SYNERESISO FCUR D
CENTRALE LANDBOUWCATALOGUS
0000 0086 6497 Promotor:Dr .Ir .P .Walstra ,hoogleraa ro ppersoonlijk e gronden Co-promotor:Dr .Ir .J . Schenk,hoogleraa r ind etechnisch enatuurkund e Y]\n
H.J.M, van Dijk
SYNERESIS OF CURD
Proefschrift ter verkrijging van de graad van doctor in de landbouwwetenschappen, op gezag van de rector magnificus, dr. C.C. Oosterlee, hoogleraar in de veeteettwetenschap, in het openbaar te verdedigen op woensdag 6 oktober 1982 des namiddags te vier uur in de aula van de Landbouwhogeschool te Wageningen.
,ÄÄl;I>üü '^HOGESCHOOL WAGENINGES
il c \'>i^(fo] BIBLIOTHEEKLH . o 1 m. -332 DNTv.TiJösewum
("c) H.J.M,va nDijk ,Melkuni eHollan d P.O.Box222 ,344 0A EWoerden ,th eNetherland s nvnMo\. opd
LAZs STELLINGEN
1.D esyneres e vanwronge l kano pbevredigend e wijze inmode l worden gebracht. Uitdi tmode l blijkt datd eendogen e syneresedruk ongeveer 1P ais . Dit proefschrift.
2. Devlokkin g vanparacaseïnemicelle ne nd epermeabiliteit , synerese(druk) en reologische eigenschappen vanwronge l hangen alle nauw samen. Dit proefschrift.
3. Indien uitvlokking vancolloïdal e deeltjes ongestoord (dusbi jafwezighei d van stroming ensedimentatie ) plaatsvindt, resulteert deze ind evormin g van éénnetwer k doord egehel e vloeistof.
4.D ehypothes e vanVa nde nTempe l datd einhomogenitei t vanee nnetwer k van uitgevlokte colloïdale deeltjes wordt bepaald door detij d dieno g niet geaggregeerde deeltjes hebben omnaa r hetcentru m vangrot e aggregaten tediffunderen , isonjuist . M.v.d . Tempel, 1979.J .Colloi dInterfac e Sei., 71:18-20.
5.D ebelangwekkend e proeven vanSchmid t c.s. overd estabilitei tva n kunstmatige caseïnemicellen vanvariabel e samenstelling zoudenme t vrucht uitgebreid kunnen wordenme tstremproeven , teneinde hetinzich t inhe tstremproce s end estruktuu r vancaseïnemicelle n tevergroten .
6. Hetmode l vanPayen s voord estremmin g vanmel k isonjuist . Veel betere resultaten kunnen worden bereiktme tee nsimulatiemode l waarbijd e volgende informatie tevens inaanmerkin g wordt genomen: -d eonderling e positie vand eK-caseïnemolecule n ophe tm ice loppervla k -d esplitsin g vandez e moleculen inaselect e volgorde -d egevolge n vanno gnie t volledige splitsing voord erepulsi e tussen micel le n T.A.J.Payens , 1979.J . Dairy Res., 46:291-306.
7.D eopvattin g vanBeltma n datsyneres e door diffusie bepaald wordt, isi n zijn algemeenheid onjuist. H. Beltman, 1975.Proefschrift , Wageningen. 8.He tlactosegehalt e vand e(verdunde )we l geeft aanvankelijk geen juist beeld van hetwaseffek t van warm water dat aand ewei-wronge l:1 s toegevoegd.
8. Het subsidie dati nhe t kader van het scheppen van werkgelegenheid aan bedrijven In het Oostene nNoorde n van het land wordt verleend, schept althans bij zulvelbedrijven geen extra werkgelegenheid.
10. Enkele door het Zuivel-kwaliteitskontrolebureau gehanteerde methoden ter beoordeling vand ekwalitei t van boter, tewete nd ebepalin gva n diacetylgehaltee nd estevigheid , kunnen misleidende uitkomsten geven.
11. Voedingswaarde-etikettering heeft voord econsumen t het meestenu t indien deze zeer globaal ise nslecht s die voedingsstoffen worden vermeld waarvan een niet onaanzienlijk deel vand econsumente n tevee l oft eweini g gebruikt. Bijd eopgegeve n gehaltene nenergie-inhou d moet vermeld wordeno fdez e relatief hoogo flaa g zijn.
12. Wiskundige statistiek ensimulatietechnieke n kunnen uitstekend worden toegepast bij het bepalen vand espeltaktie k ind erugbysport .
13. Ingevolged eWe t Gelijke Behandeling dient bij een advertentie voor 'kaasmeisjes'd etoevoegin g M/V teworde n geplaatst.
Proefschrift vanH.J.M ,va nDij k The syneresiso f curd Wageningen, 6oktobe r 1982 Aan nrCjn ouders WOORDVOORA F
Aanhe t totstan dkome nva ndi tproefschrift ,wa tmogelij ki s gemaakt doord e financiëlehul pva nd eStichtin gJ.Mesdagfond st e Leeuwarden,hebbe nvele nee nbijdrag e geleverd. Inhe tbese fnie t volledig tekunne n zijn,wi l ikd evolgend epersone nme tnam enoemen . Ind eeerst eplaat sprof .dr . ir.P .Walstra ,di ehe t initiatief heeft genomento tdi tonderzoe k endi em e erbijheef tbegeleid .Aa n deverslagleggin g heefthi j insterk emat ebijgedragen . Vervolgensprof .dr .ir .J . Schenk,di evoora lme t betrekking totd ewiskundig eweergav e adviezenheef tgegeven . Eengroo tdee lva nd e experimenten isuitgevoer ddoo rd ehee r H.Stemphe r (permeabiliteit ensynerese) ,mevrou wA.E.A .d eGroot - Mostert (reologie)e n ir.J.G . vand eGrootevhee n (experimentenbetref fendeFig .8.4) .D ehee rD . Schoonderbeek verrichtted emetinge nme t deKwantime t ImageAnalyzer ,welk e doord eStichtin gvoo rBodemkarte - ring teWageninge n terbeschikkin gwa s gesteld. Belangrijkeadvieze nhe b ikmoge nontvange nva no.m .prof .dr . A.Prins ,prof .dr .ir .S .Brui ne nmedewerker s vand eSecti eProces - kunde,dr . ir.T .va nVlie t endr .ir .Th .J .Geurts . Desymbolen -e nliteratuurlijs t zijnopgestel d doormevrou w ir.T.H .va nOijen . Debenodigd e apparatuur isgrotendee l gemaakt doord emedewerker s vand ewerkplaat sva nhe tBiotechnion . Aanhe tvormgeve nwerkte no.a .mee ,wa tbetref the t typewerk: mevrouwB.A . deJon g- va nde rLuijt ,mevrou wG.H.J .Pelleman s- Wunderink enmevrou wN.J.Walstra ;correcti e enadvie sverslaglegging : mevrouw ir.M.C .va nde rHaven ;foto -e ntekenwerk :d ehere nA . van Baaren,C .Rijpm ae nM .Schimmel . Mijnhuidig ewerkgeve rMelkuni eHollan d teWoerde nbe n ikerkente lijkvoo rd emedewerkin gverleen dbi jhe tvoltooie nva ndi tproef schrift. Mijnoprecht edan kaa nalle n dieaa ndi tproefschrif t hebben meegewerkt,voora l aandegene ndi ebetrokke nware nbi jhe to p schrift stellenva ndi tonderzoek .Bi jhe tneme nva ndez e laatstehinderni s heb ikva nu buitengewoo nvee lhul pgekregen . PERSOONLIJKEGEGEVEN S
Deauteu rwer dgebore no p 6apri l 1948t eUden .Hi jbehaald e in 1971he tdiplom ava nd eHoger eLandbou wTechnologisch eSchoo lt e 'sHertogenbosch . Indatzelfd ejaa rwer dme td estudi eaa nd eLand bouwhogeschool inWageninge nbegonnen .He tkandidaatsexame nLevens middelentechnologiewer dafgeleg di njanuar i 1976e nhe tdoctoraal exameni njanuar i 1978.D eingenieursstudi eomvatt enaas the tver zwaardhoofdva k Zuiveltechnologie enMelkkund ehe thoofdva kIndustri ëleBedrijfskunde .Va nnovembe r 1977to tme i 1981werkt ed eauteu ral s promotie-assistento phe tlaboratoriu mvoo rZuive le nLevensmiddelen - natuurkunde.Sind sme i 1981 ishi jwerkzaa mbi jMelkuni eHollan dt e Woerden. CONTENTS
List of symbols
1 Introduction
2 Materials and methods 2.1 Skimmil k powder 2.2 Rennet 2.3 Whey 2.4 Thimerosal 2.5 Concentratedmil k 2.6 Treatmento fth ege lan dstartin g syneresis 2.7 Standard conditionsfo rrenne tgel s 2.8 Standardcondition sfo raci d gels
S Endogenous syneresis pressure 9
4 Permeability 11 4.1 Introduction 4.2 Materials andmethod s 4.2.1 "Tube"metho d 4.2.2 The"torsionflux "metho d 4.2.3 Calculationo fpermeabilit y coefficient(5 ) 4.2.4 Calculationo fth eviscosit yo fth ewhe y 4.3 Results 4.3.1 Validityo fth eequatio no fDarc y 4.3.2 Resultswit hth etub emetho d 4.3.2.1 Influenceo fdeformatio no npermeabilit y 4.3.2.2Chang eo fpermeabilit yo fundeforme dcur dwit htim e 4.3.2.3Influenc eo fconcentratio n 4.3.2.4Influenc eo ftemperatur e during measurement 4.3.2.5Influenc eo ftemperatur e during renneting 4.3.2.6Influenc eo frenne t concentrationan dtyp eo fski mmil k
4.3.2.7Influenc eo fCaCl 2 addition 4.3.2.8Influenc eo facidit yo npermeabilit y 4.3.2.9 Influenceo ffa tconten t 4.3.2.10Permeabilit yo faci dgel s 4.3.3 Influenceo fdeformation ,temperatur ean dp Ho n permeabilitya smeasure dwit hth etorsionflu xmetho d 4.4 Discussion
5 The Theological behaviour of curd 32 5.1 Introduction 5.2 Methods 5.2.1 Dynamicmeasurement swit hth e"De nOtter "rheomete r 5.2.2 Creepmeasurement swit hth e"Deer "rheomete r 5.2.3 Resultsan ddiscussio n
6 The model 39 6.1 Thedifferentia l equation 6.2 Numerical solution 6.3 Parameters
7 Syneresis of thin slabs (Testing the model experimentally) 48 7.1 Introduction 7.2 Methods 7.3 Resultsan ddiscussio n 7.3.1 Testingth emode l 7.3.2 Effecto fsom evariable s 7.3.3 Therelatio nbetwee nclottin go fmil kan d permeability,syneresi s (pressure)an drigidit y ofth ecur d 7.4 Conclusions
8 Syneresis as influenced by external •pressure or deformation 73 8.1 Introduction 8.2 Methods 8.3 Results
Summary 79 Samenvatting 82 References 85 LISTO FSYMBOL SAN DABBREVIATION S a constanti nEq . 6.12 a radiuso fa tub e (m) b constanti nEq . 6.12 2 B\B, permeability (coefficient) (m) B(0) permeability (coefficient)a tth e 2 momento fth efirs treadin go f h(,t) (m) B permeability (coefficient)a tth e momentwhe nth ege li spressurize d 2 ordeformedeforme d (m)
Sn permeabilityo fth ecur dsla ba tth e starto fsyneresi s (m) 2 a constanti ntria lfunction s for P(i); a d /d£ - ^y\03 d diameter d volume-surfaceaverag ediamete r (m) dt tubediamete r (m) DS -1 jrr substantialtim ederivat eoperato r (s ) D B(1- e)3 P'/n (seeEq .6.1 ) (s"1) 2 -1 g accelerationdu et ogravit y (m» s ) 2 G' storagemodulu s (N/m) 2 G" lossmodulu s (N/m) 2 GQ instantaneousshea rmodulu s (N/m) h differencebetwee nth elevel so fth e unwetted curdan dth eadjacen twhe y (Chapter3 ) (m) h heightbelo wsurfac eo fth ege l (m) h. t;h(k,t) thicknesso fslic enumbe r k attim e t (inth emodel ) (m) h{t) levelo fth ewhe y inth etub e (Eq.4.2 ) (m) H heighto fth esla b (m) 5Q heighto fth esla ba t t =0 (m) LH shrinkageo fa sla b (m) i\i, , volumeo fconcentrate dmilk/volum e
oforigina lmilk ; h^ t/hk Q k numbero fth eslic ei nth esla b (in themodel ) K' ;K dimensionlesstim evariabl e (K' = ZK) L;L, , dimensionless thickness m numbero fslice s inth esla b (inth e model) n numbero f experiments Pr protein concentrationo fth esample / proteinconcentratio no forigina l milk PCM paracaseinmicelle s
P',Pk f syneresispressur e (Pa)
PQ pressureo fth ecur da tt = 0 (Pa) P endogenouspressur e (Pa) P* pressure onth ewhe y causedb yweigh t ofth ematri x (Pa) P| Pga tth ebotto mo fth esla b
Pt pressuredifferenc ebetwee n loweran d uppersurfac eo fth ege l inth etub e (Eq.4.1 ) (Pa) Q constantdefine d inequatio n 7.1 depending onP(i) r (surfaceo ftubes)/(surfac e ofvat ) Re Reynoldsnumbe r str, liquidvolum e fluxtha t flowsfro m slice k intoslic e k - 1 (inth emodel ) (m/s) S;5, dimensionlesspressur eP , ,/P« t time (s) t timea twhic hth epressur edifferenc e wasapplie d toth ecolum n (s) T temperature (°C) v localvelocit y ofth ewhe y inth e x-direction (m/s) v localvelocit yo fth eliqui d (whey) (m/s) v local velocity of the solid (matrix) (m/s) w u-coordinate (transformation distance coordinate) (m) WPN wheyprotei n nitrogen x x-coordinate,distanc e from the interface ofcurd/whe y (m) z s-coordinate (m)
ß dimensionless permeability (3,, tJ^n) Y shear strain
Y0 maximum shear strain r dlogff/dlog* ô phase shift orphas e angle between stress and strain (tg< 5= G"/G' ) 6 average thickness of the strands (m) e porosity (void fraction) A difference n viscosity (Pa«s) p density (kg/m ) p, density ofth ewhe y (which is assumed tob e independent of the time and position) (kg/m ) 2 a shear stress (N/m ) 2 aJ0n maximum stress (N/m ) GO angular frequency (rad*s ) V Laplace-operator
Milk samples used: A milkA ; reconstituted from 12g skim milkpowde rpe r 100g water ,use d for acidcur dan d forsom e experiments with rennet curd R milk R; 10.5g skimmil kpowde r per 100g wate ruse d forrenne t curd 1 INTRODUCTION
Thoughchees e ismad ei na noverwhelmin g varietyo ftypes ,th e techniqueo fcheesemakin gi si nprincipl e thesame .Cheesemakin g startsb ycurdlin g (clotting)th emilk .A s toth ecurdlin gmetho da divisionca nb emad ebetwee ncurdlin gwit h theai do frenne tan d curdlingwithou t rennetbu tonl yb yacidification .A smos t cheesei s madeb y rennetingw ewil lmainl ydiscus s thismethod . Afterrennetin g thecur d (i.e.a gel)mus tb ecu tslowl yan d carefully intopieces .No wwhe y isexpelle d from thecur dpieces ; thisi scalle dsyneresis .Syneresi so fthes ecur dpiece sca noccu r withoutexterna lmanupulation ,bu t isenhance db y stirring.Shrinkag e canb efurthe renhance db ymor evigorou sstirring ,temperatur eris e orincreas eo facidity .Finall y fairlysoli dcur dparticle s are collected anddrained .Accordin g toth etyp eo fchees eth e following additional treatments canb eperformed :cheddaring ,pressing ,salting , ripening. Thusa n important aspecto fth etechniqu e ofcheesemakin g isth e removalo f thegreate rpar to fth ewhe ywhic hmake su p thebul ko f themilk .Thi sproces smus tb e controlledwel la s thefina lwate r contenti sa nessentia lpropert y ofth echeese .I nindustria lpractic e thecontro l ofthi sproces s isempirical . A questionwhic h isstil lno tanswere d isho wsyneresi sproceeds . Onsyneresi s ofcur dmuc hha sbee npublished ,bu tmos tpublication s dealwit h theoveral l effecto fsom evariable s onsyneresi s oreve n onfina lmoistur e content (e.g.Walstra ,1979 ;v.d .Waarden ,1947 ; Cheeseman 1962;Stoll , 1966).Th eexperiment s canno teasil yb e compared,mainl ybecaus eth ecur d iscu tan dstirre d indifferen t ways andprecisel y thesevariable shav e alarg e effect.W ehav eonl y littleunderstandin g ofth eprocess .Befor ew eg oint oan ydetai lw e will first look atwha thappen sdurin g renneting. About 801o fth eprotei ni nth emil k isfoun di nth ecasei n micelleswhic h areglobula r particleswit h avolum e surfaceaverag e diametero f~ 100n m (Schmidt,Walstr a& Buchheim , 1973).Th eenzyme s inth erenne tremov eth eprotectiv ehair y layer (Walstra,1979 )o f themicelles .Th eresultin gparacasei nmicelle s (PCM)ar eunstabl ean d flocculate.PC Massembl e intogrowin g aggregates.A s calculations of
1 Sutherland (1967)predic tan da sobserve db yMilder ,D eGraa f& Walstra (1966)thes eaggregate shav ea ver yope nstructure ,i.e .th e volumefractio ni sabou tth esam ea sth e volume fractiono fth e originalmilk .Unles sdisturbanc e (e.g.b ystirrin go rstreaming )o r appreciablesedimentatio noccurs ,finall yon elarg eaggregate , (i.e. theentir e matrix) isformed .Th einterstitia l liquidi scalle dwhey . Electronmicrograph so fKnoo p& Peter s (1975)giv ea goo dpictur eo f thematrix .Th eschemati cdrawin gi nFig . 1.1.show stw o strands. A hypotheticalmechanis mi sproposed .Afte rth ege li sformed , thePC Msurface stha tar eno ti ncontac twit heac hothe rhav estil l manymor ereactiv esites .Possibl yth ewhol esurfac ei sreactive .B y Brownianmotio no rdeformatio nthes esurface sma ylocall ycom eclos e togetheran dstick ,thu scausin ga (higher)stres si nth estrand s (seeFig . 4.7.). Inorde rt oge tenoug h freedomfo rmovemen ti tmigh t benecessar y thata tsom eothe rplac e theyfirs thav et obreak .Th e resultingendogenou spressur ecause ssyneresis . Anothermechanis mma yb e"fusing "o fPCM ,i.e .th econtac tare a betweenan ytw oPC Mbecome s larger.Thi si sals ovisibl ei nelectro n micrographs (Knoop& Peters ,1975) . Thisi sapparentl ya slo wprocess . Accordingt oDarlin g (personalcommunication )a nexplanatio nfo rth e latterphenomeno nma yb eth erearrangemen to fcolloida lcalciu m phosphate,whic happarentl ykeep sth esubunit so findividua l (P)GM together.W e presume thiseffec tt ob esmall ,particularl ya tth e beginning. Ifth ep Hi slowere dth ePC Mshrin k (Walstra& Delsing , un published)thu scausin gsyneresis .I nou rexperiment s thep Hwa skep t
Fig. 1.1 Schematicdrawin go f twostrand so fparacasei nmicelles . constant. The stresses occurring onth estrand s ofth ematri x cause a tendency toshrin k orsynerize .Th ematri x doesno tcompl y momentarily because ofth eviscou s drag onth eoutflowin g liquid,o ri nothe r words,th e limitedpermeabilit y ofth ematrix .Thi s implies that the whey inth ematri x isunde rpressure .Th ewhe y alsoca nb epu t under pressure by deformation ofth ecurd .W e thusmus t distinguish the latter externalpressur e from theendogenou s syneresispressure . Syneresis isthu s a function ofth epressur e and the resistance against flow through thematrix ,expresse d inth epermeability . This flowan dth eresultin g change inconten t ofcomponent s should ideally be obtained from direct localmeasurement s inth e curd grains.Thi s ispracticall yimpossible . Inth eabsenc e ofinformatio n from direct measurements of localpropertie s and event,w emus t therefore rely onothe r sources,i.e .macroscopi c experiments. Permeability coefficients (B)a sdefine d inth eequatio n of Darcy (seeSectio n 4.1) canb e obtained frommeasurement s onhomo geneouspiece s ofcur dwhic h dono t shrinkdurin g theexperiment s; casein concentration and otherpropertie s canb e varied. Syneresispressur e couldno tb emeasure d inthi swa y oran y other.Evidenc ewa s found that thispressur e isalway sver y low (less than 10 Pa). Amathematica lmode l canb epostulated , anddependin g onth e assumptionsmade ,syneresi s rate canb epredicte d forvariou s con ditions. Comparison onth ecalculate d resultswit h the results on actual syneresis experimentsma y showwhethe r amode l is realistic.A s permeability and endogenous pressurebot h depend onplac e andtime , calculations are rather complicated.W ehav erestricte d ourselves to syneresis inon edirection ,a s thecalculation s becomeunwield y for thethre edimensiona l case.Moreover ,unequivoca l experiments are mucheasie r toperform . Sucha n integrated theoretical andempirica l approach canyiel d abette runderstandin g ofth eproces s and themechanism .Wher e approp riate,th eresult s of this study arecompare dwit h those found inth e literature andwit hpractica l experience. Finally someexperiment s were carried out onaci dmil k gels, producedb y addingaci dt omil ka t lowtemperatur ean dthe nslowl y warming it.Thi s enablesu s totes tth emode l fora ge lo frathe r differentproperties . 2 MATERIALSAN DMETHOD S
2.1. SKIMMIL KPOWDE R
Skimmil kpowde rwa s obtainedb y spraydryin go fon ebatc ho f lowpasteurize d skimmilk .Th edr ymatte rconten to fthi sski mmil kwa s 9.131 (m/m)(accordin g toFIL/ID F21:196 2 standard).Th edr ymatte r contento fth epowde rwa s 96.11 (m/m) (according toFIL/ID F 26/1964 standard). Forth eexperimen t 10.5g powde rpe r 100g o fdémineralize d waterwa sused .Thi sresulte d ina mil k indicateda smil kR wit hth e samedr ymatte rconten ta sth eorigina lmilk . Inth eearl y stageso fthi sstud yw edissolve d theski mmil k powderaddin g smallquantitie s duringabou t 1hou ra tabou t 45 C;whe n allth epowde rwa sdissolve dth ereconstitute d skimmil kwa skep tfo r about 1hou ra t 30t o4 5 C.I nth ecours eo fth estud y itappeare d that thepretreatmen to fth ereconstitute d skimmil ksomewha t affectedit s renneting andcur dpropertie s (seeTabl e 7.1).Therefor ew e soon standardized ourpretreatment .Afte r allth eski mmil kpowde rwa s dissolved,w ekep tth emil k for 1hou ra t4 5°C .The nth emil kwa s cooledt oth edesire d temperature.However ,th etim eunti l themil k wasuse dvarie dbetwee n about 0.5 and 5hours .Thi smay ,t oa certain extent,explai nth esprea d insom eresults ,a s ittake sabou t 24h at thetemperature suse dunti l equilibrium isreached ,especiall y inth e distributiono fCalciu mamon gth emicelle s andth eseru m (Snoeren, personalcommunication) . Undenaturatedwhe yprotei nnitroge n (W.P.N.)i nth eorigina l milkan dth epowde rwer edetermine d (AmericanDr yMil k Institute, 1971),Result swer e 6.7 mgW.P.N./ gpowde r forth eorigina lmil k and 6.3 mgW.P.N./ gpowde r forth ereconstitute d skimmilk . Forth eexperiment s with acidgels ,a differen t skimmil kpowde r wasused . Forth ereconstitutio n 12g powde rpe r 100g wate rwa s usedgivin gmil k (indicateda smil kA )wit ha highe r totalsolid s content (i.e.10.21 )tha nth eorigina lmilk . 2.2 RENNET
Commercialcal frenne t (Coöp.Stremselfabrie kLeeuwarden) , strength1 000 0unit swa suse dan ddilute d 1:10befor euse .80 %o f theactivit yi nth erenne toriginate dfro mchymosin .
