S S rheological characterizationofthe chocolateandthephysicsofcoat- shear rates(Beckett2001;IOCCC2000). tential reasonsforinconsistentmeasurements,especiallyat low rors. Otherinstrumenterrors,suchaswallslip,arerecognized po- Standardization) bobisrecommendedtominimizeinstrument er- Normung (DIN,standarddevelopedbytheGermanInstitute for concentric cylinderprobe(IOCCC2000).TheDeutschesInstite für usinga products continuestorecommend rotationalviscometry The IOCCCstandardforthemeasurement ofviscositychocolate toviscosity measurements,be completelymeltedprior that is, 40°C. Ave., Univ. ofCalifornia,Davis, CA95616. Direct inquiries toauthor Technology andDept. ofBiological andAgricultural EngineeringOne Shields thors McCarthyM.J.and K.L.arewithDept.ofFoodScienceand Wichchukit iswithDept.ofBiological andAgriculturalEngineering.Au- MS 20040648.Submitted9/23/04,Revised 11/8/04,Accepted11/20/04.Author T S and theApplicationtoCoatingFlow Flow BehaviorofMilkChocolateMelt McCarthy (E-mail: for example, 2,5,10,20,and50s ers recommendreporting shearstress values atspecifiedshearrates, standard methodformeasuringchocolateviscosity. These research- discuss asequenceoftestsandrecommendations toimprove the to 200Pa, respectively 1975,1991, 1999). (Chevalley the Cassonyieldstress; thesevaluesrangefrom1to20Pa sand10 olate. parametersThe Casson are plasticviscosityand theCasson ofthefluidchoc- (IOCCC) toquantifyrheologicalproperties tionery method by theIntl.OfficeofCocoa, , andSugar Confec- modelwasrecommended to2000,the Casson Prior asastandard todescribeflow usingrotationalviscometry properties.performed schlimann andBeckett 2000). thecorrectweight thechocolatemusthave viscosity(Ae- control, ed asitmoves through thesheet.For goodqualityandaccurate coating flows inasheetabove amoving belt. The product iscoat- S S UKANY UKANY UKANY UKANY UKANY The successoftheenrobingprocess isdependentbothonthe In study, amulti-laboratory Aeschlimann andBeckett (2000) Extensive rheologicalstudiesofmoltenchocolatehavebeen and yieldedgoodapproximationstotheexperimentalvaluesthatwerebetween1.12.7mm. and yieldedgoodapproximationstotheexperimentalvaluesthatwerebetween1.12.7mm. yield str yield str were emulsifiertypeandlevel.TherheogramdatafitbytheCassonmodeltoyield were emulsifiertypeandlevel.TherheogramdatafitbytheCassonmodeltoyield and shearstressvaluesobtainedfromanindependentpressuredropmeasurement.Theexperimentalfactors and shearstressvaluesobtainedfromanindependentpressuredropmeasurement.Theexperimentalfactors viscometric method.TheexperimentalmethodcombinesshearratevaluesobtainedfromanMRvelocityimage viscometric method.TheexperimentalmethodcombinesshearratevaluesobtainedfromanMRvelocityimage milk chocolateweremeasuredat42°Cduringsteadypipeflowusingamagneticresonanceimaging(MRI) milk chocolateweremeasuredat42°Cduringsteadypipeflowusingamagneticresonanceimaging(MRI) control