Unusually stable liquid foams - Université Paris-Saclay · Unusually stable liquid foams ... Foams...

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

Available online xxxx

Keywords:Stable foamsFoam coarseningFoam drainageFoam coalescence

Obtaining stable liquid foams is an important issue in view of their numerous applications. In some of these, theliquid foam in itself is of interest, in others, the liquid foam acts as a precursor for the generation of solid foam. Inthis short review, we will make a survey of the existing results in the area. This will include foams stabilised bysurfactants, proteins and particles. The origin of the stability is related to the slowing down of coarsening, drain-age or coalescence, and eventually to their arrest. The three effects are frequently coupled and inmany cases, theyact simultaneously and enhance one another. Drainage can be arrested if the liquid of the foam either gels or so-lidifies. Coalescence is slowed down by gelified foam films, and it can be arrested if the films become very thickand/or rigid. These mechanisms are thus qualitatively easy to identify, but they are less easy to model in order toobtain quantitative predictions. The slowing down of coarsening requests either very thick or small films, and itsarrest was observed in caseswhere the surface compression modulus was large. The detail of the mechanisms atplay remains unclear.

© 2013 Elsevier B.V. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 02. Fundamental mechanisms which control foam stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

2.1. Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 02.2. Coarsening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 02.3. Foam drainage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 02.4. Coalescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

3. Coarsening in very stable foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 03.1. Particle foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 03.2. Mixtures of oppositely charged amphiphiles and particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 03.3. Surfactant foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 03.4. Protein foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

4. Drainage of very stable foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 04.1. Foams containing hydrophilic particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 04.2. Surfactant foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 04.3. Foamed emulsions or “foamulsions” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

5. Film rupture in very stable foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 05.1. Films stabilised by mixture of oppositely charged surfactants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 05.2. Particle foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 05.3. Protein films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

1. Introduction

Foams are dispersions of gas in liquid or solid matrices [1,2]. In orderto generate the foam, some energy is needed to create bubble surfaces.

This energy is the product of the surface tension γ and of the area createdA, and is orders of magnitude larger than thermal energies. Furthermore,it is not minimised, and as a consequence, foams are thermodynamicallyunstable. However, metastable configurations can be produced, inwhich

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Please cite this article as: Rio E, et al, Unusually stable liquid foams, Adv Colloid Interface Sci (2013), http://dx.doi.org/10.1016/j.cis.2013.10.023

each bubble takes a shape having minimal area for the given configura-tion: spheres for isolated bubbles, polyhedra like the well-knowntetrakaidecahedron proposed by Kelvin, for small liquid volumefractions.

Foams being metastable, they require the use of stabilisingagents, which are generally surfactant molecules (Fig. 1), but poly-mers, proteins or particles can also be used. The stabilisers' role is toslow down the different mechanisms of foam ageing: drainage,coalescence and coarsening. Liquid foams drain rapidly under theinfluence of gravity until the liquid volume fraction ϕ reachesvalues less than a few percent. The foams evolve slowly afterwardsdue to gas transfer between bubbles (coarsening) and rupture of thefilms separating the bubbles (coalescence), until they fully disappear typ-ically a few hours later. Industrial applications necessitate larger liquid(or solid) volume fractions (frequently around 50%). To stabilise suchwet foams, the continuous phase needs to be either solid or, at leastgelified. If the continuous phase of the foam is a gel or a solid, it is meltedto allow the production of the foam and re-gelified or solidified beforedrainage takes place. The continuous phase may also be liquid andcontain polymerisation precursors allowing to gelify or solidify thefoam immediately after production.

Among the numerous applications of foams, let us mention the solidfoams, made with polymers, silica, metals, etc. They are widely used forcatalysis, thermal and sound insulation, scaffolds for drug delivery andtissue engineering, manufacture of light containers and seating furni-ture, and to obtain light and resistant materials (metallic foams in carand space industries for instance) [3]. Solid food foams include bread,cakes, and meringue among others. They are prepared in the liquidstate, frequently by in situ gas generation so their control necessitatesunderstanding the stability of liquid foams.

Foams made with liquids are mostly aqueous foams. Organic liquidslead tomore unstable foamswhich aremainly studiedwith viewof howto avoid them, because they can be damaging (in motor oils for in-stance). Aqueous foams are widely used, in detergency, food, cosmetics,fire-fighting (as barriers to oxygen), oil recovery (to exert pressure onthe trapped oil), flotation of minerals (bubbles behaving as carriers).Many aqueous foams are stabilised by surfactants. Exceptions includefood foams which are commonly stabilised by proteins.

In view of these numerous applications, obtaining stable foams is animportant issue. It was reported earlier that unusually stable liquidfoams could be made using lamellar liquid crystal dispersions [4] andmore recently using particles [5]. In this short review, we will make asurvey of a number of existing results in the area and discuss the differ-ent sources of enhanced foam stability.