2.3 WHEY
Wheywa sprepare db yrennetin gfres hskimmil ki na centrifug e tubea t3 0° Can dsubsequen tb yseparatin gth ecur dfro mth ewhe yb y centrifugingat400 0g fo r15-2 0min . o Thevalue sfo rth eviscosit ya t3 0 Cwer efo rth erenne tan d acidwhey s1.02 0an d1.02 5mPa-s ,respectively .
2.4 THIMEROSAL
25-100pp mThimerosal ,als oname dthiomersa l(CJL-.Hg.S.CJI.CO O Na),wa suse da sa preservativ ei nmil kan dwhe y ifth eexperiment s lastedove r3 hours .I twa schecke dwhethe rth epreservativ eaffecte d therennetin go rsyneresi sproces si nou rexperiments ;n osignifican t effectswer efound .
2.5 CONCENTRATEDMIL K
Concentratedmil kwa sobtaine db yultrafilterin greconstitute d skimmil ka troo mtemperature .Molecula rcut-of fo fth emembran ewa s about1 000 0Daltons .A twofoldconcentratio nwa sreached .
2.6 TREATMENTO FTH EGE LAN DSTARTIN GSYNERESI S
Rennetan daci dgel sstic kt oth esurface sof ,fo rinstance , glassan dstainles sstee lwit ha lo wnicke lconten t (Arentzen,1966; Hostëttler,1954) .Hence ,a tthes esurface sn osyneresi swil loccur . Thisenable su st operfor m fairlysimpl eexperiments .However ,th e gelsshoul db ehandle dwit hcar ea sthe yar eeasil ydisrupte dfro m thewal lsurfac ebefor ethe yar efir menough . Fig.2. 1 Interface of curd/airwit h large contact angleo f thewhey .
The syneresiswa s startedb ywettin g theupper ,fre esurfac e ofth egel .Unti lthi smomen tn osyneresi s occurred.A n explanation mayb etha tth esurfac eo fth ecasei nnetwor ktha ti si ncontac twit h airdurin g renneting isno teasil ywettable ;i nothe rwords ,th e contactangle ,a smeasure d inth ewhe ywoul db e >9 0 (seeFig .2.1) . Thecapillar ypressur etryin g toforc eth ewhe y inwardswoul d then easilyexcee dth esyneresi spressure .O fcourse ,thi sdoe sno thol d fora freshlycu tsurface .A disadvantage ofthi smetho d isa possibl e difference ofth eupper ,fre esurfac e ofth ecur d incontac twit h air anda surfac e formedb ycutting ,causin ga differen tsyneresis . However,th e layeri nwhic hth edifferenc e residesmus tb e extremely thin.Measurin g syneresis ata freshly cutsurfac ewa s expected to causeconsiderabl epractica lproblem s inapparatu sdesig nan drepro ducibility.Car ewa s takentha tth emoistur e contento fth eai rabov e thesurfac eo fth ege lremaine dhig hunti li twa swetted .Th ewettin g couldno tb edon eb y simplypourin gwhe y overth esurface ,becaus ei t causedloca ldamag et oth egel .Therefore ,th esurfac ewa swette d firstb ygentl ysprayin gwhe yo ni t (followedb y pouring).
2.7 STANDARD CONDITIONS FOR RENNETGEL S
Unlessmentione d otherwisemil k Rwa sprepare d asdescribe d in Section 2.1 anduse dbetwee n 1an d 4hour safte rpreparation ,50 0pp m rennetwa s addedan d thetemperatur e during thewhol e experimentwa s kepta t 30 C.N o CaG- wasadded .Thes ewil lb e called standard conditions. 2.8 STANDARDCONDITION SFO RACI DGEL S
MilkA wa sprepare da sdescribe di nSectio n2.1 .3 N HC lwa suse d foracidificatio na t4 C top H 4.3-4.8.Th emil kwa sthe nheate da t a rateo f0. 5 Cpe rminut et o3 0 C,whic hcause da ge lt oform . 3 ENDOGENOUSSYNERESI S PRESSURE
As statedi nSectio n 1,syneresi smus tb ecause db ya nendogenou s syneresispressure .I nprincipl e thepressur ecoul db emeasure db y fixingth ege lbetwee ntw oplate s andmeasurin gth eforc eneede dt o keepth eplate sa tconstan tdistance .W econclude dthi st ob eno t feasible,th emai nreaso nbein gth ever ylo wstress .However ,tw o experimentsworkin go ndifferen tprinciple s gavesom e ideao fth e stresses involved. Inon eexperimen t (seeFig . 3.1.),cur dwa s formedi na va tan d cutcarefull y onlyi nth evertica ldirection .Th ecur dwa sno tdis turbed,an dit ssurfac ekep tdry .I nthi swa yblock so fcur dwer e formedwit ha heigh to f2 c man dwidt ho f1 cm . Theuppe r surfaces ofsom eo fthes eblock swer ewette dwit hwhe ywhil e other remained dry.Afte r1 hou ra t3 3° Cth eblock swit h thewette duppe r surface wereshrunk ,whil e othersshrun kfa rless :th edifferenc e (h) between the levelso fth eunwette d curdan dth eadjacen twhe ywa s always below1 mm .Th estres spullin g theuppe rsurfac e downmus tb eequa l toth epressur e exertedb yth ewhe y column h, amountingt o h p g. Consequently,th esyneresi spressur ewa si nthi ssituatio n< 1 0P aa t 33 C.I tshoul db enote d thatthi si sno tth eorigina lsituatio na s thevolum eha schange ddurin gth eexperiment . Inanothe rexperimen ti twa s triedt omeasur eth epressur e exertedo nth ewhe yi nth ematrix .A smal lan dsensitiv epressur e transducerwoul db eneeded ,bu tw ecoul dno t findon etha twa s
Fig. 3.1 Syneresiso fblock so fcurd .A :Th ecur d inth eva tha sbee n cut ina numbe ro fblocks .Th euppe rsurfac eo f someo fthes eblock s arewetted .B :Afte r1 hou ra t3 3 Cth eblock swit hth ewette dsurfac e areshrun kfa rmor etha nth eothe rblock s (h =vertica l shrinkageo f blockswit hunwette d surface). electric current for
Fig.3. 2 Estimationo fth eendogenou s syneresispressur eb yrecordin g thepressur e exertedo nth e whey.
sensitiveenough .Therefore ,w etrie da nexperimen ta sshow ni nFig . 3.2. Ina va ta glas stub ewa splaced ;th etub eha da diamete ro f0. 5m m andwa s filledwit hwhey .Mil kwit hrenne twa sadde dan dafte rsettin g thecur dwa scu tloos efro mth ewall .A tfirs tth ewhe y levelwa s highertha nth e levelo fth ecur dbecaus eo fcapillar y rise. The syneresispressur eno wshoul dfurthe rrais eth ewhe y level.Onl yi f thecur dwa swarme da shig ha s4 0 C,th eleve li nth etub edi drais e perceptibly,i.e . about1 m mcorrespondin gt o1 0Pa .Th eactua l syneresispressur emus thav ebee nhighe ra sconsiderabl e transporto f wheyi sneede dfo rth emeasurement . Anothercaus efo rsyneresi scoul db eth eweigh to fth ecasei n matrix.Th elowe rpart so fth enetwor khav et obea rmor eo rles sth e networkabov ethei r level.Thi smean s thati ncur da ta leve l h below
theinterfac ea pressur eo f( p Pwhey) g hc~ 7S hc (inS.I .units ) would exist.I nChapte r7 i twil lb econclude d thatth eweigh to fth e caseinnetwor kplay sa rol ei nsyneresi spressure . Also fromcree pmeasurement s (seeSectio n 5.3)w econclude d that endogenous syneresispressur ewa sprobabl y lowertha n1 0Pa ,mayb e ~1 P aa tstandar dcondition s (Section 2.8). Consequently,a norde r ofmagnitud eca nb egiven .
10 4 PERMEABILITY
4.1 INTRODUCTION
Forth ecalculationa lmode lw ear eintereste di nth eresistanc e a fluidmeet swhe ni tflow si non edirectio nthroug ha fixe dmatrix . Ameasur efo rthi si sth epermeabilit yo rpermeabilit y coefficient.I t isth eproportionalit y constanti nth eequatio no fDarc y (seee.g . Scheidegger (1960)):
v = -~VP (4.1)
inwhich : v =superficia lvelocit y (i.e.volum e flowrate/cross-sectiona larea ) n= viscosit y VP= pressur egradient .I nou rcas ethi si salway si nth esam e x-
direction (i.e.paralle lt oth etube) .S oV P= dP t/dx.Th epressur e differencebetwee nth elowe ran dth euppe rsurfac eo fth ege li s
calledP to rPjt ) (seeFig .4.2) . B =permeabilit y coefficient.I ti sa propert yo fth ematri xan dit s geometryan dscale .Th edimensio ni slengt hsquared.(Compar eth e
laminarflo wthroug ha cylinde rwit hradiu s at where
v =- (a^/8n)dP t/da:.) (4.1.a)
Theequatio ni svali di na certai nvelocit y domain (seeSectio n 4.3.1).
4.2 MATERIALSAN DMETHOD S
4.2.1 "Tube" method
Formeasurin g thepermeabilit yo fth ecur di ti snecessar y that thecur ddoe sno tshrin k duringth eexperiment .Thi swa sachieve db y makingth ecur di ntube so f2. 0o r3. 7m minterna l diameteran d2 5c m length.Unles smentione dotherwis eth e3. 7m mdiamete rtube swer eused . The tubeswer e cleaned thoroughlys otha tth ecur dwoul dstic kt o
11 thewal lan deithe rplace di na holde rwhereb yth etub ewa s restingo n aplexigla sbas eo rseale do nlowe rsid ewit h laboratory filmi nwhic h apinhol ewa smade .The ythe nwer e slowly loweredi na va t filledwit h milkt owhic hrenne tha dbee nadded ,thereb y slowlyfillin gth etube s (seeFig .4.2) .Whe nth eclo twa s firmenoug hth etube swer edraw nou t ofth evat .Th etub eholder so rth elaborator y filmswer eremoved . Thetube swer epu ti na rac ki nth ewhey .Th ewhe y thenstarte d flowing throughth ecurd .Th ewhey-leve li nth etube swa srea da tregula r intervalswit hth eai do fa cathetoscope .Th ewhey-leve li nsom etube s withouta ge lals owa smeasured .Th eexperiment swer eexecute di n3 -o r 4-folda sabou t 101o fth ecurd sbecam eunstuc k fromth etubes .
4.2.2 The "Torsionflux" method
Whenmeasurin g B,e.g .a sdescribe di nth epreviou s Section, the geli sbein gdeformed ,becaus eo fth epressur edifferenc eapplie d(se e Section4.3.2.1) .Th edeformatio no fth ege l(i nth edirectio no fth e flow)affect sth epermeabilit yo fth ecurd .Wit hth etub emetho dw e cannot measureth edeformation .Moreove rth edeformatio ndepend so n thedistanc et oth ewal lo fth etub ean do nth erigidit yo fth e gel. Themetho ddescribe dher ewa s appliedt omeasur eth epermeabilit y asa direc tfunctio no fdeformatio no fth egel ,i fdeformatio nwa s perpendiculart oth e directiono fflow .Th ege lwa smad ebetwee na metalinne rcylinde ran da glas soute rcylinde r (seeFig .4.1) . One hourafte raddin grenne tth einne rcylinde rwa s rotatedove ra certai n anglean dkep ts ofo ron ehour .I nthi swa yth edeformatio ni spreci selyknown .The nth ewhe y inletswer eopened ,abou t5 m mo fwhe ywa s placedo nto po fth ecur dan dth ewall so fth ecylinder swer ewetted . Thewhey-leve lwa srea da tregula rinterval swit hth eai do fa cathe toscope.
4.2. 3 Calculation of permeability coefficient (B)
Generally,fo rth epurpos eo fpermeabilit ymeasurements ,a n apparatusi suse dwhic hhold s thepressur econstant .I nthi swa yth e equationo fDarc y (eq.4.1 )simpl yca nb eused .Bu tdurin gou r experi ments (seeFig .4.2 )th epressur edifferenc e (P)betwee nth eend so f
12 T i~"bean ng outlet I ^= air c whey —inner cylinder -whey
-curd
-outer cylinder
A-— whey inlet àzzzÉjzzzZi
Fig. 4.1Schemati c representationo fth e"torsionflux "apparatu s thecolum nchange ddependin go nth evelocit y (.v(t) = dh{t)/dt):
F (t) d t _d{h(« )- hjt)} _ ,. (4.2) Zt~Q-g a* u(*3 withp = densityo fth ewhe yan d g= gravitationa lacceleration .
Inthi scas eth eequatio no fDarc y (Eq.4.1 )ca nb ewritte nas :
P (tJ dh(t) = g t (4.3) M n H P(t)i scause db yth edifferenc eh(°° )- h{t) inth eleve lo fth ewhey .
fl»00- g P g{h(°>) - h(t)} (4.4) 3* n A
Integrationlead sto :
g P + h(t) =~{Ä(» )- Ä(0) }ex p (" n /* ) ÄC- ) (4.5)
Thisca nb erewritte nas : -I n M») - Ht), ln n g (4.6) 3_ kn -h(or P g t Aproble mi stha t Bwa sno tconstant :i tusuall y increaseddurin gth e measurements.Fo rsak eo fsimplicit yw eassume dg(t )t o changelinearl y withtime ;subsequen tmeasurement s showedthi st ob etru ewithi nth e
13 h(» )
PIOI P9
h(t l MO]
Fig. 4.2 Schematic representation of permeability measurement. a. formation of curd in a tube b. permeabilitymeasurement . accuracy of the experiments. If B{t) is changing linearlywit h time Eq. 4.3 turns to: dB 5(0)+ tP t(t) (4.7) St— a* H inwhic h dB/'dti sa constant.Followin g the samemetho d as described abovew e obtain: ftH - Ht) -m c •) n B dB 5(0)= M°0- ft(Q) (4.8) p 9 * a* ,dB Since B(t)i s linearwit h time BGt) B(0)+ 237-*» a™*a tB( 2t)w e find the same result aswit h Eq.4.6 . So Eq.4. 6 can stillb e used if thepermeabilit y coefficient (B)i s taken at thehal f time between the readings of/z(0 )an d h(t). Up tillno ww e have tacitly assumed that the level of thewhe y outside the tube is constant.Thi s needno tb e true.I fth e level is not constant,an d the surface ratio of the tubes to theva t is r then:
d P(tX = (4.9) 3t p g (1+ r)v(t)
14 Apossibl esmal leffec to fdifferen t v(t) indifferen ttube si s neglected.W efin di nanalog yt opreviou ssolutions :
2 .pf01 -{B(0)t+ J g t } p gO +i 0 Ä(t)-ACO)= ^Irr;sex VW^~7)p {v x —^n~ïï }- 1 (4.10) orrewritten :
5 t4 11J BC0) (1+ r )p g t 3t* -
Inth eexperiment s always r <0.01 .I fth evelocitie s inth e varioustube sdurin gon eexperimen tdiffered ,r wa smad ea ssmal la s possible (<0.001 )an dneglected . To finddB/d ta numbe ro fsubsequen treading sha d tob emad ean d fromthes eB a tdifferen ttime swa s calculated. Asmentione dalread y dB/dt indeedwa s foundt ob eno tsignificant lydependen to ftime .I nsom eexperiments ,especiall ywit hth e torsionfluxapparatu s (see4.2.2) ,th ereading swer eles saccurate . A betterestimat eo fB an ddB/d tca nb emad eb ysecon ddegre epoly nomialregression ,provide ddB/d t isindependen t oftime .W eca nus e therewritte nEq .4.1 0 foranalysis :
m {»(-)-Mt)> p ;tf + T) -
2 Ittn W -M0) }p ^ + r) - B(0)t- j g t (4.13) whereB(0 )an d làB/dt areth eregressio ncoefficients . Finally,i tshoul db enote dtha tB(0 )i sth epermeabilit y ofth e gela tth emomen ttha tmeasurement s started.Mostly ,th epressur e differenceha d tob e applied 10t o2 0minute s earlier,fo rpractica l reasons. Consequently, B i.e.B a tth emomen ttha tpressur e difference wasapplied ,ca nonl yb eha dfro mextrapolation .
4,2.4. Calculation of the viscosity of the whey
Becauseo fth elimite daccurac y ofth emeasurements ,i twa sno t necessary todetermin eth eviscosit y forever ywhe y sample,excep t
15 whenth etemperatur eo rth econcentratio nwer echanged .Accordin gt o Eilers (1945)th eviscosit ychange sconsiderabl ywit htemperatur ean d weuse dhi sresults .An yconcentratio no fth emil kwa sdon eb yultra filtration.B ythi smetho dth ewhe yi sconcentrate dalso . Theensuin gincreas ei nviscosit ywa s calculatedwit hth eai do f theexperimenta lresult so fPer i (1976).
4.3 RESULTS
4.3.1 Validity of the equation of Darcy
Itshoul db echecke dwhethe rth eequatio no fDarc yi svali di n theperforme d experiments.Thi si snormall ys oi flamina rflo woccurs . Theresul tshow showeve r thatth epermeabilit y changeswit htime .I t shouldb eprove nhoweve r thata ta give ntim e Bi sindependen to f liquidvelocity .T ocharacteriz eth eflow ,i ti scustomar yt ointro ducea "Reynold snumber " (Re)a sfollows :
Re = vp d/x\ where di sa diamete rassociate dwit h theporou smedium .I fporosit y islow , d couldb eth eaverag ehydrauli cpor ediamete ro fth estrands . We alwayskep t v <1 0 m«s ;p = 1 0 kg«m andn = 1 mPa'S .Fo r d < -1 1m mw e thenfin d Re <1 0 .Sinc ealway s d« 1mm , Re« 1.S o laminar flowca nb eexpected . Moreover,measurement swer eperforme da tdifferen tdP/dx ,b y changingth ecolum n lengthand/o rP ,an ddifferen t tubediamete r (dt). Forpractica l reasonsth emeasurement s couldonl ystar t 10-20minute s after t :th etim ea twhic h thepressur edifferenc ewa sapplie dt o thecolumn .Fig .4. 3show s thatther ei sn osignifican t difference betweenth eextrapolate dvalue s B at t .
4.3.2 Results with the tube method
4.3.2.1 Influenceo fdeformatio no npermeabilit y
As statedbefore ,cur ddeform sdurin gmeasuremen ta sa resul to f
16 Bx10,3(m2) 6-
d= 3.7 mm dP/dx =8 kPa.m"1
d= 2.0 mm dP/dx =8 ICPCMTT1
d= 3.7 mm dP/dx - 5 kPanf1
d= 2,0mm dP/dx =5kPa.m"1
0 12 3 time(h ) Fig. 4.3Permeabilit ya sa functio no ftime .Illustratin gth etim e derivativedepend so nd tan ddP t/dx.A ttim e te thetube swer eplace d inth ewhey .Th edot srepresen t thecalculate d5(0 )value s (seeEq . 4.10). theapplie dpressur egradien t (dPJàx). Forinstance ,a t8 kPa« m it wasvisibl ydeformed .Thi sdeformatio ndepende do nth edistanc et oth e wall,o ndP/dx ,o ntub ediamete r (d) an dge lstrength .Th eresult si n
Table4. 1sho wtha t largerdP t/dxan dlarge rd , whic hgav elarge r deformations,resulte di na highe rdB/dt .Eventually ,th ege l breaks.