parametersforenrobingprocessesinconfectionerymanufacture.Therheologicalofmolten control parametersforenrobingprocessesinconfectionerymanufacture.Therheologicalofmolten ABSTRACT ABSTRACT drainage theorymodeltopredictcoatingthicknessesintheenrobingprocess.Thewassolvednumerically drainage theorymodeltopredictcoatingthicknessesintheenrobingprocess.Thewassolvednumerically from 6.0to14.6Pasasafunctionofemulsifiercontent.Therheologicalparameterswereincorporatedinto from 6.0to14.6Pasasafunctionofemulsifiercontent.Therheologicalparameterswereincorporatedinto and yieldedgoodapproximationstotheexperimentalvaluesthatwerebetween1.12.7mm. yield str were emulsifiertypeandlevel.TherheogramdatafitbytheCassonmodeltoyield and shearstressvaluesobtainedfromanindependentpressuredropmeasurement.Theexperimentalfactors viscometric method.TheexperimentalmethodcombinesshearratevaluesobtainedfromanMRvelocityimage milk chocolateweremeasuredat42°Cduringsteadypipeflowusingamagneticresonanceimaging(MRI) control parametersforenrobingprocessesinconfectionerymanufacture.Therheologicalofmolten ABSTRACT drainage theorymodeltopredictcoatingthicknessesintheenrobingprocess.Thewassolvednumerically from 6.0to14.6Pasasafunctionofemulsifiercontent.Therheologicalparameterswereincorporatedinto and yieldedgoodapproximationstotheexperimentalvaluesthatwerebetween1.12.7mm. yield str yield str were emulsifiertypeandlevel.TherheogramdatafitbytheCassonmodeltoyield were emulsifiertypeandlevel.TherheogramdatafitbytheCassonmodeltoyield and shearstressvaluesobtainedfromanindependentpressuredropmeasurement.Theexperimentalfactors and shearstressvaluesobtainedfromanindependentpressuredropmeasurement.Theexperimentalfactors viscometric method.TheexperimentalmethodcombinesshearratevaluesobtainedfromanMRvelocityimage viscometric method.TheexperimentalmethodcombinesshearratevaluesobtainedfromanMRvelocityimage milk chocolateweremeasuredat42°Cduringsteadypipeflowusingamagneticresonanceimaging(MRI) milk chocolateweremeasuredat42°Cduringsteadypipeflowusingamagneticresonanceimaging(MRI) control parametersforenrobingprocessesinconfectionerymanufacture.Therheologicalofmolten control parametersforenrobingprocessesinconfectionerymanufacture.Therheologicalofmolten ABSTRACT ABSTRACT and yieldedgoodapproximationstotheexperimentalvaluesthatwerebetween1.12.7mm. drainage theorymodeltopredictcoatingthicknessesintheenrobingprocess.Thewassolvednumerically drainage theorymodeltopredictcoatingthicknessesintheenrobingprocess.Thewassolvednumerically from 6.0to14.6Pasasafunctionofemulsifiercontent.Therheologicalparameterswereincorporatedinto from 6.0to14.6Pasasafunctionofemulsifiercontent.Therheologicalparameterswereincorporatedinto manufacturing industry.manufacturing The molten chocolateor he useofenrobingtechnologyisprevalentinthechocolate K K K K K eywor eywor eywor eywor eywor A A A A A

