Introduction

Concentrated oil-in-water emulsions show a very com-plex rheological behaviour (Barnes 1994; Tadros 1993).In general, the material shear thins in steady shear(Barnes 1994), showing a zero-shear-rate-limiting vis-cosity at shear rates of order 10)4 s)1 or lower. At shearrates higher than the critical one for the onset of theshear-thinning region, the viscosity is approximatelyproportional to _cÿ1. This behaviour has been mainlyassociated to droplet de¯occulation, although othermechanisms may develop as the shear rate increases.The same behaviour is also shown by ¯occulatedsuspensions (Barnes 1995). Several well-known steady-

state ¯ow models (Ostwald-de Waele, Cross, Carreau)have been used to ®t this viscous response (Pal 1992; Paland Rhodes 1989; Partal et al. 1994).

In oscillatory shear, the evolution of the linearviscoelasticity functions in a frequency range between10)2 and 102 rad/s, for commercial mayonnaise, ischaracterised by the appearance of a minimum in theloss modulus at intermediate frequencies and a ``plateauregion'' in the storage modulus (slope values of around0.1). In addition, the frequency dependence of bothmoduli is clearly dependent on the emulsion concentra-tion, processing conditions and nature of the emulsi®erused (Franco et al. 1995, 1997; Tadros 1993). Thus, amore general picture of the oscillatory response of

Rheol Acta 38: 145±159 (1999)Ó Springer-Verlag 1999 ORIGINAL CONTRIBUTION

C. BowerC. GallegosM.R. MackleyJ.M. Madiedo

The rheological and microstructuralcharacterisation of the non-linear¯ow behaviour of concentratedoil-in-water emulsions

Received: 10 November 1998Accepted: 24 November 1998

C. Bower á M.R. Mackley (&)Department of Chemical EngineeringUniversity of CambridgeNew Museums Site, Pembroke StreetCambridge, CB2 3RA, UKhttp://www.cheng.cam.ac.uk

C. Gallegos á J.M. MadiedoDepartamento de Ingeniera QuõÂmicaUniversidad de Huelva21819 Palos de la Frontera, Huelva, SPAINhttp://reologia.us.es

Abstract This paper reports experi-mental observations on the rheologyand microstructure of concentratedoil-in-water emulsions stabilised bymacromolecular and low-molecular-weight emulsi®ers. From the fourdi�erent samples that were tested,certain general trends were identi®edand the measured linear viscoelasticand non-linear viscoelastic proper-ties were compared using a phe-nomenological factored integralconstitutive equation with a contin-uous relaxation spectrum. The self-consistency of the model was quitegood in two cases (vegetable proteinand polyoxyethylene glycol non-ionic surfactant emulsi®ers) with thegeneral exception of low steadyshear rate data where the modeloverpredicted experimental stressmeasurements. It is shown that the

®tting of the experimental data issensitive to a wide range of inter-relating factors. In addition, opticalobservations of the sheared materi-als consistently showed low shearrate surface slip and this observationwas correlated with the rheologymiss match. For some systems theoptical microstructure studies reveala range of behaviour for the emul-sions dependent on emulsi®er com-position. Wall slip, microdomainmovement, chaining and changes indroplet size distribution were allobserved under di�erent conditionsand in some cases it has beenpossible to correlate these micro-structure observations with thesample rheology.

Key words Oil-in-water emulsions ±Microstructure ± Rheology slip

emulsions stabilised by macromolecular and/or low-molecular-weight emulsi®ers presents three characteris-tic regions: a pseudo-terminal region at low frequencies,an intermediate ``plateau'' region, and the beginning ofthe transition region at high frequencies. These linearviscoelastic properties can be matched, for example, to aGeneralised Maxwell Mode, with discrete or continuousspectrum (Guerrero et al. 1996). Franco et al. (1995)have used the BSW-CW model to successfully describethe above-mentioned regions in the linear relaxationspectra of emulsions stabilised by a mixture of macro-molecular and low-molecular-weight emulsi®ers. Ma-diedo and Gallegos (1997) have used a di�erentempirical model that describes those regions in therelaxation spectra of oil-in-water emulsions stabilised bya mixture of two low-molecular-weight surfactants withdi�erent hydrophilic-lipophilic balances.