Incidentally,th egel salway sbrok ea ta distanc eo fabou t \dt from thewall ;thi si sindee dth eregio nwhere th edeformatio no fth ege l shouldb elargest .Som eresult sar eals oshow ni nFig . 4.3.
Table4. 1 Influenceo fpressur egradien t (dPt/dx)an d tubediamete r (dt)o n dB/dt. Averagevalue san drang eo fthre eexperiments .
17 dr dPt/dx dB/dt x 10 (mm) (kPa'nf') (^..-' ) 3.7 0 0.81) 3.7 5 1.4 (1.4- 1.5) 3.7 8 2.8 (2.6- 2.8) 3.7 20 gelbreak s 2.0 0 0.81) 2.0 5 0.8 (0.6- 0.8) 2.0 8 1.4 (1.3- 1.5)
h ^FromTabl e4. 2 :{B e(2h)- B eO )}/3600
17 4.3.2.2 Changeo fpermeabilit y ofundeforme dcur dwit htim e
Gels intube swer epu tunde rpressur e formeasurement s at different timeafte rrenne t addition.Fro mth e flow in4 - 12tube s theaverag e B valuean drang ean dth eaverag e dB/dt value andrang e werecalculate d (seeTabl e 4.2 andFig .4.4) .I nTabl e 4.2 also is iven ABe/A*= {Be(*2)- B e(*.,)}/ C*2- V 8 -
4.3.2.3 Influenceo f concentration
The influenceo fcasei nconcentratio nwa s studiedb yultra - filteringfres hski mmilk .Concentratio nwa s expressed asi = volum e ofconcentrate dmilk/volum eo forigina lmilk .Naturally ,w e are interestedmor e inth epermeabilit y ofhomogenou s gels concentrated by syneresis,bu t suchgel s cannot bemad ehomogenou s and theywil l showsyneresi s onholding . The lengtho fth ege lcolum nwa s takens otha t theflo wo f the wheywa s alwaysbetwee n 0.1 and 0.3 mm«s .A constant clotting time of 0.25wa sused . Theresult swer e fittedt opowe rcurves .
-1 Table4. 2 Change ofpermeabilit y with time.dP t/dx = 5kPa'm . For explanation see text andFig .4. 4 . n =numbe r of experiments t = timeafte r rennet addition
13 17 n ta Be x 10 ASe/At dB/dt x 10 x 1017 (h) (m2) (m2«s-l) (m2«s_1)
6.1 (4.2- 7.0) 8 0.5 1.5 (1.0 - 1.8) 6.6 4 0.67 1.9 (1.9 - 2.0) 2.3 (2.2- 2.8) 2.5 1.6 (1.2- 1.9) 8 1 2.2 (2.2 - 2.3) 1.1 4 1.5 2.4 (2.3 - 2.5) 1.6 (1.5- 2.5) 0.6 2.3 (1.5- 3.0) 2 2 2.5 (2.4 - 2.7) 1.1 4 3 2.9 (2.9 - 3.1) 1.6 (1.5- 1.8) 1.1 1.3 (1.1 - 1.7) 8 4 3.3 (3.1 - 3.1) 1.1 8 24 11.1 (11.1 - 11.1) 1.3 (1.0- 2.0) BxloW)
7
ü 1 2 3 k IU time after rennet addition (h )
Fig.4. 4Permeabilit y asa functio no ftime ,o fdeforme d curd during the experiment (solid line)an do fundeforme d curd (dashed lineinter connecting calculated valueso fB e).
We found:
18 17 2 4 2 1 dße/dt=8 x 10 - 2.2 x 1.0 (1 - i) ' (m -s~ ) (4.14) and:
B (i)= 2. 3x 10" 13 i2-6 (m2) (4.15) withsampl ecorrelatio n coefficients (r)o f0.9 8an d0.998 ,respective ly. Integrationan dcombinatio nyields:
B (i, f) = {8 x 10"18 - 2.2 x 10"17 (1 - i)1A} t +
+ 2.3 x 10"13 i2-6 (m2) (4.16) whichrelatio nwa suse di nth emodel .Eqs .4.1 4an d4.1 5ar eshow ni n Fig.4.5 .Not etha t B (i, t) andd B /dt fori <0. 5wer e foundb y extrapolation.Fo ri =0. 5d B /dt calculated fromEq .4.1 4ha sabou t twiceth eexperimenta lvalue .Thi swoul d onlyhav ea mino r effecto n thecompariso no fth ecalculate dan dth edetermine d syneresis since only resultsfo rAH/H Q<^0. 5 were considered.
19 BexloNm2) 36
30
24
18- dB«/dtx101Vs1) 12 12
h 6
O 0.2 0.4 0.6 0.8 1.0 1.2 i = vol. concentr. /vol.orig.m. Fig.4. 5Permeabilit yan dit stim ederivat ea sa functio no f concentrationo fth emil kbefor ecurdling .
4.3.2.4 Influenceo ftemperatur edurin gmeasuremen t
Thegel swer emad ean dtreate daccordin gt oth estandar dmethod . Onehou rafte rrenne tadditio nth etemperatur ewa schanged .Result s aregive ni nTabl e4.3 .I tshow stha t dB/dt increaseswit h increasing temperature.
4.3.2.5 Influenceo ftemperatur edurin g renneting
Forthes eexperiment s skimmil kA wa sused .On ehou rafte rrenne t additionth etube swer eplace di nwhe yo f3 0 Cwit h dP/dx =4 kPa« m . Theresult sar eshow ni nTabl e4.5a .Permeabilit ya smeasure don ehou r afterrenne tadditio n (B) increase dwit hincreasin g renneting temperature.Th einfluenc eo n dB/at wasles sconsistent .A probabl e causei stha tonl ya fe wreading so f h{t) weredone . Inanothe rserie so fexperiment sski mmil kR wa suse dan dth e temperaturedurin grennetin gwa smaintaine ddurin gmeasurement . The resultsar eshow ni nTabl e4.5b .I nthes eexperiment s B and dB/dt increasedwit h increasingtemperature .
20 Table4. 3Influenc eo ftemperatur edurin gmeasuremen to n dB/dt
17 Temperature dB/dt x 10 (°C) (m «s )
-1 dPt/ 12 < 0.05 < 0.05 25 0.7 (0.6- 0.7) 1.0 (0.9 - 1.2) 30 1.0 (0.8 - 1.1) 2.8 (2.6 - 2.9) 35 5.1 (4.9 - 7.3) 8 (7-8) 4.3.2.6 Influenceo frenne tconcentratio nan dtyp eo fski mmil k Two serieso fexperiment swer edone .I nth efirs tserie s fresh skimmil kwa suse dan di nth esecon d theusua l reconstituted skimmilk . Resultsar eshow ni nTabl e4.4 .Fro mTabl e4. 1an dFig .4. 4value so f dB/dt andB fo r50 0pp mrenne twer etaken . Theresult ssho wtha t initially Bincrease dan ddB/dt (during measurement,i.e .whil ether ei sdeformation )decrease dwit h increasing rennet concentration.Afte r 2\ hours,influenc eo frenne t concentration was small,i fexistent .Fres hmil k gavehighe r resultsfo rB an d dB/dt. 4.3.2.7 Influenceo fCaCl ,additio n CaCl2wa sadde di ndifferen t concentrationsan drenne twa s added insuc ha quantit y thatth esam eclottin gtim ewa s achievedi nal l experiments.Th eresult si nTabl e4.6 asho wtha ta tt =1 h ,B does notdepen do nth eapplie dC aconcentratio nan d dB/dt decreaseswit h increasingC aconcentration .A t t =2 h . B anddB/dt decreasedwit h a e increasing concentration. Inanothe r experiment onlyth eCaCl _ concentrationwa svaried . Theresult si nTabl e4.6 bsho wtha t Bwa sconstan to rslightl y increaseda tCaCl -concentration so f0 t o50 0pp man ddecrease da t concentrationso f740 0t o2210 0ppm . dB/dt decreasedwit h increasing concentrations. 21 — CM i-~ r~ ~3- m co r-* lO m -3- m co co co in X I o -3 co co r^ o — CM +i CS -3- en -3 «3- CM co co co CN CM m CM 00 00 m m m m co co CO co XI m o r-. H y—s. CM co 00 o m co •O ttl J, a •o vO o xr VO OtOOr-Ml ce) en -3- vO — oo CO CM CO CO CO eu — -3- W Ofi CM VO —« m \43 00 vO -3- c -3 CO -3- -3- — CM CM CM CM CJ\ O co CM •i-l -h I I I I I m I I I I 4J O CM ce) co m oo o vD CO O O H — •—. 4-> X CM co CO CO -3- O CM CM CM CU C eu Q) ^s^ 3 cj OQ 4-1 C o m o co m co m co CM et) o u o -3- CO -3- -3 ' ei CM CM CM CM CM eu 4J a» C 60 C C m •H M 4J 4-1 eu O O O O O O O O O O •rl m O S '- O CM 00 O O 00 O 00 00 o 3 o .M i—1 •H CO *4D P^ VJ3 >3- vO r-- er» CM « m i—i CJ 4-1 *— — CM CO CM co 22 Table 4.5Influenc eo ftemperatur e during renneting. a. dP\./dx " 4kPa« m .Skimmil kA Temp. B x io13 dB/dt x 1017Z ) e (°C) (m2) (m« s ) 30.2 2.4 (2.1- 2.5 ) 2.6 (2.0- 3.0) 32.8 3.0 (3.0- 3.1 ) 3.6 (3.0- 4.4 ) 35.6 6.5 (6.1- 6.8 ) 3.4 (2.9- 3.7) b. Temperaturemaintaine d duringmeasurement . dPt/da;= 5 kPa«nrl.Ski mmil kR 27 1.7 .(1.9- 2.2) 2 .(1 -2 ) 30 2.21' 1.6° 33 3.0 (2.8- 3.4) 5 (4 - 7 ) ^fromTabl e4. 1 lessaccurat ea sonl ya fe wreading so f h(t) were available 4.3.2.8 Influenceo facidit y onpermeabilit y Thep Ho fth egel swa svarie db yaddin gHC lo rNaOH .A si n Section 4.3.2.5ski mmil kA wa suse d forth eexperiment s showni nTabl e4.7 a andb . The results inTabl e 4.7sho w that B at t =1 h decreased with e increasing pH.Th eeffec to ndB/d twil lb ediscusse d later. 4.3.2.9 Influenceo ffa tconten t Thefa tconten t offres hmil kwa svarie db ytakin gwhol e milk (3.321 fat),separate d milk (0.10%) anda mixtur e (1.96»»). The results inTabl e 4.8sho w that Bdecrease d with increasing fat content. Therewa sfoun dn osignifican t correlation between dB/dt and fatcontent . 23 Table4. 6 Influenceo fCaCl „concentratio no npermeability , a.A tconstan tclottin gtim e dP^/dx = 5Pa-m m CaCl2.2H20 rennet Bex 10*3 ABI At x101 7 (ppm) (ppm) (m2) (m2.s~l) *a= 1 0 500 2.2 (2.1- 2.3) 1.6 (1.2- 1.8) 450 250 2.3 (2.2- • 2.5) 1.2 (0.6- 1.6) 1600 125 2.1 (2.1- 2.3) 1.1 (1.1- 1.2) 3200 62.5 2.3 (2.3- 2.3) 1.0 (0.7- 1.3) 0 500 2.6 (2.4- 2.7) 1.8 (1.5- 1.9) 450 250 2.5 (2.3- 2.7) 1.4 (1.2- 1.5) 1600 125 2.3 (2.1- 2.4) 1.2 (1.1- 1.3) 3200 62.5 2.4 (2.1- 2.5) 1.0 (1.0- 1.0) b.A t constantrenne t concentration äP lax = 8Pa'mr n . t = 1h t a 0 500 2.3 (2.1- 2.4) 2.7 (2.3- 2.9) 250 500 2.3 (2.2- 2.4) 2.5 (2.2- 2.8) 500 500 2.5 (2.3- 2.5 ) 2.4 (2.1- 2.6) 7400 500 2.4 (2.2- 2.6) 1.3 (1.0- 1.7) 14700 500 2.2 (2.0- 2.4) 0.8 (0.8- 1.0) 22100 500 2.0 (2.0- 2.1) 0.9 (0.7- 1.1) 4.3.2.10 Permeabilityo faci dgel s Gelswer emad ei ntube sa sdescribe d inSectio n 2.8.Permeabilit y andstorag emodulu sC 'wer emeasure d 20hour safte rheating .'Ib e resultsar ei nFig .4.6 .A tp H4. 6 thepermeabilit ywa sals omeasure d 2hour safte rheating ;i twa shighe r (i.e.1. 9 x 10~13m 2)tha nafte r 20h ,thi si ncontras tt oth epermeabilit yo frenne tgels ,whic h increaseswit htime .IXirin gmeasuremen t (dPJàx =5 kPa«m~ 1), B remainedconstan t (i.e.dB/d twa s zero)i nal lcases . 24 Table4. 7 Influenceo facidit yo npermeabilit y a.Mil kR (12g powder/10 0g water) . 250pp mrennet .Temp . .30.5° C -1 Rennetadde dMb .afte rp Hsetting .Origina lp H :6.5 .dP t/dx= 8 kPa'm ) 13 17 pH Clotting Be x 10 dB/dt x 10 time » (min) (m) (m» s ) 6.0 15 3.0 (2.9- 3.1) 1.0 (0.9- 1.2)* } 6.3 25 2.0 (1.9- 2.0 ) 0.4 (0.3- 0.7)2^ 6.6 40 1.3 (1.3- 1.3) 1.3 (1.3- 1.4) ; b. Standardcondition s (see2.7) .Renne tadditio n Jh afte rp Hsettin g -1 Originalp H :6.65 .dP t/àc= 5 kPa-m . 6.55 2.7 (2.5- 2.7)n 1.2 (1.0- 1.6)n 6.65 2.2 (2.2- 2.3 ) ; 1.6 (1.2- 1.9) ; 6.75 2.0 (2.0- 2.3 ) 2.2 (1.8- 2.3) c.Sam emil kan dconditions ;renne tadde d 3h afte rp Hadjustment . 6.55 2.3 (2.3- 2.4)n 2.2 (1.8- 2.6)n 6.65 2.2 (2.2- 2.3 ) ' 1.6 (1.2- 1.9) ; 6.75 2.1 (2.1- 2.3) 2.4 (2.0- 2.6 ) i)Result stake nfro mTabl e4. 2 2)Les saccurat ea sonl ya fe wreading so f h(t) aredon e Bx10"(m'; GINm ) CI 6.0 O 500- 5.5 400- 1.5 300- LO 200.J £1- ~ÏT 44 ZS S W Ï8 pH 43 U 4.5 46 47 48 pH Fig. 4.6Permeabilit y (B)an d storagemodulu s (G')o faci dgel sa sa functiono fpH . 25 Tabel4. 8 Influenceo ffa tconten to npermeability .Fres hmil kwa s used.dP t/dx= 5 kPa*m~' . Experiments starting Jh afte rrenne t addition (ta= {h ) Fatconten t B x10 13 dS/dt* 10 17 (%) (m2) (m2-s"1) 0.10 5.2 (5.1- 5.3 ) 4.2 (4.1- 4.5 ) 1.96 4.8 (4.7- 5.0 ) 4.5 (4.4- 4.9) 3.82 4.5 (4.3- 4.5 ) 3.1 (2.6- 3.2) 4.3.3 Influenae of deformation, temperature and pH on permeability as measured with the torsionflux method Temperaturedurin gth eexperimen twa svarie dbetwee n2 8an d3 3 C. Theresult si nTabl e4. 9 showtha t Bincrease dwit hincreasin gdefor mationan dtemperature . Bincrease droughl yexponentiall ywit hshea r strain y. Athighe rtemperature s Bdepende dmor eo ny .Mos tgel sbrok e ifY =1.0 5 (seeTabl e4.9) .Fro mFig .5. 4 itca nb ededuce dtha t gelwil lbrea ki f y e 1afte r1 hou r (standardconditions) . dB/dt (duringmeasurement )increase da littl ewit hincreasin g deformationan dtemperature . Theinfluenc eo facidit ywa sstudie db ychangin gth ep Hb y0. 1 unit.Permeabilit ywa sincreasin gwit hdecreasin gp Han dincreasin g shearstrai n (y)(se eTabl e4.9) . 4.4 DISCUSSION Thegenera lresult so fth eexperiment sare : A) Thepermeabilit yo fth edifferen tgel svarie dbetwee n^1 0 and -12 2 11n0 m. Thisresul tca nb eexpecte dfro melectro nmicrograph s (Knoop& Peters,1975 ;Mulder ,D eGraa f& Walstra ,1966 ;Green ,Turve y& Hobbs,1981) .The ysho wa naverag ethicknes s (6)o fth estrand so f ^ 250-500nm . Thematri xi sno thomogeneous .Whil e z iso naverag e about0.93 ,ther ear eregion swit ha hig hdensit yo fstrand s (locale , say0.8 )whic halternat ewit hpore s (whereloca le = 1).Th epore s 26 Table4. 9Influenc eo fdeformation ,temperatur ean dp Ho nth epermeabilit ya smeasure d with the torsionflux -1 2 17 method. dPt/dx- 5 kPa-nf' .Value so f Be arei n10 -*m » valueso f dB/dt in10~ m*-s ~ ; r ranges between parenthesis,n = • numbero fexperiments .Deformatio n started 1hou r after rennet addition,pressur ewa s applied 1h late r (t =2 h) . ' Rotationo fitmer - cylinder (degrees) Resulting shearing strain (y) 1.05 temperature (°C) 1.9(1.4-2 0) 1.8(1.5- -2 1) 2.1(1.9 -2 3) 2.4(2.1-2.7) dfi/dt 2(1-2) 1(1-1) 2(1-2) 4(3-5) n 8 6 11 4 1 2.5(2.2-2 6) 2.6(2.2--2 7) 3.0(2.4 -3 5) 3.6(3.1-4.0) 5.2 dfl/dt 2(1-2) 1(1-1) 2(1-2) 4(3-5) 12 n 1 1 1 1) M *e 4.4 5.0 5.5 dB/dt 6 5 7 33 n 2 2 2 1 Be 4.2(4.0-4 4) 4.9(4.6--5 2) 5.5(5.1 -6 0) 6.3 1) dB/dt 6(4-8) 6(4-7) 7(5-8) 15(11-20) pH n 4 4 3 2 B 3.3(3.2-3.4) 3.4(3.1-3.6) 4.0(3.6-4.5) 5.0(4.6-5.4) dfl/di 4(3-4) 4(3-5) 5(4-6) 10(8-13) 6.65 (seeT=30°C ,above ) 6.75 «4 4 3 4 Be 2.6(2.2-3.0) 2.8(2.2-3.2) 2.9(2.6-3.2) 3.4(2.9-4.0) dB/dt 3(1-4) 3(2-4) 3(2-4) 4(3-5) *)ge lbreak s (alsoa t30° Can dy = 1.05 thege lwa sbroke ni ntw oexperiments ) 27 compriseroughl yhal fth evolum eo fth egel .Typica lvalue s forpor e diametersar e 5-10ym .Th eeffectiv evolum efractio no fth epara caseinmicelle s (1-e)i stake nt ob e0.07.I nliteratur e (e.g. Scheidegger,1960 )a numbe ro fequation sar egive nwhic hpredic tth e permeability ofmode lsystems . Theequatio no f Iberalldeal swit ha mode lo fa rando mdistri butiono fcircula rcylindrica lfibres .Accordin gt othi sequatio n B = -.4 fji. ; - Y ie (4.18) 16 1- e 4- I n Re -5 -13 2 inwhic hth eReynold snumbe r (Re) ^1 0 ,w e find B^ 1 0 m .Th e Kozeny-Carmantheor yrepresent sth eporou smediu mb ya nassemblag eo f channelso fvariou scross-sections ,bu to fdefinit elength .Accordin g toth eequatio no fKozeny-Carma n (Scheidegger,1960 ) 3 ,2 B= XË (4.19) 180 (1-e) inwhic h d - volumesurfac eaverag ediamete ro fth emicelle s (A = 104n maccordin gt oSchmidt ,Walstr a& Buchheim , 1973),w ewoul dfin d B= 1x 10" m .Sinc eth e (superficial)flo wthroug ha collectio n ofpore s isproportiona lt opor ediamete rsquared ,flo wthroug hth e verysmal lpore s insideth edens eregion so fth ematri xwil lb e negligiblea scompare dt oth elarge rpore sbetwee ndens eregions . Hence,th eregion swit ha hig hdensit yo fstrands ,a sshow ni nth e electronmicrographs ,ma yb econsidere dimpermeable .Assumin gthe m tob esphere swit ha diamete ro f 10ym ,an deffectiv ee t ob e 0.5 (seeabove) ,w e findfro mEq .4.19B=3x1 0 .Experimentall -13 yw e foundunde rstandar dcondition sB = 2x1 0 and4 x-11 03 forgel s-1 3 ofreconstitute dan dfres hski mmil krespectively . Wewil lcontinu ethi sdiscussio nlate rwhe nw edea lwit hth e influenceo fth eporosit yo rconcentratio no nth epermeabilit y coefficient. B) Bchange dwit htim e Thislead st oth econclusio ntha tth estrand s inth enetwor kar e rearrangedo rchang ei ndiameter ,o rboth ,Th efac ttha t Bi s 28 increasing implies thatth ematri xbecome s lesshomogeneou s and/or thatth ediamete ro fth estrand so rth emicelle s isreduced .Th e latterindee dhold s forcasei nmicelle s andrenne tcur dwhe nth ep H falls (unpublishedresults ,Walstr a& Delsing) .Strand sa sa whol e mayb e reducedi neffectiv ediamete rwhe nth estrand sbecom eles s frayed.Thi s canb esee ni nelectro nmicrograph s (Knoop, 1975). A lesshomogeneou s gelwoul dresul tfro mrearrangemen to fstrands .Thi s canoccu rwhe n strandsar emove db yBrownia nmotio no rb y deformation (slightvibrations ,a soccu ri na building ,migh tb eenough )an dar e thusanable dt otouc han d formne w crosslinks.Tw oexample s aregive n inFig .4. 7 and4.8 .A s aresul to fth enewl y formedcross-link sth e strandswil lb eunde rstress .An d thematri xwil l eitherrela xb y shrinking (syneresis)or ,especiall ywhe nth ege li sfixed ,b y breakingo fbond s (micro-syneresis) (seeFig .4.7) .Th ebroke nstrand s whichhav emor e freedomt omov ema y fuseagai nwit hothe rstrands .Th e latterste pcertainl y enhancespermeabilit y asth einterfac ematrix - wheywil ldecreas e andmos t likely thepore swil l enlarge.Micro - syneresisma y thencontinu eunti l thestrand sar es origi dtha tthes e processes stopo rmacroscopi c ruptureoccurs . dB/dtwa s constantwit htim eunde rth eapplie d circumstances (withinth elimi taccurac yo fth eexperiments )excep t ford B /dt for a shortwhil e (i.e.withi n 1hour )afte rrenne tadditio n (standard conditions).A nexplanatio nfo rthi s linearitycoul dno tb egiven . C) Bincrease dexponentiall ywit hdeformatio n asmeasure dwit hth e torsionfluxmetho d and increasedmor ea thighe rtemperature . The strandswil lbrea ka ta certai nyiel d stress.Probabl y this impliestha tth eyiel d stressvarie s amongstrands ,an d insuc ha wa y thatth enumbe ro fstrand s thatbrea kincreas eexponentiall ywit hth e applieddeformation .Whe na stran d isbroke nth eresultin g freeend s nowhav emor e freedomo fmovement ,henc ea greate rprobabilit y to touchanothe rstrand ,formin gne wcrosslinks .Thi swoul dresul t in widerpores ,henc ea highe rpermeability . Note thatth edeformatio ni nth etube sdepend so n dPjàx and onth erigidit yo fth ege l (seeSectio n 7.3.3). 