W W W W W ess andplasticviscosity ess andplasticviscosity ess andplasticviscosity ess andplasticviscosity ess andplasticviscosity ICHCHUKIT ICHCHUKIT ICHCHUKIT ICHCHUKIT ICHCHUKIT ds: chocolate ds: chocolate ds: chocolate ds: chocolate ds: chocolate : Therheologicalpropertiesofchocolate,especiallyshearviscosityandyieldstress,areimportant : Therheologicalpropertiesofchocolate,especiallyshearviscosityandyieldstress,areimportant : Therheologicalpropertiesofchocolate,especiallyshearviscosityandyieldstress,areimportant : Therheologicalpropertiesofchocolate,especiallyshearviscosityandyieldstress,areimportant : Therheologicalpropertiesofchocolate,especiallyshearviscosityandyieldstress,areimportant [email protected]). Introduction , M , M , M , M , M ICHAEL ICHAEL ICHAEL ICHAEL ICHAEL , viscosity , viscosity , viscosity , viscosity , viscosity –1 . In addition,thechocolatemust J.M J.M J.M J.M J.M . . . . . , yieldstr , yieldstr , yieldstr , yieldstr , yieldstr The C The C The C The C The C C C C C C C C C C C AR AR AR AR AR asson yieldstr asson yieldstr asson yieldstr asson yieldstr asson yieldstr THY THY THY THY THY ess ess ess ess ess , , , , , AND AND AND AND AND , enr , enr , enr , enr , enr K K K K K obing, magneticr obing, magneticr obing, magneticr obing, magneticr obing, magneticr A A A A A THR THR THR THR THR ess r ess r ess r ess r ess r YN YN YN YN YN L.M L.M L.M L.M L.M creasing values oftheflow behaviorindex, Newtonian one. This effectbecomesmore pronounced withde- to thepower lawfluidbeingmore uniforminthickness thanthe nian fluidthanapower lawfluid. due This difference isprimarily thickness withtimeandpositionismore pronouncedforaNewto- viscosity intheNewtonian case. In addition,thechangeinfilm pronounced influenceonthefilmthicknessthanchangeof ids. Achangeinthepower lawconsistencyindex, the behaviorofpower lawfluidsascompared withNewtonian flu- Bingham plasticmodel.Insightful commentswere maderegarding el reduced totheNewtonian model,thepower lawmodel,orthe evaluated. Depending oftheparameters, onthevalues thismod- non-Newtonian fluids. Specifically, modelwas the3-parameterEllis Gutfinger and Tallmadge (1965)presented thedraining analysisfor ids by Bird andothers(2002)asfluiddrainingfrom tanksides. time waspresented inastraightforward mannerforNewtonian flu- gravitational forces. Film thicknessasafunctionofpositionand totally withdrawn fromaliquidbathisgoverned by onlyviscousand cess. The unsteadystateflow process ofaflatplatethathasbeen (1958), Gutfinger and Tallmadge (1965),andGroenveld (1970). the different regimes. Representative workincludes Van Rossum incorporates viscous,gravitational,andsurfacetensionforcesin finger (1967)citeearlyapplicationsandpresentanapproachthat andviscositymeasurement.ing, lubrication, Tallmadge and Gut- type ofphysicalsituationisimportanttocoating,cleaning,drain- as thesurfaceiswithdrawnverticallyfromabathofliquid.This 1960s andearly1970sdiscussesliquidentrainedonaflatsurface ing flow. Aconsiderable bodyofliterature publishedinthemid- predict andcontrol coatingthicknessduringthe enrobingprocess. rheological properties intoanunsteadystatedraining analysisto properties ofmoltenmilkchocolate andtoincorporatethemeasured 2003). Theobjectivesofthisstudy weretoevaluatetherheological (1994), Arola and others(1997), Yoon andMcCarthy (2002, that hasbeenreportedbyMcCarthy (1994),Powellandothers as anintegralpartoftubeviscometry andextendsthetechnique anged fr anged fr anged fr anged fr anged fr Drainage wasconsideredaspecialcaseofthewithdrawalpro- This workutilizedamagneticresonance imaging(MRI)technique C C C C C C C C C C AR AR AR AR AR esonance imaging(MRI) esonance imaging(MRI) esonance imaging(MRI) esonance imaging(MRI) esonance imaging(MRI) om 1.9to15.0P om 1.9to15.0P om 1.9to15.0P om 1.9to15.0P om 1.9to15.0P THY THY THY THY THY a; theC a; theC a; theC a; theC a; theC asson viscosityr asson viscosityr asson viscosityr asson viscosityr asson viscosityr n . K , hasamore anged anged anged anged anged

