@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Land and Food Systems, Faculty of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Wilson, Laurie L."@en ; dcterms:issued "2010-11-04T21:44:39Z"@en, "1991"@en ; vivo:relatedDegree "Master of Science - MSc"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """A study of the flow properties of four chocolate samples was conducted. These were commercial semi-sweet (HSS), milk chocolate (HMC) and two experimental samples (H1 and H2). The yield stress, an important quality indicator of the chocolate, was estimated from steady shearing flow data by extrapolating the Casson model equation to zero flow rate and, by allowing stresses to relax after shearing. As well, undisturbed samples were examined in start-up flow using Single Vane and Multiple Vane methods. Proximate and sucrose analyses were carried out to determine the chemical composition of each chocolate sample. The mean particle size and the distribution of sizes contained in the samples was determined to further characterize the chocolates. A multivariate analysis of variance indicated that there was a significant difference in chemical composition among the four test samples. The mean particle sizes ranged from 5.73 to 6.27, 6.98 and 7.15 µm for samples HSS, H1, HMC and H2, respectively. The greatest number of particles were in the size range of 4.0 to 5.0 µm. The Casson model equation was fitted to steady flow data obtained with coaxial cylinder fixtures using a Brookfield HAT viscometer, a Brabender Rheotron viscometer, and a Carri-Med Controlled Stress Rheometer. For the Brookfield viscometer, the Casson equation over the shear rate range used, was found to accurately describe the flow characteristics of chocolate samples HMC, HSS and H2, but not sample H1. For the Brabender viscometer and the Carri-Med rheometer, the Casson equation did not fit the flow data over the entire shear rate range used with each instrument. A deviation in linearity occurred below approximately 0.5 s‾1 in the flow data measured in both instruments, thereby making the yield stress determination somewhat ambiguous. Yield values recalculated using only the linear data points were higher. In addition, for the Brabender viscometer, significant differences (p<0.05) were observed in both the yield and viscosity values measured using two coaxial cylinder fixtures of different annular gap widths. Using the Carri-Med rheometer, a significant difference in viscosity (p<0.05) over consecutive test runs was found and a significant difference (p<0.01) in yield stress when samples were sheared for 12 minutes as compared to 30 minutes. Yield stress estimates obtained using Multiple Vane Method I and Method II were comparable for chocolate samples HMC, HSS, and H2, but were significantly higher for sample H1 when using Method II as compared to Method I. Method II may be a more accurate estimate of the yield value of molten chocolate because the assumption of a uniform shear stress distribution over the ends of the vane fixture could not be proven experimentally for samples HSS and H1 when using Method I. Also, the dependence of the yield value on the rotational speed was evident when the vane data were analyzed using Method I, but was not a significant factor (p>0.05) when Method II was used to estimate yield stress. In addition, the single point measurements used to estimate yield stress agreed more closely with values obtained using Method II as compared to Method I. It is postulated that the Single Vane Method or Multiple Vane Method II may provide more accurate estimates of the yield stress of molten chocolate than using the Casson approximation. For the vane methods, direct measurements were taken under virtually static conditions; whereas, in the Casson extrapolation method, yield stress was estimated indirectly from flow data over a broad shear rate range at stresses well beyond the yield point of the sample. The Single Vane Method was simple and required less time than fitting the Casson flow model to shear stress-shear rate data and, therefore, may be more suitable for routine yield stress measurements of molten chocolate in quality control laboratories."