At the outset of this article (Section 2) we will provide a brief over-view of the different mechanisms involved in the destabilisation offoams. We will then describe different types of aqueous foams whichare outstandingly stable (over months) and will be called ultra-stable,together with long-lived foams (stable over weeks), and examine ineach case if coarsening, drainage and/or coalescence are slowed downor stopped (Sections 3–5). Examples will include foams stabilised withsurfactants, protein and particles. Aqueous foams can also be stabilisedby polymers provided surfactants are added. However, only limitedresults 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 liquidevaporation. The surface monolayers can affect evaporation rates, andit is known that very compact monolayers such as those made fromfatty alcohols can significantly reduce water evaporation [7]. A recentpaper investigates this problem in detail [8]. In the following, we willnot address this issue, since in most of the reported studies care hasbeen taken to prevent evaporation.

2.2. Coarsening

Coarsening involves the transport of gas between bubbles of differentsizes, 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 ofOstwald ripening in dilute dispersions, where the gas diffuses from thesmaller to the larger bubbles due to difference in Laplace pressure. Inthe latter situation however, R ~ t1/3. The law R ~ t1/2 arises from thefact that in foams, the gas mainly diffuses trough the thin films betweenbubbles for which the diffusion path is the smallest. The characteristiccoarsening time can be estimated as:

tcoars ¼R2

Deff f ϕð Þh ð1Þ

where R is the average bubble radius, Deff an effective diffusion coeffi-cient, f(ϕ) the fraction of total area A of the bubble covered by thinfilms (A ~ 14 R2 for the tetrakaidecahedron of Kelvin, independent of ϕ)and h the film thickness [9].

Let us alsomention that the nature of the gas used for foaming plays acrucial role through the parameterDeff: gases soluble inwater 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 (bottomright). 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 andpresent in the bulk liquid.

2 E. Rio et al. / Advances in Colloid and Interface Science xxx (2013) xxx–xxx


give less stable foams than less soluble ones such as N2, because CO2

transport acrosswaterfilms is faster. The stability of CO2 foams can be im-proved by adding small amounts of nitrogen: since the gas compositionin each bubble cannot change (otherwise, the chemical potential wouldvary locally), the gas diffusion process is slowed down [10].

As in the case of evaporation, the diffusion of gas molecules throughthin films is affected by the presence of surfactant monolayers. Howev-er, it is not yet clear whether the monolayer contribution is alwayssignificant as compared to the film liquid contribution [11].

The presence of the monolayer can have another, potentially moreimportant influence on the coarsening process due to its mechanicalproperties. It was shown in numerical simulations by van Vliet and co-workers that Ostwald ripening in emulsions can be slowed down by in-creasing the compression elastic modulus E of the monolayer [12]. Thiswas verified recently experimentally in surfactant-stabilised emulsions[13].When the compression elasticmodulus E reaches the value E = γ/2, the simulations show that Ostwald ripening stops as predicted earlierby Gibbs [14]. The Gibbs argument holds for a single bubble and makesuse of the derivative of the Laplace pressure Pwith respect to the bubbleradius R. For an isolated bubble covered by layers with a compressionelastic modulus E, one has

dPdR

¼d

2γR

� �

dR¼ −2γ

R2 þ 2R

dγdR

¼ 2R2 2E−γð Þ

since E ¼ A dγdA ¼ R

2dγdR with the area of the bubble, A = 4πR2. If E b γ/2,

the pressure inside the bubble increases when its radius decreases,which leads to a self-accelerated dissolution of the bubble, and to itscomplete disappearance. If, on the contrary, E N γ/2, the pressure insidethe bubble decreases upon decrease of bubble radius. The dissolution ofthe bubble therefore slows down and eventually stopswhen the Laplacepressure approaches zero. In this case the bubble will distort and adoptfaceted shapes: this has been observed both experimentally and in sim-ulations on bubbles covered by particlemonolayers [15,16]. Note that intheir simulations, van Vliet and co-workers assume a constant surfaceelasticmodulus E, whichmight not be the case in practice, as the surfacelayers become increasingly compressed (or expanded).

Coarsening of foams is amuchmore complex issue: foams are assem-blies of close packed bubbles and coarsening depends on the number offaces of the bubbles rather than on their size [17]. A slowing down ofcoarseningwith increasing compressionmoduluswas observed recently,but attributed to the influence of the local structure of the surfactantmonolayers covering the film surface changing the film permeability togases [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 bub-ble surfaces vanishes in the long-time limit. Protein-stabilised bubblesinjected below the air–water surface also shrink and disappear [19].This is at first sight in contradictionwith themodel presented previously,because protein layers can have very large compression moduli, wellabove γ/2 and the layers exchange littlewith bulk (proteins are frequent-ly irreversibly adsorbed). However, these layers can slowly collapse uponincreasing compaction, forming multilayers.