The combined matching of the linear viscoelasticresponse, the non-linear viscoelastic response andsteady-state ¯ow behaviour of oil-in-water emulsions isa more challenging problem. Up to now a limitednumber of attempts have been made and in each casethese have involved using an integral form Wagnerequation where time and strain is separate. Mackleyet al. (1994) used this model and a discrete relaxationspectrum to predict the steady-state ¯ow behaviour ofa variety of materials, although this application tocommercial mayonnaise was without great success.Other authors (Gallegos et al. 1992a; Gallegos andFranco 1995) applied a modi®ed Wagner model, wherethe Wagner damping function was changed for theSoskey-Winter one (Soskey and Winter 1984), to ®tthe transient ¯ow behaviour of di�erent commercialand model food emulsions, achieving relatively goodresults for low shear rates, although absolute valueswere not well predicted. No precise explanations weremade for the reasons of the generalised failure ofthe above-mentioned model, although some answerscan be extracted from the conclusions of the presentwork.

It is reasonable to assume that the ¯ow behaviour ofconcentrated oil-in-water emulsions must correlate withthe evolution of the structure with shear and this paperis concerned with elucidating the primary factors thatcontrol the ¯ow behaviour of a range of oil-in-wateremulsions, stabilised using macromolecular or low-molecular-weight emulsi®ers. In order to achieve thisaim, both experimental and modelling aspects have beenconsidered. The applicability of a phenomenologicalmodel able to describe both the linear viscoelastic andsteady-state ¯ow behaviour of the emulsions has beentested. A Wager-type factored constitutive equation hasbeen chosen on the basis that it has previously beenshown to successfully bridge the gap between smallstrain viscoelasticity and steady-state shear for a numberof structured ¯uids (Mackley et al. 1994). In addition, an

attempt to correlate microstructural observations and¯ow behaviour of the deformed emulsions using aspecially designed optical shear cell (Bower et al. 1997)has been addressed.

Rheological modelling

The Wagner model derives from the more generalKBKZ model (Larson 1988). It was initially derived asan equation that empirically described polymer meltbehaviour; more recently, Wagner has attempted torelate the model to molecular parameters (Wagner andSchae�er 1993). Considering only the shear stresscomponent of the stress tensor and time-strain separ-ability, a form of the KBKZ equation is:

s�t� � ÿZ t

ÿ1

dG�t ÿ t0�dt0

h�c�c�t; t0�dt �1�

where G(t)t¢) is the linear relaxation modulus and h(c) isa damping function. Following Wagner (1976)

h�c�eÿkjc�t;t0�j �2�where the damping factor, k, is an empirical parameterwhich quanti®es the level of non-linearity in thematerial. This function can be calculated from the ratiobetween the non-linear relaxation modulus, G(c,t)t¢),and the linear relaxation modulus, G(t)t¢):

h�c� � G�c; t ÿ t0�G�t ÿ t0� �3�

In this integral equation, the relaxation modulus may bedescribed in the usual way in terms of a discrete set ofMaxwell elements, or as a continuous spectrum wherethe relaxation modulus can be related to the continuousrelaxation spectrum by the equation:

G�t ÿ t0� �Z 1ÿ1

H�k�eÿ�tÿt0�=kd lnk �4�

Substituting this into Eq. (1), the Wagner model gives:

s�t� � ÿZ t

ÿ1

Z 1ÿ1

H�k�eÿ�tÿt0�=keÿkjc�t;t0�jc�t; t0�d lnk dt0 �5�

and the apparent viscosity can be calculated from thefollowing integral equation:

g�c� �Z 1ÿ1

kH�k��1� kkc�2 d lnk �6�

In order to obtain the continuous spectrum for eachemulsion tested, the Tikhonov regularization methodwas used (Madiedo et al. 1996; Madiedo and Gallegos1997). There are now a wide range of numericaltechniques available for determining relaxation spectra,the method chosen here has been developed by some ofthe authors (Madiedo and Gallegos 1997).

