Drainage of curd
CENTRALE LANDBO UW CATALO GU S
0000 0489 0857 Promotoren Dr. Ir. P. Walstra Hoogleraar in dè Zuivelkunde Dr. Ir. J. Schenk Emeritus .Hoogleraar in de Technische Natuurkunde J.C Akkerman
Drainage of curd
Proefschrift ter verkrijging van de graad van doctor in de landbouw- en milieuwetenschappen, op gezag van de rector magnificus, Dr. H.C. van der Plas, in het openbaar te verdedigen op woensdag 29 april 1992 des namiddags te vier uur in de Aula van de Landbouwuniversiteit te Wageningen
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Stellingen
1) Door de resultaten van dit onderzoek toe te passen in de kaasfabrieken zou de aanvoer van grondstoffen voor de bereiding van smeltkaas, na een aanvankelijke stijging in de toevoer, wel eens kunnenstagneren . Dit proefschrift
2) Onderzoek naar de drainage van wrongel is zowel voor de kwaliteitsborging van kaas als voor de bereiding van weipoeder van belang. Dit proefschrift
3) Optische sensoren kunnen worden gebruikt om verschillende bestanddelen te onderscheiden in een mengsel. Dit kan op basis van verschil in brekingsindex, zoals Frijlink reeds heeft aangetoond, maar ook op basis van verschil in lichtver strooiing. J.J. Frijlink, Physical aspects of gassed suspension reactors. Ph.D.Thesis ,T U Delft (1987) Dit proefschrift
4) De door Rüegg en Moor gegeven verklaring voor de verschillen tussen het gemiddelde oppervlak van sedimenteerde deeltjes in het horizontale vlak en dat in het vertikale vlak isvermoedelij k niet de enigejuiste . M. Rüegg U. Moor, The size distribution and shape of curd granules in traditional Swiss hard and semi-hard cheeses. Food Structure 6 (1987) 35-46
6) Het effect van de wand van het draineersysteem op de drainage kan zeer groot zijn. Dit proefschrift
7) James Bond heeft nooit kunnen vermoeden dat na zijn film "For your eyes only" de grote vraag naar Maasdammer begonnen is.
Stellingen bij het proefschrift "Drainageo f Curd"va n Coen Akkermant e verdedigen op 29 april 1992
u*\ «r Table of contents 1. Introduction 1 1.1 In general 1 1.2Th e drainage of curd; an overview 2 1.3Theoretica l aspects of curd preparation 2 1.4Practica l aspects of curd preparation 6 1.5 Practical aspects of the draining of curd 8 1.6 Theoretical aspects of drainage of curd 10 1.7 Theoretical modelling of drainage of curd 13 1.8 Scope of the present work 20
2. Materials & methods 22 2.1 Curd preparation 22 2.1.1 Curd made in a small cheese vat 22 2.1.2 Cubeshape dcurd grains obtained ina ne wtyp e of cheese vat 22 2.1.3 Curd made at NIZO 24 2.2 Density of curd grains 24 2.3 Size distribution of curd grains 29 2.4 The curd flattener 29 2.5 Drainage columns 31 2.5.1 Compaction and liquid pressure measurements in radial drainage vessels 31 2.5.2 Permeability tests in a radial drainage column 32 2.5.3 Compression and permeability experiments in an axial drainage column 32 2.5.4 Pressure loss measurement in a curd column 33 2.6 Fusion of curd grains under the whey 34 2.7 Pore size distribution and porosity measurement 35 2.8 The water content of acurd block 39 2.9 Confocal Scanning Laser Microscopy (CSLM) 39
3. Curd properties 40 3.1 Characterization of curd grains 40 3.2 Whey expulsion and deformation of cube shaped curd grains 42 3.3 The fusion of cube shaped curd grains 54 3.4 Sedimentation of curd grains 57 3.5 Packing of curd grains 60
4. Effects of the drainage vessel upon drainage 62 4.1 Axial draining vessels 62 4.2 Radial draining vessels 63
5. Processes inside the curd column 72 5.1 Compaction of curd columns 72 5.2 Porosity and apparent pore size distribution in curd columns 77 5.3 Aspects of permeability 81 5.4 Computer modelling of the drainage system 85
6. General discussion and conclusions 88
Appendix A: Calculation of the permeability of a radial drainage column 92
References 97
List of symbols 102
Summary 104
Samenvatting 109
Curriculum Vitae 113 Voorwoord
Ofschoon er maar één naam op het kaft van dit boekje staat, is het natuurlijk nietzo ,da tdi twerkstu kzonde rwezenlijk ebijdrag eva nandere nto tstan di sgekomen . Zonder volledig te kunnen zijnwi l ik hier bijbedanken : - Mijn beide promotoren, Pieter Walstra en Jaap Schenk, voor de vrijheid,di e ze me gebodenhebbe nbi jd eaanpa kva ndi tonderzoe k end esteu nbi jd e realisatieva nhe t proefschrift. - Destichtin gJ . Mesdagfondsvoo rd efinancierin gva nd eAI Oplaat se nd ekoste nva n de bouw van de porositeitsmeter. - Tom Geurts voor het inzetten van zijn literatuur kennis en grote belangstelling voor dit onderzoek. - Het NIZO, met nameAa d Heijnekamp,Ja nd eWi t en de proeffabriek medewerkers voor de geboden praktische steun. - De studenten: Rudi Lewis, Frank Fox, Carla Buijsse en BeaTissing h voor hun inzet bijd e uitvoering van eenflin k deelva n de hier getoonde werk. - Maarten de Gee voor de realisatie van het rekenmodel. - Mijn collega's: Henk Jansen, Henk van de Stege, Albert Prins, Karin Boode, Lex Ronteltap, Hannemieke Luvten en Chris Bisperink voor handige ideeën, wetenschappelijk denkvoer en praktische steun. - Mijnparanimfe nAdriaa nGarretse ne nFran sde nOude nvoo r het kritisch doorlezen van het concept van het proefschrift. - De medewerkers van technische diensten van het Biotechnion: de werkplaats, de fotolokatie, de tekenkamer, de elektrische werkplaats en automatisering voor de technische uitwerking van de ideeën. -Pete rva nHaldere n (KremersLaboratorium ,Fysisch eTechnologi eT UDelft )voo rzij n steun bij de bouw van de porositeitsmeter. - El Bouw (TFDL) voor het maken van CSLMbeelden . - Het LEBfond s voor definanciël e steun bij detotstandkomin g van dit proefschrift. Abstract Akkerman, J.C., (1992). Drainage of curd. Ph.D. thesis, Agricultural University, Wageningen, (pp 113, English and Dutch summaries).
Keywords: curd, whey drainage, syneresis, curd fusion, Gouda cheese, cheesemaking equipment, curdfine s
Abstract: An extensive study was made of the factors governing drainage of curd. A basic feature of this study is the comparison of the behaviour of a single curd grain and the behaviour of batches of uniform curd grains in a drainage column. A detailed study was made of the deformation and whey expulsion from single curd grains,th e fusion of curd grains and the sedimentation of curd grains. Furthermore, drainage was studied in small scale drainage equipment. Liquid pressures, wall friction losses and compaction rates were recorded. The porosity was measured using an optical fibre technique. Furthermore the permeability was calculated from experimental results. 1. Introduction 1.1 In general Cheesei sa nimportan tfoo di nman ycountrie saroun dth eworld .Thoug hman y different varieties of cheese are produced, the basic principle of the manufacture is alwaysth e same.Cheese-makin g startswit hclottin go fth emilk , i.e.transformatio n of the liquid milk into agel . Clotting canb eaccomplishe d either by adding rennett o the cheese milko r by acidificationo fth emilk ; mostchees e ismad e byrenneting .Th ege l is cut into pieces. Whey, i.e. an aqueous solution of lactose, proteins and salts, is expelledfro mth epieces ;thi sproces si scalle dsyneresi s (VanDij k 1982). Theproces s of whey expulsion is usually enhanced by stirring the curd/whey mixture. The temperature is often raised to increase the whey expulsion rate further. Finally, fairly rigid curd grains and a large amount of whey are obtained. The whey and the curd grains areseparated .Th ecollecte dcurd grain sfor ma coheren t masstha ti spressed , salted and ripened. The order of the pressing and salting steps is reversed in the manufacture of some particular cheese types. Cheese has been knownt o mankindfo r many hundreds of years,th e product has evolved from rather primitive to (sometimes) atop-rankin g delicacy and awealt h of empirical know-how has been gained over these years. Not only the product has evolved, but also the production process. Modern cheese plants nowadays often represent highly automatedlarg escal eoperations .Th elarg escal eo f bulk production requiresclos eproces scontro lan dempirica lknow-ho wi sbecomin ginadequate .I nth e laboratory of Dairy Science and Food Physics of the Agricultural University in Wageningenan da tth eNetherland s DairyResearc hInstitut ei nEd ea nextensiv estud y ofth efundamental s of someo fth e key processes inchees e making has beenmade . Van Hooydonk (1987) focused upon the renneting of milk. Van Dijk (1982) and Van denBijgaar t (1988) performeda detaile dstud yo fth esyneresi s of rennet-induced milk gels.Zoo n (1988) investigatedth e rheological properties of rennet-induced skim milk gels and Roefs (1986) those of acid casein gels. Geurts (1972) studied the salting of Goudatype cheese. Luyten (1988) studiedth e rheological andfractur e properties of Gouda cheese. The objective of the present research project is to investigate processes occurring duringth e drainage of amas so f curd grains inwhey . Iti s amazingtha t up till nowthi sfiel d received little attention inth e literature (Walstrae t al. 1985) and basic knowledge of the processes is still largely lacking. 1.2 The drainage of curd;a n overview Thewhe y removal isa nessentia l step inchees e making: itconcentrate s most of the valuable ingredients of the milk into a small volume and it leads to a coherent mass. During draining four major processes may be distinguished: 1) Additional whey is expelled from the curd grains. 2) Curd grains aredeformed . 3) Curd grains partly fuse with each other. 4) Whey flows away through the connected pores between the grains. The processes occur simultaneously and are interrelated. For instance, the whey expulsion results in a deformation of the curd grains, thereby narrowing the pores between the curd grains through which the whey must flow away. Furthermore, the expulsion of whey contributes to the flow of whey through the channels. The water content of the cheese isno t only determined byth e drainage, but it depends also on the curd preparation, shaping and pressing of the curd block, and salting and ripening conditions. Control of the water content during salting (Geurts 1972, Guinee & Fox 1987) and ripening is generally very good, and will not be discussed in this thesis. However, fundamental knowledge about the interactions betweenth epropertie so fth ecurd a sresultin gfro mit smetho do fpreparation ,an dth e processes occurring during drainage (shaping) and pressing islackin g andwil lb ea n important topic inthi s thesis.
1.3 Theoretical aspects of curd preparation The proteins in milk can be classified intotw o main groups,casein s andwhe y proteins.Th e casein molecules are present insmal l aggregates (submicelles), which areclustere di napproximatel y sphericalaggregate s (micelles) (e.g.Walstr a& Va nVlie t
1986), as depicted in Figure 1.1.Casei n micelles in milk mainly consist of os1, a&,ß and /f-casein, calcium phosphate andwate r (Walstra &Jennes s 1984).Accordin g to Van Dijk's model (1990), micellar calcium phosphate consists of complexes of inor ganic andorgani c phosphate andcalcium ,whic hlin ku pon eb yon ean dbin danothe r limited number of Ca-, Mg- and phosphate-ions. In this way small, partly rigid and more stable ion clusters are formed by which casein molecules are interconnected. Therei sa dynami cequilibriu m betweencasei nan dcalciu mphosphat e inmicelle san d in solution (Walstra 1990), although the equilibrium between casein (and calcium o submicelle protruding chain — calcium phosphate 50n m
Fig. 1.1 Section through a casein micelle, highly schematic. The protruding chains of mainly«r-casei n are clearlyvisibl e (Walstra 1990). phosphate) and the micelles is predominantly to the side of the micelles. Van der Waals attraction would cause the casein micelles to flocculate, if there would be no repulsive interaction energy between them.Thi s repulsion of steric and electrostatic nature is primarily caused by *-casein. Rennet splits the /c-casein into para-/r-casein anda solubl ecaseino-macropeptide .Thereb yth erepulsio nbetwee nparacasei nmicel lesi sgreatl ydiminished .I fadditiona lcondition s arefulfilled ,i.e .temperatur e not below 10 °C and a sufficient activity of Ca++-ions, the paracasein micelles will flocculate, forming initially irregular aggregates. After awhile ,th eflocculatio n leadst o formation of agel ;a schemati c representation ofth etransformatio n of single micelles into age i is given in Figure 1.2.
00 « »oo ° o°0o OoO 0 °n ° 0° O
°0°°° o° 0 V °°o° A*
Fig. 1.2 Schematic representation of the change from stable casein micelles to a gel of paracasein micellesdurin gth e renneting of milk (Vande n Bijgaart 1988). The gel network consists of strands, that vary in length, thickness and pore size between them (Zoon et al. 1988).Th e network entraps fat globules. The network shows an inclination to contract. It is caused by a tendency to rearrangeth estrand stha tmak eu pth enetwork .Thi scause sa spontaneou spressure , exertedb yth ege lnetwor ko nth ewhe yenclosed ;thi sendogenou ssyneresi spressur e is, in a non-syneresed skim milk gel, some 1t o 10 Pa (Van Dijk 1982). Inth e early stages of the gelation process the build-up of pressure by theformatio n of new con tacts is only partly counteracted by relaxation due to breaking of strands and strengthening of the strands (Van den Bijgaart 1988). If the gel is geometrically constrained, the rearranging will cause local condensation of strands, leaving larger poreselsewhere .Thi sphenomeno n iscalle dmicrosyneresi s (VanDij k 1982).I tresult s ina nincreas eo fth epermeabilit y ofth ege lwit htim e (VanDij k 1982,Va nde n Bijgaart 1988).I tca nb econclude dtha tth epropertie s ofth e milk gel,an dthereb ythos eo fth e curd grains, will be affected by thetim e elapsed after renneting.Th e effect of ageing may be enhanced byth e decreasing pHdu et o theformatio n of lactic acid by starter bacteria.Th elowerin go fth e pHincrease sth e permeability ofth e network and initially alsoth eendogenou s syneresis pressure (Vande n Bijgaart 1988),an dals oaffect sth e rheological behaviour (Zoon et al. I 1989). If the gel is not constrained, expulsion of whey (syneresis) will leadt o shrinkage of the gel andthereb y to concentration ofth e matrix. It will make new contacts between the strands feasible, regenerating endogenous syneresis pressure. Shrinkage can locally promote the formation of thicker strands andthu s astiffenin g ofth ecasei n matrix (Vande n Bijgaart 1988).Th e concentration distribution of paracasein inth e gel atvariou s stages has not yet been precisely determined,bu tVa nde n Bijgaart (1988)calculate dconcentratio n profilesfo r thecas eo fone-dimensiona l syneresis,a sillustrate di n Figure 1.3. The permeabilityo f concentrated skim milk gels is decreased (Van den Bijgaart 1988).Concentratio n by meanso f syneresis always results ininhomogeneou sgels ,therefor eth e experiments were conducted with gels preconcentrated by means of ultrafiltration. These gels contain a substantial amount of whey proteins in addition to paracasein and have a slightly lower permeability thanthos e preconcentrated by syneresis (Vande n Bijgaart 1988). Permeability and endogenous syneresis pressure of the paracasein network increase considerably withtemperatur e (Vande n Bijgaart 1988). Fatglobule s impede theshrinkag e ofth e gel, probably duet oth e higher particlevolum efractio no fth ege l and a lower permeability of the matrix (Van den Bijgaart 1988). Addition of CaCI2 B=±(i 3,t) B =Ui2,t)
0.2 04 */"„ °-6 0.8
Fig. 1.3 Calculated concentration profile of paracasein asfunctio n ofth e relativedistanc e towardsth e bottom of a rennet skim milk gel, after 20 % shrinkage, where / is concentration with regard to the original milk.Tw ofunction so fpermeabilit yar etaken :B = f(r\r ) andB = t(P,t), originalheigh t ofth ege l = 5 mm.Althoug hth e permeability clearlydiffer sth e resulting concentration profilei salmos tth esam e (Van den Bijgaart 1988).
causes ap H drop.Afte r the compensation ofth e pH,th e CaCI2additio n appeared to haveonl y limitedeffec to nth esyneresi srat ean dpermeabilit y (Vande nBijgaar t1988) . Mechanical stress results ina greatl y enhanced shrinkage ofth e gel (Vande n Bijgaart 1988).Th edeformatio ninduce db yexterna lstres sresult si na nincrease dper meability of the network (Van Dijk 1982). Zoon et al. (Il 1989) assumed that at large deformations whole strands will be broken at several places in the network. This microscopic fracturing thereby causes large pores inth e gel.Furthermore ,th e defor mation will certainly facilitate formation of new contacts, and thus increase the pres sure upon the whey. After small and rapid deformations the original shape of the gel is largely recovered, but after longer lasting stresses or greater deformations it is not recovered. Hence, the gel has both elastic and viscous properties and therefore rheological behaviour of the gel is time-dependent (Zoon et al. 1988). The network consistso fstrand so fvaryin gthicknes s andsiz e (Zoone tal . 1988).Lon glastin gstres seso r greaterdeformation swil lcaus ebreakin go fsom eo fth estrands ,s oth e broken endswil lno t reformi na rando mway ,bu t insuc ha wa ytha tthe y arestress-free .Thi s processwil llea dt oa slo wyieldin go fth estrands ,afte rwhic hth eloos eend sma yfor m new junctions elsewhere (Van Vliet et al. 1991). Rapid and small deformations may also break the strands, but the yielding will not take place and the bonds will immediately be restored asth e stress isreleased .A sth e network consists of strands ofvariou s sizesan dthickness ,th erelaxatio ntime s ofth estrand s innetwor k willvary : consequently the network has awid e spectrum of relaxationtimes .
1.4 Practical aspects of curd preparation Incheesemakin gth e clotting of milk isfollowe d by cutting the gel into pieces. The cutting induces syneresis, which starts at the outer layers. Hence, in the outer layerth e concentration of paracaseinwil lsoo n be higher than inth e inner part of the curd grain.A s syneresis proceeds,th e outer layer becomes more concentrated and is sometimes referred to as a skin. The syneresis rate, defined as volume of whey expelledpe r volume oforigina lgel ,wil ldepen do nth esiz ean dth esurfac e areao fth e curdgrain s (Walstrae t al. 1985).Th efirmnes s ofth e gela tth emomen t ofcuttin g and thewa yo f cutting/stirring determineth esiz edistributio n ofth ecurd grain s (Straatsma & Heijnekamp 1988) and thus affect the syneresis rate. Van den Bijgaart (1988) attributed the permeability of syneresed curd mainly to the permeability of the outer layers.Walstr a et al. (1985) suggestedtha tth e skin may also decrease deformability, andthereb y retardshrinkage . Other important variables that affect the syneresis rate ofrenne tinduce dgel sar epH ,temperatur e andpressur eapplie dupo nth ecur dgrain s (Walstra et al. 1985). The applied pressure will depend on the process conditions in the cheese vat: the mixture of curd grains and whey is commonly stirred to prevent sedimentation of the grains and to promote syneresis. Stirring intensity and volume fraction of the curd grains during stirring determine the pressure on the grains and thereby syneresis rate (Vande n Bijgaart 1988).Th e pH,i nth e caseo f Goudachees e manufacture, will mainly be determined by the amount of starter culture and CaCI2 added.Th estarte rwil lprobabl y notproduc esufficien t lacticaci dbefor emoldin gt oac complish a significant drop in pH, but the starter contains a small amount of lactic acid, that will, together with the added CaCI2 solution, instantaneously decrease the pHb yapproximatel y 0.2 units (Walstrae tal . 1987).Th eclottin gtemperatur e isusuall y around3 0 °C, but oftenth etemperatur e israise dwhe nth ecurd iscu t andstirre dfo r a while. In Gouda type cheese manufacture, usually a part of the whey is removed before hotwate r isadde dt oth eremainin gcurd-whe y mixture.Th eexten to fsyneresi s will not only be determined by the syneresis rate, but also by the time during which syneresis cantak e place.Th e end point of syneresis, probably at acurd volum e less than0. 3time s ofth eorigina lvolum e (Vande n Bijgaart 1988),i sgenerall y notreached . Minor variations in curd preparation of Gouda cheese among various manufacturers are common and among different cheese types larger variations exist. For instance, studies onth ecur dgrai nsiz edistributio n ina cheese ,i.e .th e moststudie d parameter relevantt o curd grains, revealedwid evariatio n betweenvariou s Swisssemi-har dan d hardchees etype s (Rüegg& Moo r 1987).Heerin k (1981)foun da neffec t of curdgrai n sizedistributio n uponth edrainag e behaviour.Th ewate r contento fth echees ei sals o affected by the curd grain size (Straatsma & Heijnekamp 1988). The curd grain size may havea neffec t uponth edrainag e behaviour, butth ewate r contento f curdgrain s will vary with size as well, thereby affecting the water content of the cheese. Thedrainag ebehaviou ro fcurd ma ydepen do n(som eof )th eparameter sgive n above.Variou s empirical methods have beenpropose dt o determineth e proper time to start drainage of the curd. Scott Blair & Coppen (1940) introduced the so called pitching point technique. A cylindrical sieve was filled with curd grains and inverted after 50 seconds. Then the height of the curd cylinder was measured. Because the observedheigh tappeare dt odepen do nth econsistenc y ofth ecurd grain san do nth e filling level of the sieve, the column was reinverted and after 7 seconds it was weighted.B ytakin gth eweight/heigh t ratio,th eeffec to ffillin gleve lcoul db eeliminate d and nowth e ratio appearedt o be an adequate measure of thetim e to start pitching. An empirical relation between drainage behaviour and consistency ofth e curd grains is usedi nth efollowin gtest .Th echeesemake rsqueeze s ahandfu l of curdgrain s and thecurd isconsidere d "ripe"i fth egrain sar ereadil ytransforme d intoa coheren tmas s that can easily be divided into the original curd grains again. Sometimes, the colour ofth egrain s isuse da sa nindicatio n of ripeness (Vande r Haven &Oosterhui s 1986). Theyello w colour reflectst o acertai nexten t (depending onth efee d ofth e cows)th e concentration ofth efa tphase .Alternatively ,th eappearanc e (gloss) ofth ecurd grain s may beused .A handfulo f curd grains istake n and ifto o many ofth e curd grains are shiny,th e curd is not considered ripe (Vande r Haven & Oosterhuis 1986).Th e shiny appearance isprobabl y causedb ya fas tsyneresi sdu et oth epressur eincreas ewhe n curd is lifted out of the whey. Inlate r stages of the curd preparation the effect of the increased pressure on syneresis will be less, resulting in a less shiny surface. Replacing such more or less intangible methods by more reliable and universally applicable tests could be useful. The results of this thesis may provide relevant information to achieve that. 1.5 Practical aspects of the draining of curd Varioustype so fdrainag e equipment areuse dt o performdrainage , depending on the scale of production, variety of cheese produced, and cost/benefit ratio. Sometimes, draining is performedi nth e cheese vat itself. This is particularly done in smallscal e production unitslik echees efarms .Afte r stirring ofth e curd-whey mixture, thecur dgrain sar eallowe dt o pitch.Th egrain sar ecollecte db ymean so fa perforated stainless steel strip. Subsequently, the curd grains are left for a certain time. Direct application of a high stress causes "jamming"; a very rapid decrease of the per meability,causin gpoo r drainagebehaviour .Th ewattin gperio dseem st ob eimportan t to createfusio n betweenth e grains (Kerkhof 1979).Afte r awhile ,a pressure is often exerted uponth e collected grains by putting a perforated stainless steel plate on top and/or by removing the whey (leading to decreased buoyancy, hence increased pressure).Th ecurd mas si scu tint oblock san dpu tint ochees e molds.A tsom efarm s the curd is stirred/scalded very intensively, by which the water content will become low; immediately after stirring the curd grains are put into molds. Infactorie s two types of draining equipment are used: batch and continuous. Inth e case of batch-wise drainage the curd-whey mixture is pumped into a shallow vessel, the so called "strainer". The curd grains are evenly distributed in the vessel, and left for a while. Then the whey is removed through the perforated bottom. The curd bed is cut in blocks and put into molds. Various types of continuous drainage machines have been constructed, but the basic feature is mostly the same. Vertical pipes arefilled wit ha curd-whe y mixture,thi s mayeithe r bedon efro mth eto p orfro m the bottom of the pipe.Th e whey is removed through (sections with) perforations in the cylinder wall, i.e. in horizontal direction. The whey outlet is in most machines restrictedb ya bac kpressure .Th eus eo fcontinuou sdrainin gequipmen trequire s (due toth e curd preparation being batch-wise) abuffe rtank .Sometime s apar t ofth ewhe y in the buffer tank is removed before draining. A schematic drawing of a continuous drainage machine isgive n in Figure 1.4. Curd grains will sediment ifth e curd-whey is not stirred.Th e stirring and ageing ofth e curd grains inth e buffer tank changes the properties of the curd grains as time goes on. The changed properties of the curd grains induce avariatio n inth ewate r content amongth e cheeses after drainage.Thi s variation canb e reduced by slow cooling ofth e curd/whey mixture inth e buffer tank, thereby reducing syneresis (DeVrie s &Staa l 1974). Smarttimin g ofth e cheesepres sesfurthe r reducesth evariatio ni nwate r content (DeVrie s& Staa l 1974):Pressin go f TheCasomati cdrainag esystem :Th ecurd/whe y mixturei stemporaril ystore di na buffertank (1).A t(2 ) it is pumped into the drainage pipe. A whey inlet (3) is used to fill the pipe at the beginning and to supplement whey.Th e levelo fth ewhe yan dth e curd grainsca n be monitored ina viewglas s (4).Th e whey isremove dthroug h sieves (5) atthre e subsequentwhe youtlet s (6), (7) and nearth e bottom.Th e curd column iscu ta t (8).A nstepwis evie wo fth ecuttin g isgive ni nth eadjacen t figure.A t (1) the curd column makes a downward movement. At (2) the cutting is made and the block is shortly pressed between bottom ofth e knifean dth e piston.A t(3 ) thecur dbloc k ismove dan da t (4) the moldi sfilled .