The arrest of coarsening seems to request both a high surfaceelastic modulus and a resistance to collapse. Particle layers areirreversibly adsorbed; they resist collapse and buckle, possibly a rea-son why particle foams do not coarsen (Fig. 2) [20]. A special class ofproteins, hydrophobins, share this property with particle layers andalso inhibit foam coarsening [21].

The foam resistance to coarsening is therefore certainly linked to thesurface compressionmodulus. However, going beyond the simple Gibbsargument, 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 togravity and the liquid is collected at the bottom of the created foam:this is the phenomenon of drainage (Fig.3). When the liquid volumefraction of the foam falls below about 30%, the bubbles are no longerspherical, they distort into polyhedra, the flattened regions being theliquid films. Drainage of foams was extensively studied [1,22,23]. Theliquid flows through the interstitial spaces between bubbles, whichare composed of thin films, Plateau borders (PBs) made of connectionsof three films and junctions or nodes made of connections of four PBs(Fig. 1).

When drainage continues, the films separating the bubbles thin andeventually break. The characteristic time of drainage is given by [22,23]:

tdrain ¼ HηKρgR2ϕα ð2Þ

where H is the foam height, R the average bubble radius, ρ the liquiddensity, η its viscosity, g the acceleration of gravity, K a dimensionlesspermeability constant of order 10−2 and α an exponent between 0.5and 1; K and α depend on the mobility of the surface layers protectingthe bubbles, which depends itself not only on the compressionmodulusE but also on the surface shear viscosity [23].

2.4. Coalescence

When drainage has been completed, and the equilibrium liquidvolume fraction profile ϕ(z) reached [24], the films between bubbleshave become thin and they can then rupture, leading to bubblecoalescence.

The first point to be taken into account is the surface coverage ofthe bubbles, which should be sufficient to resist coalescence. Consid-ering that the bubbles have the shape of a tetrakaidecahedron (Kel-vin cell) and using the known calculations of bubble volumes [25],the surface concentration of the particles can be estimated asΓ = 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, Rbeing the radius of a sphere having the same volume than the bubble;all Plateau borders have the same length in a Kelvin cell). This expressionis not very different when one assumes spherical bubble geometry:Γ = C R ϕ/[3 (1-ϕ)]. Studies of monolayers have shown that the satura-tion 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. Takingthe example of foams made by turbulent mixing [26], the bubble size isabout 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 μμm

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

3E. Rio et al. / Advances in Colloid and Interface Science xxx (2013) xxx–xxx


surfactants, 2 · 10−2 wt.% for proteins and around 1 wt.% for particles.Despite the fact that particles are very good stabilisers, they have there-fore to be added in significant amounts to produce stable foams.

So far, very little is understood about the main mechanisms of filmrupture. Some authors report that coalescence in foams occurs oncethe bubbles have reached a critical size [27] as in emulsions [28], oncethe liquid fraction has reached a critical value [29] or when the appliedpressure or the capillary pressure reaches a critical value [30]. Even ifthese mechanisms are very different, it is difficult to distinguish exper-imentally between them since capillary pressure, liquid fraction andbubble size are linked as in the case of emulsions [31]. The differentbehaviours observed in the literature might also be due to differentflow conditions and accordingly to different coalescence processes.More details on this complex issue can be found in Ref. [32]. We willnot discuss here the corresponding mechanisms, since very stablefoams usually have thick gelified or solid foam films, for which filmrupture mechanisms are different.

In the case of particles, an issue is the possible rupture of the filmspromoted by the particles. Whether a particle acts as antifoam or notdepends in particular on the interfacial tensions between the threephases (air, water, particle). One generally introduces various coeffi-cients (such as the entry coefficient En and the bridging coefficient Br)to describe the particle antifoam potential [33,34]. These coefficientsEn and Br are defined as follows:

En ¼ γaw þ γpw−γap

Br ¼ γ2aw þ γ2

pw−γ2ap

ð3Þ

where γ refers to the different surface tensions and the indexes p, a andw stand respectively for the particle, air and the aqueous phase. Theentry coefficient En is linked to the potential of the dispersed particlesto penetrate into the air–water interface. It should be positive for theparticle to act as antifoam. The bridging coefficient Br is linked to theability of the particles to bridge the foam films. Positive values indicatepotentially fast antifoam. The actual antifoam action also depends onan energy barrier for entering the gas–water interface, which appearsto be the best measure of antifoam activity, i.e. how easily the dropletscan enter the air/water interface, but which is not obvious to measure[35]. Particles that cannot enter the surface of films will be trapped inthe 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 coars-ening are surface-active particles. Although the capability of parti-cles to stabilise bubbles has been known for almost one hundredyears, mainly in industrial domains such as flotation [37] and foodprocessing [38], the fundamental understanding of the underlyingmechanism preventing coarsening at the scale of individual bub-bles or of entire foams is much more recent and still incomplete(see [20,39–41] and the references therein). An important point isthe high adsorption energy of the particle at the air/water interfaceEads = πa2γW(1-cos θ)2, with a being the particle radius, γW thesurface tension of the air/water interface and θ the contact angleof the particle at the air/water interface measured through thewater [42]. This energy is maximum for θ = 90°, and about104kBT for a particle with a radius of 10 nm (kB being the Boltzmannconstant, T the absolute temperature). This is three orders of mag-nitude higher than the adsorption energy for surfactants [43] andtherefore leads to an irreversible attachment of the particles tothe air/water interface, and to the formation of solid-like surfacelayers. Together with the resistance of the interfaces to collapse,this may prevent both coarsening and coalescence [15,43–46].