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Experimental procedures

Sample preparation

Four emulsion systems were chosen and three of the emulsions weremade using sun¯ower oil (Hijos de Ybarra, Seville, Spain) andwater. The other emulsion tested was a commercial mayonnaise(Hellmanns, UK). The vegetable protein-stabilised emulsion wasmade from 65% wt sun¯ower oil, 30% wt water and 5% wt, driedpea protein (System Bio-industries, Barcelona, Spain). The peaprotein powder was dispersed in water to form a very ®nesuspension, and the oil was then slowly added to the suspensionwhilst stirring using a turbine mixer (T25basic from IKA,Germany). Two low-molecular-weight non-ionic emulsi®ers werealso used: a polyoxyethylene glycol nonylphenylether (PEG) and asucrose stearate (SS). PEG-stabilised emulsion was made in asimilar way to the pea protein-stabilised emulsion. Thus, 3% wtPEG emulsi®er (Triton N101, Sigma, St. Louis, USA) was mixedwith 27% wt water to form a homogeneous solution, at roomtemperature. Then, 70% wt sun¯ower oil was slowly added whilstunder agitation to form a stable emulsion. The sucrose ester-stabilised emulsion was made under slightly di�erent conditions inthat 5% wt sucrose ester powder (S-1570 from Mitsubishi KaseiFood Corporation, Japan) was initially mixed with 25% wt water at50 °C in order to form a surfactant solution. The 70% wt sun¯oweroil was then progressively added at that temperature whilst underagitation. After the emulsion had been formed it was allowed tocool to room temperature before any tests were carried out. In allcases the emulsions were stable for periods in excess of 1 month.

Rhelogical characterisation

Rheological characterisation of the emulsions was performed usinga RDSII dynamic spectrometer (Rheometric Scienti®c), a con-trolled-strain device that for the purpose of the experimentsperformed here, was ®tted with a parallel plate test tool (50 mmdiameter). A controlled strain or steady shear rate was applied tothe test sample and the resultant torque and normal force measuredwith a force transducer. Rheological characterisation was doneusing a series of tests, described in more detail by Mackley et al.(1994).

Firstly the extent of the linear behaviour was determined byperforming a strain sweep to measure dynamic moduli at increasingstrains. Secondly a dynamic frequency sweep (10)2 to 102 rad/s)was carried out at an applied strain within the linear region, inorder to measure dynamic moduli at variable frequencies. Thedynamic moduli from the frequency sweep data could then be usedto determine a spectrum of relaxation times for each material,either discrete or continuous. Next a series of step strainexperiments was performed, in which the sample was subjected toa precisely controlled step strain and the resultant torque measuredover the time taken for relaxation. A step strain within the linearregion was carried out ®rst, followed by a series of increasingstrains in the non-linear region. The linear and non-linear stepstrain data could then be used to calculate the Wagner dampingfactor from Eq. (3). Finally the steady shear response of thematerial was measured by subjecting the sample to increasingsteady shear rates (0.1±300 s)1). Using the damping factor and Eqs.(5) and (6), the model prediction of the steady shear behaviourcould be then compared with the experimental data. All therheological measurements were carried out at 20 °C.

Microstructure observations

In addition to the rheological characterisation, experimentalobservations of the e�ects of shear rate on the emulsion micro-structure were also performed. To this end a custom built optical

shearing cell was used, developed in Cambridge and built byLinkam Scienti®c Instruments, Surrey (see for example Bower et al.1997). The sample is placed between two circular quartz discs, andthe bottom disc rotated by a stepper motor to allow application ofa controlled shear rate. A second stepper motor allows theseparation of the discs to be varied so that the sample gap couldbe adjusted from 2500 lm down to 10 lm. Changing the wave-form on the input of the stepper motor allowed the shear applied tothe sample to be either continuous, step or oscillatory.

With this equipment it was therefore possible to generate shearconditions identical to those on the RDSII. Temperature controlwas achieved using two silver-block heating elements above andbelow the quartz discs to allow precision temperature adjustmentbetween 20 °C and 350 °C, although experiments reported in thispaper were performed at 20 °C. Full control of the shear cell wasfacilitated by a software interface running on a personal computer.Figure 1 shows the top and bottom plates of the shear cell in theassembled and dis-assembled state. The optical stage was mountedon a standard Olympus optical microscope with a JVC CCDcamera ®tter so that experiments could be recorded onto S-VHSvideo tape. Feeding the signal from the CCD into a frame grabberboard also allowed capture of digital images facilitating measure-ments of droplet size, elongation and orientation with standardimage analysis software.

