rwinmto,aditratcefre Rse 90 i n Za- and Qin 1980; (Russel forces, forces hydrodynamic interparticle and of motion, Brownian combination a by determined is behavior ute erdcinwtotpriso sprohibited is permission without reproduction Further  to inquiries [email protected]). Direct (E-mail: Genovese 14456-0462, author NY Geneva, Univ., Cornell Technology, and Carrindanga La Camino Km7,8000Bah (UNS-CONICET), PLAPIQUI with Genovese are Authors Lozano 11/14/2006. and Accepted 9/13/2006, Submitted 20060509 MS P G B. Dispersions D. Food Noncolloidal and Colloidal of Rheology The JFS hl yrdnmcfre oiaefrprilslre hnap- than larger 10 particles proximately for dominate forces dispersions, hydrodynamic sub-nanometer-size interparti- while for and equilibrate motion quickly Brownian rheol- forces size. The bulk cle particle 2003). the the Zaman therefore, on and and, depend forces ogy Qin these 2001; of others magnitude and relative (Zhou nature in tic elas- are the and forces thermal potential to are ever-present forces particles Colloidal the force. randomizing is of force motion Brownian The relative fluid. the surrounding Hydro- from forces. arise forces colloidal dynamic and Brownian, hydrodynamic, persions: liquid, another in emulsions. droplets named liquid of or solution, aqueous an usually food rhe- behavior. in and structures ological improvement desirable with the foods to of creation lead through quality should knowledge such turn, them. In between interrelationships the to- understanding food to microstructure lead a or should structure on and composition data its on Rheological data with 2006). gether (Rao level molecular microscopic the at and the changes between with links properties establish rheological to macroscopic is challenge major mi- and A molecular level. the croscopic at properties and changes the measured by affected The are nature. they However, in level. macroscopic physical the at are occur responses responses rheological those of all, not Most, if treatments. physical other thermal and as homogenization, such methods processing, processing different to media aqueous in o:10.1111/j.1750-3841.2006.00253.x doi: C 07Isiueo odTcnlgssVl 2 r ,2007 2, Nr. 72, Vol. Technologists Food of Institute 2007 he id ffre oxs ovrosdgesi lwn dis- flowing in degrees various to coexist forces of kinds Three medium, liquid a in solids either of dispersions are foods Many eair nti eiw eetsuiso olia n oclodlfo iprin nwihtertclmdl as discussed. models are theoretical employed rheological which were in on analysis dispersions bonding food structural interparticle noncolloidal as and and well colloidal loading on solids studies of recent review, role this stress, the In behavior. into yield analysis viscosity, structural insight structures, their provide complex with on models foods structure-based dimension to applied and fractal easily and be cannot forces, parameters, models theoretical interparticle rheological When size, key modulus. of and and role fraction the volume into particle insights as provide dimensions such that with exist nature equations in theoretical liquids, colloidal several regimes), in be trated solids may particles of dispersed ( dispersions The particles are noncolloidal liquids. foods larger in of gas number or A liquids, them. should in microstructure between liquids or structure interrelationships and the composition its understanding on data to with together lead food a on data Rheological ABSTRACT: theresponsesofproteins,monoandpolysaccharides,andlipids rocessedfoodsareediblestructuresthatarecreatedasaresultof ewrs olia,dsesos od oclodl rheology noncolloidal, food, dispersions, colloidal, Keywords: ENOVESE :CnieRves/Hptee nFo Science Food in Hypotheses / Reviews Concise R: ´ ıaBlanca,Argentina.AuthorRaoiswithDept.ofFoodScience µ .Frprilsi h nemdaerneteflow the range intermediate the in particles For m. ,J.E.L Introduction OZANO , AND > .A R A. M. 10 µ ) o ohclodladnnolia iprin ete ndlt rconcen- or dilute in (either dispersions noncolloidal and colloidal both For m). AO ytmadpouiga nepril oc edn orsoethe restore to tending force interparticle the an of producing energy potential and total system the increasing thereby particles, the of positions at- relative the long-range changes network the from of deformation resulting tractions, aggregation For network. spanning mi- 1999b). others of and particles (Berli larger for and dominates size gradient crometer mechanism the last by This caused field. are velocity collisions orthoki- the and where motion, Brownian aggregation, to netic due where are aggregation, encounters particle perikinetic the aggregation: of considered mechanism usually the are for cases energy limit Two interaction concentration. particle–particle particle of and magnitude the on pending 2002). Berli and concentrated (Quemada be to considered is suspension other the region, the this of In presence ones. the by hindered is particle each Brow- of the motion consequence, nian a As important. become particles collision between of probability the and interactions hydrodynamic creases, ( Brownian regime by This driven forces. medium the throughout freely particles move Thus, to radius. able are particle to compared large is particles tween m cuidb h atce nrlto otettlvlm,that volume, total fraction, the volume to particle relation the in is, particles the by occupied ume not. or aggregate particles colliding 2 if determine forces interparticle while particles, colloidal of pairs between lisions col- and promotes as suspensions, motion Brownian protein emulsion). 2003), colloidal soy (a Zaman mayonnaise milk, juices, and fruit 10 Qin cloudy 1999; to example McClements nm for 1989; 1 others be and to de- sel considered not typically is particles but Brownian) rigidly, (or fined colloidal of Olivier range and size (Sennet The properties 1965). forces system inertial governing and in interfacial significant that are simple so to enough compared small dis- large but into are molecules, subdivided that is (particles/droplets) phase units dispersed crete the where systems neous 1). (Table them in particles the of nature and size according the classified to be may dispersions Consequently, 2003). man nwal lcuae iprin,prilsfr volume- a form particles dispersions, flocculated weakly In de- flocculated, or dispersed either be can suspensions Colloidal Theparticlearrangementsincolloidalsystemsdependonthevol- heteroge- or polyphasic as defined be may dispersions Colloidal φ → )i osdrda h iuelmt As limit. dilute the as considered is 0) — ORA FFO SCIENCE FOOD OF JOURNAL φ .Atlow φ h endsac be- distance mean the , < 10 µ µ ,or m, (Rus- m φ R in- 11