Foams can be stabilised in practice by particles provided that they arenot too hydrophilic, i.e. when the contact angle between particles andwater is not too small. A number of studies weremade using fumed silicananoparticles of variable hydrophobicity, controlled by chemical coatingwith a short-chain silane reagent (dichlorodimethylsilane). Fig. 4 showsthe aspect of the foams for different silanisation degrees together withthe measured contact angles [47,48].

Themaximum in foamability corresponds to a residual percentage ofOH groups at the surface of the particles of around 35% SiOH, i.e. to acontact angle of 120°. This may seem high, but it should be stressedthat θ was measured using pellets made of compacted particles, so theactual contact angle could be different. The foams prepared with parti-cles possessing 32% and 42% SiOH were stable over years against coars-ening and coalescence [44]. Similar results have been found with othertypes of particles, of varying shape, size and surface chemistry [45].

These particle-stabilised foams are however ultra-stable only if theparticle concentration in the initial dispersion is large enough. It was re-ported, usingmultiple light scattering techniques (see in Fig. 5), that thestability of the foams produced by turbulent mixing with silica particleconcentrations below 0.7 wt.% was limited, and comparable to that ofthe foammade with a standard surfactant such as sodium dodecyl sul-fate (SDS) [46]. However when the particle concentration reaches thevalue of 0.7 wt.%, the stability becomes remarkable, with foams lastingfor months. After a drainage period where the liquid drained is clear(as compared with the dispersions which are turbid), the foam evolveslittle with time. If initially after creation the bubble surfaces are not suf-ficiently covered by particles, upon coalescence, the surface to volumeratio of the created bubbles decreases, hence the eventually releasedparticles could re-adsorb and the surface concentration of the particlesincreases. Coalescence should then proceed until the surface is suffi-ciently covered. This phenomenon was called limited coalescence [49]and was observed with emulsion stabilised by the same type of parti-cles. For foams, as can be seen in Fig. 5, the bubble size never stops in-creasing with time, even when the concentration is above the stabilitylimit. The limited coalescence has never been observed with the foamsand the reason for this being not at all obvious.

X-ray tomography of foams made by shaking revealed that somebubbles shrink, but that other bubbles become larger. This contra-diction with the previous results could be due to (i) the fact thatcoarsening might only be arrested after some time, (ii) the factthat the bubbles could be less well covered than in foams made byturbulent mixing [50] or (iii) the fact that the DWS method onlyprobes the averaged value of the bubble size. Visual observationsafter several months also revealed the presence of bubbles whichare sometimes broken, but seemingly without having influencedtheir neighbours (Fig. 6) [20]. The fact that the large bubbles arefrequently broken may perhaps be related to the fracture of particlemonolayers seen upon expansion [51].

The role of particle concentration in foam stability can berationalised by surface coverage (as explained in Section 2.4). Studiesof particle mono-layers have shown that themaximum surface concen-tration is Γ = 50 mg m−2 [52] and measured bubble radii are of theorder of 25 μm in the foams made by turbulent mixing; using Γ = C Rϕ/[3 (1-ϕ)]. Since usually comparable volumes of gas and liquid aremixed, we will use ϕ = 0.5 that leads to C ~ 0.7 wt.%, in good agree-ment with the observed behaviour. It was also checked that forC N 0.6 wt.%, the surface elastic compression modulus was larger thanhalf the surface tension in surface layers adsorbed at the surface of thedispersions, in line with the Gibbs criteria exposed in Section 2.2 [53].Note that 50 mg/m2 corresponds to an incomplete surface coverageby particles, which form rather a rigid percolated network at the surface[53]. This peculiar behaviour was also observed in particle stabilisedemulsions [54].

It has to be noted that these foams are difficult to produce. The par-ticles generally bear electrical charges and they create large adsorptionbarriers, much larger than ionic surfactants [41,46]. This means that



getting the particles onto the interfaces is difficult, and the foams areeven hard to produce by handshaking. Microfluidic techniques whichhave the advantage of producing monodisperse foams [55] are hereinoperant. In situ hydrophobising methods have been devised to sur-mount this difficulty [56] (Section 3.2).