Results

Commercial mayonnaise

The rheological data for the commercially produced oil-in-water emulsion are presented in Fig. 2. The experi-mental data obtained are typical of all the oil-in-wateremulsion studied in this paper. Starting with the strainsweep of Fig 2a, it is seen that the material response islinear over a very limited region of small strain, less than1%. Figure 2b shows data for a frequency sweepperformed at a strain of 0.4% ®tted with a continuousspectrum of relaxation times. For the continuousspectrum ®t, a time domain equivalent to the experi-mental frequency domain was chosen. For the material,the elastic modulus G¢ is greater than the viscousmodulus G¢¢ over the entire range of applied strain orfrequency, indicating the predominantly elastic behav-iour of the material at these small test strains. However,the slope of the power-law frequency dependence of G¢is higher and the minimum in G¢¢ less pronounced thanfor other mayonnaise-like products previously studied(Gallegos et al. 1992b). Figure-2c shows the continuousspectrum of relaxation times for the commercial may-onnaise, and it indicates a predominant ``plateau''behaviour in the time domain tested, with a gradualdecrease in the sti�ness constant with increasing relax-ation times. The results of step strain experiments areshow in Fig. 2d. The non-linear behaviour of thematerial is apparent from the ®gure, where an increasein the applied strain from 1% to 50% results in amarked decrease in the relaxation modulus. The stepstrain data of Fig. 2d can be used to determine theWagner damping factor to characterise the degree of

147

non-linearity. A damping factor of 0.75 has beenestimated. The damping factor can then be used tomake a prediction of the response of the material whensubjected to a steady shear rate. Figure 2e shows the

steady shear data for the commercial mayonnaisestudied. The data are ®tted with a prediction from theintegral constitutive equation with Wagner dampingfactor, using a continuous spectrum of relaxation times.

Fig. 1 Photographs of Cam-bridge/Linkam shear cell,showing top and bottom platetogether with assembly on mi-croscope

148

However, the ®t is not particularly good at either low onhigh shear rates. The overestimation of the apparentviscosity at low shear rates is thought to be due tosample slipping between the rheometer plates, as report-ed previously for other emulsions (Barnes 1995; Francoet al. 1998).

The optical microstructures observed for the com-mercial mayonnaise studied are shown in Fig. 3, for aseries of increasing shear rates. The optical observationduring shearing has proved to be a useful addition to the

rheological characterisation of the material. Figure 3ashows the microstructure of the material before shearingwithin the shear cell. A dense array of oil droplets can beidenti®ed. When the material was submitted to shearrates below of order 1 s)1 all of the droplets wereobserved to move together and with the same velocity asthe moving bottom glass disc. The emulsion under theseconditions was slipping at an interface between the ¯uidand the top stationary glass disc. As the applied shearwas increased above 1 s)1, relative movement becomes

Fig. 2 Rheological character-isation of a commercial may-onnaise a strain sweep(x = 6.28 rad/s); b frequencysweep (c = 0.4%) with contin-uous linear relaxation spectrum®t; c continuous linear relax-ation spectrum; d linear andnon-linear relaxation moduluswith continuous linear relax-ation spectrum ®t; e experi-mental and model prediction ofsteady-state ¯ow curve

149

apparent between adjacent droplets and the materialappeared to move as a continuum with little or norelative slip at the top and bottom glass interface. At

shear rates higher than 10 s)1, the size of the oil dropletswas clearly seen to increase, due to coalescence ofdroplets, as shown in Fig. 3c±e for shear rates comprised

Fig. 3 Optical micrographs ofa commercial mayonnaise:a 0 s)1; b 10 s)1; c 100 s)1;d 200 s)1; e 300 s)1; f 3000 s)1.Samples thickness of order50 lm. Photographs taken im-mediately after shear

150

between 100 and 300 s)1. At much higher shear rates(>1000 s)1) the droplets were disrupted to a sizeapproaching that of the unsheared sample. The photo-micrographs of the mayonnaise microstructure were ofsu�cient quality to facilitate in situ size measurement ofthe droplet size distribution (DSD) of the sample underdi�erent shearing conditions by using image analysistechniques.The corresponding DSD are shown in Fig. 4.The similarity of the size distributions at 10 and 3000 s)1

and the much larger size of emulsion droplets at 300 s)1

are apparent.