9 moist curd blocks effectively stops drainage byth eformatio n of awell-close d rind.Al l curd blocks of a batch are pressed at the same time. Hence, the interval between drainagean dpressin g islonge rfo rth efirs t moldedcur d blocks.Continuou s drainage equipment isgenerall y usedi nlarg escal ebul kproduction ,becaus ei ti smor e efficient thana strainer . However,continuou sdrainag eequipmen t limitsth eflexibilit yi nth esiz e andshap eo fth echeese .I nplants ,whic hproduc eman ydifferen tvarietie so fcheeses , strainers are preferred.
1.6 Theoretical aspects of drainage of curd Inth e draining equipment the packing of curd grains will initially bever y loose andth epackin gwil lbecom e morecompac t asdrainin gproceeds .Th ecompactio no f thecur d block isdirectl y linkedt oth eflo w ofwhe y out ofth e curd block. Inprinciple , thewhe y canflo w through the curd grains aswel l asthroug h the openings between them. Although only afe w experimental results have been published (Heerink1981 , Kerkhof 1979),i ti sknow ntha t acur dcolum ncompact sver y rapidly.Th e compaction will probably vary with the properties of the curd grains and the process conditions duringth e drainage. Darcy's law can beapplie d to avertica l column with drainage in axialdirection :
where
10 a skim milk gel, its relative remaining volume being 0.2), the superficial velocity, i.e. flow rate/cross-sectional area, would be 10"6 m.s'1. The compaction during 1000 seconds would be only 1 mm, i.e. orders of magnitude smaller than observed. Obviously,th e permeability of adrainin g curd block isdetermine d byth eflo wthroug h the connected pores between the curd grains and not by the permeability of syneresed curd grains.Th e flow through the curd blocks will be determined by size, shape and number of the interconnected pores, any of which will change during drainage. The compaction of acurd column may resultfro m altered packing of the curd grains (reorientation) and from deformation of the curd grains. Probably, the compaction isinitiall y causedmor eb y changes inth epackin gtha n bydeformatio n of the curd grains (Kerkhof 1979).Th e size andshap e ofth e pores presumably change slower inth e case of deformation than inth e case of reorientation.Th e reorientation isprobabl y restrainedb yfusio n betweenth ecur dgrains ,becaus e itwoul drequir eth e breakage of some of the bonds between the curd grains (Kerkhof 1979). The deformation of a curd grain will probably be determined by its surroun dings, its compliance and the exerted stress. Deformation will increase the contact areabetwee nth ecur dgrain s andthereb y extendth eare aove rwhic hfusio nca ntak e place. The fusion of curd grains is considered to result from the formation of bonds between the grains. The formation of bonds will probably be determined by the reactivity of surfaces of the curd grains and the distance between the reactive sites involved.Th e reactive sites will often not exactly matcht o one another, but Brownian motion will cause movement of the sites, thereby increasing the number of bonds formed. The process is likely analogous to the processes inside the curd grains (Green & Grandison 1987). However, it should be noted, that the outer layer of the curd grain will be almost devoid of fat globules, because the globules are lost inth e whey during cutting/stirring of the gel (Mulder et al. 1966). Hence, the formation of bondsbetwee nth esurface so fcurd grain swil lno tb ehampere db yfa tglobules ,whic h do normally not contribute to the network. Curd grains tend alsot o adheret o many materials, includingthos e commonly usedi nth echees e industry (Hostettler &Stei n 1954). Emche t al. (1967)foun d acon siderable effect of the wall upon the flow of curd grains in certain types of cheese presses.
il Duringcompactio no fth ebe dsom ebond sbetwee ncur dgrain swil lbreak .Thi s may ultimately leadt o breaking of thejunctions , i.e. allth e bonds between two curd grainstogether . Theexten t of breaking of bonds will probably depend upon the area over which fusion has taken place, the number and type of the bonds, the exerted mechanical stress andth e packing of the bed. Inadditio nt oth e drainage of curd,th e preparation of curd andth e pressingo f the curd blocks are among the factors affecting the water content of cheese before brining. Moreover it has to be taken into account that the water content of a curd block isa naverage ,becaus eth ewate rwil lb eunevenl ydistribute dthroughou tth eloa f (Geurts1978 )an di na differen tpatter na tth evariou sstage s (Straatsma& Heijnekamp 1988).Th e moisture in a curd block is composed of whey between curd grains and whey inside the grains, whileth e proportion will probably vary at the various stages. Obviously, the determination of merely the water content is of limited value when studyingdrainage .Kerkho f (1979)alread y indicatedth enee dt omeasur eth e porosity; however up till now no one has developed a method to do so. Inorde r to studyth edrainag e onecertainl y hast o controlth ecur d preparation strictly. The water content, the deformability, the shape and size (distribution) of the curd grains and the reactivity of the surface of the curd grains may affect drainage behaviour. Investigators often try to perform the curd making in a more or less reproducible way by taking "standardized conditions" (Heerink 1981, Straatsma & Heijnekamp 1988).A major problem inthi s approach istha t the results are only to a limitedexten tapplicabl et oothe rconditions .Moreover ,th echaracterizatio no fth ecurd by meaningful parameters is hampered byth e lack of suitable standard procedures. Althoughdrainin g isa nessentia lste pi ncheesemaking ,onl y afe w publications onthi s subjectexis t (Walstrae t al. 1985).Certai nimprovement s aredesirable , butth e lack of understanding ofth efundamental s of drainage hampers these developments. Current problemsare : 1)Controllin gth estandar ddeviatio no fth ewate rconten t ofth e cheese requires anextensiv etria lan derro r procedurewhe nne wdrainag e equipment is being put into use. 2)Today , the standard deviation ofth e water content inGoud a cheese manufacture isapproximatel y 0.6% (Straatsmae t al. 1984).A reductio no fthi s figurewoul dincreas eth eyield .3 )Th eproductio n ofwhe y powder ishampere db yth e presence of curd fines, a considerable reduction of the amount of curd fines in the second whey may be accomplished by appropriate drainage (DeVrie s & Van Ginkel 1985).A n additional advantage hereby isth e slight increasedyield .4 ) Theleakag e of
12 whey out of the curd blocks before, during and after pressing results in fouling, therebycausin ga build-u po funwante dmicro-organism s andphages ,an da decreas e of the quality of the whey. Whey of satisfactory microbial quality has become a valuable product andth e costs of the sanitation andth e waste water treatment have risen dramatically over last years. Hence, reduction of the amount of leaked whey is attractive. In Gouda cheese approximately 25% of the weight of the curd block obtained after draining is lost by whey leakage before brining. 5) The use of the current continuous drainage equipment restricts theflexibilit y ast o shape and sizeo f curd blocks.6 ) Certainqualit y defects of cheesear elinke dt odrainage , especiallyth e growth of molds just below the rind of cheeses made in continuous drainage equip ment occurs frequently. Other quality defects attributed to draining and/or pressing include increased firmness near the rinds and cracks (Schaller 1991). The improved process would ideally produce identicalcurd blocks,tha t do not leakwhe y anymore,wit ha wate r contento f about47 % (inth ecas eo f Goudacheese , 12 kg). Subsequently the block should be pressed, without getting a substantial moisture loss,t o obtain awell-close d rind.
1.7Theoretica l modelling of drainage of curd The draining of curd can be characterized as a particular type ofexpression , and in this section it will be considered as such. Expression means the expelling of liquidfro m asolid-liqui d mixture by squeezing or compaction (e.g.Shirat o et al. 1986, Schwartzberg 1983);mostl y the solid consists of discrete particles.Th e mainfactor s governingexpressio nar eth einteractio nbetwee nspee dan dexten to fcompaction ,th e amounto f liquidtha tca nb eexpressed ,an dth eforce s neededt oachiev e compaction (Schwartzberg 1983). Most commontheoretica l approaches are (modified) Terzaghi models (Leclerc & Rebouillat 1985) as shown in Figure 1.5.
13 P =0 P =P P =P P =0 f f t f f f P =0 P =0 P =P -P P =P m m m t f m t
Fig. 1.5Th eTerzagh imodel ,explaine d bya frictionles spisto ni na cylinderfille dwit ha n incompressible liquid, a spring,a stopcock and a load. In (a) a spring isimmerse d ina cylinderfille dwit hwater . In (b) a load isapplied .Th e piston cannot descend andth e liquid pressure isequa lt o the applied pressure. In(c )th estopcoc ki sopened ,wate rescape san dth episto nsinks .A t (d)th esprin gcarrie sth etota lloa d (Vande n Bijgaart 1988).
One of the basic presumptions in these models is that any element under stress is instantaneously deformed. Time dependent behaviour of the solid-liquid mixture is caused by restricted liquidflow . Furthermore,th e expulsion of liquidfro mth e solidi s assumed to be zero. Kerkhof (1979) applied this theory to the drainage of curd. He concludedfro mcompariso n betweenhi sexperiment s andhi smode lcalculations ,tha t instantaneous deformation of the curd grains did not take place and that the time- dependent deformation ofth e curd grains isa n essential step in drainage behaviour. Therefore Kerkhof (1979) formulated a new model. In this model, called the relaxation and expression of particles (R.E.P.),th etime-dependen t behaviour of curd istake n intoaccount . Itwa suse dt o predict uni-axialdrainag e behaviour ofthi n layers of curdfro m results obtainedfro m compression experiments. Schematic drawings of Kerkhof'scompressio nexperiment san ddrainag eexperiment sar egive ni nFigure s1. 6 and 1.7, successively.
14 displacement transducer
o. o. weicht s /o^ovw^^^^v(ys/k/s/ sieve curd/whey mixture
Fig.1. 6Schemati c representation ofth ecompressio ntest sa sperforme db yKerkho f (1979).A fairl ythi n layer of curd iscompresse d by means of a weight ontop . The compaction is measured by meanso f a displacement transducer.
^displacement level controller s transducer > > whey > whey supply > sieve pressure curd gauge sieve
whey collection
Fig. 1.7Schemati c representation ofth edrainag eexperiment sa sperforme d byKerkho f (1979).A fairl y thinlaye r of curd ispu t ina vessel .Th e bottom ofth evesse l iscovere d bya sieve.Th e compactiono f thecur dlaye r ismeasure d bya displacemen ttransduce rtha t ismounte dt oa sieveo ntop .Whe yflow s through the curd layer, while its level is kept constant by the level controller. The liquid pressure dif ference can be measured bya pressure gauge.Th e amount ofwhe ytha tflow sthroug hth e curd layer isregistered .
15 He based his model on the following presumptions: 1)Th evoi d ratio (= freewhe yvolum e peruni tvolum e curdgrains ) (e)change s when a stress (pj isexerte do nth epacke dcur dgrains ;th efina lvoi drati o (e*)depend so n the exerted stress. 2)Th evolum e ofth ewhe y inth e curd grains per unitvolum e dry matter (Q) changes due to the exerted stress; the final whey volume fraction (Q*) will depend on the exerted stress. 3)Th e rates of change infre ewhe y content andwhe y content of the curd grains are proportionalt oth edifferenc e between actualvalu ean dfina lvalu eo fthes equantities . These quantities are thus represented inth e equations (1.2) and (1.3) respectively:
£-nfc.(e-e') <1-2) where e = void ratio (m3/m3) f = time (s)
ke = first order rate constant (1/s) e* = final void ratio (m3/m3) and
^ = -ka (O - O') (1-3) where Q = volume of whey inth e curd per unit volume of dry matter (m3/m3) t = time (s)
kQ= first order rate constant (1/s) Q* = final volume of whey inth e curd per unit volume of dry matter (m3/m3) 4)I nth edrainag eexperiment s (Figure1.7 )th econtributio n ofth eexpelle dwhe yt oth e totalwhe yflo wacros sth ecurd be dwa sneglected ,becaus e relativelythi ncur dlayer s were used. Therefore the superficial velocity of the whey at any time was uniform throughout the curd bed, although it decreased withtime . 5)Th ecompactio n ratea tth eto p ofth e curd bed ishighe rtha nth e compaction rate nearth e bottom ofth e curd bed. However, comparedt oth e superficialvelocit y ofth e whey across the bed the difference in compaction ratethroughou t the curd bedwa s
16 very small, because thin curd layers were used. Therefore this difference was neglected. In Kerkhof's model,compactio n duet o decreasing porosity andt o decreasing curdvolum e aredistinguished .Relation sfo rth e decrease infre ewhe y volume andi n curdvolum ewer ederive dfro mcompressio nexperiments .Th ecompactio no fth ecurd bed in the compression experiments was assumed to result solely from whey expulsion from the curd grains after a certain arbitrarily chosen time, i.e. the change infre ewhe y contentwa sthe n assumedt o bezero . Inothe r words,th efirs t order rate constantk ewa sfa r largertha nk a. Asa resul to fthis ,a grea tpar t ofth einitia lcompac tionwa sattribute dt oth edecreas e ofth evoi dratio ,an dals oth eequilibriu mvoi drati o e* was reached in an early stage. The now remaining part of the compaction curve was usedt o fit afunctio n of curd volume versus time, according to the assumptions 2an d3 give nabove :se eequatio n (1.3).Thi sfunctio ni sextrapolate dt ozer otime .Th e difference in compaction height between total compaction and the function that describesth ecompactio n duet o decreasingcurd volume ,i scause db yth e reduction ofth efre ewhe ycontent .Subsequently ,a functio no fth edecreasin gfre ewhe yconten t isfitte d according toth e assumptions 1an d3 : see equation (1.2). Figure 1.8 depicts
h'
h'tota l ft curd grains epe 7 /»'free whey
Fig. 1.8A nexampl eo fth ecalculatio no fth econtributio no fth evolum eo fth ecur dgrain s( 17 the above relations graphically. This technique, although probably subject to anon - negligibleerror , results ina fina lvalu efo rbot hfre ewhe yvolum ean dcur dvolum ean d in proportionality constants for both variables. By conducting compression tests at various pressure levels, several values are obtained of e',k v Q*an dk Q, and plotted versusth e exerted stress.Th e obtainedvalue s are used inequation s (1.2) and (1.3), to calculate the change in curd volume andfre e whey at any stress. InKerkhof' sexperimenta lsetu pth eliqui dpressur e (pf)wa skep t constant.Th e superficial flow was calculated by Darcy's law from the liquid pressure and the total permeability, where the latter was obtained by integratingth e local permeability over the height of the column. Darcy's law could be usedt o calculate the liquid pressure at any place from the local permeability and the superficial flow. The latter was constantthroughou tth ecurd be d (assumption4) . Kerkhof modifiedth edistance sint o distances relative to the solids in the curd, whereby assumption (5) resulted in constant (relative) superficial flow. The stress upon the curd grains was calculated fromshea rstres sdu et o liquidflo wan dth epressur eexerte db ycurd upo n underlying layers due the density difference between curd and whey. The equations (1.2) and (1.3) were usedt o calculateth evoi drati o (e) andth ewhe y content ofth ecur d grains (Û). Finally the model needed a relationship to calculate the local permeability, Kerkhof used a relationship between permeability and porosity. This relationship has been sought much after, but a universal solution does not exist (Scheidegger 1960). Kerkhof dividedth e relation more or less arbitrarily into3 periods, depending onvoi d ratio. Inth e beginningth e packing of the curd is loose, andth e curd column can be compacted without altering the surface area of the curd grains, the Blake-Kozeny relation was used: B L-IB (1.4) 150 (1 - e)2 where B = permeability (m2) e = porosity (-) dp = diameter of the spherical curd grains (m) Inth e second period the decreasing porosity is accompanied by afas t decrease in 18 surface area of the curd grains, therefore the Blake-Kozeny equation (eq. 1.4) was modified.I nth ethird phas eth ecompactio nresult si nblockin go fsom eo fth eintercon nected openings, resulting in a fast decline of permeability. In neither of the above periods the permeability, as derived from theory values, exactly matched the experimental ones. To achieve this, Kerkhof needed the experimental results of the permeability test itself. Ifth estartin gcondition s areknown , thecalculatio no fth enex ttim este pca nb e executed, et cetera. The scheme is displayed in Figure 1.9. t = 0 read in curd characteristics e(0)=f(/j)ß=f(e) ft Q(0)= 1(h) f B(h,t) ZPO) I whey content (t,h) Fig. 1.9 Computer flow chart ofth e calculations ofth edrainag ethroug ha thinlaye r ofcur d according toth e R.E.P. model (Kerkhof 1979).Th e input parameters are inth e box.Th evoi d ratioa t start isuse d tocalculat eth eloca lpermeabilit yo fth e infinitesmal llayer so fcurd .Th eloca lpermeabilit y isintegrate d toobtai nth etota l permeabilityo fth ecur dbed .I ncombinatio nwit hth econstan t liquidpressur e (p,) the superficialvelocit y ( Kerkhof compared his model calculations with results of drainage experiments and concluded that the model was in harmony with his experimental results, therefore it could be concluded that the time needed to deform curd grains is essential in the 19 process of draining curd. Kerkhof considered his approach as atentativ e pilot study, i.e. application ofth e modelt o factory conditions, e.g.thicke r layers of curd, was not possiblei nit scurren tform . Furthermore,relationship s onth eparticl e level,e.g .fusio n andwhe y expulsion,wer eonl yempiricall y described.Hi sexperimenta lsetu pha dals o certain"hidden "imperfection s leadingt owron gresults ,a swil lb ediscusse di nsectio n 4.1. 1.8 Scope of the present work In spite of the fact that drainage is an essential step in cheesemaking, the fundamentalknowledg e abouti ti srathe r limited.I ti sstate dearlie rtha tfou r processes can be distinguished in drainage: 1) Additional whey is expelled from the curd grains. 2) Curd grains are deformed. 3) Curd grains partlyfuse . 4) Whey flows through the connected pores between the curd grains. However, quantification of the role of each of these processes is lacking and their mutual interactions are virtually unknown. Inorde rt ostud yth efundamental so fdrainag esevera lobstacle smus tb etaken : 1)Th epropertie so fcurd grain saffec tth edrainage ,therefor eth ecurd preparatio nha s to be closely controlled. 2) Characterization of the obtained curd was difficult, because it was not known beforehandwhic hparameter sar erelevant .Moreover ,standar dprocedure st o perform suchcharacterization swer egenerall yno tavailable ,althoug hthi sha srecentl y become feasiblefo r certainmajo rparameter s likesiz ean dshap edistributio n (Noele tal .1990) . Consequently, adequate control of the curd preparation is difficult to perform. 3)Small-scal e curd preparation results incurd grain stha t may bear little resemblance tothos eproduce d onfactor yscale . Inou rcondition s large-scalecurd productio nwa s mostly not possible. A new method of curd preparation was therefore developed. It enabled the production of almost identical cube shaped curd grains. Thereby, we were able to negotiateth efirs ttw oobstacles ,an da nadditiona ladvantag ei stha t curdgrain so fth e samebatc hcoul db euse dt ostud yprocesse slik edeformatio nan dexpressio na swel l as the overall drainage behaviour. However, our curd grains were not identical to those produced on factory scale; therefore, experiments were also conducted in 20 NIZO'sexperimenta lplant ,wher esample so fcur dgrain swer etake nfro mconventiona l cheesevats . Thecub eshape dcur dan dth ecurd obtaine da tNIZO' sexperimenta lplan twer e used invariou s experiments. The main objectives were: 1) Characterization of the curd grains. Our method of curd preparation made it possible to introduce controlled variation inth e curd properties.Th e development of relevant, measurable characteristics isthereb y feasible. 2) Determination of the role of the drainage vessel.T o that end,th e close control of the properties of the curd was indispensable, because the (variation in) construction andmod eo foperatio no fth edrainag evesse lan dth e (variationin )curd propertie sar e mutually dependent. 3)Th e distinction of thefou r processes involved (seeabove) .Th e cube shaped curd grains provedt o be highly suitablet o study expression anddeformation .Cur dfusio n andpropertie s determining transport phenomena, e.g.th e distribution andsiz eo fth e pores between the curd grains, could also be studied independently. Reliable methods to determine the above mentioned variables, e.g. extent of fusion amongth e curd grains,wer e generally not available.Therefore , agrea t parto f our effort was concentrated onth e development of appropriate methods.Th e results of the experiments were partly usedt o make acompute r model ofth e drainage.Th e aim of the model wast o improve the understanding of the drainage process; it may also be instrumental in saving on costly factory scale experiments. 21 2. Materials & methods 2.1 Curd preparation 2.1.1 Curdmade in a smallcheese vat A4 0 liter cylindrical cheeseva twit hon e rotating knifewa s usedt o make curd. The milk was pasteurized at 72 °C for 15 s and the fat/protein ratio has been standardized to make full-cream Gouda cheese, so called "48+" milk. The milk was clotted at 30 °C with 40 ml CaCI2 solution (397 g/l) per 100 kg (« 1,4 mM) and 20 ml rennet (Rademaker, 10800 Soxhlet units). No starter was used.Th e curd was cut after approximately 30 minutes and scalded at 35 °C after 30 minutes of stirring. Subsequently,th ecurd-whe ymixtur ewa sstirre dfo rabou t3 0minutes .O naverag eth e curdgrain swer emuc hsmalle rtha nthos e madei nconventiona l cheesevats ,becaus e thecutting/stirrin g intensity insmal lchees evat sha st ob ehighe rtha ni nlarge r cheese vats to prevent excessive sedimentation of the curd grains. Excessive sedimentation of the curd grains will enhance fusion between them, resulting in undesired ag gregates. Furthermore,th ereproducibilit y ofth epropertie s ofth ecurd grains ,e.g .th e size distribution of the curd grains, was unsatisfactorily. 2.1.2 Cubeshaped curd grains obtainedin a new typeof cheese vat Control of the curd preparation is essential to study drainage behaviour. Furthermore,th e costs ofth e experiments hadt o be limited andthu sth e preparation of small batches of curd was necessary. However, curd preparation on asmal lscal e often induces "scaling down" effects (see above), unless special (and expensive) precautions are taken,suc h as in the cheese process simulator of NIZO (Straatsma & Heijnekamp 1988). Curd grain size and shape will affect other properties of the grainsa swell . Ideally,cur dgrain so fconstan t shape,siz ean dcompositio n shouldb e available in drainage experiments. Therefore, it was tried to develop an alternative method of curd preparation to achieve this aim. A double walled rectangular perspex box (20 I) with external thermostat, was used to clot the milk. A grid of stainless steel wires in a frame was placed at the bottom of the vat, and another frame of horizontal wires was placed alongside of a wall. The gel was cut in horizontal slabs by moving the latter frame towards the opposite wall. Subsequently, the slabs were cut into cube shaped curd grains by movingth ebotto mfram eupwards .Th ecurd grain swer estirre db ypumpin gfou r liters ofwhe y intoth echees eva tan dsubsequentl y supplyinglarg eai rbubble sthroug hth e 22 bottom of thevat .Th e air flowwa s interrupted by a pause pulse switch (24 seconds pulse, 20second s pause) to avoid breaking ofth e curdgrains ,whil e mixing satisfac torily. The entire setup is displayed in Figure 2.1. thermostatted water-jacket curd/whey pause/pulse air switch perforated plate whey whëy/afr"çïïâ"mbé"r" iL Fig. 2.1 Aschemati c drawingo fth e cheeseva t usedt o prepare cube sized curd grains.Th e curdwa s clotted in the vat and cut into cube shaped particles; the latter were stirred by pumping whey and subsequently air through the bottom of the vat. The openings at the top of the whey/air distribution chamber were temporarily closed during clottingt o avoid mixingo fwhe y and milk. Mixedmil kwa suse dpasteurize dan dstandardize dt ofull-crea mGoud acheese . Themil kwa sclotte db yaddin g4 0m lCaCI 2solutio n (397g/l ) and2 0m lrenne t(1080 0 Soxhlet units) per 100 kg cheese milk. No starter was used. The firmness of the gel was checked by testing the cohesion by slowly lifting afinge r out ofth e gel. Theheigh t ofth e bump whichrise sabov e ofth efla t surfaceo f the gel before fracture occurred and the plane of fracture were judged. The clotting time was usually taken around 35 minutes,th e clottingtemperatur e was 30 °C. The meshsiz eo fth ecuttin ggrid swa seithe r8 m mo r 10mm .Th ecurd grain swer e stirred forapproximatel y3 0minutes .A smuc hwhe ya spossibl e (usuallyapproximatel y 5kg ) was removed and curd was scalded by adding approximately 3 kg wash water to reach a final temperature of 35 °C. Due to the lower stirring intensity and the un favorable sizean dshap e ofth e curdgrain sth e syneresiswa s slowertha n inconven tionalchees evats .Afte raddin gth ewas hwater ,th ecurd-whe y mixturewa sstirre dfo r 23 threet o six hours untilth e curd grains had reached a certain density. In spite of the prolonged stirring, the density of the cube shaped curd grains was less than the average density of curd grains in conventional cheese vatsjus t before draining. 