yielding and fracturing of concentrated emulsions in narrow gaps
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Soft Matter
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Ian Wark Research Institute, University of So
Australia, Australia. E-mail: catherine.whitb
† Electronic supplementary informa10.1039/c3sm50314c
Cite this: Soft Matter, 2013, 9, 5975
Received 30th January 2013Accepted 9th May 2013
DOI: 10.1039/c3sm50314c
www.rsc.org/softmatter
This journal is ª The Royal Society of
Yielding and fracturing of concentrated emulsions innarrow gaps†
Catherine P. Whitby,* Rebecca McVicker, Jason N. Connor and Rossen Sedev
We used rheology and confocal microscopy techniques to characterise the flow of emulsions as the
droplets were confined by increasing the drop volume fraction and reducing the distance between the
shearing surfaces. Slip was minimised by matching the density of the oil and water phases. Attractive
interactions between the drops caused them to flocculate. The contribution of the emulsion
microstructure to its shear response becomes significant when the oil drop flocs almost span the
distance between the surfaces. We found that confining the flow of droplet flocs causes a transition
from a fluid phase with shear thinning flow behaviour into a jammed, solid-like material. The large
deformations caused by flow at the maximum drop packing fraction induce droplet coalescence within
highly localised regions of the emulsion.
Introduction
Concentrated emulsions are used in applications requiringmaterials (creams, sauces, coatings) that can be spread over asurface but keep their shape aer the applied force isremoved.1 They consist of densely packed drops that canbecome stuck (or jammed) together.2 The microscopic changesunderlying this sudden, macroscopic change are surprisinglyelusive. Controlling emulsion ow behaviour and stability iscritical, however, for producing textures that are acceptable tothe consumer.3–5 Conventional rheology measurements char-acterize emulsions by shearing them between two surfacesseparated by a distance (millimetre range) that is several ordersof magnitude greater than the drop size (micrometre range).6
However, emulsions are sheared on much smaller lengthscales, for example, when spread out into thin coatings,sprayed through nozzles or pumped into narrow channels.While liquid ow has been characterised on nanometre lengthscales using surface force techniques7,8 and on micrometrelength scales using micro-rheometry techniques,9 less is knownabout the contribution of emulsion microstructure to ow inconned spaces. A unied picture of the links between the bulkproperties of emulsions and their microscopic and interfacialstructure is only now being developed.10–13 In this paper weexamine the changes in the shear response of an oil-in-wateremulsion as the drops are systematically conned by increasingthe drop volume fraction (f) and by reducing the distancebetween the shearing surfaces ( g).
uth Australia, Mawson Lakes 5095, South
tion (ESI) available. See DOI:
Chemistry 2013
Concentrated emulsions have percolated network structuresdue to attractive interactions between the drops, or glassystructures of closely packed drops.14,15 The drops in an emulsionare geometrically conned at drop concentrations larger thanabout 63 vol% (fm). The drops pack closely together and thendeform into polyhedral shapes with attened areas of contactand rounded edges as f increases. Emulsion stability is gov-erned by the thin liquid lms of the external phase lockedbetween touching drops.16–18 While dilute emulsions behavelike viscous liquids, concentrated emulsions show solid-likebehaviour. Small perturbations stretch the thin liquid lmsbetween drops in close contact. The additional excess surfacearea created determines the elastic response, which is charac-terised by the elastic storage modulus, G0. A low-frequencyplateau in G0 indicates that the drops have jammed togetherinto an interconnected network which can bear stress.19 Adetailed understanding of how closely packed drops lose theirability to ow and jam remains elusive.20–24
Flow only occurs in solid-like emulsions above a criticalvalue of applied stress (the yield stress, sy). In the solid (linearviscoelastic) regime, the yield stress at the solid–liquid transi-tion is given by
sy ¼ Ggy (1)
where gy is the yield strain and G is the emulsion elasticity.Princen16 proposed that this yield stress corresponds to thestress required to induce irreversible droplet rearrangements.Various models are used to extrapolate the yield stress from theliquid (non-linear) ow behaviour. Herschel and Bulkley simplymodelled the steady shear stress above the yield stress as apower-law function of the shear rate ( _g)
s ¼ sy + k _gn (2)
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The yield stress is taken as the lowest stress reached insteady-state ow. The Cross model is used where creep (slow,but steady deformation) is observed at very low applied stress. Itdescribes ow in terms of a limiting viscosity at low stress (h0), atransition into a shear thinning region (decreasing h as s
increases) and Newtonian behaviour (constant viscosity, hN) athigh stress
h ¼ hN þ h0 � hN
1þ�s
sy
�m (3)
where m is a material parameter. Here the critical yield stress istaken as the stress at the transition between low and high shearbehaviour.25
Rather than a gradual transition from liquid to solid ow,Coussot1 observed that there was a critical shear rate ( _gc) belowwhich steady ow could not be achieved in concentrated emul-sions. Magnetic resonance imaging of the velocity prolebetween the shearing surfaces revealed that liquid-like regions( _g > _gc) coexistwith regions of unyieldingmaterial ( _g¼ 0).Masonand Bibette26 estimated the thickness of the yielding plane (l) byassuming that the limiting elastic stress of the solid-likematerialbalances the viscous stress of the liquid-like material at the edgeof the plane. Approximating the liquid viscosity in the shearplane as the continuous phase viscosity (hc) gives
lzhcn
sy
(4)
where n is the velocity of the upper shearing surface. Masonand Bibette26 estimated that in an emulsion with a viscosity of100 mPa s and a yield stress of 104 Pa, the yield plane is 100 mmthick.