Pea protein-stabilised emulsion

The rheological data of the pea protein-stabilisedemulsion are shown in Fig. 5. The rheological behaviouris very similar to that shown by the commercialmayonnaise previously studied. The strain sweep ofFig. 5a shows that again the linear region is limited toquite small strains of less than 1%. A frequency sweepperformed at a strain within the linear region (0.4%)shows a frequency dependence similar to that of thecommercial mayonnaise, a predominantly elastic behav-iour with G¢ greater than G¢¢ for the entire frequencyrange. Figure 5b shows the frequency sweep data ®ttedwith a continuous spectrum of relaxation times, whichgives a good recalculation of the dynamic viscoelasticity

functions over the whole frequency range studied.Figure 5c shows the continuous spectrum of relaxationtimes for this emulsion. A predominant ``plateau'' regionin the time domain tested, with almost unvariantsti�ness values, is apparent. The step strain data ofFig. 5(d) showed that the pea protein-stabilised emul-sion had a more pronounced non-linear behaviourcompared to the commercial mayonnaise. Thus, arelatively small increase in the applied strain from 1%to 10% results in a marked decrease in the relaxationmodulus, which is re¯ected in a higher value of theWagner damping factor (h = 2.2). The prediction of thesteady shear behaviour using a factored constitutiveequation with Wagner damping function is given inFig. 5e. The model prediction of the steady-state ¯owresponse is similar to that for the commercial mayon-naise at low shear rates, with overestimation of theapparent viscosity. In contrast, the ®tting is fairly goodfor shear rates comprised between 4 and 100 s)1.

The optical observations for the pea protein-stabilisedemulsion are shown in Fig. 6 for a series of di�erentshearing conditions. Figure 6a demonstrates that themean droplet diameter of this emulsion before shearingwas signi®cantly lower than that of the commercialmayonnaise previously studied. At low shear rates(<4 s)1) the behaviour was identical to that of thecommercial mayonnaise; that is, the sample was seen toundergo slip between the quartz discs of the shear cell. Asthe shear rate was increased above that critical shear rate,relative movement between oil droplets visibly increased.In contrast to the commercial mayonnaise, an increase inshear rate up to 300 s)1 did not modify the droplet sizedistribution of the emulsion, as shown in Fig. 6c±e. Atmuch higher shear rates (>1000 s)1) the droplets weredisrupted by the shear stress to a size lower than that ofthe unsheared sample, as seen in Fig. 6f.

PEG/non-ionic-surfactant-stabilised emulsion

Rheological data for this emulsion, which is clearlydi�erent to those previously shown, because it isstabilised by a low-molecular-weight emulsi®er andconsequently the nature of the interdroplet interactionsis more typical of a ``particle gel'' (Dickinson and Hong1995) are shown in Fig. 7. The experimental resultsobtained show some signi®cant di�erences from theprevious two emulsions. Firstly, the linear region is verymuch smaller than before and also clear deviations fromlinearity are shown in Fig. 7a at strain levels exceeding0.3%. However, the frequency dependence of its dy-namic linear viscoelasticity functions (Fig. 7b) is similarto that of a highly ¯occulated emulsion, showing a clear``plateau'' region in G¢ and a tendency to a minimum inG¢¢, which is not reached due to the limitation in thereliability of the high frequency values because of its

Fig. 4 Droplet size distribution curves, for a commercial mayonnaise,as a function of the shear rate applied on the sample

