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 _c1. This behaviour has been mainlyassociated to droplet deocculation, 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 emulsierused (Franco et al. 1995, 1997; Tadros 1993). Thus, amore general picture of the oscillatory response of
Rheol Acta 38: 145159 (1999) Springer-Verlag 1999 ORIGINAL CONTRIBUTION
C. BowerC. GallegosM.R. MackleyJ.M. Madiedo
The rheological and microstructuralcharacterisation of the non-linearow behaviour of concentratedoil-in-water emulsions
Received: 10 November 1998Accepted: 24 November 1998
C. Bower M.R. Mackley (&)Department of Chemical EngineeringUniversity of CambridgeNew Museums Site, Pembroke StreetCambridge, CB2 3RA, UKhttp://www.cheng.cam.ac.uk
C. Gallegos J.M. MadiedoDepartamento de Ingeniera QumicaUniversidad 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 emulsiers. From the fourdierent samples that were tested,certain general trends were identiedand 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 emulsiers) 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 emulsier com-position. Wall slip, microdomainmovement, chaining and changes indroplet size distribution were allobserved under dierent 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 emulsiers 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 emulsiers. Ma-diedo and Gallegos (1997) have used a dierentempirical model that describes those regions in therelaxation spectra of oil-in-water emulsions stabilised bya mixture of two low-molecular-weight surfactants withdierent 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 modied Wagner model, wherethe Wagner damping function was changed for theSoskey-Winter one (Soskey and Winter 1984), to tthe transient ow behaviour of dierent 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 emulsiers. 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 andow behaviour of the deformed emulsions using aspecially designed optical shear cell (Bower et al. 1997)has been addressed.
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 andSchaeer 1993). Considering only the shear stresscomponent of the stress tensor and time-strain separ-ability, a form of the KBKZ equation is:
st Z t1
hcct; t0dt 1
where G(t)t) is the linear relaxation modulus and h(c) isa damping function. Following Wagner (1976)
hcekjct;t0j 2where the damping factor, k, is an empirical parameterwhich quanties 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):
hc Gc; t t0
Gt 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:
Gt t0 Z 11
Hkett0=kd lnk 4
Substituting this into Eq. (1), the Wagner model gives:
st Z t1
Hkett0=kekjct;t0jct; t0d lnk dt0 5
and the apparent viscosity can be calculated from thefollowing integral equation:
gc Z 11
kHk1 kkc2 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).
Four emulsion systems were chosen and three of the emulsions weremade using sunower 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 sunower 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 emulsiers 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 emulsier (Triton N101, Sigma, St. Louis, USA) was mixedwith 27% wt water to form a homogeneous solution, at roomtemperature. Then, 70% wt sunower oil was slowly added whilstunder agitation to form a stable emulsion. The sucrose ester-stabilised emulsion was made under slightly dierent 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 sunoweroil 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.