Emulsion ow is also conned by reducing the distancebetween the shearing surfaces (walls). Studies of the thin lmrheology of emulsions have typically investigated ow behaviourat separations small enough to conne individual drops. Gracaet al.27 showed that conningmicroemulsions into lms smallerthan the micelle dimensions causes the deformation andexpulsion ofmicelles from the gap. Clasen andMcKinley28 foundthat the largest fat droplets inmayonnaise (78.6 wt%, d# 12 mm)adhere to the walls, forming sticky layers that compress andfuse together as the distance between the walls decreases below100 mm. The dynamic response of emulsions conned in narrowspaces is likely also to be affected by structures formed on largerlength scales such as droplet aggregates and networks.29
Interactions between the drops and the walls may inuenceow behaviour in conned spaces. Slip is caused by depletion ofcolloidal particles from the liquid region closest to surfaces.30,31
The lower viscosity layer lubricates liquid ow near thesurfaces.30 Davies and Stokes32 showed that while glass spheres(f ¼ 50%, d ¼ 43 mm) jam in narrow gaps (g < 200 mm) at lowstresses, the deformation of microgels (2–20 mm in size) allowsow to take place through wall slip processes.
We combined confocal uorescence microscopy andrheology techniques to reveal the inuence of the emulsionmicrostructure on its ow behaviour. Conning the emulsioncauses a transition from a uid phase that shear thins to one
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that is a jammed, solid-like material. We show that the complexrheology of the emulsions is linked to the presence of aggre-gates that are about 100 times larger than the individual dropsand their breakdown under connement.
Experimental sectionEmulsion preparation
Oil-in-water emulsions were prepared by homogenising bro-mohexadecane (Sigma Aldrich, 99%, density of 0.999 g cm�3,passed through chromatographic alumina twice to removepolar impurities) with aqueous solutions of sodium dodecylsulphate (Sigma Aldrich, 99%) using a rotor-stator mixer(Ingenieuburo CAT X1030D, M. Zipperer GmbH) with a 19 mmhead operated at 11 000 rpm for 1 minute. At drop volumefractions, fo # 0.75 and SDS concentrations, CSDS $ 0.002 M,emulsions do not coalesce for several weeks. The density of theoil and water was matched to minimise the effects of gravity-induced separation of the phases during rheology measure-ments. The drops do, however, rapidly occulate aer forma-tion under the same conditions (discussed later). Unlessotherwise stated, CSDS ¼ 0.1 M. At this surfactant concentrationthe emulsions have a mean, volume-weighted (primary) dropdiameter, d, of 10 mm, as determined by light scattering (Mal-vern Mastersizer 2000). The distributions are monomodal witha polydispersity of 35%.
Confocal uorescence microscopy
Emulsions prepared from oil stained with Nile Red (Fluka) andcontained between glass coverslips were visualized by confocaluorescence microscopy (CFM, Leica SP5 spectra scanningconfocal microscope). Samples were excited at a wavelength of514 nm and the uorescence emission intensity collected over550 to 650 nm. The images were recorded at a depth of 260 mminto the sample. The fractal dimension, Df, of the dropletaggregates was obtained by the box counting method using theimage analysis soware, ImageJ.