151

extremely narrow linear viscoelasticity range. The con-tinuous relaxation spectrum (Fig. 7c), shows now twodi�erent regions: a transient region for the lowestrelaxation times and a ``plateau'' region, with a signi®-cant positive slope, once again typical of highly ¯occu-lated emulsions. The step strain response is shown inFig. 7d and it is reassuring to note that the relaxationmodulus predicted from the G¢, G¢¢ data is in goodagreement with the small strain, experimental step straindata. The large strain data in Fig. 7d give a dampingfactor of k = 0.62. The prediction of the steady-state

shear data using the Wagner model is given in Fig. 7e.At shear rates below 2 s)1 the ®t between model andexperimental data is poor. This poor match may againbe interpreted as a consequence of the development ofwall-slip phenomena during steady shear. At shear ratesbetween 2 and 100 s)1 the continuous spectrum data ®tcan match the steady-state ¯ow behaviour fairly well.However, for shear rates larger than 100 s)1 the model®t slightly deviates from the experimental data, in asimilar way to the lack of agreement found in this regionof the ¯ow curve for the pea protein-stabilised emulsion.

Fig. 5 Rheological character-isation of a vegetable protein-stabilised emulsion: a strainsweep (x = 6.28 rad/s);b frequency sweep (c = 0.4%)with continuous linear relax-ation spectrum ®t; c continuouslinear relaxation spectrum;d linear and non-linear relax-ation modulus with continuouslinear relaxation spectrum ®t;e experimental and modelpredication of steady-state ¯owcurve

152

This deviation can partly be explained by the truncationof the relaxation spectrum in the short time scale. If thisis extended by extrapolating the G¢ and G¢¢ data given in

Fig. 7b, a very much better ®t can be obtained in thehigh shear rate region without signi®cantly in¯uencingthe results at lower shear rates.

Fig. 6 Optical micrographs ofa vegetable protein-stabilisedemulsion: a 0 s)1; b 10 s)1;c 50 s)1; d 200 s)1; e 300 s)1;f 3000 s)1. Sample thickness oforder 50 lm. Photographstaken immediately after shear

153

Microstructure observations of the emulsion revealeda much ®ner dispersion of oil droplets compared to thepea protein-stabilised and commercial mayonnaiseemulsions. Thus, the oil droplets are so small that theyappear as a continuous background. The averagedroplet size is less than 1 lm; however, some largerdroplets (>10 lm) were also present. Application ofshear rates lower than 100 s)1 caused no visible changesin the emulsion microstructure; however, at shear ratescomprised between 100 and 300 s)1 the largest dropletswere seen to align into chains along the shear direction.

The chaining behaviour seen in this system has also beenobserved in viscoelastic polymer ¯uids (Michele et al.1977). At very high shear rates (1000 s)1) the dropletchains were disrupted and the emulsion microstructurelooked very similar to that of the unsheared sample.

Sucrose ester-stabilised emulsion

The rheology of the sucrose ester-stabilised emulsionshowed further clear di�erences, mainly due to the fact

Fig. 7 Rheological character-isation of a polyoxyethyleneglycol nonylphenyl ether-stabi-lised emulsion: a strain sweep(x = 6.28 rad/s) b frequencysweep (c = 0.3%) with contin-uous linear relaxation spectrum®t; c Continuous linear relax-ation spectrum; d linear andnon-linear relaxation moduluswith continuous linear relax-ation spectrum ®t; e experi-mental and model prediction ofsteady-state ¯ow curve

154

that this emulsion does not possess a linear viscoelasticityregion even at strains as low as 0.1%, as seen in Fig. 8a.The frequency sweeps shown in Fig. 8b therefore haveto be treated with caution. In fact, the evolution iscompletely di�erent to that found with other sucroseester-stabilised emulsions, which show a clear ``plateau''region. Consequently, strains outside the linear visco-elasticity range modify the interdroplet interactionsresponsible for this region, and also favour the appear-ance of the terminal region in the frequency rangestudied. The non-linear step strain data (Fig. 8c) follow asimilar pattern to those shown by other emulsions, butthe steady-state ¯ow results given in Fig. 8d show apeculiar response. Thus, the experimental data appear tofollow two distinct regions. For shear rates lower than10 s)1 the material behaves as Newtonian. Above thisshear rate signi®cant shear thinning is observed.