2.1.3Curd madeat NIZO Curd infactorie s differsfro mth ecub eshape dcurd obtained.Therefore , some experiments were conducted with curd grainstake nfro m aconventiona l cheesevat . At NIZO's experimental factory, curd grains were prepared in both Tebel and Ost IV cheese vats.A small portion of the curd grains were used invariou s experiments. 2.2 Density of curd grains Direct estimation of the water content of curd grains has been performed by various workers (e.g. Kerkhof 1979).Thi s water content will vary with the size of the grains; therefore, it will be an average value.Th e common technique of determining the water content of a product is by weighing the product before and after drying. However,a certai nquantit y ofwhe y inevitably adherest oth e curdgrains .A thi nlaye r of whey onth e outside of the curd grains increases the apparent water content sub stantially (Kwant 1980)."Drying "th eoutsid eo fth egrain s bywipin g (Kerkhof 1979)o r suction may induce considerable syneresis. An additional complication istha t whey contains a small amount of dry matter, so the whey content of the curd grains is slightly higher thanth e water content. Accurate calculation of the whey content from the water content is not as simple as expected, because of the steric exclusion of serum proteins (see below). The whey content can also be estimated indirectly by density measurements. Thedensit y ofcur dgrain swa sdetermine d byvariou sauthor s inorde rt o estimateth e extent of syneresis (e.g. Stoll 1966). Whereas a wide range of liquids was used in these studies, we estimated the density of curd grains by-dropping curd grains into thermostatted (35 °C) sodium chloride solutions of various densities. In case of the cube shaped curd the test was confined to a screening, because the density of the curd grains hardly varied. In other cases the percentage of floating curd grains was determined by weighing the floating and sinking fractions. Walstra et al. (1985) in dicated the possibility to calculate the loss of whey from density measurements. A basic presumption hereby istha t the sum of the volumes of the curd grains and the expelled whey is equalt o the volume of the former non-syneresed gel.A curd grain 24 consists of three components, whey, paracasein matrix plus micellar calcium phosphate (="paracaseinate") andfa tglobules .Th e amount of fatan d paracaseinate ina curd grai n hardly changes after scaldingi ncas eo fGoud acheese .Obviously ,th e ratio fat/paracaseinate can be considered constant. All experiments were conducted with standardized milk, the amounts of paracaseinate andfa t per 100k g of cheese milktha t arerecovere d inth e curd grains wereestimate dsuccessivel y at2. 7an d3. 0 kg. Thelos so fparacaseinat e andfa tt oth e whey areestimate d at0. 1an d0. 2 kg/100 kg cheese milk, respectively. The density of a curd grain can be recalculated to the fraction of paracaseinate or whey, if the densities of the three mainfraction s are known. pg = apm +ßp, + yp„ (2.1) where 3 pg = density of the curd grain (kg/m ) 3 pm = density of paracaseinate (kg/m ) p, = density of fat (kg/m3) 3 pw = density of (diluted) whey (kg/m ) a = volume fraction of paracaseinate (m3/m3) ß = volume fraction of fat (m3/m3) Y = volume fraction of (diluted) whey (m3/m3) The sum of the volume fractions will be 1: a +ß + y = 1 (2-2) Wefurthe r put: e = Ë. (2.3) a where 6 = fat/paracaseinate ratio (m3/m3) Combining (2.1),(2.2) and (2.3) yields: a = Pa ~Pw (2.4) + 0 (P< - Pj (Pm- Pj The densities of the fat and whey inth e grains at 35 °C were taken from Walstra & 25 Jenness (1984);fat : 905 kg/m3 ;whey . 1020.8 kg/m3.Th ewhe y inth e curd grainwil l be diluted by wash water. The remaining volume of whey is diluted to 85% of its original concentration and the equilibrium between whey in the curd grains and the whey around the curd grains is reached (90%afte r 25 minutes (Van den Berg & De Vries 1976)).The n the density of the diluted whey can be estimated at 1017 kg/m3. Thedensit yo fparacaseinat ewa scalculate dfro ma nequatio ngive nb y Munro(1980) : 1438 kg/m3.Th e volume ratio fat/paracaseinate then is 1.77. Some difficulties inth e use of this method are: 1) Inth edeterminatio no fth efractio no fth efloatin gcurd grains ,i ttake s approximately 30 seconds before the lastfloatin g curd grain is taken out of the beaker. During the experiment the sodium chloride penetrates into the grains, resulting in an increased density. If the replacement of whey by salt solution is solely caused by diffusion,th e masstransfe rt oa spherica lcur dgrai nca nb ecalculated ,assumin g negligible surface resistance (Heldring & Singh 1981): 2 20 = 2 R £ till sin0JLl exp-" " ' (2.5) C0 - Cs n r £? n R R'' where C = concentration as afunctio n of r and t (kg/m3) 3 Cs = constant concentration at the surface (kg/m ) 3 C0 = initial uniform concentration (kg/m ) R = radius of particle (m) r = radial variable (m) D = diffusion coefficient (m2/s) t = time (s) The following data were used: an effective diffusion coefficient of NaCI of ap proximately 10"9m 2/san d penetration during 30second s ina spherica l curd grain (fl = 0.003 m). In these circumstances approximately 15%o f the whey is replaced by NaCIsolution .Th e density increasewoul dthe n be approximately 2kg/m 3.Th eresul t is likely an overestimate, because the contact time is probably shorter and the outer layer of the curd grain has a relatively low whey content. It is thus likely that the density of the curd grains is slightly overestimated as the curd grains with a density slightly lower than the density of the salt solution will sink. The density difference between two subsequent solutions is 7 kg/m3 (in the case of factory curd we used 26 only five solutions ranging from 5t o 9% NaCI). Consequently only small shifts inth e classification of the curd grains areexpected . 2) Steric exclusion of serum proteins with respect toth e casein micelles occurs (Van Boekel& Walstr a 1989) and itshoul d betake n intoaccoun t ina paracaseinat e matrix. Wheyprotein sar econcentrate di ndomain swithou tparacasei nstrands ,leadin glocall y to aslightl y higher density ofth e"whey" . Itwil lpartl y compensatefo rth e areasdevoi d of serum protein in close environment of the strands. However, as the curd preparation proceeds, the number and size of the domains without paracaseinate strands are likely to decrease, leadingt o aslightl y lower density of the "whey". Inth e extreme case of "whey"totall y devoido f serum proteins, itsca nb ecalculate d by con sidering the density of whey proteins («1350 kg/m3) (Buma 1965) and the con centration of serum proteins in diluted whey; the latter is estimated at 0.5 wt.%.Th e density of the remaining liquid is then estimated 1012.8 kg/m3.Th e lower density of thewhe y wouldcaus e anoverestimatio no fth ewhe y content bya t most of 5percent , but this only happens when the whey content is already quite low. 3) Adherence of salt solution to the outside of the curd grains will be relatively larger for smaller curd grains andtherefor e slightly overestimate the amount of sinking curd grains, because smaller grains have usually a higher density. This is because syneresis proceeds relativelyfas tan dth elos so ffa ta tth eoute r layeri srelativel ylarg e insmal lcurd grains. For spherical curd grains,th e surface area, andthu s thevolum e of adherent salt solution, increaseswit hth e reciprocal ofth e radius ofth e curdgrain . The resulting error issmall ,eve n ifa s mucha s 20 percent ofth eweigh t would result from adherent salt solution, ifth e radii ofth e curd grains differ by afacto r 2an d ifth e true sinking/floating ratio is 1:1,th e error is estimated at 2 percent. 4) The paracaseinate content of curd grains with a decreased fat content, i.e. very smallparticles ,ma yb econsiderabl y overestimated.Moreover ,th esal tuptak eo fthes e small particles is not negligible. Therefore, the whey content can not be estimated accurately from density measurements inthi s case. If future research leads to altered figures for the densities of the fat, para caseinateo rwhe y insideth ecur dgrain ,th eresult sca nb eeasil yrecalculate dfro mth e densities of the used sodium chloride solutions (Wolf et al. 1974, Beattie 1928). Notwithstanding the difficulties mentioned above, the method was found to be satisfactorily reproducible.Th eclassificatio ni npercentage so ffloatin ggrain si nfiv esal t solutions,5 ,6 ,7 ,8 ,9 %NaCI ,respectively , incas eo ffactor y curd provedt o be useful 27 and was convenient asth e results were known immediately. The paracaseinate concentration is directly related to the whey content (both asvolum e fractions),th e latter is given asth efacto r y.Authors , likeva n den Bijgaart (1988),use dth eter mrelativ eremainin gvolum e (/"), i.e.th evolum eo fa synerese dsla b of curd expressed as fraction of the volume of the clotted cheese milk. The composition of milk changes slightly during the season, hence, we estimated the density of the cheese milk at 1024 kg/m3.Th e amount of reclaimable paracaseinate in milk was estimated at 2.7 kg per 100 kg, corresponding to 0.019 m3 paraca- seinate/m3. The relative remaining volume is then: / = — (2.6) where a0 = volume fraction reclaimable paracaseinate in milk a, = volume fraction paracaseinate inth e curd Table 2.1: The densities of the used sodium chloride solutions (p), the corresponding volume fraction paracaseinate inth e curd (a),th evolum efractio nwhe y inth ecur d (K) andth e relativeremainin g volume (O- [NaCI] P a Y / wt.% kg/m3 m3/m3 m7m3 m3/m3 5.0 1028.8 5.410" 2 0.85 0.36 5.4 1031.7 6.7 10"2 0.82 0.29 5.6 1033.1 7.3 10"2 0.80 0.26 5.8 1034.5 7.9 10"2 0.78 0.24 6.0 1035.9 8.5 102 0.76 0.23 7.0 1043.0 1.2 10"1 0.68 0.16 8.0 1050.2 1.5 10"1 0.59 0.13 9.0 1057.3 1.8 10"1 0.50 0.11 28 The relation between density and remaining volume is given inTabl e 2.1. Note: If/ 'i scalculate do n amas s base,th e relative remainingvolum e isslightl y lower, because the density of the curd grain increases with the whey expulsion. 2.3 Size distribution of curd grains Various methods exist to determine the "size distribution" of curd grains, e.g. Niederauer (1976) and Schaap (1970). Both methods use sieves to classify the curd grains in various groups. Curd grains do not have a spherical shape, therefore the results ofeac hsiev emetho dwil lb einfluence db yth e orientationo fth ecur dgrain si n the sieve. Recently a method based upon image analysis that could be used to determine size as well as shape distributions was developed (Noel et al. 1990) Schaap's (1970)metho dt o determineth esiz edistributio no fcur dparticle sha s become astandar d method inth e Dutch cheese industry. A sample of approximately 150g of curdgrain s inwhe y ispasse dsuccessivel y throughfiv esieve s of decreasing meshsize s (11mm ,7. 5 mm,5. 5 mm,3. 5 mman d 1mm) .Th e sievesar e held partly inth e whey, andth e finer particles are sieved out by gentle stirring. The curd grains are dried by gentle dabbing with filter paper andweighed . 2.4 The curd flattener The deformation and the syneresis due to stress of syneresed curd grains is a relatively unexplored topic. The deformation, due to external stresses, of non- syneresed curd slabs under the whey was studied by Van Dijk (1982). The results obtained withhi s apparatus werefoun dt o be notver y reproducible. Vande n Bijgaart (1988) studiedth e shrinkage of curd slabs withth e so-called microscope method.A porous glass filter is placed under water on top of a curd slab, the resulting compaction of the slab is followed by focusing at certain intervals at the filter. The change inheigh tca nb erea do f amicromete r knobo fth e microscope.Th e expulsion of whey occurs only at the top of the curd layer. In draining curd the sideways expulsioni sprobabl y moreimportant .Therefor ew edevelope da ne wmetho dtha tha d closer resemblance to the drainage of curd grains in a curd bed. The deformation of cube shaped curd grains was studied in uni-axial compression. A single curd grain was placed underneath a cover glass, fixed to a stainless steel bascule.Th eforc e acting upon a curd grain could be easily changed by means of adding weights or counterweights. The dimensions of the bascule were 29 takensuc htha tth ebea mstoo dalmos t completely parallelt oth e planeo fth ebottom . The bascule was placed inside a perspex tank filled with a 0.9% sodium chloride solution (having the same osmolality as milk serum). A certain exchange between whey and salt solution will occur, but this does likely not affect the compaction behaviour.Th etan kwa sthermostatte da t3 5 °C. Beforeth emeasuremen tstarted ,th e exerted force was measured by a HBM Q11 force transducer connected to a HBM MC2 amplifier. A photograph of the horizontal cross section of the curd grain was takena tstart ,3 0s an da t90 0s .Th eexerte dforc eo nth ecros ssectio n isth eexerte d stress.Th e height ofth ecurd grainwa s measured by acathetomete r atth e following times: 0 , 30, 90, 150, 300, 450, 600, 900 s. Three curd grains were studied simul taneously. A fourth curd grain was placed without any pressure upon it, next to the other grains and served as blank. The entire set-up is displayed in Figure 2.2. camera üTö thermostat o 0.9% NaCI solution cover glass ft weight curd grain bascule cathetometer Fig. 2.2 A schematic drawing of the curd flattener. The force applied was constant during each experiment, thus the increase in horizontal cross section ledt o adecreasin g stress.Th e areawa s linearly interpolated between the values at 30 s and 900 s to calculate the average stress. The volume reduction of the curd grain could be roughly estimated by taking the (interpolated) cross-sectionalare aan dth eheigh ta teac htime .Th evolum ecorrespond st oth econ centration of paracasein. 30 2.5 Drainage columns 2.5.1Compaction and liquid pressuremeasurements in radial drainage vessels All continuous drainage machines are equipped with one or more radialwhe y outlet(s). To simulate drainage behaviour therein two radial drainage vessels were constructed.Th e batch-wise operated drainage columns consisted of avertica l per forated stainless steel cylinder (diameter 12 or 20 cm, 20.7%openings , pore size 4 mmhig h and0.3 5 mmwidth ) inside aperspe x cylinder. The inner cylinder was partly filled with curd, the outer cylinder was filled with whey, sometimes hot water was added to the whey to increase the temperature to approximately 35 °C. A small spherical porous glass filterwa s mounted inth e middle ofth e curd column afe w cm above the bottom of the column, an altered packing of the curd grains in its direct environmentwa shereb yunavoidable .Th eliqui dpressur edifferenc ebetwee nth eglas s filter andth e outer ringwa s measured by aValidyn e DP45pressur etransducer , with a Dash 6-18 membrane mounted inside, connected to a Validyne CD15 carrier modulator. If the liquid pressure was lower than 5 Pa it could not be measured.Th e liquid pressure transducer had an upper limit of 500 Pa, intha t case the liquid pres sure could be measured from the difference in the water level in two capillaries (not shown). The compaction of the curd column was followed by a HBM W50 displa cement transducer connected to a HBM MC2 amplifier. Bothtransducer s were con nected to a Kipp BD41X- f recorder. The setup is displayed in Figure 2.3. iperforate d U" iwall :;whey;: < < ::y',y.'v„vY,ü:y.x:tä.x*:ü:ü.x;üx&- < ::)::::: < SCÜKft < < lltü < displacement transducer pressure transducer Fig. 2.3 A schematic drawing of the measurement ofth e liquid pressure and compaction of a curd-whey mixture in a cylindrical drainage column. The external pressure was exerted by applying a weight. 31 2.5.2 Permeability tests in a radial drainagecolumn Thegeometr yconsiste do fthre econcentri ccylinders ,a twhic ha liqui dpressur e gradient was installed betweenth e outermost andth e innermost cylinder. The middle cylinder wasfille dwit h curdgrain s anda mechanica l pressurewa s exerted atth eto p (see Fig 2.4). The whey flowed from the outermost cylinder, wherein the level of the liquidwa s highest, to the innermost. impermeable piston to balance Fig. 2.4 The experimental setup ofth e radial permeabilitytest . 2.5.3 Compression andpermeability experiments in anaxial drainage column Kerkhof (1979) used the setup displayed in Figures 1.6 and 1.7. The setup of our compression test was similar to the one used by Kerkhof. A perspex cylinder (diameter 11.5 cm) wasfille d with athi n layer of curd under the whey. Onto p of the curd adis c (25%openings , pore diameter 1.5mm ) with aweigh t onto p wasplaced . The compaction could befollowe d by means of acathetometer . Thepermeabilit ytest swer econducte di na perspe xcylinde r (diameter 11.5cm ) with a perforated stainless steel bottom (25%openings , 1.5 mm diameter pores). A weighted perforateddis cwa splace d ontop .Th ecylinde r wasplace di na vesse lfille d with water, a liquid pressure gradient was installed by keeping the level of the whey inth e perspex cylinder abovetha t of the water inth evessel .Th ewhe y level andth e level of the curd layer could be measured by means of a cathetometer. 32 2.5.4Pressure lossmeasurement in a curd column Thepressur e lossdurin g compaction ina colum ndu et o adherencet oth ewal l was measured bySchwartzber g et al. (1985).Thei r set upconsiste d of acylinde rwal l mounted on top of a load cell, during compaction and relaxation experiments the stress on the load cell was recorded. Wedevelope da nalternativ eapproach .Th epressur e(o ractuall yforce )exerte d uponth e bottom of the cylinder was measured.Th e difference between pressure on theto p plusth e pressuredu et oweigh to fth ecurd an dpressur e onth ebotto m ofth e cylinder is the pressure loss due to adherence to the wall. A perspex disc was mounted to a load cell by means of a 15 cm steel rod.Th e disc was placed in the innercylinde r of one ofth e abovedescribe d drainage columns.A layer of curd grains was put upon the disc. Another disc was placed on top. Weights were placed upon thisdisc .Th eoute r cylinder ofth ecurd colum nwa sfille dwit hwhey .Th eloa dcel lwa s connectedt o aX-f recorder (Kipp).Th esetu p isschematicall y displayed inFigur e2.5 . Measurements were conducted during at least 15minutes . load-cell perforated rod wall weight iix3C^R:XXX5C5C I L^^iv^ ^^33L whey bottom Fig. 2.5 A schematic drawing of the indirect measurement of the pressure loss in cylindrical drainage column.Th eload-cel lha sbee n mounted bymean so fa rodt oth e bottom ofth ecur d bed.Th eexerte d force onth e bottom isles stha nth e sumo fth e forces exerted due theweight s and the curd layer. Its difference isdu et o adherence of curd toth ewall . 33 2.6 Fusion of curd grains under the whey Thefusio no fcurd grain swa sstudie db y llyushkine tal . (1980).The ydevelope d adevic econsistin go ftw ocups .Th ebotto mo fth euppe r cupan dth eto p ofth e lower cupwer e equippedwit h agauze . Both cupswer efille dwit h curd grains andstacked . A load was placed on top of the upper cup, and after 2 minutes of compression the cupswer eseparate dan dth eseparatio nforc ewa srecorde do na rheo-consistometer. It is likely that the method has several disadvantages, e.g.th e curd grains adhere to the gauze, the gauze bends andth e gauze cuts intoth e upper curd layer. We tried to circumvent these disadvantages. The force needed to break the bonds between curd grains wasstudie d by placing astainles s steelpisto nwit h athi n perforated bottom (9.5 cm diameter, 100 holes of 6 mm diameter, thickness of the bottom 1 mm) upon a layer of curd grains under the whey in a 1 liter beaker. The pistonwa sfille dwit hcur dgrain sfro mth esam ebatc han da dis c loadedwit ha weigh t was placed ontop .Th e piston was mountedt o astainles s steel rod.Th e beaker was placed in athermostatte d bath.Th e curd grains inth e upper layer fused inth e open spaces inth e piston with the curd grains inth e lower layer during a certain time. To avoidth eadhesio no fcurd grain so fth elowe rlaye rt oth estainles sstee lpiston ,a filte r paper with perforations congruent and coincidingt o those inth e pistonwa s attached to its bottom bytw o sided adhesivetape . Inth ewe t environment thetap e lost itsad herence to the paper. The beaker was placed in an Overload Dynamics Material Testing Instrument, table model S 100, fitted with a 200 N load-cell. The rod of the pistonwa sattache dt oth eload-cell ,whic hsubsequentl y movedupward swit ha spee d of 100 mm/min. The force needed to break the bonds was registered by a KippX- f recorder. Thefractur e stress was calculatedfro m the contact area between the curd grains,i.e .th esu mo fth ecross-sectiona l areao fal lperforation s inth episton ,an dth e maximum required force. The results of three or four measurements were averaged to account for the deviations (approximately 10 percent of the average value). The setup is schematically displayed in Figure 2.6. 34 mounting Ç~^ whey weighted disc perforated piston curd Fig. 2.6 A drawing of the apparatus to measure the stress needed to break the bonds between curd grains. The curd grains in the top layer fuse with,th e curd inth e bottom layer at the openings inth e perforated piston.Th eforc e neededt o separate bothlayer s isrecalculate d to a fracture stress.A filte r paper, with holes congruent to those in the piston, was glued to the bottom of the piston to avoid adherence of curd to it.Th e glue becomes unstuck inth e wet environment. 2.7 Pore size distribution and porosity measurement Porosity, i.e. the volume fraction of (liquidfilled ) openings in a solid, has been estimatedi na wid erang eo fproduct s byvariou sauthor s (e.g.Scheidegge r 1960),bu t methods to determine the porosity of draining curd or similar materials could not be found in literature. The porosity itself is an important parameter, but the pore size distribution throughout the curd bed may be even more important. We developed a new method to estimate the apparent pore size distribution throughout the curd bed. Due to the characteristics of the curd bed some prere quisites had to be considered.Th e soft and highly deformable material urges a rapid and gentle method. The pores in the curd bed are generally small, therefore the resolutiono fth emetho dshoul db ehigh .Non-destructiv emethod sar et o bepreferred , because they allow the changes in one curd bedt o be measured. The method is based upon anapplicatio n of opticalfibres . Opticalfibre s enjoy a wide range of applications, e.g. in telecommunications and in surgery. The basic feature of all optical fibres is that light is harnessed in the fiber. The extremely pure 35 glass in acladdin g ensuringtota l reflection, hardly reducesth e intensity of abea mo f light. The use offibre s as anoptica l probe was described by Frijlink (1987).Wit hthi s equipment hemeasure dth e bubble size andspee d in air lift loop reactors. Ronteltap and Prins (1989) introduced the idea of a moving optical sensor to measure the bubble size distribution in foams. Our estimation of the pore sizes is based on a variant of this method. Anoptica lfibre (PCS200 ,diamete ro fth ecor e = 200^m , diameterincludin gth e cladding = 380//m ) isconnecte dt o aligh tsourc e aton eend ,wherea sth e other end hasbee nconicall y shaped,endin g ina nearl y hemisphericaltip . Light of wavelengths inth e near infra-red region, is emittedthroug h the tip into the surrounding medium. Some light is reflected into the fibre depending on the conditions inth e surrounding ofth etip .Th e reflected light isprojecte d bymean s of aY-splitte r (GTE-Ateatype Lan - Tap OCL 0102-Y) on a silicon photo-electric cell. The resulting voltage will therefore depend on the medium surrounding thetip . In Frijlink's (1987) setup,wate r andai rcoul d bedistinguishe d by differences in refractive indices between air (n = 1) and water (n = 1.33). Differences in refractive index between whey in curd grains and in expelled whey are, however, unlikely. Nevertheless, the intensity of the reflected light was clearly higher inside curd grains than in whey. This is presumably caused by the increased light scattering in curd grains. The glass fibre is held in acapillary , its tip protruding by approximately 5mm . The capillary is attached to a pneumatic cylinder. By sliding the piston,th e capillary can be moved up and down, its stroke being 10 cm.Th e position of the capillary is recorded by means of linear potentiometer (Elap pis 100), mounted alongside of the piston. The speed of the capillary is controlled by a reducing valve. A cylinder of perforated stainless steel (diameter 12 or 20 cm, 20.7 % openings, pore size 4 mm highan d0.3 5 mmwidth )wa sfille dwit hcurd grain san dwhey .Th ecolum nwa splace d ina plasti c vessel, that had beenfilled wit hwhey . Drainagewa s enhanced by putting a weight on a perspex disc on top of the curd. The capillary could be put either ver tically,throug h holes inth edisc , or horizontally,throug h holes inth ecylinder , intoth e curd column. The latter option was hardly ever used, as the positioning caused experimental problems. Initially the compression of the curd column was performed withth e perforated disc on top of the curd column, but it appeared later on that the flow of whey was influenced by the holes, so later on a solid disc was used to 36 compact the column, and was replaced by the perforated one before the measure ment started.Th e position ofth efibr eti p andth evoltag eo fth e photo-electric cellar e both registered in acompute r (HPVectr a ES12 )wit hth e aid of a Metrabyte DAS-16 data-acquisition board.Th e entire setup is graphically displayed in Figure 2.7. displacement meter lightsourc e photo electricee l Fig.2. 