R: Concise Reviews in Food Science (2) (3) (1) When s equation ’ is the viscosity of ], of the dispersed s η η m φ ] η [ φ − ] s of dispersions of rigid, nonin- η η [ r m φ η φ η + 1 − : Hydrodynamic = : Hydrodynamic-interparticle-Brownian 1 = γ r γ r η η = r High ˙ Concentrated: Entanglements and Reptation η Dougherty equation (Krieger and Dougherty – and Their Application , and the intrinsic viscosity, [ φ ] depends on particle shape, being 2.5 for rigid value of monodisperse spheres is 0.74 (in a face- η m Theoretical Rheological Models φ is the maximum packing fraction of solids. Although the is the viscosity of the dispersion, and m η φ heoretical models are derived from fundamental concepts, and they provide valuable guidelines on understanding the role of Effect of particle shape and particle size distribution. The hydrodynamic disturbance of the flow field induced by solid One relationship derived for concentrated dispersions is the particles in liquid media leads totion an and an increase increase in in viscosity the (Zhou energy and others dissipa- 2001).viscosity The of relative dispersions of solidfined particles as in a liquid medium is de- Viscosity models for noncolloidal dispersions T Theoretically, [ spheres (Barnes 2000). widely used Krieger 1959) theoretical where structure. They indicate the factors thatrameter. influence As a rheological mentioned, pa- the viscosityfected of colloidal by dispersions interparticle is forces af- rates, while and hydrodynamic forces Brownian dominate at high motion shear rates atand (Berli others low 1999a). On shear the otherdispersions hand, is the governed by viscosity hydrodynamic forces of within noncolloidal all theof range shear rates. where centered cubic array), experimental observationsloose have random shown packing that is close to 0.60, anding that is close dense to random 0.64 pack- (Quemada and Berli 2002; Servais andQin others and 2002; Zaman 2003). the continuous phase. In general, the particles are nonspherical thereand is consequently an an increase extra in energy the viscosity. dissipation In dilute dispersions teracting spherical particles (hard-sphere systems) dependsvolume on the fraction, has been well covered in texts such as(1999); those therefore, of they Steffe are (1996) not and covered Rao here. solids (Eq. 2 andregime), 3). it is At described low by the particle well-known Einstein concentrations (in the dilute m and µ 10 > m), for exam- µ 100 > liquid interface being – liquid systems, liquid food or non-Brownian. – Vol. 72, Nr. 2, 2007 ” Microscopic/colloidalMicroscopic/noncolloidal Low ˙ Hydrodynamic — Particle size/nature Forces governing viscosity m (for example, chocolate, fruit purees nez-Padilla 2005). In this case, when the ı ´ µ noncolloidal “ liquid and liquid – a m a µ m µ m Macroscopic/noncolloidal Hydrodynamic m) is formed by aggregation, with the resulting suspension JOURNAL OF FOOD SCIENCE µ µ m-100 µ Several foods contain microscopic particles that are It should be emphasized that most foods are complex polydis- In addition to solid The present review is focused on microscopic colloidal and non- Other foods contain macroscopic particles ( 100 0.1 approximately 1 nm 12 m as macroscopic. Those food dispersions are usually considered Food dispersions covered in this review. 10 > 1 nm-10 Polymers Molecular/colloidal Dilute: intermolecular-Brownian R equilibrium structure. The nonequilibrium naturegives of the a structure complex, history-dependentand rheological others 1989). behavior A (Russel colloidalculated gel systems is a where special a< state continuous of strongly network floc- of particles (often a having a very high viscosity and a finite shear modulus. Table 1 Classification --- of dispersions Rheology of food dispersions . . . particle size has atomic dimensions, the system consistsular of a or molec- ionic dispersion, althoughsystem (Sennet strictly and speaking Olivier 1965). it is a 1-phase perse systems that may contain(that is, particles both microscopic from and a macroscopic particles) broad immersedeven (or size imbibed) in range an aqueous (or lipid)be medium, a which molecular in turn dispersion may itself.systems The has rheological been behavior of coveredcoworkers such (Vitali by and several Rao groups, 1984;and including Tanglertpaibul Rao and 1996). Rao Rao and 1987; Yoo ple, vegetable or cream soups, fruits inor sauces syrups with or seeds, yogurts, and pasta dressings or meat(1997) in referred sauces. to Gondret and dispersions Petit of glass spheresµ of diameter 45 to 450 to be liquid/particle mixtures, andcolloidal sometimes dispersion the (Mart liquid itself is a up to approximately 100 foams are biphasic systems where ain gas a bubble continuous phase is liquid dispersed under phase, tension. Their with complex the rheological behavior gas ismany influenced factors, by such as airterfacial phase volume, tension liquid and phase viscosity, viscosity,shape in- bubble (Herzhaft size, 1999; size Vernon-Carter and distribution, othersothers and 2003). 2001; There are Thakur also solid and food foams (typicallyucts cooked prod- such as breads or cakes),phase dispersed which in consist a of continuous solid a phase. discontinuous Solidor foams air plastic are materials. elastic Their mechanical (rheological)yond behavior the is scope of be- this work, butdependent we on may the mention physical properties that of it the is solid primarily phase anddensity the of bulk the material (Pernell and others 2002). colloidal food dispersions. Thestructureontheirrheologicalpropertiesintermsoftheoreticalmod- objective is to discussels and the structural role analysis. of Measurement of rheological properties and sauces, starch andflocs vegetable or pastes); aggregates some ofBrownian of colloidal motion particles. them and interparticle For may forces such are be to large negligible hydrodynamic compared particles, forces. However, nonhydrodynamicsuch parameters as particle shape, particledeformability, and size liquid and polarity could size affect distribution, theresulting structure flow particle behavior and (Tsai and the Zammouri 1988). Such dispersions have been called simply

R: Concise Reviews in Food Science eaievsoiyascae ihec iceeuioa iedis- size unimodal the discrete of tribution, each product with the associated was viscosity viscosity relative resulting overall the that showed distribution size width).Farris(1968)assembledmanymonomodaldistributionsand (particle polydispersity increasing at decreases ity h rnlsi h iprin(emn -) h utr fgran- of rupture The C-D). (segment dispersion the in granules the of fraction volume the in decrease gradual and a in rupture resulting granules disintegrate, the heating, a further reaches With and (C). increases value maximum fraction volume the A-B-C), absorp- (segment water to tion due swell they heated are frac- granules low volume the As low. the at is and tion Initially state raw granules. the in starch are granules of the temperatures, fraction volume the in changes 1. Figure in viscosity, starch. dry of weight unit per granules starch hydrated of mass concentration, specific a of dispersion starch example, For a obtain. neces- in to easy data not are the model theoretical Often, a apply 2000). to (Barnes sary viscosity lower a in resulting ifrn ls sizes class different eesmlri hp,b hoiga rirr eeec frequency reference arbitrary ( an choosing profiles by the shape, in Because similar here). were shown (not frequencies oscillatory eral eainhp(q )frssesoso oshrclparticles nonspherical of suspensions Krieger for the 3) (Eq. of relationship modification a proposed who oth- (1981), and ers Kitano by studied was suspensions concentrated on shape where particles, (oblate) like atec te uigfo,increasing flow, during other each squeeze past and rest at other each accommodate can particles formable setrto(/)o h upne atce nrae;frexample, whenL/D for increases; particles suspended the of (L/D) ratio aspect where nohrwrs o ie atcecnetain( concentration particle given a for words, Mart other 2002; In others the reducing and thereby (Servais particles, larger viscosity the overall of flow the for as lubricant act particles a small the conditions, flow Under particles. larger the eue oasnl atrcreo eue ope viscosity complex reduced of curve master single a to reduced in(q ) ipefrua a endrvdb ans(00 as (2000) Barnes by derived been [ has equa- formulas Einstein Simple in 2). viscosity (Eq. intrinsic tion the by reflected is increase this . . . dispersions food of Rheology esoso oyipre peia atce nNwoinfluids, Newtonian in φ particles spherical polydispersed of pensions crystals) in cuaeyadi speeal owr ihsac rnl mass ( granule fraction, starch with disper- work starch to preferable of is deformable it fraction and accurately volume their sions determine of to Because difficult is 2000). it Rao nature, 1998; and Rao Tattiyakul and 1999; (Yang same Rao the nearly remains starch of cross-linked that while a substantially decreases volume often starch the native heating, a the of further fraction After on value. attained, been maximum has a value to maximum ungelatinized continuously the increases in it value low and a state has it dispersion; the of heating ing η ω m ] r h hp ftecrei iue1rfet h aforementioned the reflects 1 Figure in curve the of shape The agadRo(98adLa n tes(99 obtainedcomplex (1999) others and Liao (1998)and Rao and Yang feto atcedeformability. particle of Effect qain3i ai o oooa peia atce.Frsus- For particles. spherical monomodal for valid is 3 Equation = ,althe all ), shge ic ml atce a cuytesaebetween space the occupy may particles small since higher is 0.07 β β sa dutbeprmtrwoevledcessa the as decreases value whose parameter adjustable an is q η cQ η = 5 ∗ = ri η / esstmeauedt fasac iprina sev- at dispersion starch a of data temperature versus , 1(smoothspheres) 3 ,where ), ( .4(eze 95 a 1999). Rao 1985; (Metzner 0.44 ∗ φ o o-ie(rlt)prils n [ and particles, (prolate) rod-like for tmeauecre ttedfeetfeuniswere frequencies different the at curves -temperature i ,asmn oitrcin ewe h atce of particles the between interactions no assuming ), c sdysac ocnrto,ww and w/w, concentration, starch dry is η η r r = q = steailrto h feto particle of effect The ratio. axial the is β i 1 = n = 1 − η φ r β φ i m ( φ ,andwhen6 thg ocnrtos de- concentrations, high At φ i − (5) ) m 2 n euig[ reducing and ´ ı e-ail 2005). nez-Padilla η c < ] , = φ L/D φ hne dur- changes ,teviscos- the ), 0.3 – Dougherty < η q ]inEq.3, o disk- for 8(rough Q sthe is η ∗ R (4) as yslcigteaporaeepeso rmE.2t 5. to 2 Eq. from expression appropriate the selecting calculated by be can it Thus, particles. rigid of dispersion noncolloidal a of viscosity relative the generally, more or, spheres hard of dispersion h term The icst tpitDta shge hnta tpitA. point at that than higher is that D segment to point the contribute at of remnants viscosity granule image a the mirror and a amylose Thus, not leached is The dispersion. C-D ABC. starch the segment the the to 1, of contributes Figure phase that in continuous amylose the of release of the viscosity in results also ules icst oesfrclodldispersions colloidal for models Viscosity rmYn n a 19) ihpriso rmBlack- from permission with (1998), Publishing. Reprinted Rao well rates. and differ- heating Yang at and from data frequencies experimental oscillatory of swelling ent curve granule Master to rupture. due corn- and heating, a of during viscosity dispersion complex starch reduced of --- Change 1 Figure itrino h D yteserfedlast nices nthe in increase an to leads field shear the by EDL the The (EDL). of layer distortion double electrical the called interface the in charges ( distance interparticle theory. DLVO the extended of the by function predicted a ( as potential interaction particles net of or total The 2001). oth- and ers Zhou 1999; steric, (McClements forces repulsive, structural) and electrostatic hydration, (including repulsive and and bridging, (including hydrophobic, depletion) attractive attractive, as electrostatic Waals, classified der be van can They forces. colloidal cle ( faclodldseso a enmdld(gw n tes1997; others and QuemadaandBerli2002)asthesumofa (Ogawa modeled been has dispersion colloidal a of 2003). Zaman and packing maximum (Qin effective fraction the factor, 1 into lumped differ- are from factors contributions ent the effective all the which is in other method, fraction The other. volume each from individ- separated are from factors contributions ual the which into in separation method, the divided is contributions One are of technique. scaling dispersions their on colloidal based of categories 2 viscosity the predictive for The 1999a). models others and (Berli energy particles, other extra the an of demanding fields force the against move to forced particles be occur must to flow for Therefore, other. each from away particles η r h h term The hre atce na lcrlt rsn narneetof arrangement an present electrolyte an in particles Charged ntesprto fcnrbtosmto,terltv viscosity relative the method, contributions of separation the In neighboring keep forces repulsive dispersions, colloidal stable In s n a and ) η o.7,N.2 2007 2, Nr. 72, Vol. “ r h olia forces colloidal s η r c scniee ob h eaievsoiyo nideal an of viscosity relative the be to considered is f novsteices nvsoiydet interparti- to due viscosity in increase the involves η ” r otiuin( contribution — = ORA FFO SCIENCE FOOD OF JOURNAL η r hs + η r cf “ hard-sphere η r c f ) U ewe pairs between ) ” contribution r a be may ) R (6) 13