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/29792?expand=metadata"@en ; skos:note "YIELD STRESS STUDIES ON MOLTEN CHOCOLATE by Laurie L. Wilson B. Sc. (Biology) University of British Columbia, 1984 A THESIS S U B M I T T E D IN PARTIAL F U L F I L L M E N T O F T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF S C I E N C E in T H E F A C U L T Y OF G R A D U A T E STUDIES D E P A R T M E N T OF F O O D SCIENCE We accept this thesis as conforming to the required standard T H E UNIVERSITY OF BRITISH C O L U M B I A August 1991 © Laurie L. Wilson, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of A?rA vWoCfl The University of British Columbia Vancouver, Canada Date i W ^ > NftW DE-6 (2/88) A B S T R A C T A study of the flow properties of four chocolate samples was conducted. These were commercial semi-sweet (HSS), milk chocolate (HMC) and two experimental samples (HI and H2). The yield stress, an important quality indicator of the chocolate, was estimated from steady shearing flow data by extrapolating the Casson model equation to zero flow rate and, by allowing stresses to relax after shearing. As well, undisturbed samples were examined in start-up flow using Single Vane and Multiple Vane methods. Proximate and sucrose analyses were carried out to determine the chemical composition of each chocolate sample. The mean particle size and the distribution of sizes contained in the samples was determined to further characterize the chocolates. A multivariate analysis of variance indicated that there was a significant difference in chemical composition among the four test samples. The mean particle sizes ranged from 5.73 to 6.27, 6.98 and 7.15 /xm for samples HSS, HI , H M C and H2, respectively. The greatest number of particles were in the size range of 4.0 to 5.0 fim. The Casson model equation was fitted to steady flow data obtained with coaxial cylinder fixtures using a Brookfield HAT viscometer, a Brabender Rheotron viscometer, and a Carri-Med Controlled Stress Rheometer. For the Brookfield viscometer, the Cas-son equation over the shear rate range used, was found to accurately describe the flow characteristics of chocolate samples H M C , HSS and H2, but not sample HI. For the Brabender viscometer and the Carri-Med rheometer, the Casson equation did not fit the flow data over the entire shear rate range used with each instrument. A deviation in linearity occurred below approximately 0.5 s _ 1 in the flow data measured in both instruments, thereby making the yield stress determination somewhat ambiguous. ii Yield values recalculated using only the linear data points were higher. In addition, for the Brabender viscometer, significant differences (p<0.05) were observed in both the yield and viscosity values measured using two coaxial cylinder fixtures of different annular gap widths. Using the Carri-Med rheometer, a significant difference in viscosity (p<0.05) over consecutive test runs was found and a significant difference (p<0.01) in yield stress when samples were sheared for 12 minutes as compared to 30 minutes. Yield stress estimates obtained using Multiple Vane Method I and Method II were comparable for chocolate samples H M C , HSS, and H2, but were significantly higher for sample HI when using Method II as compared to Method I. Method II may be a more accurate estimate of the yield value of molten chocolate because the assumption of a uniform shear stress distribution over the ends of the vane fixture could not be proven experimentally for samples HSS and HI when using Method I. Also, the dependence of the yield value on the rotational speed was evident when the vane data were analyzed using Method I, but was not a significant factor (p>0.05) when Method II was used to estimate yield stress. In addition, the single point measurements used to estimate yield stress agreed more closely with values obtained using Method II as compared to Method I. It is postulated that the Single Vane Method or Multiple Vane Method II may provide more accurate estimates of the yield stress of molten chocolate than using the Casson approximation. For the vane methods, direct measurements were taken under virtually static conditions; whereas, in the Casson extrapolation method, yield stress was estimated indirectly from flow data over a broad