Rheology
Rheological measurements were made using a RheometricScientic Dynamic Stress Rheometer SR2000 at a xedtemperature of (25 � 0.1) �C. The emulsion was placed betweentwo parallel plates of 25 mm diameter with a set gap width, g. Inthe parallel-plate geometry, the local strain imposed by therheometer is proportional to the radial position. The highestshear rate is achieved at the rim of the rotating plate. The owbehaviour obtained using at plates with either smoothhydrophobic or sand blasted steel at large separations (2 mm)was similar to that measured using a cone and plate geometryindicating an absence of wall slip. A solvent trap was used toprevent evaporation. For ow viscometry measurements, theapplied shear stress or rate was scanned up in a series of log-arithmic steps (20 s duration). For oscillatory measurements,the amplitude was increased in a series of logarithmic steps(30 s duration) at a constant frequency (typically 0.1 Hz). Themoduli in the linear viscoelastic regions were determined from
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scans of the oscillation frequency at a constant stress. Aershearing, the rotating plate was slowly removed and the emul-sion appearance assessed visually.
Fig. 2 Stress dependence of the emulsion viscosity (h) at drop volume fractions(f) of 0.66 (blue symbols) and 0.75 (green symbols). The emulsions were shearedbetween parallel plates (25 mm radius) separated by gaps (g) of 2 ( ), 1 ( ), 0.3( ) and 0.1 ( ) mm. In narrow gaps, emulsions show yielding and thinningbehaviour. Shown is the interpolation (red dashed line) from the zero shear-plateau (h0) and shear-thinning region for determining yield stress (sy).25 Diluteemulsions show, in contrast, slightly shear thinning flow behaviour which doesnot change with g. The solid line indicates the viscosity of emulsions at f ¼ 0.50.
Results and discussion
The surfactant-stabilised emulsions studied here show a richand complex morphology. Fig. 1a shows how the emulsionmicrostructure is tuned by increasing the volume fraction ofdrops (f) of a xed diameter (d ¼ 10 mm). The surfactantconcentration is also xed (CSDS ¼ 0.1 M). The drops aggregateinto random networks at (relatively) dilute concentrations (up to64 vol%). The networks are tenuous structures that are highlydisordered and porous. Clusters of drops extending overhundreds of micrometres are observed already at f ¼ 0.5. Thestructures are self-similar, with a fractal dimension (Df) of about1.8. The aggregation is likely due to attractive van der Waalsinteractions between the oil drops. Presumably, the surfactantlayer adsorbed on the drop surfaces does not hold them suffi-ciently apart to hinder aggregation when they come into closecontact. Electrostatic repulsions between the drops arescreened by the relatively high concentration of counter-ionspresent (CNa+ ¼ 0.1 M). Depletion interactions, due to theexclusion of SDS micelles from the regions in between drops atclose separations, may also contribute to the drop occula-tion.33 Above f � 0.65 the drops close pack into a disordered,glass-like structure. This implies that the drops can be treatedas hard spheres (randomly close packed, undeformed sphereshave a packing density of about 64% (ref. 34)).
The networked microstructure in the dilute emulsions has acharacteristic length scale which depends on the drop volumefraction. The connections between the drops were graphed byprocessing images repeatedly to remove pixels from the
Fig. 1 (a) Confocal fluorescence images of the oil drop microstructure in emulsionstransition from a networked structure of drop flocs to a glass-like structure of randomsheared in a wedge shaped gap (of maximum width, g) between two glass slides adrops to jam together into a glassy, close-packed structure. Regions where clusters ofIn some areas, the drops are unstable and coalesce together.
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perimeters of the aggregates, while preserving the extent andconnectivity of the structure (Fig. S1 inset†). The diameter of acluster was taken as the shortest path between the two remotestnodes (DN). The cluster size increases linearly with f up to f �0.65 – Fig. S1.† The largest aggregates consist of about 100drops (DN y 1000 mm). These clusters were not adsorbed to thewalls as they were observed at a depth of 260 mm into theemulsion sample.
Fig. 2 summarises the emulsion ow behaviour innarrow gaps characterised under well-dened conditions with
at the drop volume fractions (f) shown on the images. At f ¼ 66 vol%, there is aly close packed drops. (b) Images of the microstructure in an emulsion (f ¼ 0.64)s illustrated in the schematic on the left. Confining the emulsion flow causes thedrops and water flow form in between the jammed zones of drops (fracture flow).