E: Food Engineering & Physical Properties Flow behavior of melt . . .

Materials and Methods Table 1—Apparatus geometry and MRI experimental parameters Apparatus geometry MRI parameters Test samples Tube radius, R (mm) 4.9 Pulse repetition time, TR (ms) 400 The test material was milk chocolate obtained directly from the Tube length, L (m) 1.25 Echo time, TE (ms) 63 manufacturer in 5 gallon containers (Hershey Foods Corp., Hershey, Reservoir radius (mm) 57.5 Number of phase encoding 32 Pa., U.S.A.). Although chemical analysis was not performed for these Reservoir height (mm) 130 Number of frequency encoding 64 particular samples, typical composition by percent for this product Number of averages 16 Field of view (mm) 60 is cocoa mass 11.8%, whole milk powder 19.1%, sugar 48.7%, added Velocity sweep width (mm/s) 188.9 20%, for a total fat content of 31.5% (Jackson 1999). The milk chocolate was manufactured without added emulsifier. Five chocolate formulations were used: milk chocolate with no added emulsifier (the control), milk chocolate with 0.1% soy lecithin, milk ity image was acquired at a position 0.50 m downstream from the chocolate with 0.3% soy lecithin, milk chocolate with 0.1% synthetic reservoir, which ensured fully developed flow. The MR velocity lecithin (YN), and milk chocolate with 0.3% YN. The emulsifiers were images were obtained using a SMIS NMR spectrometer (Surrey added by weight during the melting and mixing process. The density Medical Imaging Systems, Surrey, U.K.) connected to a 0.1 Tesla of the milk chocolate melt was 1270 kg/m3. electromagnet, corresponding to 4.2 MHz for 1H resonance frequen- Magnetic resonance imaging viscometry cy. Unshielded gradient coils produced orthogonal gradients with maximum gradient amplitudes of Ϯ 2 Gauss/cm. A pulsed gradient The experimental apparatus consisted of a temperature-con- spin-echo pulse sequence was applied to acquire the velocity pro- trolled capillary viscometer connected to a 1818-mL stainless steel files (McCarthy 1994; Arola and others 1997). The apparatus geom- sample reservoir (Figure 1). During each experimental run, the test etry and MRI experimental parameters are given in Table 1. For the fluid from the reservoir was pressure driven through a straight MR image, 32 phase encoding steps were used to characterize the length of 9.8 mm inner dimater glass tubing (Pyrex®, Corning, Inc., z component of the velocity and 64 frequency encoding steps along Big Flats, N.Y., U.S.A.) by the downward motion of a piston moving the x direction read out the radial position (r) of the volume ele- at 0.2 mm/s. The cross-sectional area of the piston was 1.04 × 104 E: Food Engineering & Physical Properties ments. The resulting matrix was zero filled to 64 × 128 and a two- mm2 and spanned the cross-section of the fluid reservoir. The con- dimensional Fourier transformwas performed. The measurement tact area between the piston and the reservoir surface was a lubri- time was on the order of 1 min and reflects multiple data acquisi- cated O-ring. The piston was connected to an actuator/control sys- tions. Data analysis of the MR velocity image was performed to tem fabricated to provide a 0.30-m stroke length and rated for 2200 characterize flow behavior using MatLab7.0.0 (R14) software (The N (Electric Cylinder Model EC2, IDC, Salem, N.H., U.S.A.). MathWorks Inc., Natick, Mass., U.S.A.). Fluid velocity at each radial A pressure measurement was acquired upstream of the imaging position was determined by the position of the maximum signal region using a pressure transducer (Model PX771-100WD1, Ome- intensity in each row of the image matrix. ga Engineering Inc., Stamford, Conn., U.S.A.). The pressure differ- To evaluate shear rate from the velocity profile, the MRI velocity ence was determined by the difference between measurement and data were fit with an even-order polynomial; the global fitting error ambient, characterizing the pressure drop over the length, L, of 1.25 for the polynomial was less than 2%. This analytic expression was m (Figure 1). then differentiated and evaluated at each radial position to yield The chocolate was melted and held at 42°C in a chocolate-temper- the local shear rate ing system (Revolation X3210, ChocoVision, Poughkeepsie, N.Y., U.S.A.) to ensure that fat was in the liquid phase and well mixed with the milk chocolate solids. The sample temperature was maintained (1) at 42°C throughout testing by jacketing the reservoir and flow tube; the heating medium was warm air (42°C). Although the target tem- perature was 40°C, there was a 2°C offset in the temperature control of the experimental system. The offset was consistent; off-line mea- where v(r) is the axial velocity of the molten chocolate during pipe surements were therefore performed at the same temperature, 42°C. flow (Arola and others 1997). The range of shear rates evaluated –1 For each flow rate and pressure drop measurement, an MR veloc- was from 1 to 8 s ; this range corresponds to shear rates relevant to the enrobing process (Steffe 1996; Aeschlimann and Beckett 2000). Local shear stress data, to correspond to the shear rate data, were obtained using the force balance

(2)

where ␴ is the shear stress, and ⌬P is the pressure difference across the pipe length, L. The shear rate and shear stress values were plot as a rheogram. The steady shear rheological data for milk chocolate melt was best described by the Casson model based on goodness of fit and the coefficient of determination. The expression for the Casson model is

Figure 1—Schematic diagram of the experimental ap- (3) paratus Flow behavior of milk chocolate melt . . .