7A schemati cdrawin go fth e porositymeter . Thesignal so fth ephoto-electri c cellan dth elinea rpotentiomete r weresample d at afrequenc y of7 kHz and6 4kbyte s weretake n at atime .Thi s corresponds to one sample per 6// m and a probe speed of 2 cm/s. The signals were sent directly to a harddis kunde rth es ocalle dDM Amod e (directmemor yaccess )an dconverte dafter wards.Externa ltriggerin gwa sused .Th eprogrammin glanguag ewa sAsys t3.10 .Con tinuous sampling of both position and voltage of the photo-electric cell results in a voltageversu s position pattern (Figure2.8) .Th ecircuitr yo fth ephoto-electri c cellwa s such that the smallest reflection corresponds to the highest voltage. The signal showed a small dent followed by a sharp rise at curd-whey transitions and a peak followedb yrapi ddecreas ea tth ewhey-cur dtransitions .Th esigna lwa sconverte dint o chordlength so fwhe y bydeterminin gth esubsequen t positions ofth e largest positive and largest negative slope. The interpretation of the signal was hampered by the occurrence of shoulders andride rpeaks ,therefor ew eassume dtha t peakswithi n0. 3 mmo feac hothe r belongedt oth esam epore .Th echor dlengt ho fwhe y isusuall y not identicalt oth e true dimensions of apore ,a s piercing of ahorizonta l cylindrical pore 37 mm porosity = fraction B Fig. 2.8 Exampleo fa part ofth eanalogu e signalo fth e photo-electric celldurin g apenetratio n ina curd bed. The conversion of the signal to a local porosity is also depicted. exactly through its poles is not likely, so the apparent dimensions will be usually smaller than the real ones.Th e sum of the apparent pore widths as afractio n of the total penetration length through the curd block isth e local porosity. Theresolutio no fthi s methodi sno texactl y known.Th efibr eti p hada diamete r of approximately 20fjm. Therefore, whey pockets smaller than thetip' s diameter will reflect, atth e maximum,onl y apar to fth ewhe y signal.I nthes e casesth esigna lmay , depending onth e limitsformulate d inth e software, be interpreted as originating from curd grains. The sample rate in the direction of the movement of the fibre is approximately one per 6 //m. Therefore, the shape of the pores may affect the resolution of the method. The resolution of the method may also depend on the characteristics of the curd grains. Curd grains are visco-elastic, therefore, the penetration of the fibre into the curd grains will be preceded by an indention of the grain,jus t liketh efina lpunctur eo fth ecurd grai nwil lb eprecede db ystretchin go fth e outer layero fth ecurd grain .Thes etw oeffect swil lcompensat e eachothe rt oa certai n extent.Th e resolutiono fth emetho d cantherefor e not exactly begiven ,bu tshoul db e estimated atapproximatel y 20/ym . Finally it hast o benote dtha t thefibr eti pwa sver y delicate and occasionally snapped. The production of identical fibre tips was until recently not possible, hence,therefor e the resolution of the method may not always 38 have beenth e same. 2.8 The water content of a curd block Thedeterminatio n ofth ewate r content of adraine d curdbloc k ishampere d by the rapid whey loss that occurs when curd blocks are taken out of the whey. The amount of whey lost will deviate, depending on the permeability of the block at that moment. Another source of experimental error isth e amount of whey clinging atth e outside of the curd block. In general,thes e two errors cause that the water content of moist curd blocks is underestimated and the water content of relatively dry curd blocks isoverestimated .T o minimize moisture loss,th ecurd block is put immediately into aplasti c container.Th e container isseale dt o prevent evaporation.Th e container is weighed, and the curd block is taken out and put into a mortar. The container is weighed again.Th e drip whey is removed and the container is weighed once more. The curd block is made homogeneous in the mortar or a mixer/blender. Three samples of 2t o 3g are driedfo r 30 minutes at 159 °C. To conform toth e NEN375 4 standard (1981) 0.3% is subtracted from the calculated dry matter content. The dry matter content of the drip whey is estimated at 6%. The total water content of the block iscalculated . 2.9 Confocal Scanning Laser Microscopy (CSLM) The inner structure of the outer layer of curd grains could be studied with CSLM.Th e major advantage ofthi stechniqu e istha t pictures canb e made atvariou s depths (up to approximately 0.1 mm) without disturbing the sample by cutting. The apparatus usedwa sa Biora dMR C600 ,fitte dwit ha nArgo nlase r (488/jm) anda BH S filter.Th e curd grains were stained with Rhodamine B.Th e samples were conserved with Thiomersal (BDH chemicals). 39 3. Curd properties 3.1 Characterization of curd grains The paracaseinate content in the curd grains will increase with time during cutting andstirring . However, syneresis ratedepend s partly on milk composition and inth e new cheese vat (see Section 2.1.2) accurate control of the stirring conditions was difficult. Preparation of curd grains of a precisely known moisture content by means of a fixed time schedule was thus not feasible. We therefore determined the density of the curd grains (Section 2.2) as a function of time and started the ex periments whenth e density of the grains reached a pre-set value. The concentration distribution of paracaseinate inside a curd grain is not homogeneous, because syneresis proceeds fromth e outside, hence,th e densitywil l be an average value. The influence of the curd preparation upon the concentration profile is not known. However, curd grains of equal density, but of different size,wil l havea differen tconcentratio nprofile ,becaus eth esurfac earea/volum erati oi spropor tional to 1/ft, i.e. larger curd grains have relatively little outer layer and a relatively large inner part. The concentration of paracaseinate in the central part of the curd grain is below the average,an dth e concentration of paracaseinate inth e outer layer of a relatively large curd grain will be relatively high and/or the concentrated outer layer will be thicker. The cube shaped curd grains were actually shaped like dice, with rounded corners (see Figure 3.3 a).Th e curd preparationtoo k longer time (4t o 6 hours) than normal (1.5 hours), because ofth e unfavorable stirring conditions and particle shape andsize .A sexpected ,th e preparation ofcurd grains cutwit h an8 m mgri dtoo k less time than that for those cut with a 10 mm grid (approximately an additional hour). The size ofth e pieces of is not determined byth e cutting alone, asth e largest curd pieces may be shattered at the subsequent stirring (Johnston et al. 1991). It is likely that the firmness of the curd pieces is also relevant hereby, as firm gel pieces may be pushed aside byth e knife instead of being cut.Th e size ofth e curd grains at NIZO's experimental plant variedfro m very small curdfine s to more than 10 mm for the largest diameter of the largest curd grains. The shape of the curd grains also varied greatly, some curd grains being angular, others rounded or disc shaped, and occasionally smallcluster s (offuse dcur d grains) werefound .W ecompare dth egrai n size distribution, determined by the method of Schaap (1970), of various batches of factory curd (see Figure 3.1) withth e density distribution (see Figure 3.2). 40 wt.% 100 80 60 7~ 40 y 20 1 o -^900404. 1 9004042 900405.1 900406.1 900406.2 900410.1 900410.2 900411.1 900411.2 900412.1 900412.2 • >11.0 (23 7.0-11.0 • 5.5-7.0 ü 3.5-5.5 [g] 1-3.5 Fig. 3.1. The curd grain size distribution in NIZO's experimental plant according to Schaap's method. The legend shows the mesh sizes of the sieves. The date and batch number are given at the labels at the X-axis before and after the dot, respectively. Wt. % 100 7~ 7: 80 60 40 20 900404.1 900404.2 900405.1 900406.1 900406.2 900410.1 900410.2 900411.1 900411.^2 S90041Z 1 900412.2 H 1028.8-1035.9 [x] 1035.9-1043.0 • 1043.0-1050.2 U 1050.2-1057.3 • > 1057.3 Fig. 3.2. The curd grain density distribution in NIZO's experimental plant. The date and batch number are given at the labels at the X-axis before and after the dot, respectively. 41 The extent of syneresis, hence density, isdetermine d byth e surface areao f the curd grains and the syneresis time. Indeed, more small curd grains were correlated to a larger fraction of curd grains of a high density. This implies that shattering of large curd grains inlate r stages of curd preparation isminima li npractice . Itshoul d beem phasized, however, that determination ofth ecur d grain sizedistributio n by means of sieveswil l be influenced byth e shapes ofth e curd grains. Moreover, it is possible to produce equal sized curd grains with different moisture content. Comparison of the curdgrai nsiz edistributio nfro m dayt o day ina chees eplan t isa usefu lempirica ltool , but comparison among various cheese manufacturers is seriously hampered due to the constraints mentioned above. Inthi sthesi s the relative remaining volume (/„), i.e. the volume of the curd grains as a volume fraction of the original volume of milk, is used.Th erelativ eremainin gvolum eca nb ededuce dfro mth edensit ydistributio n and is directly linked to the moisture content of the curd grains. 3.2 Whey expulsion and deformation of cube shaped curd grains The curd grain flattener (see 2.4) was used to study the whey expulsion and deformation of cube shaped curd grains.Cub e shaped grains of various density and sizewer ecompresse d atvariou s mechanical pressures.Th evertica lcompressio n led to whey expulsion from the sides (the bottom and the top were considered impermeable) andals ot o abroadenin g ofth ecurd grains inth e horizontaldirections . Thegrain s hardly became barrel-shaped,a sca nb esee ni nFigure s3. 3a t o3. 3d . Ap parently,th efrictio n betweentest-piec e andth e bottoman dto p plateswa sver ysligh t (Luvten 1988);thes e plates were made of perspex and glass, respectively. The compression curves showed an elastic component (immediately after application of the stress) and a viscous one (at longer time scales); an example is showni n Figure3.4 .Th eapparen telasti c deformation could beslightl y largertha nth e real one in some cases, as some curd grains were not precisely cube shaped; the height of the curd grainwa stake n atth e highest point atth e start of the experiment, atth e subsequent time intervalth eto p of the curd grainwil lb eflat , henceth e elastic deformation may be slightly overestimated. Elastic recovery was clearly visible if the stress was released within afe w seconds after the start of the compression. After 15 minutes of compression no elastic recovery was observable after release ofth epres sure. Presumably,th edeformatio n at longer timescale s leadst o irreversible changes inth e paracaseinate network. Our observation isi naccordanc e with previous results 42 Fig. 3.3 Thecompressio n of a cube shaped curd graina tvariou s times (f),0 (a),3 0 s (b),30 0 s (c) and 900 s (d), respectively. Mesh = 10 mm,/ 0 = 0.28, averagep m = 280 Pa. The dots shown are made with an analinepencil . 43 h (m) \J.\J\J\J 5C 0.005 n elastic deformation 0.004 0.003 \yiscous deformation stress released 0.002 v ~~" —* 0.001 _ \_ + * n i i 200 400 600 800 1,000 f (s) Fig. 3.4 The height (h) of a single cube shaped curd grain versus time (f) during a compression experiment. The average stresswa s 1210 Pa,/' „ = 0.28, mesh = 10mm .A tzer otim eth e compression starts, anda very rapid elastic anda slowerviscou sdeformatio nfollow . Atf = 900 sth e stresswa sre leased, but the resulting elastic recovery wasnegligible . onski mmil kgels ,thei rapparen tmea nrelaxatio ntim ebein gapproximatel y oneminut e (Zoon I 1989). The time scale of drainage is usually much longer, therefore viscous deformation will be overriding. Theresult s ofth ecompressio nexperiment s showedconsiderabl e spread. This may haveha dsevera lcauses :th e curd grains ina batc har eno t exactly identical,bu t have a, be it narrow, size distribution; the concentration of paracaseinate is only known within the restrictions of the density test; the cross-sectional area of the curd grains is slightly overestimated, because only the outer contours are taken. These complications canno t be avoided completely, butth e effect ofth eforme r two can be reduced by raisingth e number of replicates. Observation of curdgrain stha twer e left inth ethermostatte dbat hwithou t any stress,di d not reveal any detectable change in theheigh to rth ecross-sectiona lare awithi nth etim escal eo fth eexperiment s (15min) , hence, spontaneous compaction of the curd grains was small. Within the pressure range tested (up to 3 kPa) and the time interval of 15 minutes ahighe r stress uponth ecurd grai ngenerall y resultedi na greate r elastic and 44 AJA^/m2) I = 0.278 o * / = 0.234 0 A 500 1,000 1,500 2,000 2,500 Pm(Pa) Fig.3. 5Th erelativ e enlargement ofth ecross-sectiona lare a of cubeshape dcur d grains (A,s/A0) of two initial relative remaining volumes (/'<,)afte r 15 min., at various stresses (pm). Mesh = 10mm . viscous deformation. A smaller initial relative remaining volume (/„) of the curd grain resulted in a smaller elastic andviscou s deformation within the range tested (0.29 < /„ < 0.23).Th ebroadenin go fth ecurd grain sslowl y increasedwit hth estres s (seeFig . 3.5), thoughth e horizontal cross section enlarged by afacto r of at most about 1.6 in the case of 8 mm curd grains at astres s of 3 kPa (results not shown). A higher initial paracaseinate content appearedt o result inslightl y less broadening ofth ecurd grain . In theory, the extent of broadening depends on the time scale of the experiment, because curd isa visco-elasti c medium, but inpractic e variation inprocessin gtim e is hardlypossible .Therefore ,i ti slikel ytha tth elimitatio no fth ebroadenin go fcur dgrain s will also limit broadening of curd blocks, unless some junctions between the curd grainsar e broken.I tshoul d benote dtha tth ecurd grain s ina curd bedca nno t move frictionless between adjacent curd grains, as the curd grains fuse; therefore, some bulging may take place, causing a slightly larger cross-sectional diameter than that obtained underneathth ecurd flattener . Squarecurd blocks aresometime s moldedi n cylindrical molds and when the corners of the curd block fit exactly in the mold, broadening ofth ecross-sectiona lare ab ya facto r of 1.56mus tb eattained .Thi svalu e is close to the maximum found for curd grains inth e curd flattener. The deviation in 45 moistureconten ti nthos ecur dblock si susuall yincrease d (FNZ1975).I ti sals oknow n that in continuous drainage machines, e.g. the Casomatic, the dimensions of the accompanying molds can be varied only within narrow margins. Newer types of continuous drainage vessels are often equipped with interchangeable pipes. Therelatio nbetwee nth ecompressio nan dth ewhe ylos so fcurd grain sca nno t be expressed as a characteristic number. In rheological terms the volume loss (due to density increase without moisture loss) in relation to the change in height of the sample is expressed as Poisson's ratio, and by analogy we introduce a pseudo Poisson's ratio: U = 0.5 (1 - -^-) (3.1) where fj = pseudo Poisson's ratio (-) V = volume (m3) eh = Hencky strain (-) The Hencky or natural strain is a dimensionless strain corrected for the changed dimensions of the strained sample (Whorlow 1980): eh= ln £ (3.2) where h0 = height at t = 0 (m) /?, = height at f = t (m) Thepseud o Poisson's ratiowil lb esmalle rtha n0. 5whe nth evolum eo fth etest-piec e decreases. The pseudo Poisson's ratio after 15mi n of compression appeared to be virtually constant (« 0.27), regardless ofth e initial relativevolum e (although it should be notedtha tth e appliedvariatio nwa s rather small) orth e applied stress (see Figure 3.6). The ratio of compression versus volume loss is evidently constant. The spread at low pressures is the result of inevitable increase in experimental error due to the small changes in cross-sectional area and height. The results of experiments with 8 mm curd grains were almost identical to the results shown, i.e. the size of the curd grains did not affect the pseudo Poisson's ratio. If this conclusion, the pseudo Poisson's ratio being constant regardless of size, initial relative volume and applied stress, also holds inth e case of practical cheesemaking, we expect the curd grains 46 ƒ'„= 0.278 'o= °o254 '>2;234 500 1,000 1,500 2,000 2,500 A,(Pa) Fig. 3.6. The pseudo Poisson's ratio (//) for curd grains at various stresses (pj after 15 min.Th e experimentwa sconducte dwit hcub eshape dcur dgrain so fthre erelativ eremainin gvolume s(/„) . Mesh = 10 mm. ina curd blockt o expelwhe y inconstan t proportiont oth eapplie d deformation ofth e curd grains (at the conditions identical to those in our experiments; pH = 6.6, T = 35°C,fat/paracaseinat e ratio3.0:2.7) .Th ewhe yma yb eexpelle dfro mth ecurd block , butma yals oremai ni nth epore s betweenth ecur dgrains ,dependin g onth edrai nof f possibilities. Molding of round blocks of curd in square molds led to a decreased moistureconten t inth ediagona lsector s (FNZ1975),th estretchin g ofth ecur d grains towardsth ecorner s ofth emol di slarge rtha nth estretchin gtoward sth emiddl eo fth e wallo fth e mold,th e accompanyingwhe y expulsionwil l betherefor e increaseda tth e diagonal sectors. The expulsion of whey by curd has been studied by various workers (Kirchmeyer 1972, Van den Bijgaart 1988). The expression of whey from non- syneresed curd cubes was fitted by an equation introduced by Weber (1984), here given in modifiedform : M,-M m exp(-z f) (3.3) where 47 M, = mass of curd grain at f = t (kg) Mm = mass of curd grain at t = <»(kg ) M0 = mass of curd grain at t = 0 (kg) z = experimentally determined rate constant (s'1) t = time after starting syneresis (s) The density of the curd grain slightly increases due to the expulsion of whey, as the density of the latter is lower than that of the matrix. Because of this the use of mass fractions is slightly misleading,therefor e we preferredvolum e fractions.Th e mass of curd at infinity (M,») is 0.15 times the original mass (M0), according to Weber (1984). However, our experiments indicatedtha t the end point of syneresis canb e at avalu e clearly lower than 0.15 (see Figure 3.7) times the original volume.Th e minimum /„(mVnrO 0.3 1,000 2,000 3,000 4,000 5,000 Pm(Pa) Fig. 3.7 The relative remaining volume of curd grains after 15 min. (/15) of compression at various stresses (pj anddifferen t initial relative remainingvolume s(/ 0).Mes h = 8 mm. remainingvolum eo fth ecurd wil lconsis to fparacaseinate ,fa tan dmoisture .Th elatte r isestimate d byWalstr ae t al. (1985) at 1.4 gwater/ g paracasein at room temperature and physiological pH plus a little interstitial moisture for the gel of closely packed micelles.A t pH = 5.2 anda temperatur e of3 5 °C approximately 1.2 gwate r per gram paracasein is imbibed by the paracaseinate according to estimates by Walstra et al. (1985).Va nde n Bijgaart (1988)determine dth eminimu m relativeremainin gvolum ei n 48 curdslabs , preparedo f skimmilk ,a t approximately 0.10 atp H = 6.67 and0.0 7 atp H = 6.33 at 34 °C and astres s of 62 Pa.Hi s results also indicate that the end point of syneresis depends onth e exertedstress . Fatglobule s probably increase the amount of water per gram paracaseinate slightly (Walstra et al. 1985).Takin g the above con siderations intoaccoun t andestimatin gth e amounto ffa tremainin g inth ecur dgrain s andtha to fparacaseinat e at3. 0k gan d2. 7k gpe r 100k go fchees e milk,respectively , we estimate at the pressure range of our experiments the end point of syneresis at 0.10 times the volume of curd before cutting. The cross-sectional area between the values obtained at 30 s and 15 minutes was obtained by linear interpolation. Combining these results with the heights at the subsequent intervals yielded the (relative) remaining volume of the curd grains at intervening times.W etried to incor porate important factors affecting the expression of the curd grains, like exerted mechanical stress and initial relative remaining volume and initially also the surface areao fth e sides ofth e curdgrain s inth e equation (3.3).Wherea s Weber (1984) and Kirchmeyer (1972) used a factor exp(-f), other researchers, e.g. Lawrence and Hill (1974) reported a volume of whey expelled proportional to afacto r f05. Recalculation to relative remaining volume yields in the latter case a factor of about exp(-f°5). We tried various time proportionality factors, namely exp(-f), exp(-f°75) and exp(-f°5), but only the last factor matched withth e results over the entire time span,whic h agrees withth eresult so f Lawrence &Hil l(1974) .Th eproportionalit yfacto r ofth estres s upon 05 075 the curdgrain swa s alsoteste di nvariou s modes,namel y exp(-pm ),exp(-p m ) and exp(-pj; the latter gave generally the highest correlation coefficient (i2), and best graphso fth epredicte dvalue /experimenta lvalu eversu sth eexerte dstres san d/„ .Th e considerations above ledt o equation (3.4): -^L=exp(-/cpmi/T) (3-4) 'o 'oo where k = constant (Pa1.s"V4) /, = relative remaining volume at f = t /'«, = relative remaining volume at f = <» /„ = initial relative remaining volume pm = applied stress (Pa) f = time after application of the stress (s) 49 Theexerte dforc ewa skep tconstant ,bu tth ecross-sectiona l areaincrease ddurin ga n experiment. Therefore the stress exerted upon a curd grain decreased. In equation (3.4) the average stress between two successive points of time was taken. The equationwa s usedfo r bothsize so fcurd grains .Th evalu ek =4.10's Pa'Vs"*generall y gave a reasonable fit of the results (r2 varied from 0.58 to 0.74), the average of the calculated results and the experimental ones was practically identical over the total timespan . Thefi twa sles saccurat ea tver y highstress .Th esurfac e areao fth eside s is not taken into account in equation (3.4), as it did not improve the fit. Van den Bijgaart (1988) observed the permeability of skim milk gels con centratedb ysyneresi st o behighe rtha ntha to fgel sfro mski mmil kgel s concentrated by ultrafiltration. The formation of a dense outer layer in the former gels would be expectedt o diminishth e permeability ofth e syneresedgels ,bu t apparently this effect isdominate db ya nopposit eeffect . Resultsb yVa n Dijk's (1982)"torsio nflux "method , whichshowe dtha tth e permeability of age lincrease d after deforming it,point st o the importance of fracture. To investigate whether the skin cracked or not, CSLM micrographs were made of curd obtained of NIZO's pilot plant. The curd grains had aver y condensed outer layer (Figure3. 