shear rate range at stresses well beyond the yield point of the sample. The Single Vane Method was simple and required less time than fitting the Casson flow model to shear stress-shear rate data and, therefore, may be more suitable for routine yield stress measurements of molten chocolate in quality control laboratories. in T A B L E O F C O N T E N T S , i A B S T R A C T ii LIST OF T A B L E S vii LIST OF FIGURES xi N O M E N C L A T U R E xiii A C K N O W L E D G E M E N T xiv 1 I N T R O D U C T I O N 1 2 L I T E R A T U R E R E V I E W 4 2.1 R H E O L O G I C A L PROPERTIES OF M O L T E N C H O C O L A T E 4 2.1.1 Factors Influencing Flow Properties 4 2.1.2 Historical Background 6 2.2 F U N D A M E N T A L S OF ROTATIONAL V I S C O M E T R Y 10 2.3 R H E O M E T E R DESCRIPTION 11 2.3.1 Brookfield Viscometer 11 2.3.2 Brabender Rheotron Viscometer 12 2.3.3 Carri-Med Controlled Stress Rheometer 12 2.4 STRESS R E L A X A T I O N M E T H O D 15 2.5 V A N E F I X T U R E M E T H O D 18 2.5.1 Theory 18 iv 2.5.1 Theory 18 3 E X P E R I M E N T A L 22 3.1 C H O C O L A T E SAMPLES 22 3.1.1 Product Description 22 3.2 C H E M I C A L ANALYSES 22 3.2.1 Moisture 23 3.2.2 Ash 23 3.2.3 Crude Protein 23 3.2.4 Fat 24 3.2.5 Sucrose 25 3.3 P A R T I C L E SIZE ANALYSIS 26 3.4 Y I E L D STRESS D E T E R M I N A T I O N 26 3.4.1 Calibration 26 3.4.2 Sample Preparation 27 3.4.3 Indirect Methods 29 3.4.4 Direct Methods 31 3.5 DATA A N A L Y S E S 34 4 RESULTS A N D DISCUSSION 35 4.1 C H E M I C A L A N A L Y S E S 35 4.2 P A R T I C L E SIZE ANALYSIS 37 4.3 INDIRECT ESTIMATION OF YIELD STRESS 41 4.3.1 Brookfield Viscometer 41 4.3.2 Brabender Rheotron Viscometer 44 4.3.3 Carri-Med Controlled Stress Rheometer 50 4.4 STRESS R E L A X A T I O N M E T H O D 57 v 4.5.1 Single Vane Method 59 4.5.2 Multiple Vane Method I 66 4.5.3 Multiple Vane Method II 70 5 CONCLUSIONS 75 LITERATURE CITED 79 APPENDIX 86 A LISTING OF EXPERIMENTAL FLOW DATA 86 vi LIST OF TABLES 3.1 Instrument parameters for the coaxial cylinder fixtures used 28 3.2 Vane fixture dimensions 33 4.3 Composition of the chocolate samples 36 4.4 Multivariate analysis of variance for chemical composition 38 4.5 Range and mean sizes of particles in the chocolate samples 39 4.6 Casson flow parameters for chocolate melts at 40°C obtained with the Brookfield HAT viscometer using the SC4-27/13R bob and cup fixture. . 43 4.7 Casson flow parameters for chocolate melts at 40° C obtained with the Brabender Rheotron using coaxial cylinder fixtures A l and A2 45 4.8 Analysis of variance for Casson yield stress obtained with the Brabender Rheotron using coaxial cylinder fixtures A l and A2 46 4.9 Analysis of variance for viscosity obtained with the Brabender Rheotron using coaxial cylinder fixtures A l and A2 46 4.10 Casson yield stress estimates for chocolate samples at 40°C recalculated over the linear portion of the rheograms obtained with the Brabender Rheotron using coaxial cylinder fixtures A l and A2 47 4.11 Casson flow parameters for chocolate samples at 40°C obtained with the Carri-Med rheometer using coaxial cylinder fixture 5222 51 4.12 Analysis of variance for Casson yield stress of chocolate samples at 40°C over consecutive runs obtained with the Carri-Med rheometer using co-axial cylinder fixture 5222 52 vii 4.13 Analysis of variance for Casson viscosity of chocolate samples at 40°C over consecutive runs obtained with Carri-Med rheometer using coaxial cylinder fixture 5222 52 4.14 Mean Casson yield stress estimates for chocolate samples at 40°C recal-culated over the linear portion of the rheograms obtained with the Carri--Med rheometer using coaxial cylinder fixt ure 5222 55 4.15 Casson yield stress estimates for chocolate samples HI and H2 at 40°C for two run times obtained with the Carri-Med rheometer using coaxial cy-linder fixture 5222 56 4.16 Analysis of variance for Casson yield stress of chocolate samples at 40°C for two run times obtained with the Carri-Med rheometer using coaxial cylinder fixture 5222 56 4.17 Yield stress estimates for chocolate samples at 40°C using the Stress Re-laxation Method and the Brabender viscometer with coaxial cylinder fixtures A l and A2 58 4.18 Yield stress estimates for chocolate samples at 40°C using the Single Vane Method 60 4.19 Split plot analysis of variance for estimates of yield stress in chocolate samples at 40°C using the Single Vane Method 62 4.20 Yield stress estimates for chocolate samples at 40° C from extrapolating mean yield stress values for vanes at three start-up speeds to zero rpm;. . 