29 Fig. 4.7 Schematic drawings of two strands formingne wcrosslinks . This resultsher e (inthi sparticula r example)i n shrinkage of the network and thebreakin g of the strand.Arrow s indicatene wcrosslinks . D) Thedependenc eo fth epermeabilit y onconcentratio n ispoorl y predictable frompreviousl ypublishe dmodels . Themode l of Iberall predicts that B <* e/(1-e),whil eexperimen - tally B« (1/1 -e ) " was found.Th emode l restso nth e assumption thatth e thickness ofth estrand s isconstan t and that thevolum e fractiono fth estrand s iss o lowtha t anymutua l effectso f the strands onth e flowdisturbanc e arenegligible .Particularl y the latterassump tiondoe sno thol di nou rcase .Th emode l ofKozeny-Carma nwit h d = 0.1 pmgive sbette rresults . (E.g.fo r2 x concentration the equation predicts BQ (i = 0.5)/BQ (•£= 1)= 0.20,whil e experimentally 0.15 was found;nevertheles s thismode l isusuall y considered tob erestricte d tosystem swit h aporosit y lowertha n0.5 . Ifw e assumeth ecur d tob e amatri x ofimpermeabl e 'spheres'o fabou t 10ur ndiameter ,a s discussed in Section 4.4A ,thes e 'spheres'shoul d increase indiamete ro r decrease intota lvolum ewhil e edecrease s duet oconcentration ,i n Fig. 4.8 Zipperlike crosslinking of two strands 30 ordert ofi tth emode lt oth eexperimenta l results.Fo rinstanc ei f i =0. 8th ediamete rshoul dincreas et o1 1y mo rth esphere sshoul d compriseonl y 581instea do f60 $o fth evolum eo fth egel .Electro n micrographs indeedsho wtha tth emicelle si nth ecur dmad e from2 o r 4 foldconcentrate dmil kar epacke di nlarger ,mor ecompac tregion s (Green,Turve y &Hobbs ,1981) . E) Thepermeabilit yo fth eski mmil k inth eexperiment sdescribe d in Sections4.3.2. 6an d4.3.2. 9wa salmos ttwic ea shig ha sth e permeability ofth ereconstitute dski mmilk .A nexplanatio ncoul db e thatthi si scause db yth edenaturatio no fth ewhe yprotein ,althoug h lowhea tpowde rwa suse do ri scause db yth eslo wequilibratio no fth e reconstitutedski mmilk .Th epermeabilit ymigh tals odepen do nth e seasonalvariatio ni nmil kcomposition . Inth eexperiment s someothe r factorswer evarie d (composition, temperature).Fo rmos to fthes e factorsther ei sa correlatio nbetwee n clottingtime ,rat eo fsyneresis ,permeabilit y and rheological properties.W ewil ldiscus s theseaspect san dsom easpect stha tar e alreadymentione di nthi ssectio nan di nSectio n 7.3.3. 31 5 THERHEOLOGICA L BEHAVIOURO FCUR D 5.1 INTRODUCTION Theviscoelasti c propertieso fcur dca ngiv e information about gelstructur ean dchange s therein.I tma ythu s enhance understanding onwha thappen s during syneresisan dparticularl yo nth eeffec to f deformationo nsyneresis . Tuszynskie tal . (1968)studie db ymean so fa torsiomete ran da trombelastograph therat eo fincreas eo fth eso-calle d average complex rigiditymodulu so frennete d skimmilk.Thi smodulu si sa measur eo f theelasticit yo rfirmnes so fa gel .Th eprincipl eo fthes etw o apparatusi sth esame .Th ege li sforme dbetwee ntw ocoaxia l cylinders. Theresistanc eo fth ege l against deformationi smeasured .The y found, for instance,tha ti nundilute dmil ka fal li np Hfro m6.6 6t o6.1 8 doesno taffec tmaximu m firmness.Fo rth esam epurpos e Scott Blair (1957)use da napparatu s describedb ySaunder s (1953),whic h itselfi s amodificatio no fa metho dpropose dmuc h earlierb yKinke lan dSaue r CI925).Hereb yth ege li smad ei na nU-tub ean ddeforme db yconstan t airpressur eo non esurfac eo fth esample .Fro mth e volumetric dis placemento fth eothe r surfacea ta certai npressur eth erigidit y modulus (comparablet oa ninstantaneou smodulus )wa scalculated .Th e changeo fthi smodulu s during settingwa s givena sa functio no ftime . Torado (1969)an dHossai n (1976)use dth etrombelastograph .Th e influenceo fvariou s factorso nth erheologica l behavioro fcur dwa s studied.I ncontras tt oth eresult so fTuszynski ,Hossai n founda smal l influenceo fp Ho ncur d firmness,i fth ep Hwa s varied from6.7 0t o 6.51. Furtherpublication s aboutrheologica l behavioro fcur dar eb y Douillard (1973),Burnet te tal . (1963),Jacque t (1964),Marçai s (1965), Frentz (1965)an dThomaso w (1968). The typeo frheologica l parametermeasure dan dit smagnitud e depend e.g.o ntim e scale,exten to fdeformatio nan dsiz ean dshap e ofth esample .Sinc edifferen t authors generally useddifferen t types ofapparatus ,yieldin g different rheologicalparameters , comparison ofresult si sno teasy .Fo rth erheologica l characterizationo fth e curdw edefine dmodul i thatca neasil yb euse dfo rfurthe r calculation 32 andar egenerall y acceptedb yrheologists . Twotechnique swer eused .First ,dynami cmeasurement swhic har e especially suitedt oobtai nth eviscoelasti c propertieso fth ege la s a functiono ftim eafte rrenne tadditio nan da sa functio no fth etim e scaleo fdeformation .Second ,cree pmeasurement swer euse dt ostud y theregim ewher e irreversiblebreakdow no fth ege lstructur e occurred. Bothtechnique s gavee.g . informationo fth erelaxatio nbehavio ro f thegel san dth epoin ta twhic h irreversible changei nth estructur e ofth ege l starts. 5.2 METHODS 5.2.1. Dynamic measurements with the "DenOtter" rheometer Therheomete rwa sdevelope dan ddescribe d extensivelyb yDuise r (1965)an dDe nOtte r (1967).I nbrief ,th eapparatu s consistso ftw o coaxial cylinders.Th einne ron ei ssuspende dbetwee na torsio nwir e anda strai nwir ean dha sa lengt ho f1 5c man da radiu so f3.7 5mm . The outercylinde rha sa ninne rradiu so f4. 5mm .Th ege li sforme d inth espac ebetwee nth ecylinders .Th ewhol e apparatusi sthermostate d towithi n0. 1 C. The torsionwir ei sconnecte dt oa driv eshaf ttha tbring sth e wire,an dthu sth einne rcylinder ,i nharmoni c oscillation.Th efrequen - -4 1 cy (Ü)) canb evarie dbetwee n2 x 1 0 and30 0rad- s .Th eamplitud e differencean dth ephas e shift (6)ca nb emeasured . Fromthes eth e storagean dth elos smodul i G'an dG "ca nb ecalculated .Th estorag e modulus (G')i sa measur efo rth eenerg y stored duringa periodi c applicationo fstrai no nth egel ,an di sthu sa measur efo rth e elasticityo fth egel .Th elos smodulu s (G")i sa measur efo rth e energy dissipated.I nformula e G' =( ö(/Yo) C0S ô Si n 6 G"= (ö 0/Y0) inwhic h 33 an =maximu mshea r stress Yn= maximu m shear strain A comprehensive discussioni sgive nb yFerr y (1970).Correc t valuesfo r G'an dG" ar eobtaine di na neas ywa y onlyi fth evisco - elastic deformationo fth ege li slinear ,i.e .a tconstan t frequency ofth e oscillationth e deformationo fth ege lchange s proportionally toth eapplie d amplitude.Fo ral lcurd s linear behaviour appearedt o existi fy < 0.03. 5.2.2 Creep measurements with the "Deer" rheometer Withthi s rotational instrument constant stress canb eapplie db y anair-bearin g induction type electricmotor .Th emomen t canb evarie d -7 -3 between5 x 1 0 and1 0 N«m.Angula r displacementi sdetermine db ya non-contacting electronic sensorwhic hmeasure dth edisctanc e between a circular rampan dth e sensor.Th esampl ewa sbrough tbetwee ntw o -2 coaxial cylinders.Th estres sca n rangebetwee n0.0 5an d60 0N« m . 5.2. 3 Results and discussion The influenceo ftim eafte r rennetingo n G'an dG" i sshow ni n Fig. 5.1.Th emodul ikep t increasingfo ra lon g time( ~3 h) . Lower pHvalue san da highe r rennet concentrationgav ea nearlie r increase in G'an dG" (whic hagree swit hth eshorte rclottin g time)an dals o high rates.However ,th efina lvalue so f G' onlyvarie dbetwee n 110 _2 and14 0an dfo r G"betwee n3 4an d4 3N« m . As discussedi nSectio n 4.3.2.2,permeabilit y also increasedwit h time.Electro nmicrograph sa spublishe db yKnoo p& Peter s (1975)showe d a changei nth eappearanc eo fth ege lmatrix .On e hourafte r renneting thestrand si nth ematri xwer e frayed.Thre ehour s laterthe ywer e morecompact .Suc ha chang ema y causea nincreas ei npermeabilit yan d inmoduli .Th elatte rma y alsoo reve nmor e increaseb ya nincreas e ofbond sbetwee n already attachedmicelles .A sdiscusse di nSectio n 4.4,strand sma ybreak .Th eresultin gan dalread y existing spoiled strandsma yfus ewit h otherstrings .Thi s createsbot h thicker, i.e. firmer,strand san dlarge rpores .Thu smodul i andpermeabilit y increase. 34 logG INm'*) logG" INm-'l 0 1 2 3^56 time after rennet addition I h) Fig.5. 1 Storage (G')an dlos s (G")modulu sa sa function.o ftim e afterrenne taddition .Standar dconditions :ü )= 1.0rad» s .Temperatur e 30°C . pH= 6.6 5 rennet25 0pp m pH= 6.6 4 rennet25 0pp m — .— .— pH= 6.5 5 rennet25 0pp m — . .p H= 6.4 5 rennet25 0pp m pH=6.65 rennet50 0pp m Fig.5. 2 showsth emodul iG 'an d G"a sa functio no fangula r frequency.Th emeasurement swer estarte dafte rth emodul io fth ege l didno tincreas ean ymor e (e.g.3- 6 h). Therewa sn osignifican t differencei nth edependenc eo fth emodul io rangula rfrequenc yi fth e pHwa svarie dbetwee n6.4 0 and6.6 5 (seeals oFig .5.1) .G' and G" increasedwit hw ,whil e G"/G' (=t g<5 )decrease d (seeFig .5. 2) . Itca nb eshow ntha t G"i sdu et oth erelaxatio no fbonds .A nenerg y contento fonl ya fe wk Tpe rbon dwoul dthe nb esufficien tt oexplai n themagnitud eo fG" ,whil eth eenerg ydissipatio ncause db yflo wo f thecontinuou sliqui dthroug hth ematri x (eitheraroun do rthroug hth e strands)i sver ymuc hlowe r (VanVliet ,t ob epublished) .Fo rw < 0.5 rad'S ,whe nth ege li sunde rstres sfo rperiod so fir/0. 5s ,th eslop e of G' andth emagnitud eo ft gô increase da sa functio no fw .Bot h phenomenaindicat etha tth esyste mha smor eth echaracte ro fa flui d 35 log G (Nm' log G"( Nm"2) log u> ( rad s"') Fig. 5.2 G', G"an d tg6 a sa functio no fi ma t 30 Can d- .1 6h afte r rennet addition when thetim escal e increases.Thi s impliestha ta largepar to fth e bonds spontaneouslybrea kan drefor m (relax)ove rtim escale slonge r thanseconds .I tshoul db enote dtha tthi sdoe sno timpl y thatwhol e strands inth enetwor kar ebroken .Man ybond s ina stran d canbreak , stil]leavin gth estran da sa whol eintact .Fro mth ecree pcurve si t canroughl yb ecalculate d (Ferry,1970 )tha tth erelaxatio ntim eis , say,1 0- 50s . Fig. 5.3 showsth e instantaneousshea rmodulu s (GQ)a sa function ofth eprotei nconcentratio nfacto r {j?r= protei nconcentratio no fth e sample/proteinconcentratio no forigina lski mmilk) , forvariou stime s afterrenne tadditio n (t) .Fo rno tto ogrea tvalue so f -pr, pr "r . Theski mmil kwa sconcentrate db yultrafiltratio na sdescribe d in Section 2.5 Exceptfo ron emeasuremen twit ha lowervalu efo rG. , (probablycause db y a longerclottin g time)th eresult sfi treasonabl y well toth eequation : 2.7 (5.1) G0= G0(p, 1)pf Ifa nincreas e inconcentratio nonl ywoul dresul ti na nincreas ei n thenumbe ro fstrand so fth esam ediameter ,theor y (seee.g .Va n Vliet, 1978)woul dpredic tG „t ob eproportiona l top f. Therear etw o possibleexplanation s forth ediscrepanc y inth e literature.Firstly , theproportio no fspoile d strandswil l decreasewit h increasing pf. 36 logG 0(N.rf?) Fig. 5.3 Instantaneous shearmodulu s (G.)a sa functio no fprotei n concentration factor (p.).Paramete r istim eafte rrenne tadditio n (t) Secondly,th edistributio no fth estrengt hove rth estrand si swide r ata lowe rp f (Vande nTempel ,1979) .Bot hexplanation sar ebase do n anonl ypartl y effectivecontributio no fth ecasei nt oth enetwork . Aprecis ephysica l explanationfo rEq .5. 1canno tb egiven . Fig.5. 4 givesth eshea rstrai na sa functio no fshea rstres sa s determinedfro mcree pcurves .Th estres swa sapplie d1 h afte rrenne t addition.Paramete ri sth eduratio no fth eapplie dstres s (t) .Th ep H ofth ecur di nFig .5. 4 was6.65 .A tth emomen tn orea lexplanatio n canb egive nfo rth ebehavio rshow ni nFig .5.4 .I teve ni sno tknow n forsur ewhethe rth eincreas ei nGibb s freeenerg yo fth enetwor k causedb ydeformatio nstem s froma chang ei nentrop y (Flory,1953 )o r inenthalp y (Lyklemae t al.,.1978 )o rboth .Th eshap eo fth ecurve s resembles thato fa nidea lentropi egel ,althoug hth elinea rregio n ismuc hsmaller .A possible ,thoug hspeculative ,explanatio ni stha t theincreas e stems fromth esam ecaus ea sth eincreas efoun dfo rnon - idealentropi egel s (Treolar,1975 )and/o rfro ma nincreas ei nnumbe r ofelasticall y effective strandsb ymean so fa nentanglemen twhic h 37 Fig. 5.4 Shearstrai n (y)a sa functio no fshea rstres s (a).Paramete r isth eduratio no fth eapplie d stress (t) .Th ep Ho fth ege lwa s6.65 . startst owor ka thighe rdeformation s (Ferry,1970) . Besidesi ti s alsopossibl etha tenthalpi ceffect s likebendin go fstrand sstar tt o playa mor e importantpar ta thighe rdeformation s (Baileye tal. , 1977). Atp H= 6.6 5 andy ~ 1- 1th eslope so fth ecurve sincrease . Probablyth enetwor kstructur egraduall ystart st obreak .Th ecurve s endwher eth egel sbreak .Sinc efo rt =90 0sa tp H=6.6 5th ebreakin g stresso fth ematri xwa s^ 1 0Pa ,w econclud etha tth esyneresi spres sureshoul db ebelo wtha tvalue . Atp H= 6.5 4th ecur dwa s firmer.A smalle r y(a,t )fo ral l valueso f aan d t wasfound .A tp H= 6.5 4th eslop eo fth ecurve s increaseda t y~ 1- 3an dfo rt =90 0sth ebreakin gstres swa s2 5Pa . Sow econclud etha ta tp H= 6.5 4syneresi spressur ei slowe rtha n2 5Pa . Fromth ecree pcurve sals oa relaxatio ntim eo f^ 3 0s coul db ecal culated (VanVliet ,t ob epublished) . 38 6.TH EMDDE L 6.1TH EDIFFERENTIA LEQUATIO N Themode li sbase do na nanalytica ldescriptio no fth etranspor t ofwhe y insideth ecurd .Fo ra preliminar y descriptionw estar tfro m a fixedcartesia ncoordinat esystem .Late ro nw ewil ltur nt oanothe r coordinatesyste mtha trefer st oth ecur dmatri xa sa referenc e system. Thusw ewrit ea mas sbalanc eove ra stationar yvolum eelemen t àx Ay Asthroug hwhic hth ewhe yi sflowing : .rateo fwhe y , ,rat eo fwhey , , rateo fwhey , accumulation ~ goingi n " goingou t (6.1) or (informula ) Ax Ay Az j^-Ay Az {(e ^ ^ - (e Pl „* ) ^ + ^ } + vl ) + + AxAs {(ePi"J)|y- ^H yï\y+Ay } + AxAy ((EPl/)|3 -^Pl^)|2+ AB ^ where: t = time e= porosit y (i.e.volum efractio no fwhey ) p,= densit yo fwhe ywhic hi sassume dt ob eindependen to ftim ean d position v =loca lvelocit yo fth ewhe yi nth ex-directio n (i.e.e p v =bul k mass fluxpe runi tcros s section) |x =a tpositio nx Wedivid eth eequatio nb y(A xAy Ax )an dtak eth elimi ta sthes e dimensions approachzero . 3(ep ) 3(eP , v h 3C eP vb 3CeP , vh ^ i= ±—•£ _ -1 ¥ _ L_£= _ y.{ p th U 3x dy 33 E vlEV (6.3) 39 Thisi sth eequatio no fcontinuity ,whic hi nthi scas edescribe s therat eo fchang eo fwhe yconten ta ta fixe dpoint ,resultin g from thechang ei nth emas svelocit yvector .W ewan tt oreplac e v byth e permeability coefficient (5)an dsyneresi spressur e (P).Clearl ythi s ispossibl ei fw efirs t introduceth erelativ evelocit y (v - v) of theliqui dwit hrespec tt oth ecur dmatrix .I nth etheor yo fbinar y diffusionth eus eo freferenc ecomponen t centeredvelocitie sha s beendeveloped ,wher eth evelocit yo fon ecomponen ti sexpresse da s thevelocit ywit hrespec tt oth esecon do rreferenc e component. The "Fickian"for mo fth emas sbalanc ei nth ereferenc e component centereddescriptio ni st ob efoun di nth eliterature .Va nde rLij n gavea usefu l reviewi nappendi xA o fhi sthesi s (1976).Quotin gVa n derLij nw estar tfro mhi sequatio n (A39)wher ew esubstitut eou r notation. (^P S|(TPFTP-^ÄP1 •* ~ = TT + vS'V =th esubstantia lderivativ eoperator , describing changeswit htim ea ta poin t movingwit hth evelocit y y ofa loca l volumeelemen to fth esoli dmatrix . P =th edensit yo fth esoli dphas e As thedensitie s P and P\ areconstan tw edivid ebot hside s s 1 by P,an deliminat eP . ' 1 s Byinsertin gth erigh than dpar to fEq .6. 3w eobtain : 1 s 1 s (1-e)j £ (-j| -) = - V-itv } +V-{eu }= - V-leC? - u )> (6.5) Forou rexperiment sw euse da one-dimensiona l system.S oV ma y bewritte na s-- -. Introductio no fth ela wo fDarcy : r+s ->i B dP e(y - v ) = — -j- 40 ando f d(^)=d(-^) thenlead st o Herew e leaveou rorigina lstif fcoordinat esyste man dtur nt o ane wsyste mtha ti sfixe dt oth eshrinkin g solid phase ofou rmixture . Clearlyth esubstantia ltim ederivativ e inth eol dsyste mequal sth e partial timederivativ e inth ene wsystem .Moreove rw ehav et ointro ducea ne w localcoordinat e thatmus tsatisf y dw= (1- e)d x Introductioni nE q 6.6 yields ^_fJ_1=3_r B(l-e)aP , U L1- eJ 3ul n 3u If Pwer ea uniqu efunctio no fth eporosit y eth epressur egradien t inth ene wcoordinat esystem ,dP/d wma yb ewritte na sdP/de.de/dw ,whil e also (l-e)de= (1-e) d(l-e3 ) .Introductio -1 ni nth eequatio ngive s 3 r 1 ,3 ,B(1-e) P'3 f j_n L1- e } 3w x n 3w L1-£ J inwhic hP ' isth efirs tderivativ eo fP(e) . CallingB(1-e) 3P'- = Z>w eobtai nth e"Fickian "for m "3T( T^i ")= 'S « {Da? (1~)} (6.7) The latterequatio ni sth eequivalen to fVa nde rLijn sequatio n (A.46) . Boltzmann (1894)showe d (seee.g.Cran k (1975))tha t forcertai n 41 boundaryconditions ,an dprovide d Di sa functio no fe only ,e ma yb e i expressed interm so fa singl evariabl e w/lt2- andtha tEq . (6.7)ma y thereforeb ereduce dt oa nordinar ydifferentia lequatio nwit hon e newvariabl e n, where i n= \w/t2 (6.8) So that Eq. (6.7) becomes -, d 1 _ d ,n d 1 . m J ~ an VF~ "d^ ^ ~&L "FF (6.9) Iti sonl yi fth einitia lan dboundar ycondition sca nb eexpresse di n termso f nalone ,an d t and war eno t involvedseparately ,tha tth e transformation (6.8)ca nb eused .The yca nb eused ,fo rexample ,whe n syneresiso fa thi nsla boccur san dth eporosit ya tth edeepes tlaye r ofth esla bi sstil lunchange d (i.e.durin g thepenetratio nperiod) . 