8 a),tha t appearedt o befull yintact . However, after exerting a small stress upon the curd grain, in this case caused by applying a cover glass, « 100 Pa,th e skinfracture d (Figure 3.8 b).Th eflo w through crackswil l increase the permeability dramatically. The occurrence of macroscopic fracturing of rennet-induced skim milk gels at largedeformatio n ishighl y likely, according to Zoon (I11989).Th eexperimenta lsetu po fmeasurin gsyneresi so f Kirchmeyer(1972 )- cube s of curd floating in a concentrated salt solution, causing strong osmotic effects - differed from that of Lawrence & Hill (1974) - curd grains in anagitate d vat - and this may have caused the observed difference in syneresis rate. The outer layer of our cube shapedcurd grains showed already cracks before application of a stress. It is not known what isth e cause of this. The rate of the expression of cube shaped curd grains is governed by the rheological properties of the paracaseinate strands and/or by the resistance to flow. Inothe r words,th e stress exertedupo nth ecurd grain s rests uponth e paracaseinate matrix and/or the enclosed whey. The viscosity of the paracaseinate matrix can not separately bedetermined ,bu t iti spossibl et o makea tentativ ecalculatio no fth e liquid pressure. Darcy'sla wha sbee napplie dt o estimateth eeffec t of severalvalue sfo r the one-dimensional permeability coefficient on the liquid pressure. A curd grain 50 Fig.3. 8A confoca lscannin glase rmicrograp ho fth esurfac eo fa cur dgrai nobtaine dfro ma commercia l cheese vat without (a) and with (b) a cover glass. The bar is equal to 50 //m. The curd grain was conserved withthiomersa l (Merck). 51 underneath the curd flattener is visualized as a rectangular box. The top and the bottom of the box are considered impermeable and the friction between curd grain andto p and bottom plates isnegligible .Th eflo w ofwhe y isactuall ytwo-dimensional , but in this approach we simplify it to a two-fold one-dimensional flow. The box is hereto hypothetically divided in a permeable left- and right-hand side and an impermeable front and back side, respectively ina nimpermeabl e left- and right-hand side and a permeable front and back side. The flow of whey across the planes of symmetry iszero .Th ewhe y originatesfro m various places insideth e curd grain,bu t we assumedtha t allwhe y originatedfro m asourc e located atth e middle planes.Th e distance between the middle plane andth e outside of the curd grain is estimated at 3.10"3m .A s only halfo fth eflo w ofwhe y actually goes acrossth efront andbac k side (theothe r halfgoe sacros sth elef tan dright-han dsides) ,th evolum eo fexpelle dwhey , calculated from the height and the cross-sectional area of a curd grain at two subsequent times,ha st o be divided bytwo .Th etota l surface areawa s estimated at 10"4 m2.Th e following set of parameters was used:r\ = 10"3 Pa.s,x = 3.10"3 m,A = 10"4m 2. The permeability (S) was estimated at 10'14,3.10" 14o r 10'13m 2.Thes e values were combined with various results of compression experiments into the integrated Darcy's law: = (AV/2) n x {35) ' At BA where p, = liquid pressure (Pa) AV = volume decrease of curd grain in an interval (m3) n = dynamic viscosity (Pa.s) x = distance (m) At = time interval (s) B = permeability (m2) A = surface area of the sides (m2) 52 Table 3.1: The calculated liquid pressure (pf) at three time intervals (f), for each at two levels of stress (pj uponth ecur dgrain s(/' „= 0.28, mesh = 10mm )fo r variouspermeabilit ycoefficient s (S).Th ecross - sectional area ofth e curd grainsincrease s intime , causing a decreasing stress uponth e curdgrains . The values of the liquid pressure shown In brackets are larger than the exerted stress upon the curd grainsan d aretherefor e unrealistic. u 14 13 f(8 ) pm(Pa ) àV/ùt e=io S=3.10 e=10' (m3/s) (m2) (m2) (m2) A(Pa ) 0-30 227 2.010 * (2950) (983) (295) 90-150 215 1.710- 10 (252) 84 25 600-900 203 2.410" 11 35 12 4 0-30 2007 3.410' 9 (5037) 1680 504 90-150 1670 2.710" 10 404 135 40 600-900 1375 3.410" 11 51 17 5 The calculated liquid pressures (Table 3.1) are probably an overestimate due to the assumptions stated above. If the permeability were larger than 10'13 m2, the liquid pressure compared to the exerted stress becomes so smalltha t the expression of a curd grain is practically determined by the Theological properties of the network. An initial permeability smaller than 10'14 m2 is unlikely, as in that case some of the cal culatedliqui dpressure swoul dbecom emor etha nte ntime sth eexerte dstres s (Table 3.1). Wema y qualitatively conclude that, inspit eo fth e probable decrease ofth e per meability in more expressed curd grains, the stress exerted upon the curd grain will soon predominantly be carried by the paracaseinate network. In other words: the Troutonviscosit yo fth e networkbecome sth erat edeterminin gfacto r inth eexpressio n of curd grains in acur d column if the pressure on the curd-whey mixture is not very small. 53 3.3 The fusion of cube shaped curd grains The force needed to break the junctions between curd grains was measured byth e perforated piston method described inSectio n (2.6). Inprinciple ,tearin g apart thetw o neighboring curd layers can occur either by fracturethroug h the curd grains themselvesand/o r byfractur ebetwee nth ecurd grains .Th eappearanc eo fa fracture d curd grain is slightly different from that of an intact curdgrain .Carefu l examination of both curd layers after the splitting did not reveal any fractured curd grain. Moreover, a preceding coloring of the outside of the curd grains inth e upper layer with Congo Red (Merck),whic h ledt o redcolore dcircumference s afterfractur e did neither reveal any such fracture through a curd grain. These results agree with results by Luyten (1988), who concluded from her experiments that it takes at least 2 days of fusion before fracture occurs through the curd grains. Macroscopically, the fractured layers of curd matched each other quite well, even when the layers were torn apart after a contact time as short as 1 min. It is however not surewhethe r the curd grains actually contact eachothe r over the entire area. If this is not the case, the fusion areas are rather contact points that are distributed over the perforations inth e piston. Thefractur estres swa spositivel ycorrelate dwit hth efusio ntim ean dth eexerte d mechanical stress (see Figures 3.9 and3.10) . &8K mesh = 10m m mesh = 8m m o 2,000 o 1,500 o 8 * o 1,000 o * o 8 * 500 o 8 n I I I I I 200 400 600 800 1,000 1,200 1,400 f(s) Fig.3.9 .Th efractur estres s (a,)o fth ejunction s betweencub eshape dcur dgrain sversu sfusio ntim e (f)fo r cubeshape dcur d grainso ftw odifferen t sizes.T = 34.5 °C,p m = 905Pa ,/' „ =0.28 . 54 o, (Pa) 2,500 2,000 1,500 1,000 500 1,000 1,500 2,000 Pm(Pa) Fig.3.10 .Th efractur estres s{a,) ofth ejunction sbetwee ncub eshape dcur dgrain sversu sapplie dstres s (pj. Mesh = 10mm ,/ „ = 0.28, 7" = 34.5 °C,f = 7 min. Fig.3.1 0suggest stha ta minimu mstres si sneede dt oaccomplis hfusion ,bu tthi swa s caused byth e experimental conditions (thetw o layerso f curd grainswer e separated by the bottom of the piston and the lowest stress applied was caused solely by the weight of the piston upon the bottom layer, which implies that there was virtually no stress exerted atth eto p layer of curd grains,and ,accordingly , the curd grains inth e upper layer will nottouc hthos e inth ebotto m layer).I ti s alsoknown ,tha t ina settled layer of curd grains in the whey already some fusion occurs, which implies that the minimum stress neededt o createfusio n isles stha n 20 Pa.Th esprea di nth e results wasdu et osmal lvariation samon gbatches ;measurement s atvariou sfusio ntime s (or mechanical pressures) withcurd grains preparedfro m onean dth e same batchgav e less variable results. It appeared from preliminary experiments that the relative remaining volume of the curd grains (/„) was positively correlated with the fracture stress. This agrees with the observation that smaller curd grains apparently fused slightly better than larger ones (see Figure 3.9), because the concentration of paracaseinate inth eoute r layerswil lb erelativel y low,o rth econcentrate dlaye rwil lb e relatively thin, insmal l curd grains.Th e increased concentration of paracaseinate will induce two opposite effects.Th e paracaseinate strands inth e gelwil l bethicke r and 55 lessflexible ;an dt o accomplishfusion ,deformatio n isneede d andthicke r strandswil l also hinder rearrangement to a greater extent. On the other hand, at a higher con centration of paracaseinate the number of reactive sites per unit surface areawil l be larger. Iti slikel ytha tth efirs t effect isoverriding .Th e effect ofth etemperatur e is less clear: there may be anoptimu m fusiontemperatur e (see Figure3.11) . a,(Pa) £,3UU t = 420 (S) * f=720(s) 2,000 - 1,500 - o § o 1,000 _ * * o * o 500 * * * n I I 32 33 §4 35 36 T C Fig. 3.11. The fracture stress of the junctions between cube shaped curd grains versus fusion temperature after 7an d 12mi no ffusion .p m = 905Pa ,/ 0 = 0.28,mes h = 10 mm. In practical cheesemaking enhancing fusion to a certain extent is common practice.A "resting"stag e isofte n applied ina batch-wis edrainage , duringwhic hth e curdgrain sar elef tundisturbe dafte rsedimentation ;suc hrestin gma yclearl y promote fusionbetwee nadjacen t curdgrains ,althoug hthei r contact areas,henc eth ejunctio n zones, are rather small.Cheesemaker softe n put perforated stainless steel plates on top ofth e curd bed afe w minutes afterth e sedimentation.Th e exertedstres s caused by these plates will not only increase the (macroscopic) contact area, hence the junction zones, but will also increase the fusion rate. In most continuous drainage machinesth emechanica lpressur eupo nth ecurd grain si sgraduall yincreased .A con tinuous drainage apparatus isalway s equippedwit h abuffe r tank.Th e curd grains in thebuffe rtan kar eusuall yslightl ycoole dt oslo wdow nsyneresis ,bu tthi scoolin gma y affect fusion behaviour as well. Geurts (1978) observed that in a larger sized curd 56 block, amor esatisfactor y closed rindwa sobtaine dtha n ina smalle r curd block.Thi s impliestha tth ecurd grain s atth eedge so fth elarg ecurd bloc kwer efuse dbetter .Th e phenomenon must be ascribed to the faster temperature decrease of the smaller block. The curd preparation willaffec tth ewhe y content ofth ecurd grains, henceth e viscous and elastic deformation and therefore the contact area between the curd grains,bu t alsoth efusio nwil l bediminishe d at lowwhe y content inth eoutsid e ofth e curdgrains .Moreove rth econtac t areape rm 3o fcur dgrain swil lb edetermine db yth e size and shape of the curd grains. This probably caused that curd blocks of cube shaped curd grains were less coherent than the ones of factory curd. 3.4 Sedimentation of curd grains Demixing of curd grains, caused by variation insedimentatio n rate,int o layers of curd grains of various average size and density is an undesirable phenomenon in drainage equipment. Itcause svariatio n inmoistur e content ofth echees e (FNZ 1975) inbatch-wis e operateddrainag e vesselswit hon ecentra l inlet, likestrainers .Th ecurd grains insuc ha drainag evesse lar edistribute dfro mth ecente r ofth evesse lan dthe y flowwit hth ewhe ytoward s theedge s ofth evessel .T o avoida n uneven height ofth e curdbed ,th ecurd grain sar e mixedmanually . Incontinuou s drainageequipment ,lik e theCasomatic ,a thi nlaye ro ffin eparticle s canb eobserve d atth eto p ofth ecurd bed in the drainage pipe, but it is not known whether this influences the moisture distribution or not. An important characteristic in relation to sedimentation rate is the particle Reynolds number (Re): Re= ^A (3.6) n where Pi = density of the liquid (kg/m3) v = stationary sedimentation velocity (m/s) dp = particle diameter (m) n = dynamic viscosity of the liquid (Pa.s) The Reynolds number is related to the type of flow around a particle. The following parameter set was used to estimate the Reynolds number; p, = 103kg/m 3, /? = 10"3 3 Pa.s and we further assumed v = 0.05 m/s and dp = 5.10" m; this results in Re = 57 250,i.e .i nth eintermediat eregio nbetwee nlamina r (Re< 0. 1) an dturbulen t (Re> 1000 ) flow.Th efre esettlin gvelocit y of onesingl espherica l rigidparticl e ina Newtonia nflui d can be calculated (Sakiadis 1984) from the general relation: 4 g A/o dp (3.7) v = 3p,Cw where g = acceleration due to gravity (m/s2) Ap = apparent density (kg/m3) Cw = drag coefficient (-) The drag coefficient of spherical particles can begive n as afunctio n of the Reynolds number, in the intermediate region it may be represented (Sakiadis 1984) by: 07 Cw = — (1 +0.14 Re ) (3.8) w Re In practice, the free-settling velocity of curd grains can vary due to variation in diameter, apparent density anddra gcoefficient .Th eorigina lsiz eo fth e pieces of curd is decisive in this matter, unless clusters of fused curd grains are formed. The ap parent density depends not only on the density of the curd grain, thus the fat/paracaseinate ratio and the extent of syneresis, but also on the extent of the dilutiono fth ewhey ,i.e .th eamoun to fwashin gwate r addedt oth ecurd/whe y mixture. Inth e absence of clustering of curd grains, the extent of syneresis is closely related to the size of the grains, as the syneresis rate is about proportional to the surface area. Other variables, especially thetim e of syneresis may cause differences within a batch.Th e apparent density of clusters canvary , depending onth e apparent density of the fused curd grains and the amount of included whey. The drag coefficient depends onth e Reynolds number, andtherefor e apparent density anddiameter , and onth e shape ofth e particle.Th efree-settlin g velocity of spherical curd grains can be iteratively derived from the equations 3.6, 3.7 and 3.8 (Table 3.2). 58 Table3. 2 The calculatedfree-settlin g velocityan d Reynolds numbero fspherica l curd grainso fvariou s size and apparent density. tfp(m) Ap (kg/m3) v (m/s) Re 1. 10* • 15 0.061 615 5. 10"3 15 0.034 170 2. KT3 15 0.014 27 5. KV3 20 0.041 204 5. KT3 40 0.062 314 2. 1er3 50 0.031 63 Table(3.2 )show stha ti nth ecas eo fcurd grain so f identicalapparen t densityth eone s with the largest diameter will, naturally, sediment fastest. In the case of equal sized curd grains with different apparent density, the ones with the highest density will sediment fastest. Inpractice ,th e curdgrain swit hth e largestdiamete r willals o beth e ones with the lowest (apparent) density. According to an FNZ report (1975), the smaller particleswer efoun da tth e bottom ofth ecur dblock , butth e (calculated)free - settling velocity of small particles (say 2.10"3 m) is, in spite of their higher apparent density, less than that of larger particles (Table 3.2). We had similar experiences in pails filled with cube shaped curd grains and a small amount of smaller curd grains. Thecompariso n of calculatedvalue s andexperimenta l results may be not completely fair, asth e curd grains infac t areno tspherica l andth esedimentatio n rateo f particles is reduced byth e presence of other particles (hindered settling) (Sakiadis 1984).Th e fact that small curd grains were found at the bottom of the strainer does not necessarily imply that their free-settling velocity is higher, assmalle r curd grains may fillth e gaps between adjacent large curd grains and may have beensucke d down in the curd bed when the whey was removed (the experience was based upon the drainage in strainers). Such an effect also happens in the drainage of sludge and is called fines migration (Novak et al 1988). Onth e other hand, small eddies may swirl upcurd fine swhil e leavinglarge r particles motionless. Sucha neffec t may explainth e above mentioned observations at the top of the Casomatic pipes (first paragraph of this section). 59 Cube shaped curd grains rotated when freely settling.Anisometri c curd grains sank in a preferential orientation, regardless of their initial position. The preferential orien tation of an anisometric curd grain is with its longest axes perpendicular to the direction of sedimentation; this orientation is attained after a short wobbling. The Reynolds number, based upon a diameter of a sphere having the same surface area, in the range 5.5 - 200 is known to result in a stable position of maximum drag (Sakiadis 1984). 3.5 Packing of curd grains The type of flow when curd grains sediment, the angularity and the orientation of the particles and their firmness probably all affect the initial packing. The porosity is hard to estimate, and may vary with the particular conditions. '.i S I: - ' i î ; I i ! f 1111Î1 1f -1 1î ! I f S f f 1 1i ! i I ï ' 1 1! 111 1' 5 ' .:!il!!| 1 ! • i I I i S U 'Î 'J 1 Fig. 3.12. Vertical cross-sectionthroug ha curd bedafte r compression.Th e curd grainswer e obtained fromth e 40 I cheesevat . The outside ofth e curd grains had been colored with Congo red beforeth e drainage. Note that the orientation of the curd grains near the wall is altered. The dark spots on the photo are caused by curd grainsfalle n out ofth ebed . 60 Inth e preceding Section it was mentioned that free-settling curd grainsorien tated with their longest axis perpendicular to the direction of sedimentation. Section 3.2 itwa s showntha t expression of a curd grain results in a broadening and vertical compression.Th e combined effects uponth eorientatio nth e curd grain are shown in Figure 3.12. Rüegg and Moor (1987) compared vertical and horizontal cross-sections of variouschees etype san dconclude dtha tth eapparen tcur dgrai nsiz ei nth ehorizonta l direction was markedly larger than that inth e vertical direction.A s most of the whey willflo waroun dth ecur dgrains ,i ti slikel ytha tth eresistanc et oflo wo fwhe y ina bloc k invertica l directionwil l be greater than inth e horizontal directions, i.e. the curd block will be an anisotropic medium. Injection of whey provided with a tracer, Congo red (Merck), in a block of draining curd in a cylinder with a whey outlet at the top gave clear evidence of the anisotropy (see Figure3.13) . Fig.3.1 3Th eflo wpatter no fth ewhey ,injecte dint oa cur dbe dafte r7 minute so fcompressio n( ~ 400 Pa),mad evisibl ewit hCong o red. Thecur d grainswer eprepare d inth e4 0I chees evat . 61 4. Effects of the drainage vessel upon drainage 4.1 Axial draining vessels Batch-wisedrainag ewa sobserve di nvariou scommercia linstallations .Th ecur d layers produced were rarely thicker than0.2 5 m, limitingth eexerte d stress uponth e curda tth e bottomt o approximately 2.5kP a(whe nth ewhe y isallowe dt o drain).I fth e curd mass was cut in blocks in the drainage vessel, whey was expelled from the blocks,th eblock ssubside dslightly ,causin ggap sbetwee nthem .Whe yfille dth egap s inbetwee n almost to the rim.Th e drainage time, i.e. thetim e curd was in a drainage vessel, was usually around 20 to 30 min, although longer drainage times were occasionally useda tcertai n manufacturers. Itseeme dtha tth e moistureconten t ofth e curdblock s madei nbatch-wis eequipmen twa sslightl y lowertha ntha to fcur dblock s made in continuous drainage equipment. However, it will vary among the manufac turers. The experimental setup is described in Section 2.5.3. The whey in this setup flows through sieves at top and bottom of the curd bed and the sieves could in principle restrictth e flow rate through the curd bed. Experiments by Valk (1986) did notconfir mthis ;h eglue dthi nhighl y permeable spongest oth e sievesan dcompare d thecompressio n rates,whic hwer e observedt o beno t significantly dependent onth e presenceo fth esponges .Th eflo wo fwhe ythroug hth ecurd be di na drainag ecolum n (see 3.5) was made visible by adding atrace r (Congo red) to the whey percolating through it.A considerable part of theflo w leaked alongth e curd bed; Kerkhof (1979) already drew attentiont o it,bu t heneglecte dth econsequences .Th efractio no fwhe y that leaks betweenth e vessel and the curd block will depend upon the geometry of the vessel and on the packing of the curd grains;th e latter will be subject to change during the drainage, but the leakage will never be zero. It may be negligible in very largevessels , butthes e could not beapplie d inthi s study.Th edirectio no fflo w ofth e whey in a curd bed as described in the Section 3.5 - i.e. mainly in radial direction - combined with the leakage, also causes compression experiments as performed by Kerkhof (1979) to be unreliable. Drainage inou r smallscal e axialdrainag e equipment didinsufficientl yresembl eth ebatch-wis edrainag ei npractice ,therefor ew eabandone d this approach.Th eproble mo f leakage israrel y reported inliterature ,bu t itsexistenc e atothe rexpression s seemslikely ,althoug hit seffec tmayb eno ta sdramati c asi ncas e of curd grains. The location of the curd block inth e drainage vessel may affect the drainage 62 invariou s ways: 1) Demixingo fth e curd grains accordingt o size and/or shape may occur (see Section 3.4). 2) The temperature of curd blocks at the walls will be influenced by the walltemperatur e andth etemperatur e is known to be an important variable affecting syneresis (Van den Bijgaart 1988) and fusion, hence, drainage behaviour. 3)An y leakage alongth ewal laffect sth eflo w ofwhe ythroug hth e curd.4 ) The curd blocks at the wall will adhere to itt o acertai n extent, retarding subsidence ofth ecur d layer.5 )Th ecurd blocksar esequentiall y takenou t ofth evessel ;thi sma y influence the temperature of the block as well as the duration and the magnitude of the stress exerted upon it. 4.2 Radial draining vessels As far as known, radial drainage vessels are only applied in continuous drainagesystems .Start-u pan dfinishin gth eus eo fth econtinuou sdrainag eequipmen t is always the difficult part to control, resulting often in an increased variation in moistureconten t (DeVrie s& Va nGinke l 1985).Normall yth epipe sar efille dwit hwhe y before start-up.Th e curd/whey mixture issubsequentl y addedt oth e drainage pipes. Wheyan dcurd/whe y mixtureca nusuall y beadde d independently, soth ecur di skep t under thewhey .Th ecurd blocks show per batch aslo w decrease inwate r content of the subsequent blocks. In most types of drainage pipes the whey outlet is restricted by a back pressure. There is an exception: in one type, used to produce Edam cheese, no back pressure is applied. The geometry of the pipes varies, diameters range from 0.16 to 0.32 m, and the height of the pipes is between 1an d 3 m. The drainage time is usually lesstha n 10min . Thewate r content of the curd blocks after drainage, although itvarie s withtyp e of cheese, manufacturer, etc., is approximately 58 -60% . Thetota l external pressure can be broken down into the stress upon the par ticles, the liquid pressure and the loss of pressure due to friction with the wall (Schwartzberg et al. 1985): P, = Pm + Pt + Pw <4-1) where p, = total external pressure (Pa) pm = stress upon the curd grains (Pa) p, = liquid pressure (Pa) 63 pw = pressure loss duet o frictiont o the wall (Pa) The effect of the total external stress upon the liquid pressure was studied in the setup discussed at Section 2.5.1Th e flow of whey results from a liquid pressure gradient betweenth e center ofth e curd column andth e outside.A general pictureo f thedevelopmen t ofth e liquidpressur eca nb egiven :a considerabl e external pressure (p,) hadt o beapplie dt o accomplish adetectabl e (> 5Pa ) liquid pressure dropwithi n 15min .Onc e established,th e liquid pressure always increasedwit htim e (see Figure 4.1). P,(Pa) n =800 (Pa) 1000 (Pa) 500 i 1300 (Pa) i i i P= 2100 (Pa) i 400 i i i i i --—* 300 / I I I ...-"'' 200 I I I I ..-'' 100 -I ••• I .••'.• ;,I *••' l! • i i i i 200 400 600 800 1,000 f(s) Fig. 4.1 The liquid pressure inth e larger drainage column (fl = 0.10 m) filled with factory curd (f = 40 min after end of curd preparation), to approximately 0.11 m (= h0) at various exerted mechanical pressures (p,). Above this threshold value, any further increase in external pressure resulted in a faster increaseo fth eliqui dpressure .A nexterna lpressur e ofa fe whundre d Paabov e thethreshol d levelresulte d insuc ha nincreas e ofth eliqui d pressuretha tth eworkin g limito fth eliqui dpressur etransduce r (500Pa )wa ssurpasse dwithi n 15min .Th eliqui d pressure could become virtually equal to the total exerted pressure in that case (results not shown); in other words, the drainage effectively stopped. The diameter of the drainage vessel appeared to be an important variable in relation to the threshold value. In the larger vessel employed (R = 0.10 m), the 64 externalpressur eneede d (« 1000Pa )t oaccomplis ha detectabl eliqui dpressur ewa s lower than that (« 1700 Pa) inth e small vessel (R = 0.06 m) (see Figure 4.2). A?(Pa ) 600 pt=1000(Pa) fl = 0.10(m) 500 pt= 1300 (Pa) fl = 0.10(m) pt= 2100 (Pa) 400 fl = 0.10(m) p, = 600 (Pa) 300 fl=_0.06H p,= 1650(Pa) fl=0.06M 200 Pt= 2250 (Pa) fl=0.06(m) 100 200 400 600 800 1,000 Ms) Fig.4. 