63 4.21 Yield stress estimates for chocolate samples at 40°C using Method I for analyzing vane fixture data 67 4.22 Analysis of variance in yield stress estimates derived at various rotational speeds in chocolate samples at 40°C using multiple vane fixture data analyzed by Method 1 69 viii 4.23 Yield stress estimates for chocolate samples at 40°C using Method II for analyzing vane fixture data 71 4.24 Analysis of variance for yield stress estimates derived at various rotational speeds for chocolate samples at 40° C using multiple vane fixture data analyzed by Method II 73 A.25 Shear stress data (Pa) for chocolate samples at 40°C obtained with the Brookfield HAT Viscometer using coaxial cylinder fixture SC4-27/13R for steady shear tests at ascending (asc) and descending (dsc) shear rate. . . 87 A.26 Shear stress data (Pa) for chocolate samples at 40°C obtained with the Brabender Rheotron viscometer using coaxial cylinder fixture A l and spr ing C for steady shear tests at ascending (asc) and descending (dsc) shear rate 88 A.27 Shear stress data (Pa) for chocolate samples at 40°C obtained with the Brabender Rheotron viscometer using coaxial cylinder fixture A2 and spr ing C for steady shear tests at ascending (asc) and descending (dsc) shear rate. 89 A.28 Shear rate data ( s - 1 ) for chocolate samples at 40°C obtained with the Carri-Med rheometer and coaxial cylinder fixture 5222 for controlled stress tests at ascending (asc) and descending (dsc) shear stress 90 A.29 Shear rate data (s _ 1 ) for chocolate sample HI at 40°C obtained with the Carri-Med rheometer and coaxial cylinder fixture 5222 for controlled stress tests at ascending (asc) and descending (dsc) shear stress for 12 and 30 minute run times 96 ix A.30 Shear rate data (s _ 1 ) for chocolate sample H2 at 40°C obtained with the Carri-Med rheometer and coaxial cylinder fixture 5222 for controlled stress tests at ascending (asc) and descending (dsc) shear stress for 12 and 30 minute run times 102 A.31 Peak torque values for chocolate samples at 40°C using different sized vanes with the Brabender Rheotron viscometer with the A cup and spring A 108 x LIST OF FIGURES 2.1 Model rheograms for Newtonian (1), Bingham (2) and Casson (3) flow behavior 11 2.2 Schematic diagram of the Brookfield SC4-27/13R coaxial cylinder fixture and water jacket assembly (to scale) 13 2.3 Schematic diagram of the Brabender coaxial cylinder fixture A l (bob di-ameter is 54.0 mm, height is 80.0 mm and cup diameter is 56.0 mm) and water jacket (to scale) 14 2.4 Schematic diagram of the Carri-Med coaxial cylinder fixture, (bob diam-eter is 37.0 mm, height is 50.0 mm, and cup diameter is 41.5 mm), water jacket and Peltier plate (to scale) 16 2.5 Diagram of a vane fixture used to measure yield stress. The vane shown has a blade height of 40.0 mm, and four blades of diameter 25.0 mm (to scale) 21 4.6 Distribution of sizes for particles contained in the chocolate samples . . . 40 4.7 Casson flow curves of chocolate samples at 40°C obtained with the Brook-field HAT Viscometer using the SC4-27/13R bob and cup fixture 42 4.8 Casson flow curves of chocolate samples at 40°C obtained with the Braben-der Rheotron viscometer using coaxial cylinder fixture A l 48 4.9 Casson flow curves of chocolate samples at 40°C obtained with the Braben-der Rheotron viscometer using coaxial cylinder fixture A2 49 xi 4.10 Casson flow curves of chocolate samples at 40°C obtained with the Carri-Med rheometer using coaxial cylinder fixture 5222 54 4.11 Yield stress estimated at zero rpm for the chocolate samples at 40°C using mean yield values obtained from the five vane fixtures 65 4.12 Plot of 2 T m / 7 r £ > 3 versus H / D (Method I) for estimating yield stress of chocolate samples at 40°C using vane fixtures E, F, G, K and 0 68 4.13 Plot of peak torque versus vane height (Method II) for estimating yield stress of chocolate samples at 40°C using vane fixtures G, K and 0. . . . 