3.2. Mixtures of oppositely charged amphiphiles and particles

The surface of hydrophilic particles can also be rendered partiallyhydrophobic by making use of the complexation with oppositelycharged amphiphilic molecules [57–59]. Due to the ease of preparation

0,0 0,1 0,2 0,30

5

10

15

20

Average Bubble Radius R 100 μm 1000 μm 326 μm 50 μm 180 μm 900 μm 253 μm 464 μm

Red

uced

hei

ght H

* =

R /l

2 H

Liquid fraction φ

cFig. 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 sphericalbubbles. 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 heightH R/lc2, lc ¼

ffiffiffiffiffiffiffiffiffiffiffiγ=ρg

pbeing the capillary length.

Adapted from [24].

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 twoweeks 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. Particlesbecome 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 differentpercentages of surface SiOR groups (SiOR% = 100 - SiOH%) [48].



and its applicability to very different types of particles and amphiphiles,the method is becoming popular for the generation of highly stablefoams. It has also the advantage of being applicable to microfluidic de-vices, since the hydrophobisation of the particles is produced in situ[60]. Most available studies of these types of systems combine simplefoaming experiments (shaking or mixing) with investigations of thebulk properties and simple surface tension measurements. A more re-cent study of the foaming properties of aqueous dispersions containingmixtures of hydrophilic silica nano-particles (Ludox) and a short-chainamphiphile (n-amylamine) combined standard handshaking methods,microfluidic techniques and surface rheology measurements [60]. Thestudy showed that stable foams can be obtained at amine concentra-tions above approximately Ca* = 0.5 wt.%, independently of particleconcentration, which appeared to be a critical concentration for cooper-ative association between particles and amine. In contrast to foamsstabilised solely by nano-particles, these foams suffer from slow coars-ening despite their high surface elastic modulus, due to gas exchangebetween bubbles. This is possibly due to the non-permanent nature ofthe association between the amphiphile and the particle and/or to theformation of multilayers of particles under compression. Ultra-stablefoams for which coarsening is inhibited can only be produced atsufficiently high particle and amine concentrations (typically 10 and3 wt.%, respectively) for which the dispersions also gel in the continu-ous phase of the foam. Similar results were found by Gonzenbach and

Gauckler [57] who studied the same silica/amylamine system, usingstill larger particle concentrations (35 wt.%). They obtained foamsstable against coarsening, coalescence and even drainage.

Pictures of the foamsmade usingmicrofluidicmethods are shown inFig. 7. For amine concentrations Ca between 0.5 and 1 wt.% but smallparticle concentration (Cp = 5 wt.%) limited coalescence is observed,leading to a range of different bubble shapes since the shape relaxationis arrested when the surface layers are sufficiently rigid [61]. Beyondthis stage, foam destabilisation occurs via coarsening only. For higherparticle and amine concentrations, the interfaces seem to be coveredsufficiently so that coalescence is completely suppressed, giving rise toa perfectlymonodisperse foam. However, after sufficiently longwaitingtimes, these bubbles (and therefore the foams) disappear throughcoarsening. Upon further increase of Ca until Ca = 3 wt.%, bothcoalescence and coarsening are fully suppressed by bulk gelificationfor Cp = 10 wt.%.

For Cp b 5 wt.%, the foam could not be produced using microfluidicmethods. Handshaking methods were applied to produce foams withCp = 1 wt.%. The behaviour observed is similar, except that the solu-tions do not gelify at large amine concentration, so the foams arenever ultra-stable. Particle aggregation is important between 2.5 and5 wt.%, causing a fast phase separation and suppressing the capabilityof the solution to foam. Close, but below Cp = 2.5 wt.%, particle aggre-gation occurs more slowly, which seems to be responsible for the en-hanced foam stability. When Ca is larger than 5 wt.%, a bilayer isformed at the particle surface causing particle re-dispersion in bulkbut making them again so strongly hydrophilic that solutions do notfoam.

Foams generated from silica particle/amine mixtures are thereforeultra-stable only when particle and surfactant concentrations are suffi-ciently high, and when the bulk phase is gelified, otherwise coarseningpersists. Whether foams from particle/surfactant mixtures coarsen ornot, seems to depend on the surfactant type used. For instance, foamsmade from mixed dispersions of Ludox silica particles and cetyltrimethyl ammonium bromide (CTAB) [62] show the same general be-haviour as for the Ludox/amine system, whereas Ludox-dimethyldidecyl ammonium bromide mixed solutions could produce ultra-stable foams, that do not coarsen even without bulk gelation [58].Future research therefore needs to establish the conditions which aparticle/surfactant mixture needs to fulfil in order to arrest coarsening.In particular, our guess that the concomitance of a high elastic surfacemodulus and a resistance to collapse is mandatory needs confirmation.