R: Concise Reviews in Food Science is (9) tez d (12) (10) (11) ı ´ are phe- were ob- eff Max φ U 0.52 1 + p T σ + B 3 k ) m d · φ 2 ] eff 0.016 φ c η 3 [ φ 3 ( − eff = − a K ) · a eff 0.267 was obtained from Eq. 8 · T a m eff σ eff . Consequently, the effective vol- Max B T φ = φ φ /6) are numerical constants, k B ( U eff φ α k π K in a hard-sphere viscosity equation, − a = (approximately 0 for low shears) is the 1 eff k to p φ exp eff a and σ = = φ φ 1 2 ) by 1 r ) of cloudy apple juice at different pHs and c η φ φ eff ( T tez and others 2007). Values of = a ı f ´ B c r k (2 cf r η tobeshear-dependent,Buscall(1991,1994)found (theoretically η U 2 eff c a and approximately 1 tted with Eq. 8 (full lines). Reprinted from Ben c k fi Figure 3 shows In the effective volume fraction method, it is considered that re- Inthiscontext,theviscosityofacolloidaldispersioncanbesimply Byallowing particle stress (as in Eq. 32 also). pulsive forces keep particles apart from one another, thus increasing their effective radius from Figure 3 Effect --- loidal of forces particle contribution volumeent to fraction liquid relative on viscosity, mediumbols) for the conditions. differ- col- Experimental data (sym- the particle diameter, and where an approximate theoretical expression tained combining the extended DLVO theorymental and data. turbidity A experi- unique value of where ume fraction is given as ionic strengths (Ben like Eq. 3 (Quemada and Berli 2002) obtained by replacing nomenological factors. and others (2007), with permission from Elsevier. for all samples.For concentrated colloidal suspensions, Ogawaothers and (1997) derived the following expressionof based activation on processes: the theory (8) (7) for φ values ´ Alvarez r is Boltz- in terms η 0.483 was ´ f andez and B c r k = ), and pre- η • α were obtained Max U ). Several theoretical ex- 1 − φ κ tted with Eq. 8 (dashed- φ Vol. 72, Nr. 2, 2007 fi T p — Max B 5 ) with respect to the thickness of . k U a 2 (see, for example, Hidalgo- Brix (Genovese and Lozano 2006). ◦ p = α ), and ´ andez and others 2004). cf r = η ) curve. r cf r ( is the absolute temperature. The value of η U T ´ Alvarez and others 1996; Rubio-Hern values from Eq. 2. Values of s is a function of the potential in the slipping plane h r , the primary electroviscous coefficient, to the Ein- η p p wereobtainedbydifferencebetweenempirical f c r is a dimensionless proportionality constant, η α JOURNAL OF FOOD SCIENCE s constant, and ), also known as the energy barrier or activation energy predicts the stability of colloidal dispersions, and is obtained ’ potential (a measure of the particle surface potential), and the – Figure 2 shows the 3 components of Eq. 6 as a function of However, Eq. 7 only considers the contribution of electrostatic Max ζ Max 14 U where and others 1996; Rubio-Hern dicted with Eq.contribution, Eq. 6 2 (full (dashed line);semi-empirical colloidal-forces line); contribution: values theoretical ( hard-sphere Valuesof Figure 2 Cloudy --- applewith juice relative particle viscosity volume compared fraction: experimental ( viscosity due to increased energyconsidered dissipation. by This Smoluchowski and effect is wascous called effect first (Hidalgo- the primary electrovis- Rheology of food dispersions . . . at the maximum of the cloudy apple juice from 10 to 50 The coefficient or relative size of the particle radius ( the EDL, calculated as the Debye length ( R pressions have been derived for repulsive forces to the viscosity. Genoveseposed and a Lozano (2006) more pro- general, semiempirical expression for dotted line). Reprinted from Genovesewith and permission Lozano from (2006), Elsevier. and theoretical mann U obtained. from the balance between van dertion Waals, interparticle electrostatic, forces. and By applying hydra- Eq. 8, the value stein equation (Eq. 2), such that combined with Eq. 6 gives others 2004). For dilute dispersions of spherical particles,as it a appears correction of the maximum net repulsive potential( between pairs of particles