72 xn NOMENCLATURE a Ratio of bob radius to cup radius, rj,/r c. D Diameter of vane fixture. h Height of bob fixture. H Height of vane fixture. M Torque (coaxial cylinder fixture) (N-m). P Probability level for testing statistical signifl rpm Revolutions per minute. r 2 Coefficient of determination. n Bob radius. rc Cup radius. T Torque (vane fixture) (N-m). T Peak torque or maximum on start-up (N-m), V Apparent viscosity (Pa-s- 1 ). Casson viscosity (Pa-s - 1 ). Vp Bingham plastic viscosity (Pa-s- 1). i Shear rate ( s- 1 ) . IN Newtonian shear rate ( s - 1 ) . n Angular velocity (rad-s - 1). 7T pi. a Shear stress (Pa). 0~ca Casson shear stress (Pa). Yield stress (Pa). xiii ACKNOWLEDGEMENT The author wishes to express her sincere appreciation to Dr. Marvin A. Tung for his patience, advice and review of this thesis. She also wishes to thank the members of her research committee: Dr. William D. Powrie, Dr. John Vanderstoep and Dr. Timothy D. Durance for their constructive criticism and review of this thesis. Special thanks are extended to Ian Britt, Gerry Morello, Steve Owen, Agnes Papke and Dr. Alex Speers. She is especially grateful to her husband, Damir Cukor, for his patience, support and encouragement. Financial support was provided in part by the Natural Sciences and Engineering Research Council of Canada. The experimental chocolate samples were kindly donated by Hershey Chocolate Company. xiv Chapter 1 INTRODUCTION The yield stress is defined as the point at which a plastic substance begins to flow under an applied shear stress (Keentok, 1982). Many food products such as applesauce, mayonnaise, ketchup and molten chocolate exhibit non-Newtonian fluid behavior and possess a yield stress (Barbosa-Canovas and Peleg, 1983; Tiu and Boger 1974). Accurate measurement of the rheological properties and, in particular, the yield stress is important for process design and control, as well as for predicting product performance and sensory quality (Dervisogul and Kokini, 1986). Measuring the yield stress is not a simple task. There exists in the literature a variety of methods to chose from and the use of different methods can result in yield values that differ significantly. Other complicating factors may include time dependency, shear history, sample handling, temperature effects and the type of rheometer used (De Kee et al., 1983; Prentice and Huber, 1983; Paredes et al., 1989). Rotational viscometers remain the most widely used instruments for the measurement of flow properties of fluid-like materials today (Levine, 1987). The most common method of measuring yield stress is to measure steady shearing flow in a rotational instrument and extrapolate the shear stress-shear rate data to a zero rate of shear in order to obtain the yield value (Charm, 1963; Vocadlo and Charles, 1971; Nguyen and Boger, 1983). Usually one or more constitutive equations may be fitted to the flow data to form a linear relationship which may then be extrapolated to obtain an estimate of yield stress. Common rheological models used include the Bingham, Power-law, Herschel-Bulkley and 1 Chapter 1. INTRODUCTION 2 Casson models. The Casson model has been accepted as the official method used to describe the flow of molten chocolate (OICC, 1973). Although it has been reported that this equation does not fit the flow data over the entire shear rate range used, this method is commonly used in quality control and in research to estimate the yield stress of molten chocolate (Prentice and Huber, 1981; Sequine, 1986). Deviation from linearity below 5 s - 1 has been reported and it is recommended that the chocolate melt be tested within the range of 5 to 60 s - 1 (Steiner, 1962; OICC, 1973). However, it is in the low shear rate range that yielding to an applied stress (or strain) occurs and one could argue that this is where measurements should be made to estimate yield values. Modifications made to the Casson equation have brought only limited success (Heimann and Fincke, 1962c; Saunders, 1968). Furthermore, this equation, which was developed to characterize the flow of printing ink suspensions, was based on the theory of agglom-eration and disagglomeration of particles during flow which may not be true for molten chocolate (Niediek, 1980). Other flow