq. (2), the fractional area of film f(ϕ) is small, and the coarsening time is large. It is also probable that the surface layers are rigid, slowing down further or even arresting coarsening. 3.4. Protein foams Currently known protein foams are only ultra-stable if the foaming liquid is gelified, with the notable exception of foams made with hydrophobins: these proteins form solid like layers at the surface of water which have high elastic moduli E and do not collapse upon compression [21]. When standard proteins are used and when the foaming solution is fluid, the foam is nevertheless more stable than standard surfactant foams. Even when the protein concentration is small, protein foam films are thick and irregular [71–73] (Fig. 10 left). Apparently, protein aggregates are trapped in the film and stop the film thinning process. Note that the aggregates form at the film surfaces, because no aggregates are seen in the bulk solution. When the protein concentration is large enough, the films are gel-like. The coarsening of foams made from protein solutions is found to be somewhat slower than that of surfactant foams (Fig. 10 right). This feature was attributed to the larger film thicknesses according to Eq. (1) [71]. 4. Drainage of very stable foams 4.1. Foams containing hydrophilic particles Foams containing hydrophilic particles usually drain like surfactant foams and the drainage time follows Eq. (2). Exceptions occur when the particles can block the Plateau borders. A first example has been given by Friberg who noticed that foams made in the presence of small particles with lamellar structures (produced when the foaming liquid is water in equilibrium with a lamellar phase) can be very stable. When the liquid contains many particles, it becomes viscous, and one

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obvious effect is the slowing down of the drainage process. As pointed out by Friberg, a more subtle effect is due to the balance of the interfacial tensions: if the particle cannot enter the surface of films (see Eq. (3)) and if it is larger than the film thickness, it will be trapped in the Plateau borders, as he observed [4]. Similar effects were reported later in individual Plateau border experiments [74,75]. Another interesting example of particles arresting the drainage has been observed with solutions where colloidal clay, laponite, is dispersed in SDS before foaming. Laponite forms gels in aqueous solutions containing SDS, and a non-classical arrest of drainage is seen in foams made with these dispersions [76]. Whilst the foam drains, the laponite particles get confined in the Plateau borders, and since the yield stress of the dispersions increases upon confinement, the interstitial fluid gels, and drainage is arrested after a time tj. As coarsening continues, the bubble size increases, the size of the Plateau borders increases as well, and drainage then starts again at a time tu (Fig. 11). 4.2. Surfactant foams Foams made from myristic acid–CTACl mixed solutions drain very slowly as shown in Fig. 12 [66]. Whilst standard surfactant foam with the same initial bubble size and liquid fraction drains in about 1 h, the catanionic foam drains in about one day. It is furthermore noticeable that even when drainage stops, the foam remains visibly wet, i.e. that a significant amount of liquid remains trapped between the bubbles. It usually takes a few months for foam of this kind to disappear completely via coarsening. The drainage was investigated in more detail using confocal microscopy. Two examples are shown in Fig. 13 for the case of C = 0.1 wt.% and C = 1 wt.%. As liquid drains out between the bubbles (images from left to right) one observes an increasing trapping and compaction of vesicles and vesicle aggregates between the bubbles. Vesicles are also trapped within the thin films separating bubbles (inset of top right image). For sufficiently high concentrations one observes a complete blocking of Plateau borders by vesicles and hence a dramatic slow-down, and finally complete arrest of drainage [66]. A similar behaviour has been reported for foams made with mixed solutions of hydroxyl stearic fatty acid and ethanol amine. The drainage proceeds during a short period, after which it stops, probably for the same reason in view of the crowding of tubes seen in Fig. 9; the liquid volume fraction remains afterwards around 5%, much higher than for a standard surfactant foam (Fig. 3) [69]. 4.3. Foamed emulsions or “foamulsions” Mixtures of bubbles and droplets are encountered in many cosmetic and food products (such as whipped cream) or in oil recovery processes. In the most stable systems, the oil droplets are generally crystallised (at least partially) [77], and act as solid particles. Although many studies on

Fig. 9. Phase contrast microscopy image of a foam made with mixed solutions of hydroxyl stearic fatty acid and ethanol amine. Data from [70].