R: Concise Reviews in Food Science ereo grgto fasseso adt siaetevleof value the estimate to (and D suspension the a measure of to aggregation possible of is degree it 14 and 13 Eq. Combining constant. rate where where h aiu akn rcin for fractions packing maximum the h yrdnmctikeso h oye ae,and layer, polymer the plus of radius thickness hydrodynamic core the the involves which radius, hard-sphere equivalent where ie yteexpression the by given and aggregates, ouu fclodlgl ffatlflocs fractal of gels colloidal of Modulus 3) (Eq. Krieger equation modified the using by suspension soy gregating solids. describe or to surfaces, order lines, in Euclidean not 3 are and that 2, structures 1, of by dimensions coined Euclidean ventional was fractal dimensions term introduced deviates who (1982), outline The Mandelbrot object regularity. or and image smoothness an from which to degree dimension the fractal A indicates aggregates. branched highly is, that structures, Theaggregationofcolloidalparticlesleadstotheformationoffractal . . . dispersions food of Rheology intrsod(hhadohr 90,weeteeatcmodulus, elastic the where 1990), G others and (Shih gela- the threshold above well themselves. tion are that flocs gels to the applicable be than should flocs regime constant This fractal elastic be- lower links packed have the close concentrations, flocs of particle tween collection high At a particles. be colloidal to of structure network the gel considering the by gels of colloidal of properties elastic the elcsteitra tutr ftefosaddpnso h mode the on depends and flocs the of structure internal the reflects h grgts(nta of (instead aggregates the el n umd 20)pooe h olwn oe o these for chains. model following polymer systems the of proposed (2000) layer Quemada external and an Berli and polymer cross-linked of relationship: where

f srltdt h atcevlm rcin( fraction volume particle the to related is , el n tes(99 rpsdavsoiyeuto o nag- an for equation viscosity a proposed (1999) others and Berli hhadohr 19)dvlpdasaigrltosi oexplain to relationship scaling a developed (1990) others and Shih Aggregatingcolloidaldispersionsandmicrogelsuspensions. usladohr 18)pitdotta h rca dimension fractal the that out pointed (1989) others and Russel irglssesosaeprilscmoe facnrlzone central a of composed particles are suspensions Microgel rmvsoiytm data. viscosity-time from ) σ t η D c 0 m steciia ha stress, shear critical the is steEciendmnino h network the of dimension Euclidean the is steiiiltm twhich at time initial the is stevsoiyo h eimfligtesaebetween space the filling medium the of viscosity the is N steaeae ubro atce nacluster a in particles of number averaged the is χ η η m σ η = c ( = σ = G N φ ) = k 1

a = η B φ ∝ hs − 3 η T s 0 1 ), ∞ φ − φ + φ ( D m D 1 1 − k ¯ f σ N σ + a 2) χ σ stefatldmnino the of dimension fractal the is ( / (3 sarelgclindex, rheological a is t σ ( σ U N 1 → D − c − c − k (2 − D − + ≈ B D and 0 t f a 0 T φ ) f χ 1 / ) ,and 1, hs ) D ) f φ 2 ∞ σ − 2 φ →∞ “ k ytefollowing the by ) ¯ between a h aggregation the — respectively. , φ sal 3. usually 0 – and Dougherty ” a h con- the hs φ sthe is ∞ (16) (13) (18) (15) (17) (14) are ls( ulus grgto,and aggregation, epee sbt trhshvn rnlswt ihyconvoluted higher highly The with surfaces. granules having starches both as terpreted .1frCW and CLWM for 2.81 cuidb h trhgaue a acltda h rnl mass granule is, fraction the that as fraction, volume calculated was The granules amylose. starch the 19.3% by occupied with and starch, (CLWM) tuber maize substantially waxy a were cross-linked tapioca, a that other: starches each 2 from different of dispersions studied (2003a) h obelgrtmcpo eutdi esnbesrih lines straight reasonable in resulted ( plot logarithmic double The n aic trhdsesoswr lte against plotted were dispersions starch tapioca and notefo n erag t ofgrto eoesikn,thus sticking, before configuration its rearrange increasing and further penetrate floc to the particles into allows flocculation slow hand, other esostepaeueulbimvalues, equilibrium plateau the persions n tes19) h equilibrium The 1990). others and band itdi al ,ilsrt yia magnitudes. typical illustrate 2, values Table the in and listed reported obtained, been of have some data, foods, rheological of on number based them a of dimension fractal Rao on and Studies (Genovese 2003a). granules their of rigidity higher the to attributed eoeeadRo(03) ihpriso rmAACC from permission with Experi- (2003a), fraction. International. Rao volume and granules Genovese their (symbols) data of mental function dispersions starch a 2 of as modulus plateau --- Elastic 4 Figure models stress Yield inldpnec fteyedsrs ihpril ouefraction. volume particle with stress yield the of propor- a dependence found tional (1993) others and Husband fractions), volume 57% car- (27 calcium suspensions polyisobutylene In filled suspensions. bonate noncolloidal concentrated highly 1993; determination stress others of yield and on found (Husband were 2006) works others and few Marquez sur- a or Just (colloidal particles. interacting active) of face suspensions in stresses yield tified hard- a andothers2001).Mostinvestigationshaveestablishedand/orquan- (Zhou in reached is occur fraction packing not maximum will others the until stress system yield sphere and that claimed (Poslinski been forces has It 1988). interparticle in- of and magnitude size, particle creasing decreasing fraction, volume particle creasing in fte2tpso trhgaue eecluae obe to calculated were dimen- granules fractal starch the of lines, types the 2 of the slope of the sions From 18. Eq. by inferred fageain nrpdflocculation, rapid In aggregation. of R 2 rca ieso ffo dispersions. food of dimension Fractal ngnrl h antd fteyedsrs nrae ihin- with increases stress yield the of magnitude the general, In ≥ G .5 o ohsace,fliln h oe a relationship law power the fulfilling starches, both for 0.95)

oprdwt siltr rqec ( frequency oscillatory with compared ) o.7,N.2 2007 2, Nr. 72, Vol. D f oapoiaey20ad30 respectively. 3.0, and 2.0 approximately to φ D = f cQ D = G f rmpos(o hw ee featcmod- elastic of here) shown (not plots From . = . o particle for 2.5

0 .9frtpoa epciey hswsin- was This respectively. tapioca, for 2.79 auso LMsac iprin were dispersions starch CLWM of values fi — tdwt q 7 erne from Reprinted 17. Eq. with tted ORA FFO SCIENCE FOOD OF JOURNAL G

– D 0 atceageain nthe On aggregation. particle f ausotie o CLWM for obtained values G =

0 eedtrie (Shih determined were , .5frcluster for 1.75 µ eoeeadRao and Genovese ω ndaee,0%- diameter, in m ftesac dis- starch the of ) φ Fgr 4). (Figure – cluster D R f 15 =