3.3. Surfactant foams

The typically unstable nature of pure surfactant foams can becounteracted by exploiting synergies which arise in surfactant mixtures

101 102 103 104 105 106

1

2

3

4

5

SDS surfactant

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

<R

>/<

R(t

=0)

>

foam age (s)

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

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 limitbetween the two (arrow) is irregularly shaped, as expected after the rupture of a fragile film.



[63,64]. For example, foams made withmixed solutions of myristic acidand cetyl trimethylammonium chloride (CTACl) were shown recentlyto be very stable [65,66]. The two surfactants have opposite chargesand associate in the solutions in the form of vesicles [67]. These surfac-tant mixtures are sometimes called catanionic surfactants. The mixedmonolayer which is formed by vesicle rupture at the air–water surfaceis extremely rigid and prevents further vesicle rupture by avoiding con-tact of the vesicles with air. Confocal fluorescence microscopy revealedthe presence of layers of intact vesicles that are progressively creamingtowards the mixed monolayer, giving rise to an extremely thick layer[68]. The mixed monolayer not only has a large compression modulusbut behaves as an amorphous solid (glassy) with a finite shear elasticmodulus and time and temperature dependent properties.

Fig. 8 shows a typical image sequence of foam generated from a0.5 wt.% mixed solution by handshaking. The solutions show onlyreasonable foamability, but the foam stability is much better than forstandard surfactant foams. Three features have been observed: com-plete absence of bubble coalescence, very slow gravity-driven drainageof liquid out of the foam and very slow coarsening. These foams thencombine resistance to the three types of destabilisation mechanisms.Let us discuss the coarsening issue below (drainage and coalescencewill be discussed respectively in Sections 4.2 and 5.1).

The coarsening is much slower than that of standard surfactantfoams. This could be due either to the very closely packed monolayers,which act as gas barriers, to the high elasticmodulus E of themonolayer,which counteracts coarsening, or to the presence of closely packed

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 nocoalescence 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 bubblesizes are around 500 μm.Data from [60].

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 andmaintain a significant amount of liquid in comparison to standard surfactant foams with the same structural properties.From [66].



vesicles between the bubbles. It was observed that at long time scales,the average bubble size at the top of the foam increases more rapidlythan in the remaining foam (without bubble coalescence). Closeranalysis showed that this part of the foam is essentially free of vesicles,which must have drained. This leads to two conclusions. Even withoutvesicles, the coarsening is slowed down significantly, indicating animportant role of the interfaces. The presence of vesicles seems tocontribute additionally to the slowing down of coarsening, due to thethickening of films and film junctions, as in protein foams (discussedin Section 3.4).

Foamsmadewith other types of catanionicmixed solutions, hydrox-yl stearic fatty acid and ethanol amine were found to be ultra-stable[69]. At the difference of themyristic acid–CTAClmixtures, they containlong tubes which form spontaneously and reversibly, and block Plateauborders (Fig. 9). The sizes of the foam films were found much smallerthan for standard surfactant foam films, with a very thick meniscusfull of tubes. According to Eq. (2), the fractional area of film f(ϕ) issmall, and the coarsening time is large. It is also probable that the sur-face layers are rigid, slowing down further or even arresting coarsening.

3.4. Protein foams

Currently known protein foams are only ultra-stable if the foamingliquid is gelified, with the notable exception of foams made withhydrophobins: these proteins form solid like layers at the surface ofwater which have high elastic moduli E and do not collapse upon com-pression [21]. When standard proteins are used and when the foamingsolution is fluid, the foam is neverthelessmore stable than standard sur-factant foams. Even when the protein concentration is small, proteinfoam films are thick and irregular [71–73] (Fig. 10 left). Apparently,protein aggregates are trapped in the film and stop the film thinningprocess. Note that the aggregates form at the film surfaces, because noaggregates are seen in the bulk solution. When the protein concentra-tion is large enough, the films are gel-like. The coarsening of foamsmade from protein solutions is found to be somewhat slower thanthat of surfactant foams (Fig. 10 right). This feature was attributed tothe 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 surfactantfoams and the drainage time follows Eq. (2). Exceptions occur whenthe particles can block the Plateau borders. A first example has beengiven by Friberg who noticed that foams made in the presence ofsmall particles with lamellar structures (produced when the foamingliquid is water in equilibrium with a lamellar phase) can be very stable.When the liquid contains many particles, it becomes viscous, and one

obvious effect is the slowing down of the drainage process. As pointedout by Friberg, amore subtle effect is due to the balance of the interfacialtensions: 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 Plateauborders, as he observed [4]. Similar effects were reported later in indi-vidual Plateau border experiments [74,75].