2Th eliqui d pressure (p,) indrainag evessel so ftw odifferen t radii(fl ) atvariou sexterna l pressures (p,). Factory curd (f = 30 - 40 min) after drainage. h0 = 0.11 m. It should be noted that in case of an external pressure of 600 Path e line of the liquid pressure coincides withth e X-axis. The effect of the diameter of the drainage vessel upon the liquid pressure can be partlyexplaine db y Darcy's law (seeequatio n 1.1). Theflo w ratei na cylindrica lvesse l decreases with increasing distance.A n increase of the radius (ft) willg o along witha greater liquid pressure drop between the center and the outside of the vessel. Moreover, the ratio volume/outer surface areao f acylindrica lvesse l isequa lt o 2/R, hence, the flow rate of whey through the outer layer of the curd bed per unit surface area has to increase with Rt o remove the same proportion of whey in the cylinder. The diameter of the vessel also influenced the loss of exerted mechanical pressure due to friction to the wall, the experimental setup of the pressure loss measurement is given in Section 2.5.4.Th e ratio of contact area between curd and the wall of the vessel over the volume of the curd in the cylinder is proportional to 1/ff; hence,th e importance of wallfrictio n in largevessel s is relatively less (see Figure 4.3). 65 fl= 0.06 (m) p= 1230(Pa ) R= 0.10 (m) p= 1210 (Pa) 1,000 Fig.4. 3Th e pressurelos sa tth ewal l(pj , expresseda stractio no fth eexerte d mechanical pressure(p,) , asa function of time intw o drainage vessels of different radii.h 0 = 0.05 m, curd obtained fromth e 40 I curd maker. hj = 0.05(m ) fr(P 0.09(m ) fr 1,000 Fig.4. 4Th e pressurelos sa tth ewal l (pj, expresseda sfractio no fth e exertedmechanica l pressure (pj, asa function oftime ,a t variousfil llevels ,p , = 1035 Pa,R = 0.06 m, curd obtainedfro mth e4 0 I curd maker. 66 Theheigh to fth ecurd colum nwil ldetermin eth econtac tare abetwee ncur dan d wall.A sexpected ,a nincrease dfillin gleve lincrease dth efrictio nt oth ewal l (seeFigur e 4.4),hence ,th epressur eloss .A sth eheigh tdecrease di ntime ,th epressur elos sdu e to wallfrictio n also diminished.A n increased mechanical pressure resulted in amor e than proportional pressure loss due to adherence to the wall (see Figure4.5) . P,= 600(Pa) Pt=.103 5 (Pa) Pf=1650(Pa) 1,000 Fig.4. 5Th epressur eloss (pj, expresseda sfractio no fth eexerte d mechanical pressure (p,),a sfunctio n oftim e (f) atthre eexerte d mechanical pressures.h 0 = 0.09m ,R = 0.06 m, curdobtaine dfro mth esmal l scale curd maker. Schwartzberge tal . (1985)reporte dtha ta tincrease dcompressio nspeeds ,whic hals o implies higher stress levels,th e pressure loss increased moretha n proportional.Th e various factors affecting wall friction could be reasonably fitted with equation (4.2): Z *, " P. (4.2) r"\v where pw = overall pressure loss (Pa) /f, = constant (Pa15) h = height as afunctio n of time (m) p, = total exerted pressure (Pa) R = radius of the column (m) 67 The factor fc, = 6.10"6 Pa"15 gave reasonable results in the test range of our experiments (R = 0.06 m or 0.10 m, h = 0.02 to 0.13 m andp , = 600 to 1700 Pa). Equation (4.2) is not suitable for extrapolation beyondth e limit of our experiments. The vertical distance from the plane where the stress is applied has a tremendous influence uponth e localstres s uponth e curd grains.Thi swa s illustrated inth e following experiment: it was tried to measure the radial permeability of a curd bed,th esetu pi sgive ni nSectio n2.5.2 .I tappeare dtha t athig hmechanica lpressure s theto p layer ofth ecurd becamevirtuall y impermeable,wherea sa considerabl e whey flow still occurred in the lower layers. The latter made visible by adding Congo Red (Merck) to the percolating whey. Schwartzberg et al. (1985) had similar experiences for the compression of coffee grinds. In their experiments the coffee grinds were expressed in axial direction in a vertical transparent cell by an Instron machine. By placing movable, perforated cake section dividers,th e relative compaction of various sections could befollowed . Itappeare dtha tth eto p layers becameth e most compact ones,wherea sth ebotto msection swer erelativel yles scompacted .Althoug hw ecoul d not quantify it, it must be assumed that the pressure loss near the wall of the vessel was larger than that in the center of the curd column. The liquid pressure will be highest in the center of the column. Moreover, in industrial drainage equipment the heighto fth ecur dcolum nwil ldetermin eth etota lpressur eexerted ,hence ,th eexterna l pressurewil ldepen d onth e location. Inou r experimental setupth e height ofth e curd layers was so small that this effect could be neglected. The stress upon the curd grains will depend on its location, with respect to h as well as to r. The combined effects of increase in liquid pressure and pressure loss at the wall of the vessel with an increasedexterna l pressure may ultimately leadt o asmalle r stress uponth e curd grains. Applying the results above to practical cheesemaking in combination with equation 4.1, throws some light on current problems incheesemaking .Jamming , i.e. a rapiddecreas eo f permeability ofth ecur d block,frequentl y occurs.Th eeffec t ofth e external pressure upon the liquid pressure can partly explainthis : if the stress upon the curd grains issomeho w higher thanth ethreshol dvalue ,a sudde nan d rapid rise in liquid pressure occurs; hence, the permeability has become poor. In continuous drainage equipment, like the Casomatic, the outflow of whey is restricted, so a con siderable part of the exerted stress is "carried"b y the liquid.A decrease inth e back pressure may therefore lead to jamming. The whey outlets in Casomatic drainage 68 vessels have beenequippe dwit hvalves ,tha t closewhe n acurd block istake n outo f the column. Duet o the suddenfallin g down of the curd column,th e space between the wall of the vessel and the curd column is temporarily increased, and this could causea tremendou s increase ofth eflo wo fwhe yalon gth ewall , ifth evalve swer estil l open.Th e back pressure atth eto p outlet could become practically equalt oth e back pressure atth e lower outlets, i.e. far smaller; insuc h acase ,th e stress exerted upon the curd grains increases dramatically, and this would cause jamming. It may also cause a rapid flow in which large particles are dragged along toward the filter grid covering the outlet. This may result in clogging of the grid. It has to be noted that some leakage along the wall of Casomatic pipes also occurs in normal operation (Heijnekamp personal communication). The important role of friction to the wall may explain that an Edam cheese drainage vessel that operates without back pressure, nevertheless works. Without considerable pressure loss at the wall, the stress upon the curd grains would become more than 10 kPa, because the height of the pipe is approximately 1m . Sucha stres s isfa rto o hight o obtain satisfactory drainage,sinc e it would causejamming . It was tried to block the friction to the stainless steel by coating it with chlorotrimethyl silane (Beekman Instruments) or teflon, but considerable friction remained. Itmus t benoted ,however ,tha tteflo ncoate ddrainag esystem s arepopula r inth e production of Edamcheeses ,wher eth eradiu so fth edrainag e pipei sonl y 0.08 m. It isknow ntha tth e cheeses made inthi s equipment do not always havea smooth rind: sometimes the rindi s ribbed.Thi s has likely been caused by frictiont oth e wall. Besidesth epressur eloss ,th ewal lals oalter sth eorientation so fth ecurd grain s in its environment. The initial packing ofth e curd grains near thewal l isdistorte d due to steric exclusion. We have some photographic evidence (Figure 3.12) that curd grains near the wallwer e not horizontally oriented after drainage, but were turned at an acute anglet o the direction ofth e movement ofth e curd bed. In pressed cheese samples the curd grain patterns near the rind were also distorted (Rüegg & Moore 1987).A n additional aspect of thefrictio n to the wall istha t the residence time of the curd grains in the drainage vessel may depend on their location. Emch et al. (1967) showed parabola-like profiles in cheese, made of layers of colored and uncolored curd, pressed one-sided in aluminum molds. It should be noted, however, that the mechanical pressures applied in his cheese presses were at least a hundred times those applied during drainage. "Residence time distribution" of curd grains in con- 69 tinuous drainage vessels is not really an appropriate term, asth e process is notfull y continuous (unloading occurs in discrete steps). To study the residence time we added an amount of dyed curd grains (annatto coloring at 30time s the normal dose addedt o curd grains and stirredfo r approximately 20min )t oth eto p of aCasomati c drainage pipe. The curd grains at the top became slightly mixed due to the influx of new curd/whey mixture: dyed curd grains were mixed over an amount of curd that was approximately 4 times the amount of dyed curd («5 kg).Th e residence time of the curd grains was approximately 8 min. Every minute a curd block was unloaded. The height of the curd blocks cut off was about 0.2 m.Th e dyedcurd grains showed an about parabolic profile inth e curd block (Figure 4.6). -15 -10 -5 0 r(cm)5 10 Fig. 4.6 The flow pattern of curd grains after drainage in a Casomatic drainage pipe. At eachtim e acurd block is removedfro mth e pipe, plugflo w occurs, but inbetwee n this may be different. If the flow of curd in the Casomatic is considered to be completely continuous, the Reynolds number can be estimated at about 10"5, i.e. far in the laminar region. The velocity profile in case of laminar pipe flow is parabolic (Sakiadis 1984). Hence, onto the plugflo w a laminar pipeflo w is superimposed.Th e occurrence of a spread in residence time, in this case about 30 seconds, corresponding to half the height of block cut off, is relevant with respect to the productiono fchees efro msuccessiv ebatche so fcurd .Th einterva lbetwee ndrainag e 70 and pressing is varied in such way, that for the last curd of a batch the interval is shortest (seeSectio n 1.5). Ifth e curd block already contains some curd grains ofth e next batch (with a higher moisture content), it has a higher moisture content than expected. A few dyed curd grains were found at the outside of subsequent blocks; ap parently these curd grains got stuck at the grids near the whey outlets. Trailing curd grains may become problematic in case of switching from one type of cheese to another. Changing to other filter grids will probably put this right. 71 5. Processes inside the curd column 5.1 Compaction of curd columns The compaction of a column of curd grains was tested in the apparatus described in Section 2.5.1. The results of the compression of single curd grains with the curd flattener led to the expectation that the compression of a column of curd grains will increase with the relative remaining volume of the curd grains. Fig. 5.1 showsa positiv ecorrelatio nbetwee nrelativ eremainin gvolum ean dinitia lcompressio n rate. /i(m) 0.08 0.06 0.04 0.02 1,000 Fig. 5.1 The compression of a curd column filled with cube shaped curd grains of various remaining volume,p , = 388 Pa, mesh = 8 mm, R = 0.06 m. Note that the initial height was not the same. When the time after curd preparation in the case of factory curd was prolonged beyond normal (say, 30 min), the compressibility of the curd bed decreased. Effects within this period of time were not extensively studied.Th e slower compaction ofth e curdmus t beattribute dt oth ep Hdrop ,du et oth elacti caci dproductio n byth estarte r bacteria. Zoon et al. (I 1989) reported a maximum in the storage modulus at about pH=6.15. In our case, the effect may have been more pronounced as syneresis is promotedb yth elowerin g ofth e pH,whic h inturn , causesth e moisture content ofth e curd grains to decrease intime . 72 The curd beds at 35 °C were compressible to a greater extent than those at 32 °C, which is remarkable as the initial packing is probably less dense at lower temperature,du et oth efirme rcurd grains .Th ecombine deffec to fa lowe rtemperatur e and a prolonged time before drainage is shown in Fig 5.2. /i(m) 1,000 Fig. 5.2 The combined effects of a prolonged time after curd preparation and cooling upon the compaction of a curd column. The results shown pertain to the same batch offactor y curd.R = 0.06 m, p, = 1000Pa . Increasingth eexterna lpressur e alsoincrease sth ecompressio n rate (Fig.5.3) .Ther e is, however, alimit .Compactio n isonl y possiblewhe nwhe y is expelledfro mth e curd column,an dthi s mayb ebot henclose dwhe yan dwhe yexpelle dfro mth ecurd grains . At acertai n external pressure level,hencefort h calledth ethreshol d level,th e outflow ofwhe yfro mth ecurd colum n becomesa limitin gfactor .Th einitia lrapi dcompression , mainly due to the fast decrease of the porosity, is accompanied by a steep rise in liquid pressure, whereas at later stages the compression rate rapidly levels off and may virtually come to a standstill. An increased external pressure will therefore not automatically leadt o afurthe r expressed curd column (Fig.5.4) : it even may result in a less expressed curd column. 73 P,= 30 (Pa) P«= 453 (Pa) 1,000 Fig. 5.3 The compression of curd beds at two levels of external pressure.R = 0.06 m, /„ = 0.28, mesh = 8 mm Pf(Pa) 500 P= 1300 (Pa) 1 h 400 ", P =2100 (Pa) 1 h 300 — - 200 100 Fig. 5.4 The compression of curd grains and the liquid pressure drop ina curd column at two external pressure levels. Factory curd, R = 0.10 m, time after end of curd preparation 30-40 min. 74 The threshold level is primarily determined by the curd properties, but the relations strongly depend onth e drainage vessel's properties. Radius of the column, contact area between the wall of the vessel and the curd, the stress upon the curd grains andth e drainagetim e have anoverridin g effect and are mainly predetermined byth edrainag e system.Th e packing ofth ecur d grains andth e extent of fusionwer e not extensively studied, but are likely of importance. Firmer curd grains, which may result from a smaller relative remaining volume or a lower pH and/or temperature, yield ahighe r threshold level.A higher average relative remaining volume of the curd grains results in a higher liquid pressure (Fig. 5.5). It is caused by the greater whey expulsionfro mth e higher moisturecurd grain s aswel la sb yth egreate rdeformability . Nearthi s thresholdvalu e asimpl e correlation between compression rate and relative remaining volume can not be expected, since firmer curd grains cause on the one hand a higher threshold value, but on the other hand a slower initial rate of compaction. The presence of curd fines may complicate the compression behaviour even more. Itwa s observedtha t asmal lamoun t ofcrushe d curd grains addedt o acolum n ofcub e shapedcurd grain s resulted ina slightl y retarded compression ratea swel la s asignifican t liquidpressure ,wherea swithou tthes efine sth eliqui dpressur ewa sbelo w thedetectio nleve l(result s notshown) . Presumablyth einterconnecte d pores between the curd grains become plugged by the migrating curd fines. In the literature the phenomenon isknow n as"blinding " (Novak etal . 1988). DeVrie s &Va nGinke l (1985) reportedabou t6 0percen t reductiono fth ecur dfine si nwhe ydu et o drainage.W edi d notstud ythi s phenomenon indetail ,a si tmus tb ever yintricate .Takin g representative samples from a batch of curd isfa r from easy (Johnston et al. 1991). It is likely that not the amount of the curd fines will be the main factor, but rather their size relative to the pore sizes inth e curd bed. 75 100 D /, 0.16<;' 0<0.1 3 0.23<ƒ ' P,(Pa) 400 300 200 100 200 400 600 800 1,000 t(s) Fig. 5.5 (top) Thedensit y distribution -densit y being expressed as relative remainingvolum e (/0) -o f the curd grains from five factory batches. (bottom) The liquid pressure in a column filled with curd grains of these batches at otherwise identical conditions. h0 = 0.11 m,p , = 1655 Pa,R = 0.06 m, time after end of curd preparation 20-40 min. 76 5.2 Porosity and apparent pore size distribution in curd columns Visualinspectio no fcross-section so fcur dblock smad ei na Casomati cshowe d a wide variety with respectt o the (apparent) pore size and shape.Th e largest pores were approximately 5 mm,an d the shape variedfro m round to elongated, mainly in the horizontal plane, but weird shapes were found occasionally. The porosity meter is described in Section 2.7. The standard deviation in the number and apparent size of the pores was rather large. The porosity showed a relative standard deviation of approximately 50%. This inaccuracy must be attributed toth edimension s ofth esystem :th ecurd particle sar eno tver ysmal lcompare dt oth e drainage column. Hence,onl y afe w openings per measurement willb e detected.T o reduce the effects of this natural variation we conducted multiple measurements at concentric circles; to avoid ongoing compression, the weight at the top of the curd was removed. In the case of cube shaped curd grains each set of porosity measurements concerned aseparat e batcho fcurd grains ,an dth e resultsshow nar e those of different batches. Although it could not be measured atth e start of the experiment, the porosity generally decreased in time. The loose packing of curd grains before compression was disturbed by the penetration of the sensor. Depending on the conditions (see Section 3.5) the initial porosity should be estimated between 0.2 and 0.5. A higher external pressure generally ledt o afaste r decrease of the porosity. At externalpres sures below the threshold value, the porosity did not differ significantly between the "center"circl ean dth e"rim "circl e (seeFig .5.6) .A tpressur elevel sabov eth ethreshol d level, the porosity near the rind was lower than in the center (see Fig. 5.7) and the distribution ofth e openings inaxia ldirectio n becamever y uneven.I tshoul d be noted that the porosity in the outer circle was measured at 1c m from the rind and visual inspection indicatedtha t nearer toth ewal l ofth evesse lth e porosity was even lower. The large openings in the central part were also clearly visible. The decrease of porosity with time was caused by the decrease in (apparent) size as well as the decrease innumbe r of the pores (see Fig.5.8) . With respect to the latter it should be notedtha tth e probability of detection of smallpore s isles stha ntha t of larger pores. Eventual effects of the initial density of the curd grains upon the porosity of the curd bed were not significant. The applied variation in relative remaining volumes of the cube shaped curd grains was, however, relatively small compared to the differences between batches of factory made curd. The combination of dry matter content and 77 e 0.2 0.15 - 0.05 - 1,000 innercircl e outer circle —B- ...A- Fig. 5.6 The porosity (e) near the wall of the vessel and in the central part of the curd column versus timea ta nexterna l pressurebelo wth ethreshol d level.Th evariatio ni nporosit ybetwee ndifferen t batches caused the spread at identical points intime , the porosity at the outer and inner circle of one and the same batch was practically equal, ft = 0.06 m,p , = 530 Pa,/ 0 = 0.23, mesh = 8 mm. 0.15 0.05 1,000 inner circle middle circle outercircle * D A Fig. 5.7 The porosity of a curd column versus time at an external pressure level above the threshold level. The outer, middle and inner circle are located at r = 0.09 m, r = 0.05 m and r = 0.01 m, respectively, ft = 0.10 m,p , = 1670 Pa,/ „ = 0.26, mesh = 8 mm. 78 600 s 30 H 20 10 -1 1 1 r- 40 900S 30H 20 10 0 ^ 00 N ID O ^ 10 C\J (D o ^~ CO (M (D o t 00 w Fig. 5.8 The frequency distribution (A/,J?/Ax) of the apparent pore size M in a curd column at 5 points in time. R = 0.06 m, /„ = 0.23, p, = 530 Pa, mesh = 8 mm. (A/,j?/Ax) is, in first approximation, proportional to the pore volume. 79 porosity can be usedt o estimate the dry matter content of the curd grains (see Fig. 5.9). 0.15 0.05 1,000 e d.m.% curdbe d d.m.%cur dgrain s • A-.. ••• Fig.5. 9Th edr ymatte rconten to fa cur dbed , thecalculate ddr ymatte rconten t ofth ecur dgrain san d theaverag e porosityo fth ecur dbe dversu stime , ft = 0.06m ,/ „ = 530, p, = 530Pa ,mes h = 8 mm. There arecertai n difficulties herein;th e permeability ofth e briefly pressed curd blocks is very high and a certain whey loss whenth e curd block istake n out of the column can not be avoided. At later stages the whey loss is less. The dry matter content of the briefly pressed curd blocks isthu s overestimated.Th e dry matter content of the whey inth epore s inth ecur d block wasestimate d at6% .Th evolum e decreaseo fth e curd block duet oth edecreas e inporosit y isclearl y shown in Fig.5.9 .Th edr y matter content ofth e curd grains increased intime , and asmal l increase already represents a considerable volume loss of the curd grains.Thu sth e compaction of curd beds at these conditions depends both on decrease of porosity and on volume of the curd grains. A series of experiments was conducted with curd taken from Tebel and Ost cheese vats at NIZO's experimental plant. The curd was not drained immediately, because the curd size distribution andth e curd density distribution were determined first.Th e curd was drained 40 minafte r pumpingth e curd/whey mixturet o the buffer 80 tank,whic h isslightl y latertha nnormal .Th edensit y ofth ecurd grain svarie dbetwee n batches, so measurements atdifferen t intervals hadt o bedon e onth esam e batcho f curd. The same curd block was used, and 5 replicate measurements were taken at eachtime .Th e compaction of the curd column was stopped during the execution of replicate measurements, i.e.,th emechanica lpressur ewa stemporaril y suspended,t o be restored directly afterwards. This procedure may have influenced the results somewhat.Th e smallnumbe r ofreplicate s ledt o aconsiderabl e spread inth eresults . Nevertheless, the porosity showed the same trends as in the case of cube shaped curdgrains :abov eth ethreshol dleve lo fexterna lpressur eth eporosit ywa slowe rnea r the rind than at the center, whereas the porosity at an external pressure below the threshold levelwa sno tsignificantl y affected byth edistanc efro mth ecenter .Th eden sitymeasurement s revealeda wid esprea dfro mbatc ht o batch.I twa stried t o linkth e density of the curd grains to the (change in) porosity of the curd block, but no clear correlation couldb eobtained .Difference s inwate rconten t betweencurd blocks (R= 0.06 m) compressed at 1700an d60 0 Pacoul d only be partly attributedt o the higher porosity of the latter. Finally it hast o beremarke dtha t duet oth eabsenc e of any referencemethod , the results ofth e porosity meter could not beverified ,bu t wefee ljustifie dt o consider the trends to be correct. Infactor y madecurd blocks, about25 %o fth eweigh t after drainage islos tdu e to drip whey before brining. This whey must largely originate from the inside of the curd grains, as the porosity of the curd blocks after drainage is much smaller than 0.25.Th e remaining pores will be removed inth efurthe r process, but some defects, e.g. nests of holes near the rind (De Vries & Van Ginkel 1985) and the growth of molds just below the rind in cheese, must probably be attributed to incomplete removal of the last pores. That it happens mainly near the rind of the curd block is probably caused by the lower temperature in outer zone of the curd block (Geurts 1978), causing deformability and rate of fusion to be reduced. 