R: Concise Reviews in Food Science th i (26) (27) (22) (24) (25) (23) , which U ] T that is, when particles , B k m 2 φ − i ) ) 0 f ) m σ , has been correlated with the r D 3 a 2 ( v v c √ − 2 φ d d ( i U (3 1 φ χσ · φ / c B U 3 [ φ = φ = ) 0 = 0 ∝ σ σ eff 0 3 m 0 φ σ a approximately σ = ( 0 0 K σ ≈ 0 φ>φ σ is related with bond strength depending on mate- are the volume fraction and yield stress of the i B 0 σ is the maximum radius that the particle can take because and i m φ a The differences among Eq. 19 to 27 suggest that there is not From Eq. 12, Buscall (1991, 1994) derived Eq. 23, in which the Based on Eq. 9, Ogawa and others (1997) proposed a simpler This model describes the suspension in terms of particle chains Finally, it is worth mentioning the model of Berli and Quemada It should be noted that Eq. 20 and 21 only consider DLVO (van From analyses of experimental data and theoretical analysis from The power-law exponent in Eq. 25, simpler model has been suggested for calculationof of a the mixture yield suspension stress (Zhou and others 2001): are densely packed. a unique or general theoretical model to describe the yield stress component of the suspension, respectively. Unlike hard-sphere dis- persions in which polydispersity reduces the viscosity (Eq.pension 5), with a a sus- broad particle size distributionstress exhibits than higher a yield narrow size distributed2001). suspension (Zhou and others yield stress arises when the effectiveto particle produce radius a is dense high packing of enough particles, thus of the spatial constraints of the otherare the particles, same and as the other in terms Eq. 12. model, indicating that whenstrong, the there is effect an of apparent yield repulsive stress given interaction by is which is only valid if where interparticle bonds can beof soft Shih or and rigid, others (1990) similar (Eq. to 18). the study (2000) for microgel suspensions (Eq. 15 to 17),is where simply the yield given stress by where where constant der Waals and repulsive electrostatic) interparticle forces,23 while and Eq. 24 are functions ofmay include the also total non-DLVO (steric, hydration, interaction depletion, potential, and so on) interactions. several works, Zhou and others (2001) suggestederal the expression: following gen- where rial properties and system surface chemistry condition. fractal dimension, which is believed to beconnection associated and with the space-filling inter- ability of theTo network describe microstructure. this behavior, demicrorheological Rooij model and in terms others of fractal (1994) microstructures (Eq. developed 26): a ) – d (21) (20) (19) , and particle d is the dielectric , 2 0 ε Reference φ ) 2 κψ r d 0 κ ) and particle size ( π is the diameter of the κζ φ 4 εε (1999) (2003a) (1998) (1999) 0 d Z 3 exp( 3 f πεε is the Hamaker constant (a the permittivity of vacuum, f + φ + 0 Vol. 72, Nr. 2, 2007 24 A D 1 4 is a dimensionless orientation ε − − — F − φ 1.99 Marangoni2.6 and Hartel Hongsprabhas and others 2.81 Genovese2.1 and Rao Ould-Eleya and others 2.88 Marangoni and Rousseau 2 m A φ 2 – – – – – r φ H 2.90 Narine and Marangoni d − Fractal ) 2.3 F φ 1 d ( Volume fraction ( = π M 3 0 · d σ is the minimum floc concentration required 24 f π ZA φ 8 φ + = = 0 0 σ σ is the interfloc adhesive force, ) is the mean coordination number. The terms in the φ H is the total number of nearest neighbors of each sphere ( is the apparent yield stress, gels (1999)
is the surface potential of the spheres. The 2nd term in Eq. 0 2 M Z JOURNAL OF FOOD SCIENCE σ 0 ψ Colloidal dispersions. By considering the colloidal interparticle forces, Poslinski and For polydisperse spheres, the previous model is quite complex Scales and others (1998) proposed a general interactive model for Michaels and Bolger (1962) derived the following expression for canola oil blendsCaCl (1998) gel, pH 3.7 2004 pH 3.8 and 0.2M NaCl (2004) 16 Whey protein isolate Milk fat and / 1.97 Network of particles dimension, Soy protein isolate gels,Starch gelsEgg 2.3. white protein Renkema and van Vliet 2.79 1.9 Palm oil or lard fat 2.82 Cocoa butterSalatrim 2.37 Narine and Marangoni individual flocs, and where function, to form a continuous aggregate network. others (1988) derived anspheres dispersed in expression a for polymeric matrix the yield stress of solid R Table 2 Fractal --- dimensionfew foods of based structural on rheological elements data in (Rao 2006) a Unfortunately, the reasons/mechanisms of thatwere yielding not behavior clear, and noworks. theoretical models were proposed in those Rheology of food dispersions . . . and may be consulted in the work of Scales and others (1998). A bracketaccountforthevanderWaalsandEDLforcesactingbetween pairs of particles, or the strength of 1 particle bond. affect the density of thewhich interparticle in links turn and govern the the microstructure, yieldloidal stress dispersions (Zhou behavior and others of 2001). Consequently,most concentrated theo- col- retical yield stress models are mainly functions of measure of the van der Waals attractive forces), where in a particular packing configuration, the shear yield stress of flocculated suspensions.spherical For monodisperse particles, the model reducesEq. 20: to an expression similar to 20 accounts for the electrostatic repulsive forces. where and particle interactions. A representative selection of the manyfound models in the literature is presented next. suspensions of aggregated flocs, where the aggregates form tenuous networks constant of the continuous medium,

R: Concise Reviews in Food Science eeaie xrsinfrteyedsrs ffasa function a as foams properties: of structural stress their of yield the for expression generalized a proposed (2006) others and Raharitsifa 2004), others and Davis 1989; ae ihdfeetcnetain f2dfeetfaigagents in foaming resulting different white), pre- egg 2 foams and (methylcellulose juice of apple concentrations on different 5) with (Figure pared data experimental to applied (28) (2006) Eq. others and Raharitsifa observed. bubbles of number where where b ld h feto nefca tension, D interfacial of effect the clude ms) rmRhrtiaadohr (2006). others and Raharitsifa From (mesh). eladohr 00 ap n tes20) ae nE.2 and 25 (H Eq. on foams Based for 2003). models others other and (Per- Kampf stress 2000; yield others certain and a above nell liquids viscous like flow and tions, farvlm rcinadbbl endaee o dif- for function diameter as mean ( bubble foams agents: and foaming juice fraction ferent apple volume of air of stress --- Yield 5 Figure models Structural system. particular each for appropriate chosen/derived be the should instead model but dispersions, colloidal concentrated of . . . dispersions food of Rheology h lwbhvo fplmrdsesosadohrshear-thinning other and fluids. dispersions polymer characterize of to extensively behavior flow used the been has that of 30) that (Eq. is model (1965) such Cross One sample. food a of behavior rheological characterize the help experi- that with parameters of together values used, estimate are to data, They mental it. in changes of kinetics often o peia bubbles spherical For ht.Eprmna aa(symbols) data Experimental white. = 32 hs oesaedrvdfo osdrto ftesrcueand structure the of consideration from derived are models These Foams. .7( 1.37 steSue enbbl imtro ufc vrg diameter. average surface or diameter bubble mean Sauter the is d φ i stearvlm rcin parameter fraction, volume air the is R stedaee fec ube and bubble, each of diameter the is 2 om eaea lsi oisudrsaldeforma- small under solids elastic as behave Foams = tutrlMdl n Analyses and Models Structural 0.975). D 32 he n tes19;PicnadKiss and Princen 1999; others and ohler ¨ σ = 0 r = ehlells,ad( and methylcellulose, ) B d

i 3 D φ v 32 b b saftigprmtr and parameter, fitting a is d i 2 B fi i tdwt q 28 Eq. with tted

B aisfo othe to 1 from varies =

18.9, sepce oin- to expected is v = 09 and 10.9, egg ) (29) (28) acltda h qaeo h intercept, the of square the as calculated h icu otiuinwsetmtdfo h expression the from estimated was contribution important. viscous be The may attraction hydrophobic and attraction, interac- trostatic interparticle direct temperature the the Coulomb In tions, latter neglected. the be in can and dependency dependent temperature for- is The particles. mer suspended between interaction by caused stress constant ftmeaueta eeue ee10 were used were that temperature of viscosity and stress of values ofthedispersionattemperatures1and2,respectively.Typicalvalues the to refer 2 and 1 subscripts the where where Gnvs n a 2003b) Rao and (Genovese 40 nsoiial,hsbe sdt hrceiecooaeadother stress. and yield chocolate exhibit that characterize dispersions to food used been has printing originally, characterizing inks for developed although that, 1959) (Casson 1999). (Rao region shear-thinning the of Newtonian onset rate the shear zero or the plateau of end the marking rate shear critical lsi icst stesur fteslope, the of square the as viscosity plastic ain(il on)i h aets,tecnrbtoso different defor- of maximum contributions the of test, point structuralcomponentstothetotalyieldstress, vane the the in Bolger at point) and (yield balance Michaels mation energy of an work from the (1962), on Based and properties. plastic to structural weakly rise giving form a networks, to tenuous dispersion randomly and the aggregates associate bonded give clusters rates The shear stress. low yield at be finite that to flocs assumed are or units clusters flow small basic the 1962), Bolger and (Michaels particle at g. significant g/100 20 be about above to concentrations milks, found soy were the interactions for at Nevertheless, interparticle exist used. may temperatures sample different the 2 of the structure in is differences concern significant Another 1987). that (Rao products vegetable and dispersions fruit milk food as soy other such many the with of concern a phase residues, continuous solid the without of samples reliable obtain to tutrlanalyses Structural ytessedn li cniuu hs) and phase), (continuous fluid suspending the by ofo ha teso o ikb upne atce n h sus- the and particles suspended by fluid. milk pending dispersed soy of contributions a stress the of shear estimated flow structure to (2003) the others of and role Bodenstab the system. into insight valuable pro- vide can analysis structure-based information, useful provide does ◦ rma From rate, shear the For h asnmdl(q 1 saohrsrcuebsdmodel structure-based another is 31) (Eq. model Casson The ntekntco tutrlapoc orelg fdispersions of rheology to approach structural or kinetic the In hl plcto fsrcuebsdmdl orelgcldata rheological to models structure-based of application While Bdntbadohr 03.Cnieal aehdt eused be to had care Considerable 2003). others and (Bodenstab C σ s stesersrs asdb h icu ocsgenerated forces viscous the by caused stress shear the is α o.7,N.2 2007 2, Nr. 72, Vol. c σ = 0 . 5 1 oprdwith compared ’ / ehnclfito ocs yrgnbns elec- bonds, hydrogen forces, friction mechanical s γ ˙ c Generally, . γ η ˙ σ c a where , 0 = . 5 σ s = η σ — = ∞ = K γ ˙ ORA FFO SCIENCE FOOD OF JOURNAL + η c γ 0 ˙ σ s c η ie nodro antd fthe of magnitude of order an gives 0 s σ η 1 + . a 5 1 1 + η + = K lt h asnyedsrs is stress yield Casson the plot, − − 0 σ c ( − ( p α η σ ( η ◦ γ 2 2 c ˙ σ η n 25 and C 0 γ ˙ ) ∞ 0 0 ) + c . η m 5 = Ca η ( σ ∞ K = 0 ) s 0 / ,maybeestimated ( c ◦ ,teCostime Cross the 2, K ) ,ad20 and C, 2 c σ n h Casson the and ) 2 p . steshear the is ◦ and C R (33) (32) (31) (30) 17