␩ ␴ where, is the shear rate, CA is the Casson viscosity, and ␱,CA is the wide by 50.8 mm height, on each side. The mass of chocolate was al- ␴ Casson yield stress. The yield stress, o, was also determined directly lowed to solidify and was then scraped and weighed to determine an from the MR image with the plug radius, Ro, and is designated as average film thickness on each side of the plate. Soy lecithin was added to the milk chocolate to a level of 0.1%. ⌬P ␴ ␱ = R ␱ (4) The dipping procedure was repeated. The 0.1% lecithin mixture was 2L brought to a level of 0.3%; the dipping procedure was repeated. The sample preparation, dipping, and weighing procedure were The image analysis procedure was developed and documented followed for the synthetic lecithin YN as well, starting with emulsi- by Sadikin (1999) and Choi (2003) and utilized the graphic user fier-free milk chocolate. interface feature of MatLab. In addition to the MR viscosity measurement, the flow behavior Results and Discussion was measured off-line by rotational viscometry (CVO, Bohlin Instru- igure 2 illustrates representative magnetic resonance phase en- ments, Gloucestershire, U.K.) utilizing the concentric cylinder ge- Fcoded velocity images of molten milk chocolate at 42°C. Figure ometry and the vane method. The chocolate melt temperature was 2a represents the MR reference location of fluid at rest (v = 0); Fig- controlled at 42°C by a circulating water bath (RTE-111, NESLAB ure 2b illustrates a velocity profile at a volumetric flow rate of 2.4 mL/ Instruments, Inc., Newington, N.H., U.S.A.). A DIN bob with a diam- s. Figure 3 illustrates velocity profiles of the molten milk chocolate eter of 25 mm and a cup with a diameter of 27.5 mm operated under under the experimental conditions. Typical of these velocity pro- the controlled rate mode over a shear rate range of 1 to 8 s–1. A 4- files, the velocity is maximum at the center of the pipe and de- blade vane with a diameter of 25 mm and the same cup were used creases toward the pipe wall. The maximum velocity value in- over a shear rate range of 0.05 to 10 s–1 in the controlled rate vane creased as the amount of the emulsifier increased from 0% to 0.1% method to measure the yield stress (Steffe 1996). to 0.3%. The velocity values are 38 mm/s, 40 mm/s, and 41 mm/s, respectively, and did not differ significantly with type of emulsifier. Enrobing Wall slip is also observed as the velocity is nonzero at the pipe wall. The emulsifier-free milk chocolate, described above, was stored For comparison purposes, the apparent viscosity values of test for several days before the experiment to ensure constant temper- fluids were determined using rotational viscometry data and MRI ature and mixed thoroughly before removing 1 kg samples. The 1- viscometry data. The apparent viscosity (␩) was calculated by kg milk chocolate samples were prepared in the tempering bowl of the Revolation X3210, chocolate tempering system (ChocoVision, (5) Poughkeepsie, N.Y., U.S.A.). The chocolate was maintained be- tween 40 Ϯ 0.5°C. Flat plastic plates with dimensions of 101.6 mm × 101.6 mm (4 × 4 Figure 4 illustrates apparent viscosity compared with shear rate inch) were prepared for dipping into the chocolate. The plastic plates of milk chocolate melt for MRI viscometry and rotational viscome- were paper covered; the adhered paper was removed from the bottom try in the shear rate range of 1 to 8 s–1. Overall, the apparent viscos- 50.8 mm on each side of the plate using an Exacto knife. Three plates ity ranged from 7 to 48 Pa s. Shear-thinning behavior is observed as were dipped into the molten milk chocolate for each trial and then the apparent viscosity decreases with increasing shear rate. For gently shook for 20 s over the tempering bowl. The plates were then both emulsifiers, the apparent viscosity decreased as the amount hung in a controlled environment chamber, which was maintained at of the emulsifier increased. As the emulsifier level increased to Ϯ

40 1°C by two 1500W heaters (Steinel, Model HG3002LCD, Howard 0.3%, the Casson viscosity values decreased by more than a factor E: Food Engineering & Physical Properties Electric Instruments Inc., El Dorado, Kans., U.S.A.). After 30 min, the of two. Likewise, the Casson yield stress decreased significantly plates were removed from the chamber and any excess chocolate was with increasing emulsifier level (Table 2). scraped from the side and bottom edges of the plate, the protective Wall slip, in part, plays a role in the discrepancy between the paper was removed from both sides of the top portion of the plate. Casson parameters determined for the MRI data and the rotational The chocolate remaining on the plate had dimensions of 101.6 mm viscometry data (Table 2). Wall slip occurs when a layer of fluid that

Figure 2—Representative MR image of milk chocolate flow at 42°C: (1) at rest and (2) at a volumetric flow rate Flow behavior of milk chocolate melt . . .