equations proposed include constants that relate to some physical properties of the chocolate, but no further research using these equations has been carried out (Charm, 1963; Sommer, 1974). An alternative approach would be to use direct methods of yield stress measurement. One technique in which the residual stress after shearing is measured, uses the equilibrium stress value at rest as an estimate of the yield stress value of the sample. As well, a method using vane fixtures, which has been used to estimate the yield values of clay suspensions (Nguyen and Boger, 1983), could be applied to molten chocolate. In this method, yield stress can be estimated from torque readings at the onset of vane rotation from a resting state. Chapter 1. INTRODUCTION 3 The objectives of the present research were: 1. To study the application of the Casson flow model for the determination of the yield stress value of molten chocolate from steady shear and controlled stress flow data. 2. To assess the validity of a stress relaxation and vane fixture methodology for the direct determination of the yield stress value of molten chocolate. Chapter 2 L I T E R A T U R E R E V I E W 2.1 R H E O L O G I C A L PROPERTIES OF M O L T E N C H O C O L A T E Molten chocolate, like many food products, displays non-Newtonian fluid-like behavior and is characterized by the presence of a yield stress (Charm, 1963). When subjected to slowly increasing stresses below the yield point, the chocolate behaves like an elastic solid, deforming in proportion to the applied stress, until the yield stress is exceeded. At higher stresses, the melt flows as a viscous fluid. From a rheological standpoint, materials that have a yield stress but can be made to flow at higher stresses are said to have plastic properties. Chocolate in the melted state is pseudoplastic or shear rate thinning which is a reversible effect in which the the resistance to flow (apparent viscosity) decreases with increasing shear rates (Motz, 1964; Malm, 1968; Kleinert, 1976). This thinning effect is more apparent in low fat chocolates (Chevalley, 1975). 2.1.1 Factors Influencing Flow Properties Molten chocolate is essentially a suspension of finely ground solid particles in a continuous liquid fat phase (Rostagno, 1974). The flow properties of this suspension are influenced by chemical composition, temperature, particle size and solids content (Chevalley, 1975; Kleinert, 1976). In particular, yield stress is thought to be due to interactions between suspended particles that form a kind of structure (Davis et al., 1968; Hunter and Nicol, 1968; Kleinert, 1976; Wildemuth and Williams, 1985). 4 Chapter 2. LITERATURE REVIEW 5 Chocolate is a particularly complex food, consisting of fats, proteins, carbohydrates, minerals, cellulose and water. Simple model systems of cocoa powder and fat, with added sugar and/or emulsifier, and specifically formulated chocolates, have provided some insight into which components influence flow (Rostagno et al., 1974; Kleinert, 1976). Cocoa particles are hydrophobic and interact with the fat phase, whereas the sugar crystals are hydrophilic (Tscheuschner and Markov, 1986). The presence of milk protein and the type of milk protein used would further affect the nature of the interactions occurring between particles in the chocolate melt (Heathcock, 1985). When lecithin, an emulsifier, is added at very low concentrations of 0.1 to 0.5%, it acts primarily as a surface active agent reducing the friction between the sugar, protein and cocoa particles, during the conching process, and causes a reduction in both yield stress and viscosity (Kleinert, 1976; Tscheuschner and Wiinsche, 1979). Increasing the fat content will also cause a decrease in measured yield and viscosity values (Chevalley, 1975). Increasing the solids content and/or decreasing the particle size during refining will, not surprisingly, increase the viscosity and yield values (Malm, 1967b; Kuster, 1985). Molten chocolate is usually tested at a temperature of 40°C and a variation of 1°C at this temperature will result in a 2-3% change in viscosity and a 0.5-1% change in yield stress. When temperature is increased over the range of 40 to 60°C, the viscosity decreases and the yield stress