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8 7 6 5

R / R(t=0)

4

SDS

3

2

β-casein

1 100

1000

10000

time (s) Fig. 10. Optical microscopy pictures of foam films made with SDS (top left) and β-casein solutions (bottom left) showing that thickness is heterogeneous when proteins are used. Right: coarsening of a β-casein foam compared to an SDS foam; the lines are fits with a squared root of time variation. Data from [71].

food grade foamed emulsions have been performed [78,79], fewer studies exist on simpler systems. Introducing fluid oil drops into a foam is the classical approach to suppress the foaming of a solution and to destabilise existing foams [33,34,80]. In a pioneering work with dilute emulsions, Koczo et al. showed that bubbles and fluid oil droplets can coexist without destabilisation of the foam [81]. All oils are therefore not necessarily antifoaming systems and Goyon et al. used a highly concentrated emulsion as a model yield-stress fluid to study shear induced drainage in foams [82]. In a recent study, the stability of foamed emulsions has been studied in more detail [83]. Two oils were chosen for their different bridging and spreading coefficients: dodecane, En = 18 mN/m, Br = 740 mN2/m2 and rapeseed oil, En = 3 mN/m, Br = −57 mN2/ m2. From these numbers, one expects dodecane to be an antifoam and rapeseed oil to be a foam stabiliser but, surprisingly, they were both found to stabilise the foam under certain conditions. The surfactant used to stabilise both the foam and the emulsion was SDS. A criterion of good foamability was found, where the concentration of SDS must be

higher than a critical concentration such that there are enough SDS molecules to cover the surfaces of both the emulsion drops and the gas bubbles [83]. The foams made from rapeseed oil emulsions drain and coarsen like classical foams made from SDS only. This suggests that the oil droplets are only transported through the water, and do not interfere with the gas–liquid interfaces, which is consistent with the very small value of entry coefficient En. In contrast for dodecane, for which both En and Br are large and positive, the foams are much less stable. The dodecane foams have a lower lifetime than oil-free foams, and foam destruction occurs before drainage is completed. This implies that dodecane acts as slow antifoam; the oil droplets do not enter in the films, but break the foam only after being squeezed inside the Plateau borders. At larger oil volume fractions, very different features are observed, in particular an outstandingly long lifetime with the rapeseed oil with ϕoil = 0.7. When ϕoil N 0.63 (random close packing of spheres), the emulsion droplets are densely packed [84], and the emulsion becomes viscoelastic, with a finite shear modulus and yield stress. Microscope images of such a foam (ϕoil = 70%) are shown in Fig. 14. One can see that droplets are actually confined and crowded between bubbles, which stay anomalously far from each other. The presence of such a dense assembly of droplets trapped and jammed in between the bubbles has several effects. The local viscosity increases, slowing down both film thinning and Plateau borders shrinking (slower drainage) as in the case of particles. In addition, for initial bubble diameters of the order 100 μm, hydrodynamic stresses in the Plateau borders become comparable to the yield stress of the emulsion (of the order of a few Pa [85,86]). Drainage can therefore not only be slowed down, but also even be arrested if the yield stress of the emulsion becomes higher than the local hydrodynamic stresses as seen before for the laponite–SDS foam [76] and confirmed by Goyon et al. [82]. 5. Film rupture in very stable foams

Fig. 11. Time evolution of the normalised liquid fraction at a fixed position inside the foam, for SDS foams and various concentrations of laponite CL. On the curve at CL = 16 g/L, the times tj and tu are indicated. After [76].

The stability of foams is controlled by the stability of the thin films which separate bubbles. Foam films of standard surfactant solutions thin until they reach an equilibrium thickness controlled by the interaction forces between liquid surfaces (h ~ 5–20 nm) [87]. The properties

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Fig. 12. Evolution of the foam volume generated from a myristic acid–CTACl mixed solution (C = 0.5 wt.%) using turbulent mixing. A period of slow drainage is followed by a long-term stability. From [66].

of isolated, horizontal films can be conveniently studied using various devices such as the Thin Film Pressure Balance (TFPB) [88,89].

5.1. Films stabilised by mixture of oppositely charged surfactants Let us take again the example of the foams made with mixed myristic acid–CTACl solutions, for which thin films were also studied with the TFPB [66]. The films ruptured immediately when the pressure was applied without an equilibration time, whilst the stability increased significantly with equilibrium time. The films were then resistant to rupture, rendering coalescence difficult, at least on the time scales and pressure conditions accessible in the TFPB. The observations correlated well with the slow adsorption dynamics witnessed by the surface tension measurements: the film stability is greatly enhanced once the gas/liquid interface

is sufficiently covered by the surface active mixture. The film stability also depends significantly on the surfactant concentration. Fig. 15 shows representative examples of the time evolution, i.e. the progressive thinning of such films for three different concentrations (C = 0.01 wt.%, 0.05 wt.% and 0.1 wt.% after 24 h of equilibration) once a pressure of 2000 Pa is applied. As can be seen by the variation of the interference colours, the film thickness is highly heterogeneous. The fact that the typical object size is of the order of 10 μm suggests that vesicles remain trapped in the film without destruction. Films created from C = 0.1 wt.% (bottom of Fig. 15) were extremely stable and could be observed for more than 8 h. These films were also resistant to applied pressure ramps or pressure steps exhibiting the same appearance, before and after the cycle. This indicates that there is no rearrangement of the structures at the film surface and it may be concluded that, at sufficiently high concentrations, the vesicles form gel-like networks