has lower viscosity than the main fluid forms at the walls of the vis- For a milk chocolate with a Casson yield value of 15 Pa, the fluid cometer and has been observed in many food suspensions and would ultimately drain to a final coating thickness of 1.2 mm, high fat products. The lower apparent viscosity values of the rota- whereas a Newtonian fluid would theoretically drain to an infinite- tional viscometer compared with the MRI technique are consistent ly thin layer. with wall slip in the concentric cylinder geometry. In addition, the Equation 6 is most appropriately used for the evaluation of a values of wall slip can be determined directly from the MR image. static film or coat. However, the enrobing process is a transient The values of slip velocity for the lecithin trials ranged from 17.7 to processing as chocolate drains away from vertical surfaces. The first 19.0 mm/s. Similar slip velocities were observed for the synthetic step of extending the drainage flow analysis to Casson fluids is to lecithin (YN), though accurate wall slip velocity could not be deter- evaluate steady state drainage from a vertical surface. The flow of mined due to lower signal-to-noise ratio at the tube wall. fluid on the vertical surface is controlled by the balance of gravita- Table 3 shows reasonable agreement between the yield values tional and viscous forces (Bird and others 2002). Schematically, the obtained from the vane method, and the values based on the plug flow is illustrated in Figure 6a, where x is the vertical downward dimension obtained from the MRI viscometry (Eq. 4). However, direction and y is the horizontal axis. these yield values are considerably higher that the Casson model Mathematically, the problem is formulated as yield values and may well represent static yield stress due to the conditions required to initiate shearing flow. It is not unusual that yield stress values obtained by 1 method are different than those (7) obtained by a different method (Steffe 1996). where the left hand side of the equation is the gravitational forces Application of rheological parameters (g is the gravitational acceleration and ␳ is the fluid density) and the to the enrobing process right hand side of the equation is the viscous force. For a Newtonian Much of the focus of process rheology is the application of the fluid, the relationship between the shear stress and shear rate in information to real-time decision-making. For instance, will this terms of the velocity gradient is given by particular milk chocolate provide adequate coverage on a wafer during the enrobing process? Figure 5 illustrates a typical enrobing E: Food Engineering & Physical Properties (or coating) process with the chocolate flowing in a sheet from a bin above a moving belt. As the chocolate covers the wafer, excess drains from the vertical sides of a wafer due to the force of gravity. Choc- olate is a special case of coating because a phase change occurs during the process. The following analysis is relevant for the time interval immediately following the enrobing of the product when the chocolate is in the molten state prior to solidification of the fat. For fluids with a yield stress, like chocolate, flow ceases when the yield stress is greater than or equal to the shear stress. Therefore the

coating thickness, Ho, supported by the yield stress is (Steffe 1996; Lang and Rha 1981)

(6)

Figure 4—Apparent viscosity of milk chocolate melt for the 2 emulsifiers: (a) soy lecithin and (b) synthetic Figure 3—Representative velocity profiles of milk choco- lecithin. In each figure, circles represent 0% emul- late obtained from the MRI viscometry. ␴, 0% soy lecithin; sifier, squares, 0.1% emulsifier, and triangles, 0.3% ␪, 0.1% soy lecithin; and ␯, 0.3% soy lecithin. emulsifier. The filled marks are MRI data; the open marks are CVO concentric cylinder data. Flow behavior of milk chocolate melt . . .

Table 2—Casson parameters from the MRI-based viscometry and rotational viscometry, T = 42 °C Sample MRI-based viscometry Rotational viscometry Casson Casson R2 Casson Casson R2 viscosity yield stress viscosity yield stress (Pa s) (Pa) (Pa s) (Pa) 0% 14.6 15.0 0.995 6.7 16.4 0.986 0.1% lecithin 12.5 3.1 0.996 4.2 12.7 0.994 0.3% lecithin 6.0 2.6 0.977 2.1 10.4 0.999 0.1% YN 12.7 3.9 0.980 4.3 12.1 0.994 0.3% YN 6.6 1.9 0.978 2.6 9.6 0.998

(8) (12)

This approach assumes that the average velocity at a given ver- where u is the downward velocity of the fluid and ␮ is the Newto- tical position can be approximated by Eq. 10, with the fluid thick- nian viscosity. This expression is substituted into Eq. 7. Equation ness H replaced by h(x,t) (for example, a typical lubrication approx- 7 is integrated to yield the fluid velocity as a function of position (y- imation). Equation 12 is useful because the average fluid thickness direction) and the steady-state fluid thickness (H). () at a time t is determined by integrating the expression over the height of the region draining for

(9) (13)

By integrating over the velocity profile with respect to y, the av- As an example, if the height of coverage is L = 5 cm, the average erage velocity () under steady state conditions is fluid thickness at 20 s is 2 mm for a Newtonian fluid with a viscosity of 60 Pa s and density of 1270 kg/m3. In concept, this approach was used by Cisneros-Zevallos and Krochta (2003) to evaluate coating (10) thickness applied to fruits and vegetables. The limitation of this approach is that the solution is valid only for Newtonian fluids and for finite values of x/t. This expression is useful because it gives the relationship be- In contrast to Newtonian fluids, the unsteady state mass bal- tween the drainage velocity and fluid properties, the more dense ance (Eq. 11) cannot be solved analytically for Casson fluids (Eq. 2). the chocolate, the greater the drainage velocity; the higher the vis- However, Eq. 11 can be numerically evaluated using the analytical cosity, the lower the drainage velocity. expression for the average velocity of the Casson fluid. The Casson The next step is to consider the unsteady state nature of the model, with the shear rate expressed in terms of velocity gradient, chocolate enrobing process. An unsteady state mass balance over E: Food Engineering & Physical Properties was substituted into Eq. 7. Equation 7 was integrated to yield the a volume of fluid between x and x + ⌬x yields fluid velocity as a function of position