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Fig. 3 Frequency (u) dependence of (a) elastic storage moduli (G0) and (b)viscous loss moduli (G0 0) of the emulsions at drop volume fractions (f) of 0.50 ( ),0.66 ( ) and 0.75 ( ). At 0.62 < f < 0.68, the moduli vary with the gap width (g)and the values shown are for gaps of 2 ( ) and 0.3 ( ) mm. The moduli undergo atransition from being dependent on the oscillation frequency to showing a low-frequency plateau when confined in g # 0.5 mm. The lines are shown to guidethe eye.
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a stress-controlled rheometer. At (relatively) low volume frac-tions (0.50 < f # 0.62) these emulsions show slightly shearthinning ow behaviour (slightly decreasing h as s increases) –black line in Fig. 2. There was no change in the ow responseover the range of gap widths studied (100 mm < g# 3000 mm). Incontrast, emulsions with intermediate f, show shear thinningbehaviour (h decreases as s increases) that is also highlysensitive to g (f¼ 0.66, blue symbols in Fig. 2). At small stresses(s < 2 Pa), the viscosity increases as the gap between theshearing surfaces decreases, indicating increasing resistance toemulsion ow. In the narrowest gap (g ¼ 0.1 mm, blue dia-monds in Fig. 2) there is a dramatic decrease in viscosity over anarrow range of stress values, typically by about four orders ofmagnitude as the applied stress increases from 2 to 10 Pa. Thesteady state viscosity achieved at high shear rates decreases as gincreases, indicating there is greater disruption to the emulsionmicrostructure in narrower gaps.
Concentrated emulsions (f $ 0.70) show a pronounced zeroshear plateau over the range of gap widths studied (f ¼ 0.75,green symbols in Fig. 2). This is similar to the behaviour ofemulsions at intermediate f in narrow gaps. This apparentlysteady ow cannot be reached at s < 1 Pa for emulsions connedin gaps of width g # 2.0 mm. Instead the ow stops abruptly.Similar behaviour is observed when small shear rates (<0.01 s�1)are imposed (instead of applying a low shear stress). Themagnitude of the zero shear viscosity (h0) measured in thesteady ow regime increases slightly as the gap width decreases.The value of the constant viscosity measured at low stressdepends on how long the stress is applied. It is best described asan apparent viscosity. The viscosity seems to increase inde-nitely with the measurement time, suggesting solid-likebehaviour under conned conditions.35
Above a critical stress, extreme shear thinning is observedwhere the viscosity decreases by several orders of magnitude.The value of this critical stress increases as g decreases. Steadystate ow, similar to that observed in dilute systems, is appar-ently achieved at higher applied stresses.
Although the Herschel–Bulkley model (eqn (2)) could modelthe emulsion ow above the critical (yield) stress, the data showan apparently constant viscosity at very low and high appliedstresses. The Cross model (eqn (3)) was favoured for modellingthe ow curves at f > 0.66. The steady state achieved at highstress is independent of the strain rate for the most concen-trated emulsions. When the shear rate ( _g) is varied the stress isnearly independent of _g (Fig. S2†). The Herschel–Bulkley model(eqn (2)) is a poor t to this data (Table S1†). The yield stress wastaken as the intercept between the low shear and shear thinningregions. This means that concentrated emulsions (and closepacked emulsions in narrow gaps) do not behave as ideal plasticmaterials in narrow gaps, but instead fracture. The ttingresults are discussed shortly.
Fig. 3 summarises the response of emulsions at different f toa small amplitude oscillatory strain. Dilute emulsions (f¼ 0.50,black symbols in Fig. 3) are only weakly viscoelastic and theirelastic storage moduli (G0, Fig. 3a) and viscous loss moduli (G00,Fig. 3b) increase with the frequency (u) of the oscillatory strain.Their response to oscillatory shear does not change with
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connement. At volume fractions around the maximum frac-tion for randomly close packed spheres (fm), G0 increases tovalues that are about an order of magnitude higher than G00 atlow frequencies. The sharp increase in G0 at f� fm is consistentwith behaviour observed for monodisperse emulsions.18 Themoduli vary with g (cf. f ¼ 0.66, blue symbols in Fig. 3a and b).In narrow gaps, G0 is nearly independent of u, as shown inFig. 3a. This indicates that the conning pressure causes theemulsionmicrostructure to become robust enough to be elastic.The formation of a stress-bearing, interconnected networkmeans that the emulsion is behaving like a jammed solid.19 Athigher f, the emulsions are clearly elastic with G0 [ G0 0 overthe range of frequencies studied (cf. f ¼ 0.75, green symbols inFig. 3a and b). They show a dominantly solid-like behaviour thatis consistent with their viscous ow behaviour (Fig. 2).