Another interesting example of particles arresting the drainage hasbeen observedwith solutionswhere colloidal clay, laponite, is dispersedin SDS before foaming. Laponite forms gels in aqueous solutions con-taining SDS, and a non-classical arrest of drainage is seen in foamsmade with these dispersions [76]. Whilst the foam drains, the laponiteparticles get confined in the Plateau borders, and since the yield stressof the dispersions increases upon confinement, the interstitial fluidgels, and drainage is arrested after a time tj. As coarsening continues,the bubble size increases, the size of the Plateau borders increases aswell, and drainage then starts again at a time tu (Fig. 11).

4.2. Surfactant foams

Foams made from myristic acid–CTACl mixed solutions drain veryslowly as shown in Fig. 12 [66].

Whilst standard surfactant foamwith the same initial bubble size andliquid fraction drains in about 1 h, the catanionic foam drains in aboutone day. It is furthermore noticeable that even when drainage stops,the foam remains visibly wet, i.e. that a significant amount of liquid re-mains trapped between the bubbles. It usually takes a few months forfoam of this kind to disappear completely via coarsening. The drainagewas investigated in more detail using confocal microscopy. Two exam-ples 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 andvesicle aggregates between the bubbles. Vesicles are also trapped with-in the thin films separating bubbles (inset of top right image). For suffi-ciently high concentrations one observes a complete blocking of Plateauborders by vesicles and hence a dramatic slow-down, and finally com-plete arrest of drainage [66].

A similar behaviour has been reported for foams made with mixedsolutions of hydroxyl stearic fatty acid and ethanol amine. The drainageproceeds during a short period, after which it stops, probably for thesame reason in view of the crowding of tubes seen in Fig. 9; the liquidvolume fraction remains afterwards around 5%, much higher than fora standard surfactant foam (Fig. 3) [69].

4.3. Foamed emulsions or “foamulsions”

Mixtures of bubbles and droplets are encountered inmany cosmeticand food products (such aswhipped cream) or in oil recovery processes.In themost stable systems, the oil droplets are generally crystallised (atleast partially) [77], and act as solid particles. Althoughmany 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].



food grade foamed emulsions have been performed [78,79], fewer stud-ies exist on simpler systems. Introducing fluid oil drops into a foam isthe classical approach to suppress the foaming of a solution and todestabilise existing foams [33,34,80]. In a pioneering work with diluteemulsions, Koczo et al. showed that bubbles and fluid oil droplets cancoexist without destabilisation of the foam [81]. All oils are thereforenot necessarily antifoaming systems and Goyon et al. used a highly con-centrated emulsion as a model yield-stress fluid to study shear induceddrainage in foams [82].

In a recent study, the stability of foamed emulsions has beenstudied in more detail [83]. Two oils were chosen for their differentbridging 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 andrapeseed oil to be a foam stabiliser but, surprisingly, they were bothfound to stabilise the foam under certain conditions. The surfactantused to stabilise both the foam and the emulsion was SDS. A criterion ofgood foamability was found, where the concentration of SDS must be

higher than a critical concentration such that there are enough SDSmolecules to cover the surfaces of both the emulsion drops and the gasbubbles [83].

The foams made from rapeseed oil emulsions drain and coarsen likeclassical foams made from SDS only. This suggests that the oil dropletsare only transported through the water, and do not interfere with thegas–liquid interfaces, which is consistent with the very small value ofentry coefficient En. In contrast for dodecane, for which both En and Brare large and positive, the foams are much less stable. The dodecanefoams have a lower lifetime than oil-free foams, and foam destructionoccurs before drainage is completed. This implies that dodecane actsas slow antifoam; the oil droplets do not enter in the films, but breakthe foam only after being squeezed inside the Plateau borders. At largeroil volume fractions, very different features are observed, in particularan outstandingly long lifetime with the rapeseed oil with ϕoil = 0.7.

When ϕoil N 0.63 (random close packing of spheres), the emulsiondroplets are densely packed [84], and the emulsion becomes viscoelas-tic, with a finite shear modulus and yield stress. Microscope images ofsuch a foam (ϕoil = 70%) are shown in Fig. 14. One can see that dropletsare actually confined and crowded between bubbles, which stay anom-alously far from each other.

The presence of such a dense assembly of droplets trapped andjammed in between the bubbles has several effects. The local viscosityincreases, slowing down both film thinning and Plateau borders shrink-ing (slower drainage) as in the case of particles. In addition, for initialbubble diameters of the order 100 μm, hydrodynamic stresses in thePlateau borders become comparable to the yield stress of the emulsion(of the order of a few Pa [85,86]). Drainage can therefore not only beslowed down, but also even be arrested if the yield stress of the emul-sion becomes higher than the local hydrodynamic stresses as seen be-fore for the laponite–SDS foam [76] and confirmed by Goyon et al. [82].

5. Film rupture in very stable foams

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

1

2

3

4

5

6

7

8

100 1000 10000

R /

R(t

=0)

time (s)

β-casein

SDS

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].