R: Concise Reviews in Food Science extension de- – 2 / 1 , respectively 2 − b 2 / 1 1 − K ◦ K ◦ Nomenclature Acknowledgments constants in Eq. 9, dimensionless energy barrier between pairs of particles, J constants in Eq. 25 and 28, N and N.m time, initial time, s Sauter mean diameter of bubbles, m square root of Casson yield stress, Pa plateau modulus, Pa = maximum particle radius, m = square root of Casson plastic viscosity, (Pa.s) fractal dimension, dimensionless Boltzmann constant, J/ = mean coordination number, dimensionless elastic modulus, Pa Cross exponent, dimensionless aggregation rate constant, s total interaction potential between pairs of particles, J interfloc adhesive force, N averaged number of particles in a cluster, dimensionless phenomenological factor in Eq. 12, dimensionless Euclidean dimension, dimensionless swelling factor, dimensionless absolute temperature, 2 orientation function, dimensionless = Hamaker constant, J = particle diameter, m primary electroviscous effect coefficient, dimensionless axial ratio, dimensionless phenomenological factor in Eq. 12, dimensionless particle radius, m constant in Eq. 28, dimensionless ’ dry starch concentration, dimensionless = distance between pairs of particles, m ======0 Finally, it is worth to mention that foods are subjected to exten- ======0 = = = ,c = = Max = = f 32 = = = =

C 0c = = m B 1 a ¯ t, t b B, B U q Q r M N p G D D A T D G U AuthorsGenoveseandLozanoaregratefulforfinancialsupportfrom CONICET.Author Rao acknowledges support from USDA-NRI com- petitive grants. a a k K m These models provide valuable guidelines with respect tokey the rheological role parameters of such as volume fraction, size, anddimension fractal of the particles, as welldue as to interparticle the forces. complex, However, including nonrigid,food nature dispersions, of those particles models in have been most modifiedcosity to describe data. vis- Also due toanalyses have the been complex developed that structure are based of onlogical experimental foods, rheo- data structural on dispersions and they provideof insight food into microstructure. the nature sional shear in the mouth and in somespinning unit operations and (such as dough fiber mixing). Therefore,its extensional measurement viscosity are and also ofids, techniques interest. based Briefly, for on low-viscosity creatingbetween flu- a opposing stagnation jets point such andoped. as For filament high-viscosity flow and stretching semisolid foods, have biaxial (compression- extension) been devel- deformation techniqueFurther, to has better understand beenelongational how flow used food at structure the (Rao deforms microscale,visualize food under equipment 1999). structure behavior was under compression developed to formation by combining confocal microscopy and compression ap- paratus (Nicolas and Paques 2003).rheo-optical One studies will can be anticipate conducted, that whichvisual should more and provide rheological both data on foods at the microscale. F H k k d c c K K ˙ γ ∞ (34) (35) η is the , yield = n 0d v σ σ σ m, and others (for µ m. Theoretical models 10 µ n < σ 10 , and the dynamic, 0d Vol. 72, Nr. 2, 2007 + 0s σ > v — σ σ − + 0s σ b σ = = b s σ 0 Conclusions σ -carrageenan on the contribution of bonding λ ´ arrega and others 2006), the influence of starch . As 1 example of structural analysis of processed n σ is the stress required to break the bonds between the flocs, and b

b σ JOURNAL OF FOOD SCIENCE σ ome food dispersions (for example, cloudy applecolloidal juice) contain particles with dimensions

is the stress dissipated due to purely viscous drag, and The stress to break the bonds between the flocs may be calculated Atexturemapcanbecreatedbyplottingyieldstressvaluesagainst 18 v where example, tomato concentrates, orange juice)colloidal contain particles larger, with non- dimensions σ R Figure 6 Texture --- map of cross-linkedamioca waxy maize (ami), (cwm), andundisrupted tapioca (u) (tap) andovese starch disrupted and dispersions Rao (d) with (2003b). structures. From Gen- S Rheology of food dispersions . . . is very small in most dispersions,tions one can estimate the 2 contribu- foods, the contribution of bonding to theucts static that yield were stress homogenized, of such prod- as53% mayonnaise, ranged and between 65%, whilesuch that as of apple finished, sauceanother was nonhomogenized about study products 20% (T (Genovese and Rao 2005). In stresses of the samples withrespectively. undisrupted and disrupted structure, have been derived assuming thatviscosity, the yield particles stress, are and rigid modulus to predict of both types of dispersions. as the difference between the static, stress required to break the aggregate network. Given that in skim milk-based dispersions was examined. the corresponding values of the deformation.heated The starch dispersions texture based map on static of and dynamic 3 yield stresses compared with deformation isRao shown 2003b). Unlike in a Figure traditional texture 6 map,and a (Genovese map dynamic based and on yield static stressesboth indicates undisrupted the and disrupted behavior structure, of andin should a evaluation of be food product valuable quality. with concentration and