2 Ifth etransformatio ni sallowe di tals ofollow stha t w a t(fo r i constante )an d M a t2; Ml= shrinkag eo fa thi nsla b (seeFig .6.1) . Somemethod s ofsolvin gEq . (6.9)ar egive ni nth eliteratur e (Crank (1975),Philli p (1969)). 6.2NUMERICA L SOLUTION Theapproac hdescribe di nsectio n6. 1 isno tsatisfactor y for several reasons:w eha dt opostulat eP an d Ba sa uniqu efunctio n ofe .S o thequantit y Dintroduce di nequatio n (6.7)shoul db e exclusivelydependen to ne t oallo wa nanalytica lsolution .Bot h assumptionsar euntenable . Asw ehav esee ni nSectio n4.3.2. 3B changeswit htime ,eve ni fe remain sconstant .I nChapte r7 i twil l beshow ntha t Pchange swit htim ea swell .Sinc ei ti sver yunlikel y that B.P' remainsconstant ,thi simplie stha t Di stim edependent . Weno wstar tth esearc hfo ra numerica lsolutio nwit ha mor e generalvalidity . Inthi ssectio nw e reporta nexplicit edifferenc e scheme.Fo rtha tpurpos ew econside ra thi nsla bo fcur dwit hinitia l thickness H devidedint o mthi nslice so fthicknes s Ä „-Theorigina l "-'° th thicknesso fth eslice svarie swit hth eposition ,tha to fth e k 42 whey Fig. 6.1 Schematicdrawin go fa thi nsla bo fthicknes s H at t =0 ando fthicknes s H. -A5 ,a tt • T .Th esla bi sdivide di na numbe r ofslice stha tcorrespon dwit hth emathematica lgrid . Inth e experiments thesla bwa s ina horizonta lposition . slicebein g1. 2time stha to fth e(fc-1 ) .Durin gth eshrinkag eth e thickness Ho fth esla b (andconsequentl yth ethicknes so fa tleas t someo fth eslice s k) changewit htim e it) andwit hpositio ni nth e slab (k; 1« k 4 m). Wedefin e actualvolum e h _1 "e0 relativeremainin gvolum e k,t {i) volumea tt» 0 1-e. 'fc,0 k,t In Section 4.3.2.3 i wasalread y definedi na different contexta svolum eo fconcentrate d milk/volumeo forigina l milk. Darcy's lawfo rth eflo wo fwhe yi nth ecur dwa sgive ni nSectio n6. 1 Forth epresen t calculationi ti srewritte na s AP= str, n àx/B where str, isth eliqui d volume flux that flows from slice k into slicfc-1.e Consequentl yw ehav eA P= P .- P , , For(Aar/B )w eintro + duce along thesam e lines Hih-jB,^) C\/Sfe)},bein ga ninter mediate value between theslice s kan dfe-1. Wit h these substitutions the formulao fDarc y turnst o 43 Inou rmode lo fth eshrinkin gproces sth eshrinkag ei sexclusivel y causedb yth elos so fwhey .S ow ema ystat e bkk,t = (strM,t- st%t) At Note that tJ%, isnegative .Substitutin gth eformul ao fDarc yw e obtain p F h +h 1 MM w,t ~ ^ ( w.* ±A_r - P P fe k,t ~ fe-1,tr\, £ fe-1,t .-1 Inorde rt oarriv ea ta mor e convenient calculationprocedur ew e introduce dimensionless variablesfo rth epressur e P, the permeability Ban dth ethicknes s h: \t = \t /P0>& = \t /B0 ™d Lk,t =\ t /Ho , where PQ, BQ and HQar e the values of pressure, permeability and total thickness of the curd slab at t = 0. Introduction of these reduced quantities in the equation yields -1 ALC, . == Ax AX' US.{(S fc+.. 1 . t-~ S,S.A .1 f JÇîliÉ( g^-. +^ -A+ -± ^l ) We have introduced in this formula the dimensionless time variable 2 AX' = (2S0 P0 A*)/(n HQ ) 44 Thevalu eo fAX 'wa s increased foreac htim einterva lb ya facto r 1.005t o1.05 .Durin g the calculation itwa s checkedwhethe r k atr. , A* "*.,—if- being thedifferenc ebetwee nth eshrinkag e calculatedb y additiono f theshrinkag e ofal lth eslice s andth eshrinkag e calculatedb y the flowo fwhe y outo fth eslab ,whic h shouldb e zerotheoretically ,wa s smallertha n1 0 .I-9f itsabsolut e valuewa s greaterth etim e interval was loweredb y 51. ., Finally Aff,/5Qwa sslotte dversu s Kwher e M. =- EZAft ,, an d K= HAK' = \ (6.11) Amajo rproble mi nth eapplicatio no fdifferenc e schemes tohighl y non-linearpartia l differential equationsi stha ti ti softe n difficult toprov e stability and convergencet oa tru e solution.Her e toother ei s no suchproof . However,i nliteratur ew e findmany succesful examples:e.g .Va n derLij n (1976),Kerkho f (1975),Schoebe r (1976)an dD eWi t (1972). Moreover,th enumerica lmetho dwa s checkedb y comparingwit h the resultso fth e analytical solutionwheneve rpossible .Result swit ha n unequally spaced 15compartment s slabwer e accuratewithi n 21. Further moren osubstantia l changes couldb e detectedwhe n thenumbe ro f compartmentso rth e timeinterval swer emodifie dwithi n limits.There forethes esolution s seem tob ereliable . 6.3PARAMETER S (DEPENDENCEO FPRESSUR EO NRELATIV ESHRINKAG EAN DTIME ) Equation (6.10)permit s calculationo fth e changeo fthicknes s (Ai, ,) a tan ypositio n k anda tan y time t ifth econdition sa ttha t time (i.e. L-, )ar eknow n foran y k. Toobtai nnumerica l results, however,w estil lnee dvalue s forth epermeabilit y (3)an d thepressur e (S). Forth epermeabilit y the reader isreferre d toSectio n4.3.2. 3 where thebehaviou ro fth epermeabilit y asa functio no fshrinkag e and timei s already discussed. Inth epresen t sectionw ewil l restrict 45 ourselvest oa discussio no fth epressure .A si s discussedi n Giapter3 ,th epressur eexerte do nth ewhe y iscause db yth eendogenou s stressi nth estrand s (P) an db y theweigh to fth ematri x (P^): p = pS + F& As thematri xshrink sth epressur eo nth ewhe y diminishes,sinc ea ta certaindegre eo fshrinkag e (i.e.whe n i =1/3) ,syneresi s stops,s o P= 0 .I fonl yendogenou s syneresis occurs,P = 0 mean stha tth e tendencyo fth ege lt o swellexactl ycompensate s thetendenc yt o shrink.I fonl ygravit y acts,P = 0 mean stha tth eelasti cforc e resulting fromcompressio no fth ematri xcompensate s theweigh to fth e matrix. IfP ^= 0 ,als oP =0 bu ti ti sno tknow ni nwhic hwa yP an d P° decreasewit h i. However,i tmus tb e assumedtha ta s longa s endogenous syneresisoccur s (i.e.P >0) , alsoP ^> 0 .Thi si s becausea matri xwit h anendogenou s tendencyt oshrin k (P) wil lals o yieldt oan yexterna l force (sucha s P*). Itma yb es otha t P°= àp'g-h isindependen to f i andonl y s *" 2 becomes zerowhe nP does;however ,i ti smor elikel y thatP 6wil l startt odiminis ha thighe rvalue so f i. Iti sver y likely thatP . , willmonotonousl y andrathe r smoothly decreasewit h increasing -i, .Therefor e fivetria l functionswer e introduced,takin gthi s intoaccount .A sa genera l formo fou r relationbetwee n P7 and i, ,w eadop t Fk,t =P D {a{ik,t "1/3) 2+ b(-%t "1/3) } (6-12) withdifferen tvalue s for aan d b. AsP , =P « for i =1 w ehav e Aa+ 6b =9 . Fouro fou rtria l functions areno wfoun db yvaryin g thestartin g valued(Pj * /PQ)/di at i =1 ,tha tw ecal l a. Wese ea tonc etha t c= (4 a+ 32>)/3 .Solvin g a and bwit hrespec t to aw e find b =3- a and a= 3/2 e- 9/4 . Introducingc = 3 ,8/3 ,7/ 3 and2 successivel yw efin dth efou r parabolic trialfunction srepresente d inFig .6.2 .Th efift htria l functiono fFig .6. 2i sdefine das : 46 P(k,U/P(k,0) 1.2-1 O 0.2 0A 0.6 08 1.0 h(k.l)/h(k,OI Fig. 6.2Tria lfunctions ;S-shape d curvean d (goingupwards ) o= 3 , 8/3,7/ 3 and2 (seetext) .Syneresi spressur ea sa functio no f porosity. pk t= 27Po {("i3+ 2 *2" * )/4}+^ (6-13;) which leadst oa hS-shape dcurve . Forsak eo fsimplicity ,w eassume dth eeffec to fgravit y either todiminis h linearlywit h i ort ob e constant for i > \ andthe nt o diminish linearlywit h i, P&becomin g zero for i =1/3 .Othe rtria l functions didno tmateriall y improveth efi tbetwee n theory and results.P ?depends ,o fcourse ,als oo nth ethicknes so fth e layer above k.Thes econsideration s leadt oth efollowin g formulafo rth e pressure (onth ewhey) : k -(? \o - ihk^ p + J V3 ) (6J4) \t - lt * b T0 t-^M" inwhich : P?= pressur e causedb yth eweigh to fth esla ba tth ebotto mo f thesla ba tt =0 . 1.5(H +" 1/3 )denote s the fractiono fth epressur etha ti slef t incas eP &decrease s linearlywit h i incas eP 8decrease s linearlywithi . Aswil lb e shown later P andP *als odepen do ntim ewhe n ii s keptconstant . InEq .6.1 1P „i ssubstitute db yP. . 47 7 SYNERESISO FTHI NSLAB S (testingth emode l experimentally) 7.1 INTRODUCTION Asmentione dearlie r (Section6.1 ) themechanis mo fsyneresi si s easiestexamine di fth eflo wo fth ewhe yan dth eshrinkin goccu ralon g thesam eaxi s (one-dimensionalmodel) .Moreover ,th eflo wan d shrinkageshoul dno tb edisturbe db ysid eeffects .Thi sca nb e achievedb yusin grelativel ythi nslab so fcurd ,s otha ta regio ni n thecentr eo fth esla bremain spla nparalle l (i.e.withi nth eaccurac y ofmeasurement) . 7.2 METHODS Whencur di sforme di na va tan dth ecur dkeep sadherin gt oth e wallsi twil lno tshrin kb ysyneresis .Als oa tth ecurd-ai r interface thecasei nmatri xwil lno tshrink ,becaus ethi ssurfac ei sno teasil y wetted.Syneresi sstart safte rth ecur di scu to rth esurfac ei swette d (seeSectio n 2.6).Th elatte rwa s donei nth e experiments. Drops falling onth ecur dsurfac ean dwhe y floodingth edr y surfaceeasil ydamag eit .Therefor eth efirs tportion o fwhe y(o r water)wa spu tont oth esurfac eb ymean so fa fin espray . Twomethod swer e employed formeasurin gth eshrinkag eo fa sla b: I "Shadow"metho d Theapparatu suse di sshow ni nFig .7.1 .Th etriangula rblad ewa s sliddow nunti li ttouche dit sshado wo nth esurfac eo fth ecurd .Th e heightwa srea dof fo na scal egauge di n0. 1mm .Th efirs treadin gwa s donebefor eth ewhe ywa spoure dont oth ecurd .B ythi smetho da numbe r ofvats ,whic hwer estore di na thermostate dtan kcoul db eexamine d simultaneously.Ever y5 t o1 0minute sa va twa splace dunde rth e apparatusan dth eheigh twa smeasured .Afte rabou t2 hour sha drelapse d longerinterval swer etaken .Th eradiu so fth esla bwa s9 cm .Thi s methodwa sespeciall yuse dt ofollo wth eshrinkag eo fa sla bfo ra longtime ,allowin gth esla bt oshrin kt oequilibrium . 48 I light source lens W. Fig. 7.1Schemati cdrawin go fth eapparatu sude d tomeasur eth e syneresisb yth eshado wmethod ,wit hfiel do fvisio ndraw ni nth e circle.Th eradiu so fth esla bwa s9 cm . II "Microscope"metho d Amicroscop ewit h obliqueillumination ,employin ga water - immersionobjectiv ewa suse di nconjunctio nwit ha speciall y designed thermostatedva tholdin gth esla bo fcurd ;se eFig .7.2 .A ta fixe d timeth ecur dwa swette db yfirs tsprayin gan dthe nfloodin gwit h whey.Syneresi s thenstarted .Th emicroscop ewa s focusseda ssoo na s possibleo non eo fa fe wcorundu mgrain ssprinkle do nth esurfac eo f thecur dan dth efocussin gheigh twa s reado nth escal eo fth e micrometerkno bo fth emicroscope .Th efirs treadin gcoul db emad eon e ortw ominute safte rstartin gth ewetting .Ever y3 0second sth e microscopewa sfocusse dagai nan dth e (reduced)heigh to fth esla bwa s readoff .Afte r 10an d2 0minute sth etim e intervalwa sdoubled , and latero neve nlonge rtim einterval swer etaken .Th edept ho ffocu swa s M pman don euni to nth emicroscop e scale correspondedwit h2 ym . Theradiu so fth esla bwa s5 cm .Thi smetho dwa smor eaccurat etha n thepreviou son ei nth esemi-interva lbetwee n1 o r2 minute san dabou t 1hour ,thoug hth eabsolut ezer ocoul dno tb edetermined . 49 objective I water -—• two-fluid spray nozzle whey tube curd Fig. 7.2Schemati cdrawin go fth eapparatu suse d tomeasur eth e syneresisb yth emicroscop emethod .Th eradiu so fth esla bwa s5 cm . 7.3 RESULTSAN DDISCUSSIO N 7.3.1 Testing the model Thefirs t experimentswer edon ewit hslab so fvariou s diameter andheight ,i norde rt ofin dth einfluenc eo fthes evariable so nth e shrinkagei nth emiddl eo fth eslab ,wher eth esyneresi swa smeasured . The shadowmetho dwa sused .A sth esla b stuckt oth ewal lth eheigh t ofth esla bremaine d thesam ether ean dshrinkag ewa sa tmaximu mi n themiddl eo fth eslab .W efoun dtha ti fth eradiu so fth esla bwa s v|0time sth eorigina lheigh to fth eslab ,th eshrinkag ei nth e middleo fth esla bremaine duninfluence db yth esiz eunti l equilibrium wasreached .The na nare ai nth emiddl eo fth esla bwit ha radiu so f 2t o3 c mremaine d flat (differencei nheigh t lesstha n0. 1 mm). InFi g7. 3doubl elo gplot so fth eresult so fth eshado wmetho d aregive nfo rslab so fdifferen t thicknessunde r standard conditions (seeSectio n 2.7).A curv ewa smanuall y drawn throughth eexperimenta l points resulting from3 t o1 0replicat eexperiments .Th eaverag e deviationo fth eexperimenta lpoint sfro mth ecurv ewa s0. 1mm . The graphssho wtha t initiallyth eshrinkag eo fth esla bwa sindependen t ofit sorigina l thickness.Th ethinne rth esla bth esoone rth ecurv e deviatedfro mthos eo fthicke rslabs .Th edeviatio ni sexpecte dt o occurafte rth epenetratio nperiod ,i.e .a ssoo na sth eslab sals o startt oshrin ksignificantl ya tth ebottom . Afterabou ton eda yth ethicknes so fth eslab sha ddecrease dt o about1/ 3(rang e0.2 7- 0.37 )o fth eorigina lvalue .Th eresult so f 50 time(h ) Fig. 7.3Shrinkag e (Äff)a sa functio no ftim e (botho na lo g scale). Parameteri sth eorigina lthicknes so fth esla b (inmm) .Th edot s (•) indicate2/ 3o forigina l thickness.Number s indicateorigina lthicknes s ofth esla bitself . theslab so f1 0an d2 0m mwer e fittedt oa straigh tlin eb yregressio n analysis;her e r= dlogAH /dlog t= 0.78 . Fig.7. 4show sdoubl elo gplot sfro m4 experiment sunde rstandar d conditionswit hth emicroscop emethod .Th ethicknes so fth esla bwa s 5mm .Fo rth eshrinkag eo fth esla bdurin gth efirs tminut e0.0 4t o 0.08m mwa staken .I nthi swa yth eresult so fthi smetho dagree dwel l withth eresult so fth eshado wmetho dfo r0. 2h < t < 3 h wher ebot h methodswer eused . For t <0. 1h ,r i sno treliable .A swil lb ereasone dlate rr i s expectedt ob e"x-0. 5fo rsmal lvalue so f t. Theresult sobtaine dwit h thismetho dar eno ta tvarianc ewit hsuc ha value . Fig.7. 5show sWa s afunctio no f* o na linea rscale .Agai nth e experimentswer edon ea tstandar dcondition san dth emicroscop emetho d wasused .Th ethicknes so fth eslab swa s5m mexcep tfo ron ewhic hwa s 10mm . Fig.7. 5suggest stha tth eshrinkag erat eo fth eslab stend st o bever yhig ha s t •*•0 . Fig.7. 6show scalculate dresult sfro mth emode l (Chapter6) . Because Band ,a swil lb ediscusse dfurthe ron ,als oP depend so n t 51 Fig. 7.4 Shrinkageo fa sla ba sa functio no ftim e (bothlo g scale). Forth eshrinkag edurin gth efirs tminut e0.0 5m mwa staken .Origina l thicknesso fth esla bwa s5 mm . independentlyo f i andmoreove rP isdetermine db yth esu mo fP and P^,th egraph sca nonl yb euse dfo ron ecombinatio no fth e characteris 2 p tictim e t/K =n HQ /(BQ PQ)an dPf/ o* Forsak eo fclearnes sno tthes eterm swhic hwer euse di nth e calculationar enote di nFig .7.6 ,bu tspecifi cvalue so fn , SQan d HQ. n ands weretake na stypica lfo rth eexperiment sa tstandar d timeIs ) Fig. 7.5Shrinkag eo f 11slab sa sa functio no ftime .Origina l thicknesso fth eslab swa s5 m mexcep tfo ron esla bwhic hwa s 10mm . 52 conditions.Fo rÄ „ 10m mwa staken ,bu tcalculation swit hothe rvalue s gaveanalogou sresults .Th eothe rparameter swer evaried .Althoug hth e graphsar eonl ycorrec tfo ron ecombinatio no f t/K andP|[/PQ , they approximatecalculation swit hothe rvalue so f t/K andP|f/Pn - Generally 101deviatio ni nth ecurv eresult sfro ma 50%deviatio no f t/K ora 10°*deviatio no f P£/PQ. Onth eX-axi s t = 1h isindicate d witha narrow .I nal lfigure sth eexperimenta lresul twit ha sla bo f 10m m thickness isindicate dwit ha broke nline . Theresult so fth ecalculatio nwer eonl ycompare dfo r t >oO. 1 h and bH/Hç.< v|/3 .A s statedbefor eth evalu eo f Hcanno tb edetermine d accurately for t <'UJ. Ih .Th evalu eo f H(t <0. 1 h)tha tca nb e expectedo ntheoretica lground swil lb edeal twit hlater .Fo r AÄ/Ä« > M/3 themode lwil lb eles saccurate .Th epermeabilit y for i <0. 5 is foundb y extrapolation.Moreove rth epermeabilit yo fa ge lforme db y rennetingultrafiltere dmil kma yb esomewha tdifferen tfro mtha to f a gelforme db ysyneresi sa tlowe rvalue so f i (ifth epermeabilitie s differ). s s Thoughal l fivetria lfunction sfo r P* = P, Ai) (seeFig . 6.2) wereuse di nth ecalculations ,onl y threear eshow ni nth egraph so f Fig. 7.6.Fo rth eto pcurve si neac hgrap h (exceptFig .7. 6G an dH ) theS-shape d curvewa sused ,fo rth emiddl ecurve s a = 7/3an dfo rth e lowercurve s a =3 .Th ecurve sfo r a = 2an d a =8/ 3 gavecomparabl e results. Fig. 7.6 showsth eresult so fth ecalculations .Th eshap eo fth e trialfunction sfo rP , =P , Ai) hasonl ya smal l effecto nth e results.Th edifferenc e isno tonl ydetermine db y theaverag evalu eo f F j, +0-)/PQ . IfP f f {i) decreases more slowlywit hdecreasin g i, the gelnea rth e interfacecurd/whe ywil lshrin kfaste r (seeFig .7.8) . Thusth epermeabilit ywil lals odecreas emor ehere .Th eshrinkin go f deeperlayer swil l thereforeb eretarded . Fig. 7.6 showsth eresult so fcalculation s if Ban dP ar e independento ftim e (atconstan t i). As ist ob eexpecte dfro mEq . 