(11) (14) which is written in terms of the local fluid thickness, h, as a function of time (t) and vertical position (x) (Figure 6b). This approach is based on the draining of a viscous fluid down a tank wall (Bird and others 2002). The solution to Eq. 11 for fluid thickness of a Newto- nian fluid is

Figure 6—Downward flow of fluid from a vertical surface: (a) Figure 5—Schematic of the enrobing process steady state and (b) unsteady state Flow behavior of milk chocolate melt . . .

Table 3—Yield stress values of milk chocolate using MRI- Table 4—Average film thickness measured experimentally based viscometry and the vane method, T = 42°C and estimated theoretically based on the MRI-based Casson parameters given in Table 2 MRI Vane Experimental Theoretical Sample with Yield radius Yield stress Yield stress film thickness film thickness emulsifier (R ) (mm) (Pa) (Pa) o Ϯ SD (mm) (mm) 0% 0.98 51 54 Soy lecithin 0% 2.3 Ϯ 0.3 3.0 0.1% soy lecithin 0.98 37 29 0.1% 1.2 Ϯ 0.1 1.7 0.1% synthetic lecithin 0.98 38 30 0.3% 1.1 Ϯ 0.1 1.2 0.3% soy lecithin 1.00 18 19 0.3% synthetic lecithin 0.75 19 20 Synthetic lecithin 0% 2.7 Ϯ 0.2 3.0 0.1% 1.6 Ϯ 0.1 1.8 0.3% 1.2 Ϯ 0.1 1.2

␴ ␳ Ј Ј where Ho = o,CA/( g), and y is 0 at the film surface and y = H at the solid vertical surface. Equation 14 is valid in the shearing region differential equation (Eq. 11) was solved numerically for Casson Ј from Ho to the solid surface at y = H. The value of the velocity from fluids with a MatLab finite difference program using central differ- the film surface to Ho is the maximum velocity of ence for the time derivative and central difference for the spatial derivative (Haberman 2004). The finite difference program was validated by limiting cases (for example, Newtonian fluid) and by (15) decreasing ⌬t/⌬x to ensure numerical stability. The average film thickness over a 20-s time interval is illustrated The velocity profile of milk chocolate with no added emulsifier (Table 2) is illustrated in Figure 7. The plug region, with fluid trav- eling at the maximum velocity, is at the surface of the film. To rein-

E: Food Engineering & Physical Properties force the difference in flow behavior of Casson fluids relative to Newtonian fluids, the velocity profile of a Newtonian fluid is also shown. The Newtonian fluid has a viscosity equivalent to the ap- parent viscosity of the milk chocolate at a shear rate of 1 s–1(59.2 Pa s). The average velocity over the film, for Eq. 11, is calculated by in- tegrating Eq. 14 and 15 over the relevant region and dividing by the film thickness. In Figure 7, the Newtonian fluid has an average ve- locity of 18 mm/s; the average velocity of the Casson fluid is 13 mm/s, which is 28% lower due to the yield stress. The final step in extending the drainage flow analysis to Casson fluids is to determine the film thickness during the enrobing pro- cess. The local film thickness, h(x,t) is substituted for H in Eq. 14 and 15 for the unsteady state mass balance (Eq. 11). This partial

Figure 7—Steady state velocity for a film thickness of 5 Figure 8—Average film thickness as a function of time for mm for milk chocolate melt with a plastic viscosity of 14.6 (a) milk chocolate with soy lecithin and (b) milk chocolate Pa s and Casson yield stress of 15.0 Pa (solid line) and for with synthetic lecithin, YN. The solid line is 0% emulsifier, a Newtonian fluid with the same apparent viscosity (59.2 the dashed line is 0.1% emulsifier, and the dotted line is –1 0.3% emulsifier. Pa s) at 1 s . Flow behavior of milk chocolate melt . . .