R: Concise Reviews in Food Science χ η ζ eff cf Subscripts η Ben BarnesHA.2000.Ahandbookofelementaryrheology.1sted.Wales:CambrianPrinters. σ ε ε Z v . . . dispersions food of Rheology σ φ φ φ φ η σ σ σ σ σ η γ σ γ β σ η ψ el L,Die A A JA, Deiber CLA, Berli parti- microgel of potential interaction the of Prediction 2000. D. Quemada CLA, Berli el L,Die A A JA, Deiber CLA, Berli oesa ,JilrtM ae ,Sme .20.Sprtn h oeo particles of role the Separating 2003. K. Sommer W, Bauer M, Juillerat S, Bodenstab η hs σ α α κ [ ai P ogdn A asnF.20.Eetottcefcso h il tesof stress yield the on effects Electrostatic 2004. FK. Hansen EA, Foegeding JP, pseudo- Davis for equation flow new a fluids: non-Newtonian of Rheology 1965. MM. Cross type. ink printing the of suspensions pigment-oil for equation flow A 1959. of N. Casson viscosity non-Newtonian the of model hard-sphere effective An 1994. R. Buscall concentrated of viscosity the on forces repulsive long-range of Effect 1991. R. Buscall η ˙ ˙ η c 0 ∞ 0 s r m a C 0 m f = 0s 0d 0 v s p n c b = = = = = 0 0 p. 200 lsfo hoercdt.Cmaio ihdfeetmdl.Lnmi 16:10509 Langmuir models. different 14. with Comparison data. rheometric from cles 21(1):100 Hydrocoll Food theory. DLVO extended the of application turbidity: upnin.Remti aaadtertclitrrtto.JArcFo Chem Food Agric J interpretation. theoretical 47:893 and data 13:507 Rheometric Hydrocoll suspensions. Food suspension. protein soy a of 15. interactions colloidal and n h upnigfudfrtefo fsymls odSi68(5):1722 Sci Food J milks. soy of flow the for fluid suspending the and re Letters Greek hypoenioaefas olSr :Bonef34:13 Biointerf B: Surf Coll foams. isolate protein whey 20:417 Sci Colloid J systems. plastic 82 p Press. Pergamon York: New systems. disperse 104. of Rheology editor. CC, Mill In: 83:33 A Surf Coll stabilized particles. sterically microgel for for data data with further and with lattices comparison dispersions: colloidal model. stable hard-sphere effective an 87:1365 with Trans Faraday data Soc Chem experimental J of comparison lattices: = = ] ======, ======´ = = = = ı ======φ e ,Gnvs B oaoJ.20.Efc fp n oi tegho pl juice apple on strength ionic and pH of Effect 2007. JE. Lozano DB, Genovese E, tez = ilcrccntn ftecniuu eim dimensionless medium, continuous the of constant dielectric osati q 5ad2,dimensionless 28, and 25 Eq. in constant iprinvsoiy Pa.s viscosity, dispersion eaptnil V potential, zeta = eirclDbelnt,m length, Debye reciprocal osati q ,dimensionless 8, Eq. in constant ouefato ftedsesdpae dimensionless phase, dispersed the of fraction volume osati q ,dimensionless 4, Eq. in constant ha ae s rate, shear ha tes Pa stress, shear hooia ne,dimensionless index, rheological oa ubro ers egbr fec pee dimension- sphere, each of neighbors nearest of number total less olia forces colloidal rtclserrt,s rate, shear critical ovn icst,Pa.s viscosity, solvent eaievsoiy dimensionless viscosity, relative emtiiyo aum F/m vacuum, of permittivity eoservsoiy(paetvsoiyas viscosity (apparent viscosity zero-shear paetvsoiy Pa.s viscosity, apparent hard-sphere ∞ ha tescue yfo ftessedn li,Pa fluid, suspending the of flow by caused stress shear iiu lcvlm rcin dimensionless fraction, volume floc minimum rtclsersrs,Pa stress, shear critical ha tesdsiae u oprl icu rg Pa drag, viscous purely to due dissipated stress shear il tes Pa stress, yield effective ha tesrqie obektebnsbtenfos Pa flocs, between bonds the break to required stress shear ha tescue ypril neato,Pa interaction, particle by caused stress shear nrni icst,dimensionless viscosity, intrinsic tesrqie obekteageaentok Pa network, aggregate the break to required stress rs iecntn,s constant, time Cross ufc oeta,V potential, surface iln eimvsoiy Pa.s viscosity, medium filling niieservsoiy(paetvsoiyas viscosity (apparent viscosity infinite-shear aiu akn rcin dimensionless fraction, packing maximum ttcyedsrs,Pa stress, yield static yai il tes Pa stress, yield dynamic – = 900. φ m for − σ 1 n ˜ → n nM.19a oncinbtenrelgclparameters rheological between Connection 1999a. MC. on ˜ ´ nM.19b etidcdpeoeai o protein soy in phenomena Heat-induced 1999b. MC. on ´ and 0 − 1 References σ – →∞ – 70. 37. − 1 , – 23. γ ˙ → – 42. γ ˙ ) Pa.s 0), →∞ – 30. ,Pa.s ), – 9. – – – arsR.16.Peito ftevsoiyo utmdlssesosfo unimodal from suspensions multimodal of viscosity the of Prediction 1968. RJ. Farris aggregating weakly of Elasticity 1994. J. Mellema D, Ende den van A, Potanin R, Rooij De aieS,MrnoiA 99 h ifrnebtenccabte n salatrim and butter cocoa between difference The 1999. A. Marangoni SS, Narine ihesA,Ble C 92 h lsi lwbhvo ffocltdkoi suspen- kaolin flocculated of behavior flow plastic The 1962. 29(6):739 JC. Rheol Bolger J AS, liquids. Michaels polymeric in suspensions of Boca Rheology techniques. 1985. and AB. Metzner practice, principles, emulsions: Food 1999. DJ. McClements Mart aqe ,Rbe ,GayB,Rb .20.Vsoiyadyedsrs euto in reduction stress yield and Viscosity 2006. I. Robb BP, Grady A, Robben M, Marquez the on interesterification chemical crystal of fat influence The of 1998. D. analysis Rousseau AG, structural Marangoni and Visualization 1998. Freeman. RW. WH York: Hartel New nature. AG, of Marangoni geometry fractal The 1982. BB. Mandelbrot ioHJ atyklJ a A 99 uepsto fcmlxvsoiycre during curves viscosity complex of Superposition 1999. MA. Rao J, Tattiyakul H-J, Liao suspensions in flow non-Newtonian for mechanism A 1959. of TJ. viscosity Dougherty relative IM, the Krieger of equation empirical An 1981. T. Shirota T, Kataoka T, Kitano ap ,Gnae C ordn G ee .20.Efc ftogm nthe on gums two of Effect 2003. M. Peleg MG, Corradini MC, Gonzalez N, Kampf ubn M ke ,Gesl .19.Teeitneo ttcyedsrse nsus- in stresses yield static of existence The 1993. W. Gleissle N, Aksel DM, Husband eoeeD,RoM.20a oeo trhgauecaatrsis(ouefraction, (volume characteristics granule starch and of Role viscosity 2003a. the MA. Rao to DB, forces Genovese colloidal of Contribution 2006. JE. Lozano DB, Genovese ioa ,Pqe .20.Mcohooy neprmna ehiu ovsaiefood visualize to technique experimental an Microrheology: 2003. M. Paques Y, Nicolas eoeeD,RoM.20b aeyedsrs fsac iprin.JFo Sci dis- food Food structured of J stress yield dispersions. vane starch of Components of 2005. MA. stress Rao DB, yield Genovese Vane 2003b. MA. Rao DB, Genovese PernellCW,FoegedingEA,DaubertCR.2000.Measurementoftheyieldstressofprotein viscoelastic of analysis fractal and Scaling 2004. S. Gunasekaran S, Ko MM, Ould-Eleya gw ,Ymd ,MtuaS kjm .19.Vsoiyeuto o concentrated for equation Viscosity 1997. K. Okajima S, Matsuda H, Yamada A, Ogawa Hidalgo- ezatB 99 hooyo qeu om:altrtr eiwo oeexperimental some of review literature a foams: aqueous of Rheology 1999. B. Herzhaft ode ,PttL 97 yai icst fmcocpcssesoso bimodal of suspensions macroscopic of viscosity Dynamic 1997. L. Petit P, Gondret olnk J ynM,GpaR,Ssar G rcet J 98 hooia be- Rheological 1988. FJ. Frechette SG, Seshadri RK, Gupta ME, Ryan AJ, Poslinski enl W ogdn A ukP,DvsJ.20.Poete fwe n g white egg and whey of Properties 2002. JP. Davis PJ, Luck EA, Foegeding CW, Pernell ogpahsP abtS aagn G 99 h tutr fcl-e hyprotein whey cold-set of structure The 1999. AG. Marangoni S, Barbut P, Hongsprabhas H ekm M,vnVitT 04 ocnrto eedneo yai ouiof moduli dynamic of dependence Concentration 2004. T. Vliet van JMS, McClements Renkema In: rheology. food on microstructure applications. food of and Influence principles 2006. foods: MA. semisolid Rao and fluid of Rheology 1999. MA. Rao Math- origin: plant of suspensions food of properties flow the Predicting 1987. MA. Rao for foams juice apple of Characterization 2006. C. Ratti DB, Genovese N, comparison Raharitsifa suspensions: colloidal concentrated of Viscosity 2003. AA. Zaman K, Qin umd ,BriC 02 nryo neato nclod n t mlctosin implications its and colloids in interaction of Energy 2002. C. Berli J emulsions. D, concentrated Quemada highly and foams of Rheology 1989. AD. Kiss HM, Princen uslW.18.Rve fterl fclodlfre nterelg fsuspensions. of rheology the in forces colloidal of role the of Review 1980. WB. Russel Rubio-Hern he ,ChnAddS saisA 99 hooia eoyefc naqueous in effect memory Rheological 1999. A. Asnacios S, Cohen-Addad R, ohler ¨ icst aa rn o ho 12(2):281 Rheol Soc Trans data. viscosity 49(4):3038 E Rev Phys dispersions. latex polystyrene isi h irsrcueo h a rsa ewr.JA i hmssSc76(1): Soc Chemists Oil Am J network. crystal fat the of 7 microstructure the in lies in.IE ud1:153 Fund I&EC sions. 75. Press. CRC Fla.: Raton, niern.Fac:ELSPbihr,UEC.p323 p UNESCO. Publishers, EOLSS France: engineering. ufcat n/rnnpril diin olItr c 9:374 295: Sci Interf Coll J addition. nanoparticle and and/or polymers surfactants with modification surface by suspensions concentrated noncolloidal 75(11):1633 of Soc Chemists fractality Oil and Am Rheology J III. network. systems. crystal the fat complex of properties physicochemical 52(9):46 Technol Food networks. eaiiaino trhdseso n og.JFo rcs n 22:215 Eng Process Food J dough. and dispersion starch of gelatinization 3:137 Rheol Soc Trans spheres. rigid of 20:207 Acta Rheol fillers. inorganic various with filled melts polymer eeomn,relgclpoete n tblt fegabmnfas ho Acta Rheol foams. 42:259 albumen egg of stability and properties rheological development, esoscnann oclodlprils ho 37(2):215 Rheol J particles. noncolloidal containing pensions iiiyadfatldmnin nterelg fsac iprin ihadwith- and 80:350 with Chem dispersions Cereal starch of amylose. rheology out the on dimension) fractal and rigidity 20:767 Hydrocoll Food juice. apple cloudy of stability tutr eairudrcmrsinetnindfraincniin.JFood J conditions. 68(6):1990 deformation Sci compression-extension under behavior structure esos odSi70(8):E498 Sci Food J persions. 68(7):2295 om yvn hoer.JFo c 65(1):110 Sci Food J rheometry. vane by foams 18(2):315 Hydrocoll Food gels. protein heat-induced of properties upnin fcagdclodlprils ho 41(3):769 Rheol J particles. colloidal charged of suspensions ok.OlGsSiTcnl54(5):587 Technol Sci Gas Oil works. ie oi pee.JRel41:1261 Rheol J spheres. solid sized airo ildplmrcssesI il tesadsertinn fet.JRheol J effects. shear-thinning and stress Yield I. 32(7):703 systems polymeric filled of havior rti om.Cl ufA204:9 A Surf Coll foams. protein slt espeae ihCa with prepared gels isolate polymer of kinetics 67:1 Sci aggregation Interf Coll and Adv colloids. stability colloidal properties, Electrokinetic om.Erpy et48(1):93 Lett Europhys foams. etidcdsypoengl.Fo yrcl 18(3):483 Hydrocoll Food gels. protein soy heat-induced foods. complex of microstructure Ltd.. the Publishing Woodhead controlling U.K.: Cambridge, and Understanding editor. DJ, 433. p Publishers. Aspen Md: Gaithersburg, rheological 41(3):85 Technol and Food composition behavior. between relationship the clarify help models ematical Sci Food J methylcellulose. and protein white 71(3):E142 egg with prepared drying foam-mat 266:461 Sci Interf Coll J models. bidisperse of hooia oeig d olItr c 8 51 98: Sci Interf Coll Adv modeling. rheological 128(1):176 Sci Interf Coll ho 24(3):287 Rheol J nclodlssesos d olItr c 107:51 Sci Interf Coll Adv suspensions. colloidal in – 13. ´ ı e-ail P 05 odssesos nBarbosa-C In suspensions. Food 2005. LP. nez-Padilla lae ,Mart R, Alvarez – ´ 68. – ne J arqeF uzRiaE 04 h rmr lcrvsoseffect electroviscous primary The 2004. E. Ruiz-Reina F, Carrique FJ, andez ´ 35. – – o.7,N.2 2007 2, Nr. 72, Vol. 301. 51. – 4. – 317. ´ ı nA,Fern – 62. – 87. ++ – – ne ,Bso ,Mart D, Bastos A, andez ´ 8. ees isUTcnl32(4):196 Technol U Wiss Lebensm . – – 504. – – 118. 21. 8. – 51. — 5. – – 74. ORA FFO SCIENCE FOOD OF JOURNAL 96. – 52. – 301. – 7. – – 4. 85. – 60. – 49. – 73. ´ ı – e ,d a ivsF.1996. FJ. Nieves las de F, nez 6. – – 38 7. nvsG,eio.Food editor. GV, anovas ´ – – 85. 35. – – 23. 87. – – 202. 9. – 34. R 19 –