Experimental observations of the sucrose ester-stabi-lised emulsion microstructure in the optical shear cellcon®rmed the peculiarities raised by the rheologicalcharacterisation. At rest, the sucrose ester-stabilisedemulsion was seen to be a relatively uniform dispersionof oil droplets, visible as light circles in the photomi-crograph of Fig. 9a. The sucrose ester was also visible asdark regions between the oil droplets. It is thought thatthe sucrose ester formed a continuous matrix interdis-persed with oil droplets. Application of small steadyshear rate of 10±50 s)1 led to coalescence of the oildroplets and a disruption of the gel-like sucrose estermatrix. Figure 9b and 9c clearly shows the increased sizeof the oil droplets and the separation of the sucrose ester(black regions) into discrete clusters within the micro-structure of the emulsion. Slippage of the samplebetween the quartz discs of the shear cell was alsoapparent, but in addition to this, movement of ``micro-domains'' within the emulsion matrix was also observed.The sample was seen to fracture into irregular domainsseveral hundred of micrometres across which movedrelative to one another as a result of the applied shearstress. These microdomains were similar in appearanceto the grain boundaries in crystalline materials, withemulsion droplets inside the domains showing norelative movement. At intermediate shear rates of 20±300 s)1 the emulsion became much more ¯uid-like withincreased mobility and relative motion of the oil dropletswithin the sample. At shear rates of 200±300 s)1

chaining of the oil droplets was apparent. As was seenwith the PEG non-ionic surfactant-stabilised emulsion,the oil droplets formed chains consisting of severaldroplets aligned along the direction of the applied shear.At high shear rates (600 s)1) droplet alignment disap-peared and the larger oil droplets were disrupted to yielda more uniform emulsion similar to the originalunsheared material. Shearing of the sample at 1000 s)1

for a period of approximately 5 min resulted in theformation of large gel-like particles of the sucrose ester.

Once the emulsion reached this condition it was notpossible to return to the original state without theapplication of heat to melt the sucrose ester aggregates.

Discussion and conclusions

In this paper the rheology and microstructure of fourdi�erent oil-in-water emulsions has been experimentallysurveyed and the ®t of the rheological data to one classof constitutive equation has been attempted.

At small strains all of the emulsions had a signi®cantviscoelastic response and two systems had a clear linearviscoelastic region. The linear viscoelastic frequencyresponse was ®tted to a continuous relaxation spectrum.From the data presented in this paper it is clear thatthree of the emulsions tested possessed a broad relax-ation ``plateau'' within the time domain examined (10)1±102 s); this observation is consistent with the ®ndings ofothers where a wide ``plateau region'' has been reportedfor the viscoelastic spectrum (Gallegos et al. 1992b).

Good self-consistency was observed between thelinear relaxation modulus generated from G¢ and G¢¢data and that obtained from small strain, step straindata. For larger strain, step strain data exhibited theclassic hallmark of factorability for strain, characterisedby a reduction in the relaxation modulus without amajor change in the slope of the stress decay. This is akey point and supports the justi®cation for ®tting theexperimental data to a Wagner-type equation. Thestrain softening of the materials was characterised usinga Wagner damping factor k, with values for k rangingfrom 0.6 to 2.2. This compares with a typical value of 0.3for a polymer melt and con®rms the experimentalobservation that emulsion viscoelasticity is delicate,and limited to smaller strain deformations than mostpolymer systems.

The model predictions for steady shear were com-pared with experimental data and the quality of theobserved match varied depending on both shear rateregime and material composition. A key feature of thesteady shear data observed for all samples is that thepredicted low shear data are greater than that experi-mentally observed. This is consistent with the observa-tion of slip seen at low shear rates using the optical shearcell. This observation of slip is also consistent with theconclusions of others (Barnes 1995; Franco et al. 1998)and obviously has important consequences in terms ofinterpretation of any steady shear data from emulsionsystems. Thus, low-shear-rate wall-slip e�ects appear tobe a generalised problem in emulsion rheology. It mayalso in¯uence the width of the linear viscoelasticityregion, as previously stated by other authors (Diogo1995). This may explain why no linear viscoelasticityregion has been found in the sucrose stearate-stabilisedemulsion. In fact, this system shows the largest wall-slip

155

e�ects, with a ``pseudo''-Newtonian region at shear ratescomprised between 0.1 and 10 s)1.