6.9 F =0. 5 (inthi scase )durin gth epenetratio nperiod ,i.e .th eperio d whereth etota l shrinkageo fth esla b isindependen to fth ethicknes s ofth esla bbecaus eth eshrinkag eprofil eha sno tye treache dth e deepestpoin to fth eslab . 53 B= B (constant withtime ) Trialfunctions : e= 3 ,7/ 3an d S-shapedcurve . oê = 0. B= B{t) (see Eq.4.16) . S P 0- !Pa . Trialfunctions : o =3 ,7/ 3an d S-shapedcurve . Pg =0 . J LI M fil L_J I I I I I II J 1 l_l lllll 3 S K -7 3 S i« -1 3 S i« B= B(t )(se e Eq.4.16) . F®= 0 .1Pa . Trialfunctions : a =3 ,7/ 3an d S-shapedcurve . =8 1Pa . Trialfunction : -I 1—I I I I, I U I I L LI II II I I I I I I Ml 3 5 ie -2 3 S i« -1 . 3 S 1» »0 1.5tfM- 1/3) K- b EI gy h H.*) Fig.7. 6Experimenta l ( )an dcalculate d ( )syneresis . HQ= 1 0 B. =0.2 3 pm2. n= 1mPa-s .Th earrow sindicat e t =I h . 54 PQ~ 0.5 Pa. Trial functions: o * 3, 7/3 and S-shaped curve. "Î 1 Pa Trial function: 1.5(iM- 1/3) I I I I I I II P0» • Pa - Trialfunctions ; c=3, 7/3an d S-shapedcurve . P\ -1 Pa. Trialfunction : 1/3) 1« »0 pô • 2 Pa- Trialfunctions : o- 3 ,7/ 3an d S-shapedcurve . P^= 1Pa . Trialfunction : -2 3 5 ,. -. 1.5«fct- 1/3) K- t 8,13V (a H.1) Fig.7. 6Continued . 5- •B(t) (seeEq .4.16 ) 55 PQ 0.8Pa . Trial function: . G a =3 . UI =g 0.8Pa . s • tl I " Trial function: N 'y// I 7 i Us for i > J. J ; S yT III SyS D u) 6(ife É - 1/3) m for 1/3 < i < \. i i i i ili i 11 i i i i i 1 11 i i i i I Mil 3 S u -2 3 5 IJ -1 3 5 10 po = K2Pa- Trial function: a = 3. P? « 0.8 Pa. D Triag l function: P D8 ^0 for i > \. I L_l_l_LLLI_ _l t_]_l_LLU -2 3 S 1< -1 3 6( H 1/3) K- tB.P.V UH. 1) 'M for1/ 3< i < £ . Fig. 7.6Continued . Upper full curve: P independent oftim ea t constant i. Lower curve: Eq.7. 4used . B - B(t) (seeEq .4.16) . If Bincrease swit htim ea tth erat egive ni nEq .4.16 ,th e resultsar ea si nFig .7. 6B .r increase sfro m0. 5fo rt <0.0 1ht o ^0.8fo r K= 0.05 . Upunti lher ew ehav eneglecte dan yeffec to fgravit y (P^= 0). Ifonl yP 8wer eactiv e (i.e.P s= 0),th einitia lr woul db e1 ; if P8 were zeroan donl yP swer eactive ,initia lr woul db e0. 5 (see above).I fbot hact ,a si sth enorma lcas ei nou rexperiments ,r wil l 56 be inbetween .Figs .7. 6C- F showresult sfo rfinit evalue so f Pp and s s (J P«;th ecurve sca nsignificantl y improvean dP „= P ?= 1 P agive sth e bestone .Her eP* *varie s from0 t oP rfro mto pt obottom ;se eSectio n 6.3. Inthes eexample sw eassume dtha tP ?, =P fQ (a:)1.5(i , . -1/3) , where x isdistanc e fromth eto po fth eslab ;i nothe rword sP8(i ) linearlydecrease swit h i until i - 1/3.I nFigs .7. 6G an dH a differentassumptio nwa smade ,viz . P? =P? n for i > \an d an ' ' K t = Fk 0^ 6 ^"k t ~1 ^3-'^ or1 /3< i < \. Thisassumptio nma yb e morerealistic .However ,n osignifican t improvemento fth efi ti s attained.Th ehighe raverag eP ma yb eoffse tb yth emor e rapidly decreasing Bnea rth ecurd/whe yinterface . Stillr = 0. 5fo r t ->-0 .Thi si st ob eexpecte d sincea tth e startshrinkag eonl yoccur sver ynea rth esurfac eo fth e slaban dP ^= 0a tth esurface .A st increasesP decreases fastestnea rth esurface , deeper layerso fth esla bcom eint opla yan d P%become smor e important. Nearth een do fth epenetratio nperio d (when ÙJl/Hç.= 0.1 ) theprofil e ofP isroughl yth esam ea sth eprofil eo fP* ,eithe rha s aboutth e samecontributio nt oth esyneresis ,an dr wil lb eabou tmidwa ybetwee n 0.5 and1 . Iti sals opossibl etha tP depend so ntim e independentlyo f i. Approximatevalue so fthi sfunctio nP(t )ca nb eobtaine d fromth e relationbetwee nP „an d dAH/dt. Ifth e influenceo fdB/dt anddP/d t ando fp fca nb eneglecte dw e findth efollowin g relation,deduce d fromth enumerica lcalculatio na sshow ni nFig .7. 6A : Where Qdepend so nth etria lfunctio n Ps(-t)an dvarie sbetwee n 0.58 and 0.62.Differentiatio nyields : d d B pS ^/y ^/y . d* lfl K-i o o r7 n —dT~ = —dx dJ=2QK "TT t7-1-) nff0 Eliminationo f# Qyields : s ar-»«^' (7-2) 57 Or,rewritten : n t AùJl/àt ,2 (7.3) 0 As longa s Ban dP depen do n i onlywhic hi snearl ytru efo rsmal l t, penetrationtheor yma yb eapplie dfo rsmal l t (Section6.1 )an di n thatcas er = 0.5 .A ssee ni nFig .7. 6thi si sindee dfound ,bot hi n theexperiment san dfro mth enumerica lsolutions ,eve nu pt o t =50 0s . Weconclud etherefor etha tEq .7. 1i sindee da usefu lapproxima tionfo rth esyneresi sdurin gth efirs t1 0minutes .W edi dsom e experimentsusin gth emicroscop emetho di nwhic hw evarie dth eperio d betweenrenne tadditio nan dth estar to fth esyneresi s (t) .A sshow n inFig .4. 4w eals odi dthi si nth epermeabilit yexperiments . The resultso fth ecalculatio no fP Q fromEq .7. 3ar eshow ni npar to f Table7. 1an dFig .7.7 .Fo rth emode lth eequation : Ps= P s(i)(0.2 5- 0.2 5ex p(-9. 9x 10 -4 t/s)+ +ex p(-6. 6x 10 t/s) (7.4) wasuse dfo ral lvalue so f i. (althoughi twa sonl ydetermine dfo r i =1) .Result sar eshow ni nFig .6. 7G an dH .Th eresult sfi tpoore r 1A- 10 Q6 02- u 1 2 3 4 5 18 time after rennet-v additio n ( h) Fig. 7.7P asa functio no ftim eafte rrennetin gunde rstandar d conditionsa scalculate dwit hEq .7.3 ,i nwhic h Q= 0. 6 ( ).Soli d andbroke n ( •)line sfollo wEq .7.4 .Th esoli d linewa suse d inth e model (seeFig .7. 6G an dH) . ( )i sa nassume dextrapolation .Th e arrowindicate sth eclottin gpoint . 58 toth eexperimenta l results.I tshould ,however ,b etake nint o accounttha tth estres si nth estrand seithe rrelaxe sb ysyneresi s orb ymicro-syneresis ,whil eapplicatio no fEq .7. 4implies ,a si t were,tha trelaxatio noccur stwice .Therefor ei ti sno tt ob eexpecte d thatEq .7. 4hold sfo ri « 1. Ofcours ei ti spossibl et ofi tth eresult so fth e calculations withcertai nassumption s exactlyt oth eexperimenta l results.W e couldno t (directly)determin e B{i,£) and P(i,t) foral lvalue so f i andt. Iti sals opossibl e that Ban dP depen do ndi/dt .Bette r resultsca nfo rinstanc eb eobtaine di f Bo rP o rbot hincreas emor e stronglywit htim efo rt - \h .I nadditio nt oth etota lsyneresis , shrinkageo fth esla ba sa functio no fdistanc ebelo wth ecurd/whe y interface (x)i so fimportance .W etrie dt omeasur eit ,bu tdi dno t succeed.Nevertheless ,mode lcalculation sma yoffe rsom e interesting results.Fig .7. 8i sa typica lexampl eo fsuc hresults .Her e PQ => P^ = 1P acombine dwit hEq .7. 4wa staken .P hasth elarges teffec tfo r smallervalue so f xwhil eP *ha sth elarges teffec to nth eshrinkag e atth ebotto mo fth eslab .Thi s explainswh yth ecurve ssho wa maximum.Suc ha phenomeno n (strongersyneresi sa tth ecentr eo fa pieceo fcur dtha na tsom edistanc eo fth ecentre )wil lneve roccu r incur dpiece sfloatin gi nwhey .I ti sa consequenc eo fou rexperimen talconditions ,wher eth eeffec to fgravit yi scomparitivel ylarge . Fig. 7.8 Shrinkageprofile so fa sla ba tdifferen tvalue so fth e dimensionlesstim e (X)an ddifferen ttria lfunction s forP S(-£)/?§ .Fo r t/K -4.3 5 x 105, K= 0.08 5an d0.1 2 correspondends to t - 10an d 14h respectively. X/HQ isth erelativ edistanc ebelo wth ecurd/whe yinter face a= d(Ps/P§)/dt at i » 1.S mean sS-shape d trialfunctio n Ps(i)IPff 59 7.3.2 Effect of some variables Syneresisrate swer eals odetermine da sa functio no fsom e externalVariabl e (seeTabl e7.1) . A) Pretreatmento fth emil k Inth efirs tserie sth emil kpowde rwa s dissolvedan dstirre d for1 h a tdifferen ttemperatures .I nth esecon dserie s themil kwa s cooleda t4 ° Cafte rdissolvin ga t4 5° Can dstore dunti l thenex t day.Th emil kwa s thenheate dfo r1h a tdifferen t temperaturesbefor e rennetwa s added.I nbot hserie sther ewa sa significantl yhighe r syneresisrat ei nth egel so fth emilk stha tha dbee nheate dt o4 5 C ascompare dt o3 0°C . Ifth emil kha dbee nrennete dth esam eda yth e higher temperature mightspee du pattainin gequilibriu m (especiallyo fCalciu mdistri butionbetwee nmicelle san dserum )i nth emil k afterdissolvin g (Jenness& Patton ,1959 ;Walstr a& Va nde rHaven ,1979 ;Snoeren , personalcommunication) .I fmil kha sbee ncol dstore d ß-casein migratest oth emicelle swhe nth etemperatur ei sincrease d (Schmutz& Puhan, 1981).Howeve ra ttemperature s above3 0° Cn ofurthe rmigratio n isfound .Th emigratio noccur swithi nminute s (VanHooydonk ,persona l communication).A bette rexplanatio nfo rth eeffec to ftemperatur ei s againtha tth edistributio no fCalciu mamon gmicelle san dseru m dependso ntemperatur ehistory . B) Temperaturean dp Hdurin gth eexperimen t (including renneting) Inaccordanc ewit h generalexperience ,th esyneresi srat e increasedwit h increasingtemperatur e (27- 3 3 C)an dwit hdecreasin g pH.Thi swa scause db yincreasin gpermeabilit yan dincreasin g syneresis pressure.A t2 7 C Hwa salmos t linearwit h t above t =50 0s . Accordingt oth e modelthi swoul dmea ntha t P « P°. Whenafte r rennetingth etemperatur ei slowere dt o1 5 Co rbelo wn osyneresi s occurs.S obot hP and P° mustb ezero .Th ege l becomesfirme ri fi t iscoole d (VanHooydonk ,persona lcommunication )an dth estati c pressurecause db ygravit yi spresumabl ycounteracte db ya yiel dstres s ofth egel . 60 Table 7.1 Effecto f someexterna lvariable so nsyneresi srate so frenne tgels . #Q =origina l thickness, n = numbero fexperiments .Atf/A t• {H(t =*3000 )- H(t «500)}/2 5s .S ofro mtable s inChapte r4 ,fro m inter-o r extrapolation,o rfro m themos t similar treatment (e.g.effec to fpretreatmen t on BQwa sno tdetermined) . P§calculate d withEq .7. 3 (Q= 0.6) . factorvarie d n 100dAff/d t ÄS/Äi. 100dAff/ d (t-500s) (t-3000s) > (mm) um ) (Pa) pretreatment sameday : 1h a t30° C 5 2 13(12-14) 12(11-12) 11(11-11) 220 0.4 2 1 19 12 8 220 0.9 5 8 22(17-22) 16(12-17) 14(11-15) 220 1.2 10 1 22 19 18 220 1.2 day before:0. 5 ha t 30C 5 5 20(17-22) 18(17-20) 15(14-16) 220 1.0 " 45°C 5 4 22(20-25) 19(18-20) 16(15-17) 220 1.2 5 3 23(20-27) 18(17-19) 15(11-17) 220 1.3 temperature 27°C 5 5 10(09-11) 10(08-11) 10(10-11) 180 0.3 10 1 12 11 10 180 0.4 33°C 5 4 31(29-32) 24(22-25) 19(18-20) 280 1.9 10 4 32(29-34) 27(26-30) 24(32-26) 280 2.0 cooled to5 o r 15C 5 3 1*0 ^0 %o 220 •xd pH* 6.55 5 3 28(26-29) 21(20-22) 16(15-17) 270 1.6 6.75 5 3 20(18-23) 16(12-18) 15(13-16) 200 1.1 timeafte rrenne tin g 0.75h 5 5 15(12-17) 16(14-18) 16(14-16) 200 0.6 2 h 5 3 24(22-26) 21(19-22) 18(16-20) 250 1.3 4 h 5 5 21(18-24) 13(12-15) 12(10-14) 330 0.7 M 8 h' 5 2 13(13-13) 10(09-10) 8(07-08) 1000 0.09 M8 h" 10 2 18(16-20) 12(11-13) 10(09-11) 1000 0.2 water instead ofwhey 5 CaCl-additio n 500pp mCaCl,.2H, 0 5 1 30 18 25 220 2.3 1600 " " 5 1 40 24 19 230 3.9 3200 " 5 1 45 28 21 230 4.9 CaCl,(const,clott . t.)* 250pp mCaCl,.2H, 0 5 1 24 18 15 230 1.4 500 " " 5 1 29 22 22 250 1.9 rennet concentration 200pp m 5 1 20 15 13 250 0.9 1000 " 5 1 22 16 14 230 1.2 acid gels (pH4.6 ) timeafte rpreparatio n 0h 5 1 31 19 11 2.87 1h 5 1 16 8 5 190 0.8 3h 5 1 9 4 3 0.27 M8 h 5 1 4(2-5) 4(2-6) 1(0-1) 120 0.07 i.Da yo nwhic hth e samplewa sprepare d and time(min.)an d temperature (°C)treatmen tafte r thepowde rwa s dissolved,or ,i ncas eth emil kwa sprepare d theda ybefore ,th emil kwa s stored at+ 4° Can d thenheate d at theindicate d time (min.)an d temperature (°C). 2.Rennetin gan d syneresisa tindicate d temperature,excep texperiment s at 5an d 15°Cwhic hwer erennete d at 30°C. 3.Origina lpH :6.65 . (pH:0. 1 unit lowero rhigher ) BQ fromtable s inChapte r4 ,fro m inter-o rextra polation,o rfro mth emos t similartreatment . "i.Tim eafte rrenneting :1 6t o2 0h .On eo fthes eexperiment s proceededfo r2- 3h .Afte r1 h th ecurve swer elinear . 5.Instea d ofwhe ywate rwa suse d tomoiste nan d flood thesurfac eo fa norma lgel . 6.Renne tconcentratio n adjusted toge t thesam eclottin g time (15min. )a swit h50 0pp mrenne tan dn o calciumaddition . _ _|_ 7.Assumin g BQ/T\ = 190ym 2-Pa l-s 1 61 C) Waterinstea do fwhe y Ifwate rwa suse do nto po fth esla b insteado fwhe y syneresis wasno tsignificantl ydifferent .I tma yb eexpecte dtha tdilutio no f whey alsoha s littleeffect .Ther eseem st ob en oappreciabl eosmoti c effecto nsyneresis . D) CaCl2 Syneresisrat eincrease dwit h increasing CaCl,additio n (250- 3200pp mCaCl 2.2H20).Würste r (1934)foun da decreas ei nsyneresi srat e ifmor eCaCl ~wa s added.I tmus tb enote d thatals oth ep Hi sdecrease d byaddin gCaCl- .Whe nth ep Hi sadjuste d LBjH- decreaseswit h increasing CaCl-additio n (0-1500pp mCaCl-^H-O ) (Cheeseman,1966) . E) Acidgel s Qualitatively,th eeffec to fth evariatio no fth eperio dbetwee n formingth ege lan dth eonse to fsyneresi s [t )ha dth esam eeffec t cL onaci dan drenne tgels .B Q,howeve rslightl ydecrease dwit h t in acid gels,whil ei tincrease di nrenne tgels .Thes eresult s suggest thatth eincreas ean ddecreas e (relaxation)o fP occurfaste ri n acidgels . 7.3.3 The relation between clotting of the milk and permeability 3 syneresis (pressure) and rigidity of the owed InChapter s4 ,5 an d7 th einfluenc eo fvariou s factorso n B, P, syneresisrat ean drheologica lbehaviou rwa s determined.I nth e literaturemor e informationabou tthi ssubjec tan dabou tth einfluenc e onth eenzymi can daggregatio n stageo frennetin gi sfound .W ewil l discussal lth eresult si nconnectio nt oeac hother .I tshoul db enote d thatw espea ko fcross-linkin g whenstrand sconnec twit hon eanother , andtha t formationo fbond si smean tt ooccu ro na molecula rscal e betweenmicelles. Th etrend sobserve dar eshow ni nTabl e 7.2. The curvesar eonl ymean tt oillustrat e trends,an dar ethu sver y approximate;moreove r theprecis erelationshi pma yvar ywit hothe r conditions. Whenw ecompar eth evariou sresult sth efollowin gconsideration s 62 Table7.2 .Effec to fsom evariable so nclotting ,permeability , syneresis (pressure)an drigidit yo fcurd .Ver y systematican donl y meant toillustrat etrends ;arrow sindicat edirectio no fchang eonly ; (....) indicatesprobabl erelation . MP= (caseino-)macropeptide . dA/dt •aggregatio nrat e (allK-casei nsplit) . Be =permeabilit yon e hourafte rrenne taddition . dB/dt( )= rat eo fchang eo fB ewit h time (nodeformation) . dB/dt( )= rat eo fchang eo f Bwit htim e(wit h deformation).P |= initia l syneresispressure .dAff/d t= shrinkag erat e at50 0s afte rstar to fsyneresi s &H<*/H0= maximu msyneresis .rig .= rigidity,measure dwit hdifferen t instruments;( )= rigidit yafte r 1h ;= ( )= rigidit yafte r4 h .t = wit htorsio nflu xmethod . factorvarie d range clotting permeab. syneresis rig. AMP &A *e dB dAH dt dt dt n dt ^o" 0-1 / deformation(y ) if 1^ y 1,2,1 temperature (°C) 0-40 M ,y 3/ ^y / _s^ pH 6-7 X ^*. 1.2 c* V K V> 5^"^ rennetcone . (/oo ) 0-1 v f— / 7 r~v --. •'T CaCl2add . (%) % a)const.renne tc . 0-2 / — •%>_. /•••... A. /. A. >/ b)const ,clott .t . 0-2 jt /•••.../"-.. ./^ . c)cons .p H 0-2 •i ,k , 10 -.-4'"•••- I 5">i'o '"••Ù. '•••> ""•••> F *a(»» ) i—10 r-^, /\- /N^_ — r proteincone . (%) 3-7 ? .jS / y S ^ N fatconten t (%) 0-4 If — '"-•i "'•A "'"••A N acidgel s timeafte r -1-20 preparation (h) =^VV l.Foltmann ,1959 ;2 .Berridge ,1942 ; 3.Va nHooydonk ,p .c .; "• .Gree n& Marschall, 1977;5 .Hossain ,1976 ;6 .Scot tBlai r& Burnett ,1957 ; 7.Walstr a& Va nde rHaven ,1979 ;8 .Dalgleish , 1980;9 .Beeby ,1959 ; io.Cheeseman , 1962;n .Nitschman n& Bohren ,1955 ;12 .Torad o &Alais , 1969;13 .Va nVliet ,1982 ;it .Va nVlie t &Dentener-Kikkert ,1982 ;15 . Kowalchyk& Olsen ,1977 . 