5.3 Aspects of permeability The permeability of the curd column could not directly be measured and a description of the failed approaches was given in Sections 4.1 and 4.2. It can be roughly estimated by using the Blake-Kozeny equation (equation 1.4)fo r curd beds with a porosity larger than 0.10.Th e permeability of acurd bedwit h a lower porosity 81 can be calculated by taking the volume reduction of the curd column (AAJ * A), the liquid pressure (p,) andestimatin gth ewhe y expulsionfro mth e curdgrain s (equation 3.4). A description ofth e mathematics requiredt othi sapproac h isgive n inAppendi x A.Th e permeability as afunctio n of time canthe n be derived (Fig.5.10) . ß(m2) 1E-08*- 1E-09 1E-10 1E-11 1E-12 - 1E-13 200 400 Ms) 600 800 1,000 Fig. 5.10 The calculated permeability of a column filled with cube shaped curd grains as a function of time, p, = 820 Pa, R = 0.06 m, mesh = 8 mm, ;0 = 0.25 It is seentha t the permeability changes over several decades over the time interval. Thever y highpermeabilit y atth estar to fth edrainag e hasconsequence sfo rth eprac tical cheese making. In continuous drainage machines, e.g.th e Casomatic, the first whey outlet ismounte d relatively closet oth eto p of the pipe.Althoug hth eflo w ofth e whey at this outlet is restricted by a back pressure, the amount of whey flowing out of this outlet is large, because of the high permeability of the curd/whey mixture (leakagebetwee nth ewal lo fth evesse lan dth ecurd ma yals ocontribut esignificantly) . The curd grains may ultimately become uncovered, and therefore whey (usually first orsecon dwhey ) issupplemente d independently. Inolde r drainagesystem swhe ywa s recirculated hereto, but this causes microbial contamination. Heijnekamp(persona lcommunication )foun da tNIZO' sexperimenta lplan tlarg e deviations in moisture content in adjacent sectors taken from curd blocks after 82 drainage in aCasomatic .Straatsm a et ai. (1984) gave results ofth e moisture content during cheesemaking.Th evarianc ewithi n achees e contributed for about40 %o fth e total variance in moisture content of the daily production.Th e spread inth e number and (apparent) size of the openings in a curd bed will affect the spread in moisture content. To investigate the flow of whey through a curd block, colored whey was injected in a block of draining curd, the coloring became visible at the outside of the curd block at various places and at variable intervals of time.Th e latter observation pointst o variations inflo w ratethroug hth e interconnected pores betweenth egrains . TheHagen-Poiseuill eequatio ni svali donl yfo ra straigh tcapillar yo f uniform diameter: = _n_V dp, (5 1} 8/7 äx where 0 = flow rate (m3/s) R = radius (m) n = dynamic viscosity of the liquid (Pa.s) p, = liquid pressure (Pa) x = distance (m) This equation cannot be used as such to predict the permeability of a curd column. It may, however, be useful to apply this formula to an infinitesimally small capillary insideth e complicated network of channels.Th e smallest pore radius in a channel is the limiting factor for its total flow. Small differences in this limiting pore radius will according to the Hagen-Poiseuille equation, leadt o rather largedeviation s inth eflo w rate. Andth etota l flow willthu s mainly becontrolle d by the channels withth e largest minimum porediameter , i.e. asmal l number. Poissonstatistic s may beappropriat e to explain large variation inwhe y flow. Interconnected pores become more narrow and may eventually become disconnected.Thi s process, caused both by reorientation of the curd grains and by deformation can beaccelerate d byth e presenceo f curdfine s that plug the pores. The whey flow from isolated pores is considerably retarded, because ofth e lowpermeabilit y ofth e curd grains (sayS = 10"13m 2,se eSectio n 3.2) as compared to that of the pores between the curd grains in the drainage column. Straatsmae tal . (1984)reporte dtha ta lowe rmoistur econten ti nth ecurd grain sbefor e drainagele dt oa smalle rdeviatio ni nmoistur econten twithi nth echeese . Experiments 83 by Geurts (1978) also showed a reduced unevenness in moisture distribution in cheese made of curd grains stirred very dry. Curd grains containing more moisture have to expel more whey to attain the desired moisture content, the permeability of these curd beds should be higher hereto. However, the porosity of these curd beds at external pressures below thethreshol d level is lower or equaltha n that of beds of drier curdgrains .Th edecreas e inporosit ywil llea dt o considerable narrowing and/or sealing of most ofth e (initially) interconnected pores,causin g (locally) a considerable decreaseo fth epermeability .Th eloca lsealin gwil lhappe n inth emor emois tcur dbe d beforeo r atth esam etim etha t itwoul d happeni na drie r curdbed ,hence ,a ta highe r moisture content.Th earea so f ahighe r moisture content havet o becompensate d by relatively dry areas to obtain the desired average moisture content, hence, the standard deviation in moisture content will be considerably increased. Intheory ,considerabl esealin go fpore sma yoccu rwithou ta significan tincreas e inth eoveral lliqui dpressure ,a sth eoveral lliqui dpressur ei spredominantl y determined by the largest interconnected pores. Even inth e case of a liquid pressure below the detection level,th e existence of isolated pores can not be ruled out. The moisture content of curd blocks of Casomatic drainage vessels is usually around 58-60% and estimating the porosity of those blocks to be a few per cent implies that the amount of the whey inside the curd grains is only slightly reduced in the vessel. Directly after drainage, the pressure exerted upon the lower layers inth e curd block is dramatically increased, due to the sudden decrease in buoyancy. The average distance to the outside of the curd block decreases as result of the cutting ofth ecur dcolumn ,wherea sth e permeability, especially ofth ecentra l parto fth ecurd block,i sstil lconsiderable .Pressin ga freshl ycu tcurd bloc k betweentw o impermeable horizontal plates as illustrated in Fig 1.4 is, due to these plates, unlikely to be very effective with regardt o whey expulsion.Afte r molding,th e outflow ofwhe y really gets going,resultin gi nconsiderabl ewhe y lossdurin gtranspor tt oth echees epresses ;du e to the unavoidable microbial contamination the spilled whey is practically worthless. Cuttingth e collected curd mass in blocks ina batc h drainage systems also results in a rapid and considerable whey loss, but this whey is usually retained in thevessel . Applicationo f highstresse s ina nearl y stageo fth edrainag e does not resulti n extensivewhe y expulsion,bu tcause sjamming .Thi s phenomenon is probably due to thefollowin g mechanism.A highexterna lpressur e leadsinitiall yt o arapi dcollaps eo f the curd grain packing, causing a substantial whey expulsion from the pores. The 84 whey inth ecentra l partca nonl yflo w outthroug hth eoute r layerso fth ecurd column . Due to the rapidly decreasing permeability, the transport of whey from the center towardsth e rimbecome s insufficientt o keepu pwit hth efas twhe y expulsionfro mth e outer layer, leading to afurthe r and more rapid narrowing of the pores in the outer layers.This , inturn , retards further whey transporttoward s the outer layer, causing a rapid sealing of the pores near the rind. 5.4 Computer modelling of the drainage system Itwa strie dt o modelth e compression of acurd/whe y mixturei na colum n and thereby predictth echang ei nporosity .Th einpu tdat awer eobtaine dfro m compaction of cube shaped curd grains inth e small column R = 0.06 m (Section 2.5.1). Thetota lexerte dpressur e (p,)ca nb ebroke ndow nint othre epartia lpressures : + + 4 1 P. = Pm P, Pw ( - ) The weight of the (submerged) curd grains is neglected hereby. At relatively low external pressure, the overall liquid pressure gradient between the center and the outside of the column was below the detection level,hence ,virtuall y zero.Th e voids between the curd grains, which were assumed to be uniformly distributed over the curdbed , do not carrya significan t parto fth epressure .Th eexterna lpressure ,i nfac t force per m2, is carried by a smaller cross-sectional area of curd grains, hence the stress upon the curd grains can be (locally) higher than the overall pressure. The average local stress (pm') upon the curd grains is equalto : , = Pi-Pt- PW (5.2) (1-e) where pm' = average local stress upon the curd grain (Pa) p, = total exerted pressure (Pa) p, = liquid pressure (Pa) pw = pressure loss due to friction (Pa) e = porosity (-) 85 Thetota l pressure loss (pj atth e wall can be described with equation (4.2): 2 *, h p, (4.2) Infac t the pressure loss depends on the vertical distance from the plane where the externalpressur e isapplie d (Section4.2) ,bu t hereth e pressure losswa s assumedt o beconstan t throughout the curd column.Th etota l pressure losswa s divided by two to obtain an average.Th e volume of the curd column is composed of the volume of the pores andth e volume of the curd grains. Ifth evolum e of the curd grains can be predictedan dth evolum e (infact ,height ) ofth ecurd colum ni smeasured , theporosit y can be calculated.Th e initial porosity was estimated and initialvolum e of curd grains (Vg(0)) can then be calculated. It was tried to predict the decrease of the volume of curdgrain s byequatio n (3.4),whic hwa soriginall y derivedt o describeth e expression of a single curd grain: ILL!?- =exp( - k pm JF) (3.4) 'o '» The calculation scheme is given in Figure 5.11. h =f(t) w V°> < - vjt) m m Fig.5.1 1Th e schemet ocalculat eth e porosity(e )fro mmeasuremen t ofth eheigh t ofa cur dcolum n(/? ) andth evolum eo fth ecur dgrain s (Vg). Thevolum eo fcur dgrain si scalculate db ymean so fth eequatio n for the compression of a single cube shaped curd grain (equation 3.4). 86 At external pressures below 400 Pa, the porosity decreased monotonically. The predictedporosit ydepend st oa larg eexten to nth eunknow ninitia lporosity ,bu ttakin g reasonablevalue sfo rth e latterth ecalculate d porosity asa functio n oftim e appeared realistic, althoughw eha dn oporosit y measurements atsuc ha lo wexterna lpressure . This impliestha tth e behaviour of asingl ecurd grain is probably areasonabl e model forth eexpressio no f acolum n ofthes ecurd grain s inthi scase .A t external pressures above 400 Pa, the calculated porosity increased after an initial decrease. This happened at an earlier stagefo r the higher external pressures.A significant increase of porosity isunrealisti c and must beattribute dt o anoverestimate dvolum e decrease of the curd grains. At high external pressure levels (say, greater than 1000 Pa) the liquid pressure soon plays an important role and in the relatively simple model this factor isno ttake n intoaccount ; it leadst o anoverestimate d stress uponth ecurd an d thus to an overestimated decrease of thevolum e of the curd grains. The increase in porosity at external pressures in the range 400 - 1000 Pa, as followed from the calculations,wa scontrar y to our expectation. Inreality ,th e expressiono f curd grains ina colum n maywel l beles stha n isth ecas efo r asingl ecurd grain;thi s may be due to the limited deformation possibilities inth e curd column and/or the locally retarded flow of whey (although anoveral l liquid pressure between the center andth e outside was notfound) .Th eincreas ei ncross-sectiona l areai nth ecas eo f asingl ecur dgrai n isno tidentica lt otha to fthes egrain si na batch ,whic h impliestha tth estres s uponth e curd grains (pj in a column may decrease faster than is implicitly assumed in equation (3.4). Itshoul d berealize dtha tth esituatio ni na curd colum n isfa r more complicated than assumed in most filtration models, e.g. (modified) Terzaghi models (Leclerc and Rebouillat (1985).I nou rcase ,th eparticle sar edeformabl e(visco-elastic) ,the yca nb e expressed andthe y partially fuse with eachother . Nevertheless, our model seems to work fairly well, up to pressure of about 400 Pa, and maybe higher pressures if the curd grains are more rigid. That the model does not work for pressures above the threshold level is only to be expected. In the intermediate pressure range, some elaboration of the model could be tried. 87 6. General discussion and conclusions Varioustype so fdrainag evessel sexis tan deve nfo r identicaldrainag e systems the mode of operation varies among plants, whereby the way of curd preparation and/or the shaping/pressing of the curd blocks may be tuned to the particular drainage system inuse .Apparentl yther ear esevera ldifferen tway st oachiev eth etw o aims of the drainage: separation of the curd grains from thewhe y andth e formation of a coherent block of curd. Nevertheless,th eidea ldrainag e process hasno t beendevelope dyet .I tshoul d yield identical curd blockswit h amoistur e content of about 47%(i nth e caseo f 12k g Gouda cheese), for which pressing is only neededt o obtain awell-close d rind. The study of the drainage of curd is complicated by the many, often mutually dependent parameterstha t determineth e process.Th e properties ofth e curd grains play an important role, and to eliminate variations in drainage behaviour due to variation in the curd grains a standardized curd preparation was developed for this study. The new curd preparation process resulted in practically uniform curd grains thatcoul deasil y becharacterize d bythei r density. Besidesth euniformity , other major differences betweenth e model curd grains andthos e prepared infactorie s were:th e presence of cracks inth e outer layer ofth e curd grains before stress application and the absence of starter culture.Th e density of the curd grains can be recalculated to the relativeremainin gvolum e(/ 0)and/o r whey contento fth ecurd grains . Besidesthi s property, there could be other (minor) factors that had some influence upon the drainage behaviour ofthi s modelcur d grains.Th esam echaracterizatio n was applied tocur dgrain stha twer eproduce di nNIZO' spilo tplant ;again ,th edensit y (distribution) appeared to be an important variable. But there are parameters that may become important too, such as pH and temperature. These were (mostly) not varied in the caseo f modelcurd grains .Th esiz edistributio n ofth ecurd grain si susuall y monitored in cheese plants, but in experiments with model curd grains of two different sizes its importance for thedrainag e process seemedt o be minor. Onth e other hand, adding a small amount of curd fines to the model curd grains did cause appreciably slower drainage. Further research on the role of curd fines in the drainage process will be useful. The drainage system affects the drainage process in various ways. Obvious characteristics ofth edrainag evessel s are:drainag etim ean dtemperature ,manne ro f whey discharge, and duration and magnitude ofth e exerted pressure upon the curd 88 grains. But there are also less known parameters that play an important role in the drainageprocess . Leakageo fwhe y betweenth ewal lo fth evesse lan dth ecur dmas s can become a major factor. Friction at thewal l can limitth e stress exerted upon the curd grains to only a smallfractio n of the total exerted stress.Thes e two processes maydominat eth edrainag ei f iti sperforme d inrelativel y smallvessels .Th ewal lo fth e vessel alters the orientation of the curd grains close to it. Inside the drainage system various processes take place, and it was tried to study them separately. The deformation of and whey expulsion from a single cube shapedcurd grai nunde rstres swer eclosel ycorrelate dwit heac hother .A ninterestin g result was that such a curd grain could be expressed to a very low whey content within areasonabl etime . Importantvariable s likedrainag etime ,applie d pressurean d initialwhe yconten twer eth e (major) parameters determiningth eexten to fexpression . Therheologica lpropertie s ofth eparacaseinat estrand sbecom esoo nth edeterminin g factorfo rth erat eo fexpression .Th eoute rlaye ro fa factor ymad ecur dgrai ni sinitiall y very dense and no cracks were observed. Onth e other hand, application of a small stress (say10 0Pa ) uponth ecurd grai nle dt oimmediat eformatio n ofnumerou ssmal l cracks in the outer layer; consequently, it may be expected that the behaviour at expression of a cube shaped curd grain still is an adequate model for factory curd. The expression of a single curd grain was compared to the expression of a column ofcurd grains ,bu tther ear etw ofundamenta ldifferences :i na colum nth eflo wo fwhe y frombetwee nth ecur dgrain sca nb erestricte dan dth edeformatio no fcurd grain sca n be limited duet o geometrical constraints. A simple computer model indicatedtha t at low external pressure the expression of a single cube shaped curd grain could be used as a model for the expression of a column of these curd grains. At pressures abovethi s levelth e model indicated thatth e expression of curd grains wasretarded , although a liquid pressure between the center and the outside of the curd column could not always befound . It should be realized,however , that despiteth e formation of many isolated pores, some interconnected pores may still remain, and the liquid pressure is predominantly determined by the latter and may be still be below the detection limits. Application of pressure upon the loosely packed curd grains leads to their reorientation, and this causes a rapid decrease of size and number of the openings betweenthem .At th e contact areas betweencur dgrain sjunctions , i.e.ensemble s of bonds between two adjacent curd grains, areformed . Thesejunction s may limit the 89 extent of reorientation. Itwa strie d to study thefractur e stress of thejunction s inwel l definedconditions .A ta constan tmacroscopi cfusio nare ath efusio ntime ,th eexerte d pressure,temperatur ean dprobabl yth ereactivit yan dstiffnes so fth eoute r layero fth e curdgrain swer eamon gth edominatin gfactors .Th econtac tare abetwee ncur dgrain s in a curd column is difficult to determine, but it will certainly increase in time. The extent of fracturing of thejunction s depends on their strength, the exerted pressure andth egeometrica l possibilities.Th eporosity , i.e.th evolum eo fth ewhe yfille dpore s as a fraction of the total volume of the curd bed, decreases in time due to the reorientation and deformation of the curd grains. Reorientation probably causes a faster decrease.Th e compression of acur d column is directly linkedt o flow of whey leavingth edrainag evessel .Th eflo woccur spredominantl ythroug hth einterconnecte d pores,whereb yth e largestpore scontribut e most.A decrease d porositywil lgenerall y leadt o adecrease d permeability. The permeability can become so smalltha t aliqui d pressure between the center and the outside of the curd column can be measured, the value of the exerted pressure at which this occurs is called threshold level. It is primarily determined by the curd properties, butth e relations strongly depend onth e properties ofth e drainage vessel. Pressures aboveth e threshold level usually cause a lower porosity near the outflow surface and an increased inhomogeneity of pore distributionthroughou tth ecur dcolumn .Unfortunately ,th ethreshol dleve li srathe rlo w in practical cheesemaking. Inth e current equipment the removal of whey is hampered by the fact that a largeamoun t ofth ewhe y remainsinsid eth ecur dgrains .Th estres sexerte dupo nth e curd grains inside the curd column is insufficient to drive out all whey. The major question istherefore : howca nthi s stress upon the curd grains be increased without narrowing the pores between the curd grains to such an extent that the permeability of the curd block becomes a limiting factor in drainage. A solution could be creating verythi ncur dlayer stha tca ndrai na tal lside san d experiments indicatetha t relatively lowwate r contents (approximately 53% ) can indeed beobtaine d ina shor t periodo f time (15 minutes), but from the perspective of current cheesemaking, especially for hard and semi-hard cheese types, curd blocks should be large. In the upper layer in a continuous drainage pipe, e.g. Casomatic, a loose packingo f curdgrain sca nb efound .Thi spackin go f curdi ss o permeabletha twhe n whey is discharged the curd grains at the top of the curd column can become un covered. The amount of removed whey can be adapted by changing the back- 90 pressure or the drainage time, which is relevant because steady states are not reached. Ideally so much whey should be removedtha tth e occurrence of asizeabl e liquid pressure can just be avoided. This is difficult to achieve in liquid pressure controlled drainage vessels, asth e amount of removed whey can becontrolle d only indirectly. Direct control of the actual whey removal rate, possibly combined with a well-controlled curd/whey mixtureinput ,ma yb ea bette r option.Thi sca nonl y bepar t ofth e solution as a large amount of whey insideth e curd grains still remains. A high pressure is necessary to accomplish considerable whey expulsion ofth e curd grains within anacceptabl e period oftime .Th e resulting reorientation ofth e curd grains can be limited when strongjunction s between the curd grains have beenformed . It may therefore be taken into consideration to create conditions that promote fusion. Drier curdblock sar eles sdeformabl ean dsatisfactor y rindformatio nma ynee dthe nspecia l attention, but the reward:a considerable reduction of the amount of drip whey, may be worthwhile further efforts. 91 Appendix A:Calculatio n of the permeability of a radial drainage column Thepermeabilit y ofa colum no fcurd grain si scalculate dfo ra nidealize dsyste m of uniform particles.Th e Blake-Kozeny equation is usedt o calculate the permeability inth e region porosity larger than 0.10: 2 3 dp e B (1.4) 150 (1 - e)2 3 The diameter of the curd grains dp was estimated at 6.10" m , and results of various porosity measurements were used. The initial porosity (e) is estimated at 0.3. At a porosity smaller than 0.1, the Blake-Kozeny equation was not applied. Porosity data forthi sregio nwer ecalculate dfro mth eexperimenta lresults ,obtaine dfro mexpressio n testswit hth e arrangement described in 2.5.1.Th efollowin g assumptionswer emade . Theflo w of whey is completely determined by theflo w between the curd grains.Th e porosity and permeability are uniform throughout the column. Wall friction and the apparent weight of the curd grains are not taken into account, therefore the exerted pressurei sconstan tthroughou tth ecur dcolumn .Th emai nconsequenc eo fthes eas sumptions is that we introduce an overall value for the permeability of the whole column,tha t may be considered as a practical calculation quantity. Fig. A.1 A schematic drawing of a horizontal cross-section through the curd column showing the cylindrical coordinate system. ft, isth e radius ofth e glassfilter , R2i sth e radius of the curdcolumn . 92 The flow rate of whey atr (see Fig.A.1 ) can be calculated by Darcy's equation S dp, 0 = -2nrhÊ.^l (1.1) n dr At r + dr the flow rate is equal to: 0 + d0 = -2 rrr h ä ^ - 2 nh Ê. ±(r — >* (A1) /7 dr r/ dr dr Thene tflow o fwhe y resultsfro m bothcompactio n ofth ecolum nan dwhe y expulsion from the curd grains. The net change in "free"whe y volume per unit of time at r can be described as: ÛZ = —(2 n r h e) dr (A.2) df where Z = net free whey volume change (m3/s) e = porosity (-) r = radial variable (m) h = height (m) t = time (s) Thewhe y expulsion ratefro mth ecurd grains isa functio n ofth eexerte dstress ,initia l moisture content andtime : !L!± = exp(- kp mvT ) (3-4) The resulting function is complicated and therefore less suitable for further handling. To avoid this difficulty the amount of expelled whey was calculated at times 30, 90, 150,300 ,450,60 0an d90 0s fro m (equation3.4) .Th ewhe yexpulsio n ratewithi neac h of these intervalswa s assumedt o beconstant . Furthermore thewhe y expulsionwa s linkeddirectl yt oth estres s uponth ecurd grains .S oth efollowin gfunctio ni sobtained : O = *, pm (A.3) where Q = volume of whey expelled per volume of curd grains per unit of time (m3/m3s) 93 1 1 /cq = time dependent constant (Pa .s' ) Avolum e balance results in: 0 + d0 - 0 = -—(e 2 n r h)är + 2 rrr h är Q (A.4) or, accounting for (1.1) and (A.1): Ë. 1 ±(A =- O • .Ë£ (A.5) n r dr dr df Thetota lexerte dmechanica lpressur ei sequal ,i ncas eo fnegligibl ewal lfriction ,t oth e sum of the liquid pressure and the stress upon the curd grain: + 4 1 P, = Pm P, ( - ) Equation (4.1) can be used to link the whey expulsion rate (equation A.3) and the liquid pressure. Equation (A.5) then turns to: ßj d ,, dp,, . .t . , t „ . ds l^(r^) = -/cqpt+/cqp(+°£ (A.6) n ir ôr or q q df With boundary conditions: r = fl, •* p,-p, (A.7) and r = R2 - p, = 0 (A.8) As reference liquidpressur eth eliqui dpressur e atth e outer surface istaken .T osolv e equation (A.6) a new dependent variable n is introduced: n = *q (P, - P, • ^ ^f) (A.9) Wherep ,an dde/d far eassume dt ob eindependen to fr (seeforgoin gconsiderations) . Equation (A.6) then changes into: 94 l± r = fl, - n, = A, (p, - p, + 1 *) (A.11) r = R2 - n2 = *, (-p, + 1 *) (A.12) Thenumerica lvalu ep ,i sobtaine dfro mexperimenta ldat ao nth eliqui dpressur ea tth e center, fl, = 0.01 m, and the wall of the vessel, R, = 0.06 m. Furthermore we introduce: B r-ï (A.13) n K Introduction in equation (A.10) yields: d2 n 1 dn n = 0 (A.14) äf + f df The boundary conditions turn into: n ft, (A.15) f, =«i B - n = n. n K (A.16) f, = R2 B n = n, Equation (A.14) represents the modified zero order differential equation of Bessel. It has two solutions, namely l0(fl and K„(f). The general solution is: n = a l0(f) • ß K„(f) (A.17 ) The boundary conditions yield the coefficients a andß: 95 a l0(f,) + ß KoK) = n, (A.18) a l0(f2) +ß KotfJ = n2 (A.19) From (A.18) and (A.19) the coefficients a and ßhav e to be solved with reference to (A.11), (A.12), (A.15) and (A.16).T othi s endw e need anumerica lvalu efo r de/df for the time interval concerned. The unknown permeability (B) is maintained as such in our solution for the sake of the iteration procedure. To evaluate the mathematical solution the derivatives of the Besselfunction s must beobtained : Uz) = 1,(7) (A.20) and <{z) = -K,(z) (A.21) The values of l0(z),K0(z),l1(z) and K,(z) were taken from Olver (1965) and partly calculated using IMSLroutines . Introducingth esolutio n (A.17) in (A.9)w eobtai np ,a s function of r for the time interval concerned. Substitution of this p, in equation (1.1) yields a relation between B " (P„A dn)2 " *< (A.22) 2 n H. n 2 df 3 Itwa s solved iteratively. The dynamic viscosity was estimated at 10" Pa.s ,R 2= 0.06 m, 0,p ,an dh were obtainedfro mth e results ofth e compaction of acurd column. It hast o benote dtha tth efacto rk q isprobabl y slightly overestimated (seeSectio n 5.4). Moreoverth eter mde/d fwa sno texactl y knownfo rth ecircumstance sgiven ,therefor e it was assumed to bezero . 