An additional striking feature of the steady shearrheological data can be seen if the steady shearpredictions for the continuous spectrum model areexamined for all the emulsions. Over the shear raterange of order 10)1±102 s)1, the steady shear ¯ow stressis almost constant for each sample. The value of the ¯owstress varies for each emulsion and ranges from 10 Pafor the non-ionic surfactant emulsion to 100 Pa for thesucrose ester emulsion. The origin of the stress atdi�erent shear rates can be correlated as originatingfrom the components of the relaxation spectrum where kis of order 1= _c. This may have important consequencesin interpreting the mechanism associated with stressgeneration in emulsions.

The optical microstructure observation made duringshear revealed a number of additional features. Incertain systems such as the vegetable protein-stabilisedemulsion little or no change in droplet size distribution(DSD) was observed as a consequence of shear formuch of the shear rate examined and in this casereasonable agreement was found between model steadyshear data and experiment. For the case of mayonnaise,

however, droplet coalescence was observed at interme-diate shear rates (probably due to a wrong storage,which induced lower viscoelastic characteristics thanexpected) and, in this region of the ¯ow curve, arelatively poor ®t between the model and experimentwas found. These observations suggest that when thechange in microstructure with shear is mainly related toa de¯occulation process, a factorable constitutive equa-tion can be used; if, however, the DSD does change, thisassumption cannot necessarily be made. Consequently,if the wall-slip phenomena and DSD changes areavoided, the Wagner constitutive equation shouldpredict the steady-state ¯ow behaviour of emulsions ina very wide range of shear rate. This fact is con®rmed inFig. 10, where the experimental steady-state ¯ow curveof the vegetable protein stabilised emulsion, obtained ina controlled stress rheometer using a serrated plate-plategeometry, is matched with that predicted from theWagner model, in a shear rate range comprisedbetween 10)6 and 10)3 s)1.

Concentrated emulsions appear to fall into a generalrheological class of behaviour characterised by a``plateau'' relaxation spectrum and a factorable strainsoftening damping factor. Although concentrated emul-

Fig. 8 Rheological character-isation of a sucrose ester-stabi-lised emulsion a strain sweep(x = 6.28 rad/s); b frequencysweep (c = 0.3%); c non-linearrelaxation modulus; d experi-mental steady-state ¯ow curve

156

sions have high viscoelasticity at small strain deforma-tions, they also strain soften to give an essentiallyviscous ¯uid at large strain deformations and in steady

shear. The Wagner integral equation appears to do areasonable job in characterising the steady-state ¯owbehaviour of concentrated emulsions, although it is

Fig. 9 Optical micrographs ofa sucrose ester-stabilised emul-sion: a 0 s)1; b 10 s)1; c 50 s)1;d 200 s)1; e 300 s)1; f 600 s)1.Samples thickness of order50 lm. Photographs taken im-mediately after shear

157

almost certainly not a unique constitutive equation thatcan describe the observed behaviour. Wall slip, changesin droplet size distribution and microdomain ¯ow are all

factors that may cause deviation from the base emulsionbehaviour.

This paper has provided a microscopic and phenom-enological description of the rheology of concentratedoil-in-water emulsions. It has not proved possible to linkcompletely the observed microstructure changes with therheological behaviour. However, the observed low shearslip does, for example, correlate with the overpredictionof the model steady shear stress, in relation to theexperimental values, for low shear rates. In addition, thesmall change in observed droplet size for the shear rangetested also supports the view that the material can bedescribed using a factored memory function. What isnow required is a greater depth in understanding themechanism of viscoelasticity for concentrated emulsions,task that has been already addressed by several authors[see, for example, Princen (1983) and Kraynik et al.(1991)].

Acknowledgements We would like to thank Acciones Integradas, aBritish Council/Spanish joint collaborative fund for providingsome ®nancial support for this work. C. Bower would also like tothank the Cambridge Colloid Technology Programme for ®nancialassistance.

Fig. 10 Experimental and model prediction of steady-state ¯owcurve, for vegetable protein-stabilised emulsion, using a smooth plate-and-plate geometry in a controlled-strain rheometer, and b pro®ledplate-and-plate geometry in a controlled-stress rheometer

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