in Figure 8 for each of the milk chocolate samples using the Casson y’ H-y parameters determined by MRI-based viscometry (Table 2). The z axial direction higher viscosity fluids have greater film thickness. As the emulsifier Greek letters level increases, the film thickness decreases. The predicted average pressure drop, Pa film thicknesses at t = 20 s are given in Table 4, with the experimental shear rate, s–1 average film thicknesses (Ϯ 1 standard deviation). The unsteady ␩ apparent viscosity, Pa s ␩ state mass balance (Eq. 11) yields a good approximation to the ex- CA Casson viscosity, Pa s perimental values. Experimentally, the film thicknesses are lower ␮ viscosity, Pa s due to the draining that took place during the 30 min in the con- ␳ melt density, kg/m3 trolled temperature chamber. The experimental film thicknesses ␴ shear stress, Pa were approximately 30% lower than the film thicknesses would have ␴␱ yield stress, Pa ␴ been had they been measured at 20 s. This approximation is based ␱, CA Casson yield stress, Pa on weighing the chocolate mass that collected in the tray beneath the draining plates. Specifically, 62 g chocolate was collected after References the synthetic lecithin trials; a total of 217 g had adhered to the 9 Aeschlimann JM, Beckett ST. 2000. International inter-laboratory trails to de- termine the factors affecting the measurement of chocolate viscosity. J Texture plates. Stud 31:541–76. Arola DF, Barrall GA, Powell RL, McCarthy KL, McCarthy MJ. 1997. Use of nuclear magnetic resonance imaging as a viscometer for process monitoring. Chem Eng Conclusions Sci 52:2049–57. he flow behavior of molten milk chocolate was evaluated ex- Beckett ST. 2001. Model for chocolate, friends or foe? Manufactur Confection March:61–7. Tperimentally using an MRI-based tube viscometer. The choc- Bird RB, Stewart WE, Lightfoot EN. 2002. Transport phenomena, 2nd edition. New olate was best characterized by the Casson model; as the emulsifier York, N.Y.: John Wiley & Sons. Chevalley J. 1975. Rheology of chocolate. J Texture Stud 6:177–96. level increased from 0% to 0.3%, the Casson yield stress values de- Chevalley J. 1991. An adaptation of the Casson equation for the rheology of choco- creased from 15 to 1.9 Pa and Casson viscosity values decreased late. J Texture Stud 22:219–29. Chevalley J. 1999. Chocolate flow properties. In: Beckett ST, editor. Industrial choc- from 14.6 to 6.0 Pa s. Deviation of the Casson parameters between olate: manufacture and use, 3rd ed. Oxford: Blackwell Science Ltd. the MRI-based method and rotational viscometry was due to uncor- Choi YJ. 2003. Application of tomographic techniques for rheological properties and rected wall slip during the rotational measurements. The MRI- process control [PhD dissertation]. Davis, Calif.: Univ. of California, Davis. 257 p. Availability of Choi, YJ dissertation: http://wwwlib.umi.com/dissertations/search. based viscometer Casson parameters were incorporated into an Cisneros-Zevallos L, Krochta JM. 2003. Dependence of coating thickness on vis- unsteady state mass balance to predict the average film thickness cosity of coating solution applied to fruits and vegetables by dipping method. J Food Sci 68(2):503–10. of the milk chocolate during enrobing. As the emulsifier level in- Groenveld P. 1970. Withdrawal of power law fluid films. Chem Eng Sci 25:1579–85. creased from 0% to 0.3%, the predicted enrobing thicknesses de- Gutfinger C, Tallmadge JA. 1965. Films of non-Newtonian fluids adhering to flat plates. AIChE J 11(3):403–13. creased by 60%. Experimentally, this trend was verified. Haberman R. 2004. Ch 6, Finite Difference Numerical Methods for Partial Dif- ferential Equations. In: Applied partial differential equations with Fourier series and boundary value problems, 4th ed. Upper Saddle River, N.J.: Pearson Acknowledgment Education, Inc. p 222-31. We appreciate the donation of chocolate from Hershey Foods Corp. [IOCCC] Intl. Office of Cocoa, Chocolate and Sugar . 2000. Viscos- ity of cocoa and chocolate products, analytical method 46. Brussels, Belgium: Assn. of the Chocolate, & Confectionery Industries of the EU. Notation Jackson K. 1999. Recipes. In: Beckett ST, editor. Industrial chocolate: manufacture g gravitational constant, 9.8 m/s2 and use, 3rd ed. Oxford: Blackwell Science Ltd. Lang ER, Rha C. 1981. Determination of the yield stress of hydrocolloid suspen-

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