Thus increasing f drives a transition from a uid phase thatshows shear-thinning behaviour into a solid-like material. Thewhole trend is illustrated in Fig. 4 which shows the emulsionviscosity at low applied stress as a function of the oil volumefraction. The dilute emulsion consists of an interconnectednetwork of droplets that is readily disrupted by shearing anddoes not possess signicant elasticity. The drops (and anyaggregates of drops) are not caged (restricted in their move-ment) by other drops because the smallest gap is 10 times larger
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Fig. 4 Volume fraction (f) dependence of the apparent emulsion viscosity at lowapplied stress. For slightly shear thinning ( ), shear thinning ( ) and yielding andthinning ( ) flow behaviour, the viscosity measured at a shear stress of 1 Pa(hs¼1 Pa) is shown. For apparently creeping ( ) flow, the apparent zero shearviscosity (h0) is shown. At f > 0.62, the emulsion viscosity varies with the gapwidth (g) and the values shown ( ) are for g ¼ 2.0, 0.5, 0.3 and 0.1 mm (frombottom to top). At 0.62 < f < 0.68, the emulsion flow behaviour changes fromliquid-like to a jammed solid as flow is confined by reducing g.
Fig. 5 (a) Gap width (g) dependence of the yield stress (sy) at oil volume frac-tions (f) of 0.66 ( ), 0.70 ( ) and 0.75 ( ). Yield stresses were derived from theemulsion response to dynamic ( ) and steady ( ) shearing. The gap width isscaled by the average drop diameter (d).
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than the individual drops. The solid phase (concentratedemulsion) consists of droplets organized into a glassy arrange-ment that can bear signicant stress and shows a low-frequencyplateau for the elastic modulus.
For unrestricted ow between widely separated shearingsurfaces, the transition from liquid to solid-like behaviouroccurs above fc � 0.62 (shaded region in Fig. 4). This isconsistent with the maximum volume fraction at whichmonodisperse hard spheres (oil drops18 or air bubbles36) canpack together into a mechanically stable structure (0.63).18
Below f¼ 0.70, ow is homogeneous throughout the emulsion,while for higher f, the emulsion fractures. Mason et al.18 alsoobserved a history-dependence of the shearing behaviour inconcentrated emulsions. Our results show that conning theemulsions into narrow gaps reduces the ability of the drops tomove and rearrange into different congurations. Thusreducing g causes jamming to occur at lower volume fractions.
Jammed emulsions (see image in Fig. 1b) are re-uidized byapplying a uni-directional stress that exceeds their yield stress.Above the yield stress, the measured stress does not varysmoothly with the shear rate in narrow gaps, indicating inho-mogenous ow.26 This suggests that shearing causes spatialvariations in the emulsion microstructure (fracturing). Toreconcile the macroscopic rheology with the physical picture ofthe emulsion structure, some shear was applied duringmicroscopy experiments where the emulsions were connedbetween two glass cover slips. The distance between the slideswas varied by altering the volume of emulsion conned betweenthe slides or inserting a thin spacer at one edge so the slideswere not exactly parallel. Shear was applied by gently pushingthe upper slide several millimetres in one direction across thebottom slide. Concentrated emulsions appear to ow unevenlyin narrow spaces, forming zones where droplet clusters andliquid ows in between stationary regions of closely packeddrops. A heterogeneous (fractured) structure is observed oncemechanical steady state is reached, as shown in Fig. 1b. Sheared
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emulsions consist of regions with low concentrations of dropsclustered into aggregates and regions where the drops areconcentrated and randomly close packed together. In contrast,the drops in dilute emulsions (f < 0.6) are not crowded and donot interact while owing. The emulsion structure remainshomogenous and the fractal character and size of the dropnetworks are preserved.
Shearing concentrated emulsions in narrow gaps also causesthe drops to become unstable to coalescence (Fig. 1b). Milli-metre-sized oil drops were observed in concentrated emulsionssheared in gaps of width g < 0.5 mm (using the controlled stressrheometer) at stress values above the yield stress. The coalesceddrops were located at relatively well-dened radial positions,indicating that destabilization occurs above a threshold shearrate of about 1000 s�1. Using eqn (4), the yield plane is esti-mated to be about 5 emulsion drops thick (�50 mm). Presum-ably the large strain applied to drops located within the fractureplane causes them to coalesce.