R: Concise Reviews in Food Science 20. – 9. – 22. 20. – – 207. 81. – – 98. – 50. – concentrated metal oxide suspensions. Chem Eng Sci 56:2901 viscosity and effect of pulp content. J Food Sci 49(3):876 dispersion during gelatinization. J Food Proc Eng 21:191 effect of concentration and finisher screen size. J Texture Stud 27:451 dispersions during and after heating. Carbohydr Polym 43:215 design on the continuous manufacturing of food foams. J Food Procconcentrated Eng suspensions. 60:9 J Rheol 32(7):737 of foaming agents on the stability,rheological properties, dryingretention kinetics of and flavour tamarind foam-mats. Food Res Int 34:587 Zhou Z, Scales PJ, Boger DV. 2001. Chemical and physical control of the rheology of Vitali AA, Rao MA. 1984. Flow properties of low-pulp concentrated orange juice: serum Yang WH, Rao MA. 1998. Complex viscosity-temperature master curve of cornstarch Yoo B, Rao MA 1996. Creep and dynamic rheological behavior of tomato concentrates: Tattiyakul J, Rao MA. 2000. Rheological behavior ofThakur cross-linked RK, waxy Vial maize C, starch Djelveh G. 2003. InfluenceTsai SC, of Zammouri operating K. conditions 1988. Role and of impeller interparticular van derVernon-Carter Waals EJ, force Espinosa-Paredes in G, rheology Beristain of CI, Romero-Tehuitzil H. 2001. Effect 5. – -carrageenan addition. λ 92. – 9. – 44. Vol. 72, Nr. 2, 2007 – — 8. – 60. – JOURNAL OF FOOD SCIENCE dispersions in skim milk: effect of starch concentration and Food Sci Tech Int 12(3):253 Mich.: Freeman Press. p 418. affected by particle size and methods of concentration. J Food Sci 52:141 processing of food. J Food Eng 51:201 properties of colloidal gels. Phys Rev A 42(8):4772 cept of zeta potential.Washington In D.C.: American Gushee Society DE Publications. p editor. 73 Chemistry and physics of interfaces. Cambridge, U.K.: Cambridge Univ. Press. p.525. lated colloidal suspensions. AIChE J 44(3):538 20 ´ arrega A, Costell E, Rao MA. 2006. Vane yield stress of native and cross-linked starch T Steffe JF. 1996. Rheological methods in food process engineering. 2nd ed. East Lansing, Tanglertpaibul T, Rao MA. 1987. Rheological properties of tomato concentrates as Servais C, Jones R, Roberts I. 2002. The influence of particle size distribution on the Shih W-H, Shih WY, Kim S-I, Liu J, Aksay IA. 1990. Scaling behavior of the elastic R Sennet P, Olivier JP. 1965. Colloidal dispersions, electrokinetic effects, and the con- Russel WB, Saville DA, Schowalter WR. 1989. Colloidal dispersions. Ed. G.K. Batchelor. Scales PJ, Kapur PC, Johnson SB, Healy TW. 1998. Shear yield stress of partially floccu- Rheology of food dispersions . . .

R: Concise Reviews in Food Science