96 References Beattie, J.A., Density (specific gravity) and thermal expansion (under atmospheric pressure) of aqueous solutions of inorganic substances and strong electrolytes, In: Washburn, E.W. (ed.) International Critical Tables III (1928), Mc Grawhill, London 79 Berg, G.va n de & E. de Vries,Th e use of curd washing water, Zuivelzicht 68 no 40 (1976) 878-879 and no 42 924-926 Bijgaart, H.J.CM. van den, Syneresis of rennet-induced milk gels as influenced by cheesemaking parameters, Ph.D. thesis, Agricultural University, Wageningen, The Netherlands (1988) Boekei, M.A.J.S. van & P.Walstra , Steric exclusion of serum proteins with respect to (paracasein micelles, Neth. Milk Dairy J. 43 (1989) 437-446 Buma,T.J .Th e true density of spray milk powders and of certain constituents, Neth. 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(1985), NATO ASISerie s E no. 88, Martinus Nijhoff Publishers, Dordrecht, 356-391 Luyten, H., The Theological and fracture properties of Gouda cheese, Ph.D. thesis, Agricultural University, Wageningen,Th e Netherlands (1988) Mulder, H.,J.J .d eGraa f & P.Walstra , Microscopical observations onth e structure of curd and cheese, XVII International Dairy Congress (1966) München D:413-420 98 Munro, P.A., The densities of casein curd particles and caseinate solutions, New Zealand Journal of Dairy Science and Technology 15 (1980) 225-238 Nederlands Normalisatie-instituut. Fysische en chemische methoden van onderzoek. Bepaling van het vochtgehalte. NEN 3754 (1981) Delft, The Netherlands Niederauer,T. ,Ein eeinfach eMethod efü rdi eKorngrößenbestimmun gvo nKäsebruch , Deutsche Milchwirtschaft 16 (1976) 464 Noel, Y., P. Chevanne, A. Dasen, R. 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Milk Dairy J. 43 (1989) 35-52 101 List of symbols A area m2 B permeability m2 C concentration kg/m3 c, surface concentration kg/m3 3 Co initial uniform concentration kg/m cw drag coefficient dp diameter of particle m e void ratio e final void ratio 2 9 acceleration due to gravity m/s h height m m h0 height at t = 0 fy height at t = t m / relative remaining volume of curd 'o initial relative remaining volume of curd 'o initial relative remaining volume of curd at infinity 't relative remaining volume at t = t k constant Pa"1** K first order rate constant s1 15 *i constant Pa 1 1 *, time-dependent constant Pa- .s" 1 ka first order rate constant s Mx mass of a curd grain at t=t kg M0 mass of a curd grain at f=0 kg M„ mass of a curd grain at t= < » kg Pt pressure on the liquid Pa Pa Pm stress upon the curd grains Pa Pm' average local stress upon the curd grains Pa Pt external pressure Pa Pw pressure loss due to wall friction/adhesion 1 0 relative whey expulsion rate of the curd grains s f radial variable m 102 R radius m t time s V stationary sedimentation velocity m/s V volume m3 v „ volume of the curd grain m3 X distance m z experimentally determined rate constant s1 Z net "free"whe y volume change m3/s a volume fraction of paracaseinate - milk - a0 volume fraction of paracaseinate in Ox volume fraction of paracaseinate in a curd grain - ß volume fraction of fat - Y volume fraction of whey - e porosity - eh Hencky strain - 0 volume ratio fat/paracaseinate - n dynamic viscosity Pas fj pseudo Poisson's ratio - 3 P, density of fat kg/m 3 Pa density of curd grain kg/m 3 Pi density of liquid kg/m 3 Pm density of paracaseinate matrix kg/m 3 Pw density of diluted whey kg/m 3 0 flow rate m /s n volume of whey in the curd per unit volume of dry matter - Q* finalvolum e of whey inth e curd per unit volume of dry matter - 103 Summary Cheese making starts with transformation of the liquid milk into a gel by proteolytic enzymes and/or acid producing bacteria. The gel is cut into pieces.Th e protein matrix contracts, by which whey is expelled from the pieces,thi s process is called syneresis.Th e process of whey expulsion is enhanced by stirring and usually heating. Finally fairly rigidcur d grains and a large amount of whey are obtained.Th e subsequent separation of whey andcur d grains is calleddrainag e of curd. For most typeso fcheese ,th eobtaine dcurd mas si ssubsequentl y pressed,salte dan dripened . This study is mainly aimed at the drainage in case of Gouda cheese, but some aspects may be applicable to other cheese types as well. Drainage of curd not only separates (most of) the whey from the curd grains, but it also leadst o theformatio n of acoheren t mass.Th e drainage is not an isolated process,bu t itsoutcom e depends heavilyo nth e preceding curd preparation andth e subsequent shaping and pressing. The study of the drainage process therefore requires awell-controlle dcurd preparation.I nou r conditions large-scalecur d produc tionwa s often not possible, but scaling down ofth e curd making process ledt o curd grainstha t hadonl y littleresemblanc et othos e producedo nfactor y scale.A newwa y of curd preparation was therefore developed. It enabled the production of almost identicalcub eshape dcurd grains .Th ebasi cfeature s ofth e newapparatu s were:th e gel was cut in cubes by two wire grids, andth e cubes were stirred by subsequently pumping anamoun t ofwhe y andlarg eai r bubblesthroug h holes inth e bottom ofth e cheese vat. The delicate curd pieces were hardly broken up by the resulting gentle stirring. As the used air istoxi c to starter bacteria curd was prepared without starter. Thecurd grain swer echaracterize db ymeasurin gthei rdensit yi nthermostatte d sodium chloride solutions of various concentrations. Thedensit y can be recalculated to a moisture content or relative remaining volume, i.e. the volume of curd grains as afractio no f itsvolum e beforesyneresis .Th edensit y measurement could,i nth e case of uniform curd grains, replace the various empirical methods currently applied to determineth e momentt o beginwit hdrainage . However, incas eo ffactor y madecurd otherfactor sma yals ob eo fimportance ,e.g .pH ,temperatur e andth eamoun to fcur d fines. Theunifor mcur dgrain swer euse dt ostud yth eexpressio n anddeformatio no f a single curd grain in a uni-axial compression setup. The compression led to an instantaneous (elastic) and aslowe r viscous compression of the curd grain. Release 104 of the stress within afe w seconds after the start of the compression ledt o a clearly visible recovery; this was not the case after 15 minutes of compression. The elastic and viscous compression increased with the exerted stress (pj and initial relative remainingvolum eo fth ecurd grai n(/'„) . Theexten to fcompressio n increasedwit htim e (f). The relative remaining volume at time t of a single curd grain (/',) could be expressed as: -^L=exp(-/fpmN/T) (3.4) where/'« ,i sth erelativ e remainingvolum ea t infinity andk isa constan t (4.10sPa" 1.s"*). The expression also led to horizontal broadening of the curd grain. The broadening increased with the exerted pressure and decreased slightly with decreasing initial remaining volume of the curd grain. At maximum, the broadening increasedth e originalcross-sectiona l areat o about 1.6times .Th eexten to fcompres sion and volume decrease of the curd grain appeared to be closely correlated. The rheological properties of the paracaseinate strands probably become soon after the startth e rate-determining factor atexpression .Th e resistancet oflo w ofwhe y mayb e a rate limiting factor at the start of the expression. It was observed in CSLM photographstha tth esurfac e layer ofth ecub e shapedcurd grain s showedcracks .I n the outer layer of curd grains obtained from factory made batches no cracks were observed, but, after application of a stress, cracks wereformed . The fracture stress of fused curd grains could be studied at constant macroscopic fusion areawit h a newly developed technique. The fracture stress was positivelycorrelate dwit hth efusio ntim ean dth eexerte dpressure .Th einitia lremainin g volumeals oshowe da positiv ecorrelatio nwit hth efractur estress ,withi nth esmal ltes t range. The temperature also had an effect upon the fracture stress: the highest fracture stress was obtained at about 35 °C and higher or lower temperatures both led to somewhat lower values. The sedimentation rate of curd grains mayvar y due to differences in apparent weight anddensity , butth efac ttha t smallcur d grains are usuallyfoun da tth e bottom of a settled layer of curd grains can not be attributed hereto. Small curd grains can, however, fill the gaps between adjacent larger curd grains. The cube shaped curd grains rotated when freely settling. Anisometric curd grains sank with their longest 105 axes perpendicular to direction of sedimentation, regardless of their initial position. Due to preferential orientation of the curd grains and the deformation of curd grains the curd bed has to be considered an anisotropic medium.Th e flow of whey occurs mainlythroug hth e interconnectedopening s betweenth ecurd grains,an dth e permeability of the curd bed inth e horizontal direction will be greater than that inth e vertical direction. Varioustype so fdrainag eequipmen t areuse dt o performdrainage ,dependin g onth escal e of production,th evariet y of cheese produced andth ecost/benefi t ratio. Batchdrainag esystem sar emostl y usedi nsmal lscal eproductio nunits ,wherea scon tinuous drainage vessels are commonly used in bulk cheese production. Both types have been realized inseveral ,somewha t varying constructions and alsoth e modeo f operationvarie sfro m plantt o plant. Itwa strie dt o studyth eeffect s ofvariou s designs uponth e drainage byth e construction of small scaledrainag e vessels. Scaling down of the often applied batch drainage vessels could not be done adequately, as the leakageo fwhe ybetwee nth evesse lwal lan dth ecompresse dcur dcolum ncontribute d significantly to the flow of whey. Vertical perforated cylindrical pipes were used as a modelfo rth econtinuou sdrainag evessels .Obviou sparameter s aredrainag etim ean d temperature, whey discharge conditions, and duration and magnitude of the exerted pressure. Other relevant parameters are the pressure loss due to the friction of the wallan dth eleakag e ofwhe y betweenth ewal lo fth evesse lan dth ecurd .Th epackin g near the wall is less dense due to steric exclusion. The friction at the wall alters the orientation of the adjacent curd grains: the curd grains are turned to an acute angle to the direction of movement of curd column. Experimentswit hcolore dcurd grain si na Casomati cdrainag epip eshowe dtha t curd grains were slightly mixed at the top. The flow of curd grains through the pipe can be considered as a plugflo w with a parabolic flow superimposed on it.A trailo f colored curd grains at the rind of the subsequent blocks was observed, these curd grains probably got stuck at the filter grids near the whey outlets. Thecompactio no fa curd/whe y mixturei nth evertica ldrainag ecolumn sinitiall y increased whenth e exerted pressure and/or the initial remaining volume of the curd grains increased. However, above acertai n external pressure, calledthreshol dlevel , thetranspor t ofwhe y out of the column becomes rate determining;th e compression then is accompanied by a fast increase in liquid pressure. The threshold level is primarily determined byth e curd properties, butth e relations strongly depend on the 106 drainage vessel's properties. Whey discharge conditions, the contact area between curd andth e wall,th e exerted stress uponth e curd grains andth e drainage time are mainly determined by the drainage vessel.Th e packing of the curd andth e extento f fusionar elikel yt ob erelevant ,bu twer eno textensivel ystudied .Th ewhe yconten t and thefirmnes s ofth ecur dgrain s andth e presence of curdfine s hadsignifican t effects. Visualinspectio no fcross-section so fcurd block smad ei na Casomati cshowe d pores in various sizes and shapes, the largest ones being about 5 mm. The curd blocks lost a considerable amount of whey after the drainage. This drip whey originated largely from the inside of the curd grains. The porosity of a curd column could be measured with a newly developed porosity meter. The working principle of the apparatus is a moving optical fibre that penetrates the curd bed. The difference in scattering properties of curd grains and whey inth e pores allows discrimination betweeneither .Th e porosity of acurd beds o estimated, showed a large standard deviation, as the number of pores was rather small. The porosity generally decreased in time, which was due to decrease in the number and inth e (apparent) sizeo fth e pores.Significan t effects ofth einitia l relative remaining volume upon the porosity were not detected. The compaction of a curd column at an external pressure level below the threshold value resulted from the decrease of porosity aswel l asfro mth e whey expulsionfro mth e curd grains. Inthi s case, the porosity did not differ significantly between the central part and the outer regions. A higher external pressure led to a faster decrease of the porosity. At an external pressure above the threshold level the porosity of the outer region became lower than that of the central part. The permeability of a curd block decreases over several decades during the drainage process. Initially the permeability is very high. The permeability is mainly determined by the interconnected pores,whereb y the largest pores contribute most. Thepore sca nbecom e disconnected duet oreorientatio nan ddeformatio no fth ecurd grains.Applicatio n ofpressure sabov eth ethreshol dleve lfinall yd ono t resulti nfurthe r expressed curdcolumns , butcaus ejamming .Th ehig hpressur e causes asubstantia l reorientationan ddeformation ,hence ,th epermeabilit ydecrease sver yrapidly .Th eflo w of whey from the central region becomes insufficient to keep up with the fast whey expulsion fromth eoute r layer, causing afurthe r decrease ofth e porosity inth eoute r region.This , inturn , retardsfurthe r transporttoward s theoute r layer, causing arapi d sealing near the rind. 107 A simple computer modelwa s made.Th e expression of asingl e cube shaped curd grain was used as a model for the expression of a batch of these curd grains. Itappeare dtha tth e model gave reasonable results at lowexterna l pressures.A t high externalpressure sth emode lwa sinadequate ,a sth etranspor t ofwhe yfro mth epore s between the curd grains becomes a rate determining factor, and this factor is not taken into account in the model. In the intermediate pressure range the model predicteda to ofas t expressiono fth ecurd grains ,althoug hth eoveral lliqui dpressur e was below the detection limits. The latter does not rule out the existence of isolated pores, henceth e liquidflo w may locally be retarded.Th e deformation of curd grains in a curd bed may also be retarded due to fusion and geometrical constraints. 108 Samenvatting Kaasmaken start met het stremmen van melk door stremsel toe te voegen en/of aant e zuren (doorgaans m.b.v.zuurvormend e bacteriën). Degestremd e melk wordt instukje sgesneden .We itreed tuit ,di tnoem tme nsynerese . Desyneres eword t versnelddoo rt e roerene nveela look doort everhitten . Naverloo pva ntij d heeftme n vrij stevige deeltjes en een grote hoeveelheid wei verkregen. De scheiding van de deeltjes en de wei noemt men drainage van wrongel. De wrongelmassa wordt vervolgens geperst, gezouten en gerijpt. In dit proefschrift is de bereiding, zoals die voor Goudse kaasword t toegepast, het uitgangspunt geweest. Het doelva n het drainageproces is meestaltweeledig ; het afscheiden van het grootste deel van de wei en het bereiden van een samenhangend wrongelblok. De drainage kannie tlo sworde ngezie nva nd ewrongelbereidin g enhe tperse nva nwron - gelblokken kan eventuele tijdens de drainage ontstane verschillen weer ongedaan maken. Destudi eva nhe tdrainageproce s vereistda noo k eenzee rgoed ebeheersin g vand ewrongelbereiding .Ee nextr acomplicati ehierbi jvorm td ebereidin gva nwronge l op kleine schaal. De conventionele methode van wrongelbereiding resulteert, bij de bereiding op kleineschaal ,i nzee r fijngesnede n wrongel,welk e niet representatief is voor de fabrieksmatig bereide wrongel. Een verwant probleem is de karakterisering van wrongel, aangezien op voorhand niet bekend was welke kenmerken van de wrongeldeeltjes doorslaggevend zouden zijn. Een nieuwe methode van wrongel bereidingi sontwikkel do maa nbovenstaand eeise nte kunne nvoldoen .D egestremd e melk werd hiertoe met twee draadramen in kubusjes gesneden, waarna er een hoeveelheid wei in de wrongelbereider werd gepompt. De grote luchtbellen, die vervolgens werden ingebracht, zorgden voor een zeer milde menging. De wrongel werd bereid zonder zuursel. Devrijwe luniform e deeltjeswerde ngekarakteriseer d m.b.v.ee ndichtheidsme ting. De deeltjes werden hiertoe in een serie zoutoplossingen met toenemende dichtheid gestrooid. De dichtheid is direkt gerelateerd aan het weigehalte van de deeltjes enaa nhe tzogenaamd e relatievevolum e (/„),di t ishe tvolum eva nhe t deeltje t.o.v. hetvolum e van de uitgangsmelk. Ook in het gevalva nfabrieksmatig ewrongel bereidingblee kd emethod ebruikbaar ,maa rander eprocesvariabele nkunne noo kee n rolspele n bijd e drainage, bijvoorbeeld pH,temperatuu r end ehoeveelhei d stofwron- gel. De kubusvormige wrongeldeeltjes werden gebruikt om de uitpersing en 109 deformatie vanéé nafzonderlij k deeltjete bestuderen. Dedeeltje s zijnvisco-elastisch . Het uitoefenen van een uni-axiale druk leidt tot een momentane indrukking gevolgd dooree nlangzam eviskeuz evervorming .Indie nd edru kbinne nenkel eseconde nwer d weggenomen trad momentane terugvering op. Na 15 minuten compressie bleef de terugvering achterwege. Zowel de elastische als deviskeuz e vervorming namen toe met de druk (pj en het initiële relatieve volume van de deeltjes (/'„).Toepassin g van hoge druk leidde ertoe, dat de deeltjes konden worden uitgeperst tot een zeer laag relatief volume. Deuitpersin g kan grofweg worden samengevat in onderstaande vergelijking: i^l=exp(- kPm JT) (3-4) waarin /'«, het relatieve volume is op (tijd) t = «>,e nk = 4.10"5Pa' 1.s"v'. Naast de uitpersing resulteerde de compressie ook in een vergroting van de dwarsdoorsnede van de deeltjes. Deoptredend e vergroting waswa t hoger voor een hogere druk en een hoger initieel relatief volume. Het oppervlak van de doorsnede werd hoogstens ongeveer 1,6maa ld e oorspronkelijkewaarde . Devergrotin g vand e dwarsdoorsnede isondermee r relevant bijhe t"stoppen "va nwrongel . Bijhe tstoppen , d.i. hetoverbrenge nva nd ewrongelblokke ni nee nkaasvat ,moge nd edimensie sva n de wrongelblokken niet teveelverschille n van die van het kaasvat, omdat anders de wrongeldeeltjes denoodzakelijk evervormin gmoeilij kkunne nbereiken .Teven sbleke n uitpersing envervormin g van wrongeldeeltjes in hoge mate gecorreleerd te zijn. Het stoppen van ronde blokken in vierkante kaasvaten, leidt danook to t grotere vochtgehaltespreiding binnen eenkaas . Uit de resultaten van deze compressiemetingen bleek datd e reologische eigenschappenva nd eparacaseïnematri xwaarschijnlij k algau wd esnelheidsbepalen - defacto r vormen. Deafvoe r vanwe i uit een deeltje zou beperkend kunnenzij n inhe t begin van de compressiemeting. Uitmicroscopisch e beelden bleek date r in de oppervlaktelaag van de kubusvormige deeltjes scheuren aanwezig waren. In fabrieksmatig bereidewronge lwa sd ebuitenlaa ggesloten ,echte r nahe t aanbrengen van een (geringe) druk ontstonden ook daarin scheuren. Dewrongeldeeltje s vormenonderlin gbindingen ;di tnoem t menvergroeien .Bi j constant macroscopisch contactoppervlak werd de kracht nodig voor het verbreken van deze bindingen gemeten. Deze kracht nam toeme td evergroeiingstijd ,d e 110 persdruk, enhe tinitiël evolum eva nd edeeltjes . Bij3 5 °Cware nd ebindinge nstevige r dan bij lagere en hogere temperaturen. Verschil in valsnelheid van wrongeldeeltjes kan leiden tot ontmenging. De kubusvormige deeltjes hadden geen voorkeursoriëntatie, maar de anisomere wrongeldeeltjes wel. Als gevolg hiervan en de optredende afplatting (t.g.v. de uitgeoefende druk) isd e permeabiliteit,di eword t bepaald door deopeninge n tussen de deeltjes, in vertikale richting kleiner dan in horizontale richting. Het gebruikte type draineerapparatuur is afhankelijk van de bedrijfsvoering. Batch draineersystemen worden veelal gebruikt bij de ambachtelijke kaasbereiding. Continuedraineerautomate nworde nuitsluiten dtoegepas t ind eindustrie . Erbestaa n verscheidene uitvoeringenva n beidetypes . Hetnabootse nva nd ebatc hdraineerma - chines op kleine schaal bleek niet mogelijk, omdat lekkage van weitusse n wand en wrongelee noverheersend ero lblee kte spelen .Vertikal egeperforeerd e pijpenwerde n gebruikt als model voor continue draineer automaten. Belangrijke parameters zijn: draineertijde n-temperatuur , wijzeva nwei-afvoe r endruk(verloop) . Hetdrukverlie sal s gevolg vanwrijvin g met de wand bleek zeerfor s te kunnen zijn. Deoriëntati e van de deeltjes wordt ook door de wand beïnvloed. Bij praktijkproeven in een continue draineerautomaat bleek dat er behalve propstroming ook sprake was van een zekere parabolische pijpstroming. In de roosters voor de weiaftap bleven nogal wat deeltjes achter. Zolang de weiafvoer geen belemmering vormt, kan de uitpersing van de wrongel/wei massa worden versneld door de druk te verhogen. Maar, als de uitgeoefende druk te hoog wordt, ontstaat er een aanzienlijke vloeistofdruk in het wrongelbed. De druk waarbij dit gebeurt noemen we de drempelwaarde. De hoogte van de drempelwaarde hangt zowel af van de deeltjeseigenschappen als van de eigenschappen van de draineermachine. De poriën in een wrongelblok uit een draineerautomaat blekenzee ruiteenlopen d vanvor m engrootte . Dewrongelblokke n verliezen,nada tz eui td edraineermachin e komen,no gcirc a25 %aa nlek -e nperswei ; deze wei komt grotendeels uit de deeltjes. De porositeit, dat is het volume wei in de poriën als fractie van het totale volume,va nee nwrongelblo k konworde ngemete nme tee nzogenaamd e porositeits- meter. Hierbij wordt een optische sensor, die onderscheid kan maken tussen de deeltjes en dewe i ind e poriën,i nee nwrongelbe d gestoken. Deporositei t nama f in detijd ,waarbi jzowe lhe taanta lal sd egroott eva nd egedetecteerd eopeninge nafnam . 111 Devolum everminderin gva nee nwrongelkolo mblee kzowe lte wijte naa nafnam eva n de porositeit als aan afname van het deeltjesvolume. Bij toepassing van een druk bovend edrempelwaard e werd de porositeit aand ebuitenkan t vand e wrongelkolom lager dan in het centrum. Bij lagere druk werden hierin geen significante verschillen gevonden. Depermeabilitei tva nee nwrongelblo k neemtenor ma ftijden s dedrainage .D e stroomva nwe iverloop tvrijwe lgehee ldoo ree nnetwer kva nverbonde n poriëntusse n de deeltjes. De grootste poriën leveren de grootste bijdrage. Indien de poriën als gevolgva nreoriëntati e endeformati eva nd edeeltje s plaatselijk wordengeblokkeerd , neemt de permeabiliteit snel af. In het geval van "dichtslaan" treedt er een sterke verdichting opvla k langs het uitstroomoppervlak waardoor hetweitranspor t insterk e mate belemmerd wordt. Een computermodel werd gebruikt ter vergelijking van de uitpersing van één afzonderlijk deeltje end e uitpersing van eenverzamelin g van deze uniforme deeltjes. Het model gaf aan dat de uitpersing bij lage druk in grote lijnen hetzelfde verliep. Bij hogedru kspeel td esne ltoenemend evloeistofdru kee nwezenlijk erol ,maa raangezie n dezegroothei dnie twa sopgenome ni nhe tmodel ,ware nd evoorspeld eresultate nnie t inovereenstemmin g metd ewerkelijkheid .Tusse n40 0e n100 0P averlie pd euitpersin g van één afzonderlijk deeltje sneller dan die van een kolom met deeltjes. Twee mogelijke oorzaken hiervoor zijn: een deel van de wei bevindt zich in geïsoleerde openingen, danwe l de uitpersing van de deeltjes inee nwrongelbe d isvertraag d als gevolg vanvergroeiin g en/of beperkte mogelijkheden voor deformatie. 112 Curriculum Vitae JanCoe nAkkerma nwer do p3 1 augustusgebore nte Ouwsterhaule .I n198 0behaald e hij zijn atheneum diploma op het Nassau College te Heerenveen. In hetzelfde jaar begon hij aan detoenmalig e Landbouwhogeschool. Tijdens de studie werd er stage gelopen bij Melkunie Holland te Woerden en Opmeer en bij Marigold Foods Inc. te Rochester, MN., USA. De doctoraalfas e bestond een3 maands vak bij informatica, een6 maand sva k bijproceskund e eneveneen s een6 maand sva k bijzuivel . In198 7 werd de studie afgerond,waarn a dit vier jarige onderzoek werd begonnen. 113