Emulsion stability in the conned space depends on thesurfactant concentration. The yield stress shows a sharpincrease around the critical micelle concentration (Fig. S3†).The emulsions studied here were stabilised by surfactantconcentrations above the critical micelle concentration (0.008M). In this surfactant-rich regime, the yield stress is indepen-dent of the surfactant concentration (Fig. S3†). The oil–waterinterface is saturated with surfactant and there will be a (rela-tively) thick stable lm between touching drops. The largestrain applied to drops located within the fracture plane mustdeform the lms sufficiently for the maximum in the disjoiningpressure to be reached and hence for rupture to occur.
Fig. 5 shows that sy increases with the geometric connementthat occurs as f increases and with the ow connement thatoccurs as g decreases below 1000 mm. At f¼ 0.7 (blue symbols inFig. 5), the yield stress is highly sensitive to changes in the gapwidth. The restrictions to droplet movement caused by theconning pressure increase the stress required to induce ow. Atf ¼ 0.75 (green symbols in Fig. 5), the yield stress remainsconstant in gaps <1000 mm. Presumably this is due to the dropvolume fractionbeing very high and comparable to themaximum
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random packing fraction achieved by ellipsoids (0.74),37 sincethe drop shapes in these concentrated emulsions will havedeformed16 into polyhedral shapes. The dramatic increase inyield stress in gaps of widths comparable to themaximum size ofthedroplet aggregates suggests there is localized inhomogeneousow of droplet clusters where the emulsion fractures. This isconsistent with the observations of droplet clusters owingbetween regions of jammeddrops in themicroscopy experiments(image of fractured emulsion in Fig. 1b).
Our results indicate that inhomogeneous ow of concen-trated emulsions conned in sub-millimetre sized gaps is dueto fracturing of the jammed drops. Other possible causes for theunusual ow behaviour are wall slip or aging and thixotropy.There was no evidence for wall slip, since similar ow behaviourwas obtained using at plates with either smooth or roughenedsurfaces. Since the drop interactions are dominated by attrac-tive forces, it could be argued that the formation of liquid-likeand solid-like regions during shearing (shear localisation) wasdue to aging of the emulsion microstructure. Møller et al.38
argued that shear localisation is due to differences in the agingdynamics of aggregates in different regions. They measuredlonger structural relaxation times in the solid-like regions of agelled particle dispersion being sheared.38 This type of shearlocalisation has been linked to pasty materials that are thixo-tropic, their viscosity and yield stress depending on their shearhistory.39 In the case of concentrated surfactant-stabilisedemulsions (f ¼ 80%, d < 1 mm), however, Fall et al.39 found itnecessary to add colloidal particles to cause thixotropic behav-iour and inhomogeneous ow in millimetre-sized gaps. Thesurfactant-stabilised emulsions studied here do not showevidence of thixotropy.
Our results show that connement inuences the ow ofocculated (adhesive) emulsions at length scales that arecomparable to the size of the droplet ocs. The transition from ajammed solid to a owing liquid must involve the breakdown ofthe glassy structure into the clusters which act as ow unitsuntil they are broken down by further increases in shear.Meeten40 also observed a change in the yield stress of pastes(including mayonnaise and hair cream) squeezed betweenparallel plates increased as the uid thickness decreased belowa critical gap width. Meeten40 argued that there had to bedisconnected regions of large yield stress and a size similar tothe gap width in the uid. We have shown that changes in theow behaviour of the emulsions studied here are linked toclose-packed drops jamming into gaps where g # 1000 mm zDN, the maximum size of the droplet aggregates in the uidphase of the emulsions.
Conclusions
A complex rheology arises when the characteristic length scaleover which shear is applied to a compressed emulsion becomescomparable to its microstructure. A sequence of ow transitionsoccurs at the maximum packing fraction as the drops jamtogether. Reuidisation requires breaking the jammed struc-ture down into droplet clusters, leading to a viscosity and yieldstress that are highly sensitive to the gap width.
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Acknowledgements
CPW acknowledges receipt of an Australian Research CouncilFuture Fellowship. This work was supported by the Departmentof Innovation, Industry, Science and Research (AustralianGovernment) through the Australia-India Strategic ResearchFund. This research was also supported under AustralianResearch Council's Discovery Projects funding scheme(DP110103391).
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