Fig. 13. Confocal microscopy images of foams created from myristic acid–CTACl mixed solutions at bulk concentrations of C = 0.1 wt.% (top) and C = 1 wt.% (bottom). The larger (N50 μm) dark circles are air bubbles, the smaller (b20 μm) circles are vesicles. One can clearly identify the vesicles and the bubble surfaces, due to their affinity for the fluorescent dye (Oregon Green 488).

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Fig. 14. Optical microscopy photograph of a foam made from a rapeseed oil emulsion with ϕoil = 70% immediately after preparation (left) and 6 h after preparation where the Plateau borders are still very thick (right). After [83].

in the film. In all cases, the equilibrium film thickness remains unusually thick, with thicknesses above 100 nm, i.e.at least an order of magnitude thicker than for films made of standard ionic surfactant solutions (a few tens of nanometer). Interestingly, the foam films made from hydroxyl stearic fatty acid and ethanol amine mixed solutions drained down to thicknesses of the order of 20 nm, the tubes being completely expelled from the films. Therefore, these tubes did not contribute directly to stabilisation against coalescence [69].

that render these foams very stable. The films may however be broken upon expansion (Fig. 6) [91]. Let us recall that, surprisingly, the limited coalescence observed in the Pickering emulsions made with the same particles has never been observed: the long term stability is reached above C* = 0.6 wt.% (for foams made by turbulent mixing), R is constant and equal to R*; just below this concentration, the bubble radius increases with time (Fig. 5) without stabilising at a value corresponding to the optimal surface coverage: R being proportional to Γ, the limit value should be such that R = R* C*/C. The origin of the differences between the foam and emulsion behaviour remains to be elucidated.

5.2. Particle foams Stratification phenomena have been reported for foam films made of dispersions of monodisperse hydrophilic silica particles until the particles are expelled from the films [90]. However, TFPB studies showed that the films formed by the partially hydrophobic silica do not exhibit such behaviour. They are very thick and solid-like, resisting to breakage unless very large pressures are applied. This is one of the many reasons

5.3. Protein films It was reported that protein foams become stable once the thickness irregularities of the foam films become connected and the films gelify [71]. Similar observations were made in foam films containing preformed protein aggregates [92].

Fig. 15. Progressive thinning of films made from mixed solutions of myristic acid and CTACl for various concentrations (a) C = 0.01 wt.%, (b) C = 0.05 wt.% and (c) C = 0.1 wt.% after 24 h equilibrium time. The applied pressure difference is 2000 Pa. Time difference between pictures: 10 min. Data from [66].

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6. Conclusions One drawback systematically encountered with very stable foams is that they are difficult to produce. Special procedures such as in situ hydrophobisation in microfluidic devices for particles for instance have to be used to produce them in a well-controlled manner. Many examples of very stable and ultra-stable aqueous foams were reported recently in the literature. The origin of the stability is related to the slowing down of either coarsening, drainage or coalescence. In some cases, the three effects are impacted simultaneously as in the case of the myristic acid–CTACl foams. In other cases, they are frequently coupled, not always to enhance stability, as for instance in the SDS–laponite foams, where coarsening is responsible for the re-start of drainage. Coarsening is slowed down when the films between bubbles are thick and/or small, and it can be arrested when the surface compression modulus E is large enough. Drainage can be slowed down when particles accumulate in the Plateau borders or if they locally gel there if the yield stress increases upon confinement. Drainage can be arrested if the liquid of the foam either gels or solidifies. Coalescence is slowed down by gelified foam films, and it can be arrested if the films remain very thick and/or rigid. There have been significant advances in our understanding of the stabilising mechanism leading to the creation of very stable foams. The phenomena leading to arrest of drainage and coalescence are qualitatively easy to identify, but they will be less obvious to model in order to obtain quantitative predictions. The different mechanisms leading to the slowing down and to the arrest of coarsening remain less obvious. A full comprehension is still eluding us, which would allow for the complete control over the ageing of foams. Further investigations are clearly desired, combining experiments at different scales: surface layers, films, Plateau borders and bubbles and foam itself. Indeed, the mechanisms evidenced so far can act at any of these scales and partial measurements can miss important features.

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[65] [66]

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