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



of isolated, horizontal films can be conveniently studied using variousdevices 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 foamsmadewithmixedmyristicacid–CTACl solutions, for which thin films were also studied with theTFPB [66]. The films ruptured immediately when the pressure was ap-plied without an equilibration time, whilst the stability increased signifi-cantly with equilibrium time. The films were then resistant to rupture,rendering coalescence difficult, at least on the time scales and pressureconditions accessible in the TFPB. The observations correlated well withthe slow adsorption dynamicswitnessed by the surface tensionmeasure-ments: the film stability is greatly enhanced once the gas/liquid interface

is sufficiently covered by the surface activemixture. Thefilm stability alsodepends significantly on the surfactant concentration.

Fig. 15 shows representative examples of the time evolution, i.e. theprogressive 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 variationof the interference colours, the film thickness is highly heterogeneous.The fact that the typical object size is of the order of 10 μm suggeststhat vesicles remain trapped in the film without destruction. Films cre-ated from C = 0.1 wt.% (bottom of Fig. 15) were extremely stable andcould be observed for more than 8 h. These films were also resistantto applied pressure ramps or pressure steps exhibiting the sameappear-ance, before and after the cycle. This indicates that there is no rearrange-ment of the structures at the film surface and it may be concluded that,at sufficiently high concentrations, the vesicles form gel-like networks

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

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 fluorescentdye (Oregon Green 488).



in thefilm. In all cases, the equilibrium film thickness remains unusuallythick, with thicknesses above 100 nm, i.e.at least an order of magnitudethicker than for filmsmade of standard ionic surfactant solutions (a fewtens of nanometer).

Interestingly, the foam films made from hydroxyl stearic fatty acidand ethanol amine mixed solutions drained down to thicknesses ofthe order of 20 nm, the tubes being completely expelled from thefilms. Therefore, these tubes did not contribute directly to stabilisationagainst coalescence [69].

5.2. Particle foams

Stratification phenomenahave been reported for foamfilmsmade ofdispersions of monodisperse hydrophilic silica particles until the parti-cles are expelled from the films [90]. However, TFPB studies showedthat the films formed by the partially hydrophobic silica do not exhibitsuch behaviour. They are very thick and solid-like, resisting to breakageunless very large pressures are applied. This is one of the many reasons

that render these foams very stable. The films may however be brokenupon expansion (Fig. 6) [91].

Let us recall that, surprisingly, the limited coalescence observed inthe Pickering emulsions made with the same particles has never beenobserved: the long term stability is reached above C* = 0.6 wt.% (forfoams made by turbulent mixing), R is constant and equal to R*; justbelow this concentration, the bubble radius increases with time(Fig. 5) without stabilising at a value corresponding to the optimalsurface coverage: R being proportional to Γ, the limit value should besuch that R = R* C*/C. The origin of the differences between the foamand emulsion behaviour remains to be elucidated.

5.3. Protein films

It was reported that protein foams become stable once the thicknessirregularities of the foam films become connected and the films gelify[71]. Similar observationsweremade in foamfilms containing preformedprotein aggregates [92].

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 Plateauborders are still very thick (right).After [83].

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.% after24 h equilibrium time. The applied pressure difference is 2000 Pa. Time difference between pictures: 10 min.Data from [66].



6. Conclusions

One drawback systematically encountered with very stable foams isthat they are difficult to produce. Special procedures such as in situhydrophobisation in microfluidic devices for particles for instancehave to be used to produce them in a well-controlled manner.

Many examples of very stable and ultra-stable aqueous foams werereported recently in the literature. The origin of the stability is related tothe slowing down of either coarsening, drainage or coalescence. In somecases, the three effects are impacted simultaneously as in the case of themyristic acid–CTACl foams. In other cases, they are frequently coupled,not always to enhance stability, as for instance in the SDS–laponitefoams, where coarsening is responsible for the re-start of drainage.Coarsening is slowed down when the films between bubbles are thickand/or small, and it can be arrested when the surface compressionmodulus E is large enough. Drainage can be slowed down when parti-cles accumulate in the Plateau borders or if they locally gel there if theyield stress increases upon confinement. Drainage can be arrested ifthe liquid of the foam either gels or solidifies. Coalescence is sloweddown by gelified foam films, and it can be arrested if the films remainvery thick and/or rigid.

There have been significant advances in our understanding of thestabilising mechanism leading to the creation of very stable foams.The phenomena leading to arrest of drainage and coalescence are qual-itatively easy to identify, but they will be less obvious to model in orderto obtain quantitative predictions. The different mechanisms leading tothe slowing down and to the arrest of coarsening remain less obvious. Afull comprehension is still eluding us, which would allow for the com-plete control over the ageing of foams. Further investigations are clearlydesired, combining experiments at different scales: surface layers, films,Plateau borders and bubbles and foam itself. Indeed, the mechanismsevidenced so far can act at any of these scales and partial measurementscan miss important features.

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