63 shouldb enoted : Therat eo fth eenzym e reactiondoe sno t affectth efina l properties ofth eparacasei nmicelle s (PCM).Bu ti fth erat ei s variedan dth emeasurement sar estarte da ta constan t timeafte r rennetadditio nthi sma yhav ea naffec to nth eresults ,sinc e notal l K-caseinma yhav ebee nsplit .Fo rth eeffec to fth evarie d factoro n theaggregatio nrat e (dA/di)i t isassume d inTabl e 7.2 thatthi si s donei na nexperimen ti nwhic hal lth eK-casei n issplit . Themicelle s aggregate sinceth eenzymi csplittin go fth e K-casein causesa decrease drepulsio nbetwee nth emicelles .Aggregatio nma yb e duet oVa nde rWaal s attractiono rt ospecifi cbond s (e.g.electro static ones),o rboth .Littl e isknow nabou t theseinteraction sbetwee n micelles.A lowactivatio nfre eenerg yfo rth eaggregatio no fmicelle s (whethercause db ywea krepulsio no rstron gattraction )wil lbot h enhanceth eclottin g reactionan dth e formationo fne wcros s links betweenstrands . Itmus tb e assumed thata nactivatio nfre eenerg yexist sfo rth e breakingo fbond san dthu so fstrand s (atleas tth ebon d free energy). InChapte r 5i ti salread ydiscusse dtha tth erelaxatio ntim eo fth e bonds isa fe wtime s 10s. Thevariable smentione dma yals oaffec t thisfre eenergy .T owhic h extentth evariatio n inthi s activation freeenerg y affectsth eobserve deffect si sno tclear .W e assumeth e influencet ob e small formos tvariables .A nexceptio nma yb eth e effecto fCaCl „ (seelate ron) . If,becaus eo fa differen t compositiono rtemperatur emor ebond s existbetwee nmicelles ,thi sdoe sno t imply that theclottin g reaction orth eformatio no fcros s linksi nth ematri xar eenhance d also.Bu t fewerstrand swil lbrea kunde rstress .Consequently ,micro-syneresi s isdecrease d andth ege lwil lb efirmer . An increasei nth enumbe ro fcros slink sresult si na highe r stress inth estrand san da mor erigi dgel . Thenumbe ro f"spoiled "strand s (i.e.strand sonl yconnecte d on oneen dwit h thematrix )decrease sb y cross-linking. Therelatio nbetwee nth evarie dan d themeasure d factorsca nb e explained asfollows : 64 A) Deformation (byshea rstrain ) Theeffec to fdeformatio n isdiscusse d inconnectio nwit hth e othervariable san d inSectio n4.4 .Generally ,deformatio ncause s an extrastres so npar to fth estrands .Strand sma ybreak . Inthi swa y thestres s inth estrand scausin g thesyneresi spressur ema y faster relax.Deformatio na ssuc hwil lhardl yaffec tth epermeability . However,i fsom estrand sbrea k thebroke nstrand s separate (asa resulto fth erelaxatio no fth estres s inth esurroundin g strands)an d cross-linking ofth ebroke nstrand sma yoccur ;thi sresult s inlarge r poreshenc e ina nincrease dpermeability . B) pHan dtemperatur e Ifth ep Hdecrease so rth etemperatur e increases theactivatio n freeenerg y forcontac tbetwee n themicelle sprobabl y decreases.I ti s wellestablishe dtha tth evoluminosit y ofth emicelle s decreaseswit h increasing temperature (seee.g .Walstra ,1979 )o rdecreasin gp H (Walstra& Delsing ,unpublished) ;thi sma y goalon gwit h increased Vande rWaal sattractio nan ddecrease dsteri crepulsion .A changei n pHma y influence theelectrostati c interaction.Lowe rp Han dhighe r temperatureenhanc eth eclottin greactio nand ,th eformatio no fne w cross linksbetwee n strands inth enetwork ,an dbetwee n "spoiled" strands inth enetwork .Thu sth epermeabilit ywil l increasefaster . B isals olarge rbecaus eo fa shorte rclottin gtime .A n increased rateo fcross-linkin gwil l result ina nincrease d stress inth estrand s anda faste r increaseo fth erigidit y ofth ege l (Hossain,1976) . If strandsbrea kbecaus eo fdeformation ,th eincrease dstres san dth e lowerfre eactivatio nenerg ywil l locallyresul t inwide rpore s (i.e. B increases).A 0.2 units decrease inp Hroughl ygav ea 501increas e inrat e foral lphenomena ,whil e a 6 C increase intemperatur egav ea two- t ofiv efol dincreas e inal lrates .Thi sagai npoint st oa clos e relationbetwee nal lphenomena . Thehighe rpermeabilit y andhighe rsyneresi spressur e causea highersyneresi s rate.Th efina lvolum e (A5/50)wil l decreasebecaus e ofth e lowervoluminosit y ofth emicelle s (Walstra,1979 ;Waltr a& Delsing,unpublished) . Theeffec to ftemperatur e onth erigidit y ofth ege lafte r4 h 65 isno tclear .Hossai n (1976)foun dth esam erigidit y ingel s renneted at 28an da t 31.6° Cafte r 2h bu t at 28° Cth erigidit ywa s still increasing.H ean dTorad o &Alai s (1969)foun da decreas eo fth e rigiditya ttemperature s above 30C . Ifa ge lforme db y rennetinga t 30°C i ssubsequentl ycooled ,i tbecome smor e rigid (VanHooydonk , personalcommunication) .A nexplanatio n forth elatte rresult sma y be thatb y cooling the voluminosity ofth emicelle s increases (e.g. Walstra, 1979). Iti sno t inconceivable thatbeside s the temperature ofmeasuremen t thato fge lformatio naffect s itsrigidity . Asth esyneresi s rate isabou t zeroi fth ege l iscoole dt o5 or 15 Cw econclud etha tP and P° are zeroa tthes etemperatures , unless h isver y large.P gwil l onlyac t ifth epressur ecause db y theweigh t ofth ematri x (whichdepend so nA p g h )surpasse sth e yield stresso r ifP > 0.Wit hsom e simplificationP gwoul deithe r be zeroo rsignificantl y largertha n zero.I fth etemperatur e is increasedP ^wil lbecom epositiv e ata certai ntemperature ;s o P° will alsobecom e significant,independentl y of h .Moreove rth eyiel d stresswil ldecrease ,s o P° willbecom e significantbelo wa certai n distance fromth eto po fa ge l (h ),irrespectiv e ofP (thecritica l h willb e smaller fora highe rtemperature). Tabl e 7.1 shows that dAfl/dichange smuc h lesswit h timea t 27 C.A sdiscusse dbefore ,thi s canb e causedb y P° being largecompare dt oP .Calculatio no fP „ indeedyielde d a lowervalu e (0.3an d0.4 )whil eP ?wa s 0.4 and 0.8 for# „= 5an d 10mm ,respectively .A thighe rtemperature sP does increasewhil e P° would remainconstant ,thu sr decreases . Theeffec to facidit yo n dB/dt (obtainedb y thetub emethod ;se e Table4.7 ) deviates fromth eresult s inTabl e4. 9 (obtainedb y the torsionfluxmethod) . Thisca nb eexplaine db ya highe rrigidit y of thege lresultin g inles sdeformatio n inth etub ea t constant dP./dx asth ep H isdecreased . C) Rennet concentration Increasing rennetconcentratio nwil l result ina nincreasin g enzymicreactio nrate .Th efina lresul thoweve rwil lb eth esam ei f concentrations areno textreme .I fth eperio dbetwee nrenne t addition andmeasuremen t iskep tconstant ,renne tconcentratio nma yhav e some 66 effect,especiall y ifth emeasurement sstar t ina nearl ystag eo fth e formationo fth ematrix .I nsuc ha nearl ystage ,th ege li sno tye t Completely formedan da ttha ttim eth egreates tchange soccur . D) CaCl2 addition Increasingth eamoun to fCaCl -adde d increasesth erat eo f coagulationo fmicelles. Th eincreas e inth erat eo fcoagulatio ni s onlycause db y adecreas eo fth epH . Ifth ep H iskep tconstan tth e clotting time isconstan t too (Cheeseman,1962 )excep tfo r lowC a concentrations (<1 0mW ) (e.g.Gree n &Marschall ,1977 ;Yamauch i & Yoneda, 1978). Sinceth erat eo fcoagulatio n increases atincreasin g CaCl- addition,on ewoul dexpec t thata sa resulto fa lowe ractivatio n free energy ofth emicelle s forcoagulatio nals oth epermeabilit ywoul d increasemor e (increasing B, dB /dt and dB/dt). This isno t so.Th e activationfre eenerg yappear sonl yt ob e loweredb ya decreas e in pH.Apparentl y theextr aC aion sar eonl y involved inth eformatio no f extrabond sbetwee nmolecule so falread yaggregate dPCM .Thi sresult s instronge rstrands .Fewe rstrand swil lbrea k ifstres s isexerte d onthem .Thi s isi nagreemen twit h theexperiment so fYamauch i & Yoneda (1978).Th ephosphorylate d Calciumcaseinat esolution s coagulated almosta sfas ta snativ e Calciumcasei na tCalciu mconcentration s above 20mW .Th eyiel do fcoagulate dprotei nwa s thesam efo rbot hcaseins . Calciumconten t ofth ege lmad eo fdephosphorylate dcasei nwa s less thanon efourt ho ftha to fnativ ecasein .Dephosphorylate d caseingav e amuc hsofte r geltha nnativ e casein.W econclud etha tbot hphosphat e groupsan dCalciu mar e involved inth estronge rbond sbetwee nth e micelles.A s aconsequenc eo fth edecrease d activation freeenergy , causedb yp Hreductio nmor ecros s linksform ,whic hresult s ina highe r syneresispressure .Als o therigidit y increases asa resul to fCaCl ~ addition (Scott Blair,1957 ;Hossain , 1976).Thi s isprobabl yno t causedb y anincrease dnumbe ro fmicelle sbein gboun dt oothers ,bu t by anincrease dnumbe ro fbond sbetwee nan ytw otouchin gmicelles. E) Time afterrenne tadditio n Thegreates t changes inth ematri xoccu rshortl y afterth ematri x 67 isformed ,sinc eman y "spoiled"strand sstil lwil lb eavailabl ean d morebond sbetwee nalread yaggregate dmicelle sca nstil lb e formed. Thestrand sbecom eles s frayed (so B increasesan dd B/d tdecreases ) andstronge r (sodB/d tdecrease san dth erigidit y (ff')an d (GQ) increases). Aftera fewhour s B and G' still increase,thoug ha ta lowe rrate , andP ^decreases .Thi sca nb eexplaine da sfollows :Ther eexist s a distributiono fyiel dstresse s inth estrand so fth ematrix .Th eweake r bondsbetwee naggregate dmicelle s cannotresis t thecontractin gstres s ofth ematrix .S othe ywil lbreak .Th eresultin g"spoiled "strand swil l cross-linkwit hothe rstrands .Thi sresult s ina lesshomogeneou s matrix (increasingpermeability) ,relaxatio no fth estres s (decreasing £Q) andmor erigi dstrand s (increasei nrigidity) .Thi sproces swil l continuea s longa sther e isa distributio no fbon dstrength sbetwee n theaggregate dmicelle san da s longa sth eoveral lstres s islarge r thanth eyiel d stresso fth eweakes tbonds . F) Proteinconcentratio n Concentrationo fprotei nwa sachieve db yultrafiltratio n (see Chapter 2). A higherprotei nconcentratio nwil lresul t ina highe r rateo fsplittin g (VanHooydonk ,persona l communication).Jus ta s in thecas eo frenne tconcentration ,thi swil l influenceth eothe r phenomena. VanHooydon k (personalcommunication )foun da nincreas e inth e initialrat eo fchang ei nrigidit y (ameasur e forth eaggregatio n rate)wit hconcentratio ni nth emilk swhic hwer erennete dnormally , i.e.no tal l theK-casei n isspli twhe naggregatio nstarts .I fal l theK-casei n isspli tther ei sn o indicationtha tth éactivatio nfre e energy forth eformatio no fbond sdepend so nth ePC Mconcentration . Hence,thecoagulatio nca nb e describedb y abimolecula rreactio n accordingt oSmoluchovsk i (Overbeek, 1952). Thusth eaggregatio nrat e is proportionalt oth ePC Mconcentratio nsquared .Th einfluenc eo f theenzymi creactio nrat ean do fth eaggregatio nrat eo n B~, P!!, syneresisan d rigidity,a sa chang e inrenne tconcentration ,appeare d tob e small.I ti sexpecte dt ob esimila ri nthi scase .Th eeffec t ofprotei nconcentratio no n BQ and dB/dt isdiscusse di nChapte r4 . 68 Wedi dn oexperiment s insyneresi swit hvaryin ginitia lprotei n concentrations.Cheesema n (1962)foun da decreas ei n ^MJ^Q iftn e concentrationwa sincreased .Thi si st ob eexpecte dsinc eth efina l concentrationwil lt oa lesse rexten tb e influencedb yth estructur e ofth ematri x (seeeffec to f£ ) .Gree n (1981)foun dtha tth ebasi c 3. structureo fth ematri xwa s laiddow ndurin gth ecur dformin gproces s andwa sno tfundamentall yaltere dlate ri ncheesemaking .However ,he r resultsd ono tsho wwhethe rther ei sa neffec to n ÛHJHQ. AS is generallyth ecase ,th erigidit yincrease swit hincreasin gprotei n concentration (seeFig . 5.3).Afte r 1hou ra nS-shape d curvei s obtained (seeTabl e 7.2).Thi swil lb ecause db y adecrease drennet / caseinrati oa thighe rcasei nconcentrations ,whic hresult si na slowe r firming. G) Fatconten t (unhomogenized) Ifth efa tconten tincreases ,th erati oo frenne tt ocasei nwil l slightlyincreas e (atconstan trenne tadditio nt oth emilk) .Th e permeability slightlydecreases ,probabl ydu et oa decreas ei n porosity.Als od B /dt willdecrease ,a sa smalle rpar to fth esolid s canchang ei nstructure . dB/dt decreasesa sth ege lwil lb eslightl y weakeri fpar to fth ematri xi sreplace db y fatglobule stha tar eno t parto fth ematrix.(Th ematri xwil lb eles sdense. )Thi swil lals o causea lowe rP!J .P ?wil l lowera sth edensit yo fth efa ti slowe r thanth edensit yo fth ewhey .A lowerP Q andS Qwil lcaus e dH/dt tob e smallerinitially .Late ro ndAff/d twil lmainl yb e lowerbecaus eo fa lowerP§ . WJHQ willdecreas esinc eth efa tglobule sar eimcompressi - ble. H) Acidgels .Tim eafte rpreparatio n Thesyneresi so faci dgel si sbasicall ysimila rt otha to frenne t gels.Bu tther ear edifferences .Th eexperiment sdi dno tsho wa maximumi nth erat eo fsyneresi swit htime .Thi s isprobabl ycause db y thenatur eo fth eexperiment so rb y theirlimite dnumber .P ~wil l initiallyincreas efro mzer ot oit smaximu man dsubsequentl ydecreas e by relaxation.Th emaximu mmigh talread yb ereache ddurin gpreparation . Apossibl eexplanatio nfo rth edecreas eo fS flan dP Qma yb etha tth e micellesswell . 69 7.4 CONCLUSIONS Inthi sChapte r theshrinkag eo fslab so fcur dwa s investigated. Bothth eshado wan dth emicroscop emetho dgav egoo dresult s andwer e supplementary. Thefirs t serieso fexperiment swer edon eunde r standardcondition swhil eonl y thethicknes so fth esla bwa svaried . Itwa s foundtha t for M/HQ (#n = 10mm) . Thismode lfitte d the results fairly good. Fromth e syneresis rate,th epermeabilit y coefficient andth eviscosity ,th e S s initial syneresispressur e (P„)ca nb ederived .P „wa s foundt ob e a functiono ftim eafte rrennetin g (thusindependen t of i). However,th e applicationo fsuc ha relatio n intoth emode l didno t improveth efi t toth eexperimenta lresults . Aperfec t fitwil lprobabl yb e obtained ifeithe r Bo rP increases morestrongl ywit htim eu pt o t =0. 5 h.Ou rexperimenta l evidence neithersupport sno rcontradict s suchbehaviou r; further experiments wouldb eneede d tosettl e thepoints . Inthi sChapte rw e also investigated theeffec to fth e composition andtemperatur e onth esyneresi s rate.Syneresi s rate increasedwit h increasing temperaturedurin g reconstitutiono fth e skimmilk , increasing temperature during theexperiment ,decreasin gp H and increasing Calciumaddition .Renne t concentration didno t affectth e syneresis.A s discussed inSectio n 2.1 pretreatment ofth emil kha s a largereffec to nsyneresis . 70 Finallyth erelation sbetwee nclotting ,permeability ,syneresi s andrigidit ywer ediscussed .Th emai nconclusion sar e(unde rth e conditionso fthes e experiments): Temperature andp Haffec tth efre eactivatio nenergy ;probabl y viaeffect so nsteri crepulsio nan delectrostati c attraction.Thi s affectsth erate so fal lphenomena . Additiono fCalciu m (>-v2 0mM )onl yaffect sth estrengt ho f bondsbetwee nalread y aggregatedmicelles . Aftera ge lha s formed,formatio no fcros s linksstil l goeson . Thisresult si na stres si nth estrands ,whic h causesa tendenc yo f thematri xt oshrink .I fth ematri xi sfixed ,th estrand swil lbrea k atwea k spotsthu scausin gth estres st orelax . Thepermeabilit y increaseswit htime .Initiall y thisi smainl y causedb yth estrand sbecomin g less frayed,late ro nb ybreakin go f strands. Table7. 3 Tentativerelatio nbetwee nphysico-chemica l parametersan d curdproperties . high low high temperature pH tea] ' \ * lowactivatio nfre e highactivatio nfre e energy forformatio n energyneede dfo r ofbond sbetwee nPC M breakingo fbond s 1 highrat eo f strongcros slink s aggregationan d inth ege l cross-linking 1 little high high •— micro gel endogenous syneresis rigidity syneresis pressure ^ highrat eo f syneresis muchmicrosyneresi s 1 rapidincreas e high ofrigidit y perinea sility withtim e 71 A tentativeexplanatio no fth eeffec to ftemperature ,p Han d additiono fCalciu mi sgive ni nTabl e 7.3. Ifw ecompar ethes eresult swit hth efinding si npratica l cheesemakingw e seetha tth esam erelation sar efoun dbetwee nth e compositionan dtemperatur ean dsyneresis .However ,whe y expulsion happensmuc h fasteri npractica lcheesemaking . Inth enex tChapte ri t willb eshow ntha texterna lpressur eca nincreas eth esyneresi srat e by orderso fmagnitude . 72 8 SYNERESISA S INFLUENCED BYEXTERNA LPRESSUR EO RDEFORMATIO N 8.1 INTRODUCTION Inth eexperiment smentione di nChapte r 7th ecur dwa sno t deformed. Itwa sou rintentio nt otes tth emode l alsounde rcircum stanceswher e thecur di sdeforme db yexterna lpressure .I nth emode l the flowo fwhe y occursonl yi non edirectio ni na cartesia ncoordinat e system.Thi s geometry canb eapproximate di na cylinde ro fcurd ,wher e pressurei sapplie do n thefla tside s andth etranspor to fwhe y occurs only throughth ecurve dsurface .Moreove rth ediamete ro fth ecylinde r shouldno tb e solarg e thatth eshrinkag ei ntangentia ldirectio nca n beneglected . Whena pressur e isexerte do nth etw ofla tsurface so fth ecylin der,th estrand s arecompresse d inth eaxia ldirectio nan delongate d inradia lan dtangentia ldirection .Th ematri xunde rstres swil l tend toshrin kmomentaril ybu t cannot dothi sbecaus eo fth eviscou s resistance ofth eoutflowin gwhey .Thi s situation iscomparabl e to syneresiswithou texterna lpressure ;th edifferenc e istha tth e pressure ishigher .Externa lpressur ema y inprincipl e affectth e permeabilitybu tw e cannot findconsideration s tosuppor tth evie w thatsuc ha chang ewoul db esignificant .Th eheigh to fth ecylinde ra s a functiono ftim eca nb epredicte d inprincipl e fromth eresult so f creepmeasurement sb ywhic hmean san ysyneresi s inth eaxia ldirectio n couldb epredicted ;axia lsyneresi s canoccu ri fth e flatsurface s are notmad e impermeable towhey .Moreove rextr acros s links cani n principleb e formed inth eaxia ldirection .Howeve rcalculatio no fth e heighto fth esla b inth eabsenc e ofsyneresi sprove dt ob eo f littleuse becauseth emeasurement s ofth evolum eo fth esla bwer e insufficiently accuratean dbecaus e thedeformatio nmostl y occurredoutsid eth e linear visco-elasticregion . 8.2 METHODS Itturne dou tt ob e impossiblet operfor mexperiment swit h a cylindero fa heigh tmuc h largertha nth ediameter ,becaus e of 73 buckling.Ultimatel yw ehav e chosenfo rfla tcylindrica l slabswit ha diametero f9 o r1 4c man da heigh to f5,1 0o r1 5mm .Mil kwa s rennetedi na bottomles smoul dwhic hwa splace di na thermostate d vat (seeFig .8.1) .I nth e vatwhe ywa spoure d aroundth e mould.5 0 Minutes afterrenne tadditio nth ecur dwa scu tfre efro mth einne r wallo fth emoul dan dmoistene db ysprayin gwhe yo nth euppe rsurfac e toth eslab .Th emoul dwa sremove dan dth esla bcu tfre e fromth e bottom.Mor ewhe ywa s added.Th ewheigh to fth eplat ewa scounter balancedb ymean so fa counte rweigh tan da pulley ,t oassur eth e pressure exertedb yth eplat e itselfbein g zero.Pressur eo nth ecur d slabi sintroduce db yplacin gweight so nth escal ea tth eto p (seeFig .8.1) .Th eheigh to fth esla bwa srecorde dwit ha displace menttransduce ran dit scros ssectio nwa sdetermine d fromphotograph s ofth ebotto mo fth eslab sb ymean so fa Quantime timag eanalyser .I n thiswa yth evolum eo fth esla bwa s calculateda sa functio no ftime , givingth esyneresis . Onehou rafte r rennetadditio na weigh twa splace do nth e scale. Two serieso fexperiment swer edone .I nth efirs tserie spressur ewa s scale on which to put weights ^ t ^fv-pulley 4T milk, rennet h -counterweigh t whey ! mould displacement U~transduce r £—plate - i — a ac \ \jb|—camera Q b C Fig. 8.1 Schematicrepresentatio no fth eapparatu s forapplyin g pressureo na sla bo fcurd . a.Mil kprovide dwit hrenne ti sbrough tint oa moul d ina thermostatedvat .Whe y isadde dt oth evat . b. Whenth ecur dha sforme di ti scu tfre efro mth ewall so fth emould . Themoul d isremove d and thesla bi scu tloos efro mth ebotto mo f thevat . Thebotto mi scleaned . c.A horizonta lplat ei sbrough tint ocontac twit h thecur dsla ban d thefirs tphotograp h istaken .Weight sca nb eplace do nth euppe r plate. 74 appliedfo ron eminute ,followe db y5 minute swithou tpressure . Inth esecon dserie sth éweigh twa splace dan dremove d fromth escal e eachtim efo r5an d1 0s ,respectively .Thi swa sdon e1 2time s (i.e. during3 minutes )whereupo nn opressur ewa sexerte dfo r3minutes . Thetota ltime ,durin gwhic hth esla bwa sunde rpressur e thuswa s the samea si nth efirs tseries .Afte r6 minute sth efollowin gschem ewa s usedfo rbot hseries :10 ;0 ;50 ;0 ;10 0g ,eac htim efo r1 minut e(se e Fig.8.2) . 8.3 RESULTSAN DDISCUSSIO N A typicalresul ti sgive ni nFig .8.2 .Th ecurve sgivin gth e heighto fth esla ba sth eresul to fth eputtin gi nan dremovin go f weights,hav ea shap eanalogou st ocree pcurves .Th ecur di sa visco - elastic system.A tth emomen to fapplyin gth epressur e elastic deformationoccur s;afte rtha tth edeformatio ni sa resul to fretarde d elasticityan dviscou sdeformation . height of slab (mm) 1 '/o syneresis 20 time after rennet addition (h) Fig. 8.2 Heighto f thesla b (ff,ful lcurve )an d% syneresi s (bottom line)o rrelativ evolum ereductio na sa functio no ftime .Exampl eo f anexperimen to fth efirs tserie s (50g fo r1 minute .Furthe rexpla nationi nth etext) .Origina lcros ssectio no fth esla b 153cm^ .Ori ginalheigh t 10mm .A t t =0 th epressur ewa s 30Pa . 75 pressure(Pa ) Fig. 8.3 Syneresis during the first 5minute s of the experiments (see Fig. 8.2) as a function of pressure at t = 0.Withou t pressure the relative volume reductionwa s estimated at 0 - 4%.Th e curves indicate the function: % syneresis = 0.58 Ki; where K is for total pressure (external and endogenous) D O V O =wheigh t on scale for 1minut e continuously. • • f • =wheigh t on scale for 1minut e intermittant. V ? =heigh t of the slab: 5mm , cross section 153 cm„ O • = height of the slab: 10mm , cross section 153 cm„ O + =heigh t of the slab: 15mm , cross section 153 cm O# = height of the slab: 10mm , cross section 62 cm -«— = arrows indicating % syneresis after 5minute s of a slabwithou t external pressure (see Chapter 7) FromFig .8. 2i tals oappear s thatextr apressur e enhanced syneresis.Withou tpressur e thevolum e reduction after 5minute so f a slabo f 1c mthicknes swa sestimate d at0 - 41 .Whil ea nexterna l pressure ofabou t 30P aresulte d inabou t 101syneresis .Th eextr a syneresis occursa slon ga spressur e isexerte do nth eslab ,an dfo r a short timeafterwards .Th elatte ri simaginabl e ifon econsider s thatafte rth eweigh ti sremove dth estres s inth ematri x doesno t momentarily relax.I na numbe ro fexperiment s thepressure ,th e height andth esurfac eo fth esla bwer evaried .Th eresult s aregive n inFig .8.3 . Thesyneresi s isshow ni nFig .8. 3a sa functio no fth epressur e atth emomen tth eweigh ti splace do nth escale .Directl y afterwards the slab isdeforme dan dtherefor e thecros s section areai senlarge d 76 whichimplie s thatth eeffectiv epressur ei ssomewha tlower . Theresult so fth emeasurement swit hth eapparatu swer e foundt o beno tver y reproducible.Hence ,th eresult sar eonl yapproximat ean d it cannot beconclude dtha tth eintroduce dvariation si nheigh tan d diametero fth esla ba swel la sth etim eschem eb ywhic hth epressur e was exertedo nth esla baffecte dth esyneresi srate .Bu tth eincreas e insyneresi srat ewit h increasingpressur ei sunmistakable . InFig .8. 3als oEq .7. 1i sshow nfo rtw ovalue so f HQ, i.e.5 2 and1 0mm .Othe rparameter swer e BQ =2. 3x 10 m , t =30 0s ,n= 1mPa-s . ForP Qth eexterna lpressur e+ 1 P afo rendogenou spressur e was taken.I ti ssee ntha tth ecurve sfi tth eresult sobtaine dfro m theexperiment sbot hwit h andwithou t externalpressur ewithi na n ordero fmagnitude . Theresult so fthes eexperiment s showth esam etren da sth e results givenb yVa nDij ke tal.(1979 ) (seeFig .8.4) .Her eals o thepressur eha da grea teffec to nth esyneresis .Th efirs tpoin ti n Fig.8. 4(lowes tpressure)pertain st ocur d grainsi nwhe ykep t stirringfo r2 h ;th epressur eher ei sroughl ycalculate d from Bernoulli's equation fromth evelocit ygradient si nth ewhey .Th e secondpoin tpertain st ocur dmerel ypresse db yit sow nweigh tunde r thewhey ;hence ,thi spressur ei sals osomewha tuncertain .I fth e mmwate r 10 100 1O00 Fig. 8.A Waterconten t (%) ofcur dfro mwhol emil kafte r 1h stirrin g and 1h pressin gunde rth ewhe y atvariou spressures ;temperatur ean d pHwer ekep tconstant . 77 samecur dha dbee n leftundisturbe d for 2h ,an dha dbee n subject only toit sow nsyneresi spressur eo fsom e 1Pa ,it swate r content would onlyhav ebee n lowered from itsorigina l 871t osom e85° s according tomeasurement s onthi nslab so fcurd .Finall y itshoul db e noted that Fig.8. 4 mayno tb e taken asrepresentativ e ofactua l cheesemaking practice,becaus e experimental conditionswer esubstan tiallydifferent . Fromth eresult s ofth eexperiment s itca nb e concluded that in practical cheesemaking externalpressur e onth ecur dgrain s isver y important.Suc hpressur e isexerte d inpractica l cheesemaking by stirring,drainin gan dpressing . 78 SUMMARY H.J«M.va nDijk ,Syneresi so fcur d Thisstud ydeal swit hth esyneresi so fcurd .Renne tgel sar e primarilyconsidered ;som ecomparison swit haci dmil kgel sar egiven . Aftercurdlin gth emilk ,th ecur dtend st oshrink ;i nothe rwords , thenetwor ko faggregate dparacasei nmicelle s (PCM)wil lb eunde r stress. Ifth ecur di scu to r- a swa sth ecas ei nou rexpirement s- a curdsurfac ei swetted ,syneresi sstarts .Th erat ea twhic hth ewhe y isexpelle ddepend so nth epressur egradien ti nth ewhe y ando nth e permeabilityo fth enetwork . InChapte r 2th ematerial san dmethod sgenerall yuse dar e described.Unles smentione dotherwise ,standar dcondition swer euse di n theexperiments .B ystandar dcondition s ismeant :reconstitute dski m milkwit hth esam edr ymatte rconten ta sth eorigina lmilk ,t owhic h 500pp mrenne twa sadded ;th etemperatur edurin gth ewhole experimen t waskep ta t3 0°C ;n oCaCl 9wa sadded . s Theendogenou ssyneresi spressur e (P) appeare dt ob ever ylow , about 1Pa .I nChapte r3 tw omethod sar edescribe dwhic hgiv ea norde r ofmagnitud eo fth estresse sinvolved .Moreover ,th eweigh to fth e networkca ncaus ea nadditiona lpressure .Th emaximu mpressur ecause d byth eweigh t (P^)a ta level h belowth einterfac ei s (^curP j-Pid Kwhey. )J 9 y h„C - 75fe cP a {hv c i n m)•*. Thepermeabilit ymeasurement sar edescribe d inChapte r4 .Tw o methodswer eused ;i nboth ,th eflo wo fwhe y througha vertica lcolum n ofcur dwa smeasure da sa functiono fhea dpressure .A proble mi stha t thecur di sdeforme ddurin gth eexperiment .I nth e"tube "method , deformationi sa functiono fth epressur egradien t (dP.làx), the diametero fth etub eholdin g thecur d (df), andth erigidit yo fth e gel. Inth esecon dmetho dth e"torsionflux "method ,th edeformatio n wasadjustable .Th etub emetho dle dt oth e followingresults : -13 2 Thepermeabilit y iso fth eorde ro f 10 m . Permeability increaseswit htime ,whic hi sascribe dt o "microsyneresis",i.e .syneresi sa tloca lsite si nth egel .Th e rateo fincreas ei sapproximatel yconstant . 79 The increase inpermeabilit y (dB/dt)i shighe rfo ra highe r pressuregradien to ra wide rtube ;bot h leadt o largerdeformatio n ofth ecurd . Thechang eo fth epermeabilit ywit htim e inth eabsenc eo f deformation (dB /dt) wasobtaine db yapplyin g thehea dpressur e atdifferen ttime safte radditio no frennet .Shortl yafte r clottingpermeabilit y increasesfastest .Betwee n 1an d2 4h dB/d twa sconstant . Thepermeabilit yo fcur dmad e fromultrafiltere dski mmil k (B(£)) and itschang ewit htim e (dB(£)/d£)wer edetermined .Thi syielde d thepermeabilit y asa functiono fconcentratio nan dtim e (B(•£,£)). Thepermeabilit y alsodepend so ntemperature ,CaCl ~concentration , acidity,fa tconten tan dtyp eo fski mmilk . Inaci dmil kgel dpermeabilit ywa s ofth esam eorde ro fmagnitude , buti thardl ychange dwit htime . TheTheologica lbehaviou ro fcur d isdiscusse di nChapte r 5.Th e dynamicmeasurement swit hth e"De nOtter "rheomete rsho wtha tth e moduliG 'an dG "kep tincreasin gfo ra longtim e 03 h)afte rrenne t addition.Fro mth edependenc eo fG 'an dG "o nth eangula rfrequenc yi t was deducedtha tG " isdu et oth erelaxatio no fbond san dtha tth e relaxationtim e isa fewtime s 10s . Theinstantaneou s shearmodulu s (Gn)wa s determineda sa functio n ofprotei nconcentration .Th eobtaine d relationca nb e explainedi n termso fa nonl ypartl yeffectiv econtributio no fth ecasei nt oth e network;thi scontributio nbein g relatively smallera t lower concentrations.Als o fromth ecree pmeasurement s itwa sconclude dtha t theendogenou ssyneresi spressur ewa s lesstha n 10Pa . Ifbot hpermeabilit y andpressur ear eknow n foral lvalue so f concentration (orrelativ eremainin gvolum e (?'))an dtim e (t),th e syneresisca ni nprincipl eb e calculated.Thi s isi nth emode l describedi nChapte r 6, inwhic hth eequatio no fDarc y iscombine d with theequatio no fcontinuity .A numericalprocedur e isdeveloped , fora on edimensiona l case;th esyneresi so fa thinslab . Thepressur e inth ewhe y isth esu mo fth eendogenou s syneresis pressure (P) an dth epressur ecause db y theweigh to fth enetwor k (Pg). For P {%)an dP^(-i )som etria lfunction swer econsidered . 80 InChapte r 7th esyneresi so fslab si sstudied .Th eresult s of theexperiment s showtha t initiallyr = dlogM/dlog t isabou t 0.5. For t >0. 5 h r increasest o^0.78 . ri sindependen t ofth eorigina l thicknesso fth esla b (#Q) during a certainperio d (penetration period).Th e lengtho fthi sperio ddepend so n HQ. Afteron eda y Hdi dno tchang ean ymor ean d H^jHç. wasabou ton e third.Th ebes t fitbetwee nmode l calculations and experimental resultswa sobtaine d ifi twa s assumedthat : thepermeabilit y increaseswit htim e(t )an ddecrease swit h i3 aswa s foundi nth eexperiments , endogenous syneresispressur e (Ps)decrease sonl ywit hshrinkage , maximumgravitationa l pressure (Pg)i sconstant , PQ =p S= 1P a (#0 = 10mm) . PQ was foundt ob ea functiono ftim eafte rrenneting ,a t first increasing,the n (after 1- 2 h )decreasing .However ,th e introduction ofsuc ha relatio n inth emodel di dno t improveth efi tt oth e experimental results.Afte rall ,th epressur ecanno trela xtwice ,bot h by shrinkagean db y "ageing". Theeffect so fsevera lparameter s (pH,temperature ,C aconcentra tion,etc. )o nmil k clotting,ge lpermeability ,syneresi s andcur d rigidityar einterrelated .A surveyi sgive ni nTabl e 7.2 anda tentative explanation issummarize d inTabl e 7.3. InChapte r 8i ti sshow ntha texterna lpressur eha s adramati c effecto nth esyneresi srate .Extrapolatio nt o zeroexterna lpressur e yields,again ,a nendogenou s syneresispressur eo fabou t 1Pa . 81 SAMENVATTING H.J.M,va nDijk ,Syneresi so f curd Deze studiebehandel t de synereseva ngestremd emelk . Onder synereseword tverstaan :he t samentrekken vanee nge londe rhe tuit drijvenva nvocht .Syneres e treedtme tnam eo pbi jmelkgelen . Bijd e kaasbereidingword tdi tproce sbovendie nbewus tbevorderd . Hierdoor worden deeiwitte ne nhe tmelkve tva nhe tgrootst e deelva nhe tvoch t gescheiden. Doordi tproce s telate nsamengaa nme t eenbeheerst e verzuring doormelkzuurbacterië nword t eensmakelij kproduk t verkregen, datbovendie nvee l langerhoudbaa r isda nmelk . Hetge lword t inhe talgemee nverkrege n dooraa nd emel k stremsel toet evoege ne nsom s doord ehiervoo r genoemdebeheerst e verzuring. Bijbeid emethode ngaa nd ecaseïnemicelle n ("kaasbolletjes"me t een diameterva nongevee r ééntienduizendst e millimeter),di e ind emel k zweven,aa nelkaa rkleven .Hierdoo rworde nvlokje s gevormd diever volgens ookwee r aanelkaa rkleven .Tenslott eword t ééngroot ,ij l netwerk gevormd;d eruimte n daartussen zijnopgevul dme twei .Doo r in degestremd emel k tesnijde no fhe toppervla k tebevochtige n kan ze zichgaa nsamentrekke n totwrongel .Daarbi jword twe iuitgedreven . Waardoor dit gebeurt,i nwelk emat ee nwa the t effect isva n veranderingen insamenstellin g entemperatuur ,alsmed e de verklaring daarvan,ware nd evoornaamst evrage ndi ew e indi tonderzoe k aand e orde stelden. Hetnetwer kheef td eneigin g omsame n tekrimpe ne no m int e zakken;he teerst egebeur t spontaan (endogene synerese),he t tweede onder invloedva nzwaartekracht .Dez eprocesse nworde n echterver traagd doordatwe iui the tnetwer kmoe t stromeno mhe tnetwer k te latenkrimpen .Hierdoo rkom t dewe i inhe tge londe rdru kt estaan . Indiendez e syneresedruk end edoorstroombaarhei dbeken d zijnka nhe t verloopva nd esyneres ebereken dworde n (Hoofdstuk 6). Desynerese drukblee k overigens teklei nt e zijno m zeme t een instrument te kunnenmeten ,maa r zeko nwe l indirekt bijbenaderin gbepaal dworden . Inhoofdstu k 3worde n twee experimenten beschrevenwaaruit deze druk indirektval t tebepalen .D econclusi e luidt dat desyneresedru k van 82 deord eva ngroott e isva n 1P a (overeenkomendeme t0. 1 mmwaterkolom) . Onafhankelijkhierva nvolg tdi too kui td ereologisch emetinge n (Hoofdstuk 5)e nui td eexperimente nbeschreve n inHoofdstu k 8. Desyneresedru k end edoorstroombaarhei dbleke nbehalv eva nd e samenstellingva nd emelk ,d etemperatuu re nd emat ewaari n de synerese alha dplaat s gevondenoo kafhankelij kt e zijnva nd etijd , dieverlope nwa sn ahe ttoevoege nva nstremsel .D e doorstroombaarheid werdsteed sgroter ;d esyneresedru kna maanvankelij k toemaa r later weeraf . Omhe taanta l factorenda t invloedheef to pd esyneres et ever kleinen,wer dgewerk tme tee nééndimensionaa lmodel ,bestaand eui t horizontale dunneplakke nwrongel .Di t isoo kd eeenvoudigst emanie r omd euitkomste nva nhe twiskundi gmode lva nhe tsynereseproces ,da t wijopstelden ,t evergelijke nme td eresultate nva nproeven .Verde r kono pdez emanie ree npraktisc hproblee mworde nopgelost .D epla k begonnamelij kpa st esynerere nnada t zebevochtig dwas . Zoko no p eeneenvoudig emanie ree nexperimen t gestartworden . Deuitkomste nva nd emodelberekeninge nkome nhe tbest e overeen metd euitkomste nva nd eexperimente nal shieri nhe tvolgend eword t aangenomen: Dedoorstroombaarhei d isee nfuncti eva nd e indikking end e tijd (zievergelijkin g 4.16). Deaanvankelijk e endogenesyneresedru k (P„)i sgelij kaa n 1Pa. Dedru kveroorzaak tdoo rhe tgewich tva nd ewronge l (P?) isgelij k aan 75x d eafstan d (inmeters )to the toppervla kva nd ewrongel . P en P° nemena fnaarmat ed esyneres evoortschrijdt ,maa rd e wijzewaaro p datprecie s gebeurt,heeft ,bi j dedoo ron s geprobeerde functies,slecht see ngering e invloedo phe t resultaat.D e endogene syneresedrukva nno gnie tgesynereerd ewronge lverander tme td etij d nahe t toevoegenva nhe tstremsel .Zodr asyneres eoptreed te ndaarme e indikking,za ldez erelati eme t detij dechte rgehee lander s zijn:d e drukka nimmer snie ttwe emaa lrelaxeren ,doo r indikkingè ndoo r veroudering.D ebest eovereenkoms t tussenmodelberekeninge n enexperi mentenwer dgevonde ndoo rd einvloe dva n tijdal s zodanig teverwaar lozen. De invloedva nenkel eparameter s (pH,temperatuu rC aconcentra - 83 tie,enz. )o pd estremmin gva nmel kd edoorstroombaarhei dva nhe t gel,syneres ee nd estevighei de nhu nonderling ecorrelatie sworde n gegeveni nTabe l 7.2 enee nvoorlopig everklarin gword tgegeve n inTabe l 7.3. 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