increases dramatically (Heimann and Fincke, 1962d; Rostagno, 1974). In the solid form, chocolate is a relatively stable food product when stored at tem-peratures between 18 and 20°C. Higher or lower temperature fluctuations over a period of months may adversely effect the texture and appearance of the chocolate. As well, chocolate and compound chocolates are best stored at a relative humidity ranging from 50 to 70%. Chocolates will absorb moisture if the relative humidity is above 78% for milk chocolate and above 82 to 85% for dark chocolates (Minifie, 1980; Abbink, 1984; Chapter 2. LITERATURE REVIEW 6 Cockinos, 1985; Reade, 1985). For practical applications, the rheological behavior of chocolate and the factors which influence flow are of the utmost importance when sizing pipes and designing pumps, and when using the chocolate for molding or coating. Therefore, an accurate description of flow and, in particular, the yield phenomenon, is necessary for process and product control. 2.1.2 Historical Background Over thirty years ago, the Bingham model was used to describe the rheological behavior of molten chocolate. This model is represented by the following equation, tT = c T J / + 7 / p 7 (2.1) where a is the shear stress (Pa), ay is the yield stress (Pa), T)v is the the plastic viscosity (Pa- s - 1 ) , and j is the shear rate ( s - 1 ) . If the material is a true Bingham plastic, the shear stress-shear rate data will form a straight line on linear coordinates where the slope is the plastic viscosity and the intercept is the yield stress. In studying the work of other researchers, Steiner (1958) concluded that the Bingham equation did not adequately describe the rheological behavior of molten chocolate. The flow curves were relatively linear over a shear rate range of 15 to 100 s - 1 , but there was a pronounced curvature concave to the shear rate axis at shear rates under 15 s _ 1 . Using flow data over a wide range of shear rates with extrapolation to zero shear rate would result in an over-estimation of the yield value. A slightly more complex two-parameter model was derived theoretically by Casson (1957) and tested by Bantoft (1957) on dispersions of pigments in castor oil (Steiner, 1958; Casson, 1959). A simplified form of this equation is written as, y/o- = y/O^a + \\J Tfca^f (2.2) Chapter 2. LITERATURE REVIEW 7 where crca is the Casson yield stress (Pa) and rjca is the Casson infinite shear viscosity (Pa-s - 1 ) . Steiner (1958; 1962) found this model fitted the chocolate melt flow data more accurately than did the Bingham model. He found that a linear relationship existed when the square root of shear stress was plotted against the square root of shear rate over a shear rate range of 1 to 100 s - 1 when several types of chocolates were tested using different rotational viscometers. The Casson flow model was first applied to oil suspension data using cone and plate fixtures with a rotational rheometer. In this type of sample fixture, the shearing volume or gap increases in thickness from the center of rotation out to the edge of the fixture in proportion to the increasing relative velocity between the cone and plate surfaces, therefore the rate of shear is constant throughout the volume of the sample. In coaxial cylinder fixtures, the annular gap between the cylinders would subject a Newtonian fluid to a shear rate which varies inversely with the square of the radial position. Therefore, the rate of shear for Newtonian fluids is not constant across the gap and the shear rate profile for non-Newtonian fluids is more complex. The Reiner-Riwlin equation corrects for non-Newtonian shear rates in Bingham materials (Van Wazer et al., 1963). An equiv-alent correction was calculated by Steiner (1958) and later by Hanks (1983). Although the mathematical approach differs among the three separate groups, the correction is essentially the same. Darby (1985) applied the power-law shear rate correction (Krieger, 1968) to the Bingham and Casson models and estimated the percentage error in shear rate to be approximately 6% for Casson materials in narrow gap coaxial cylinder fixtures. Steiner's original equation for the exact relation between shear rate and shear stress for Casson flow is as follows: 7 fe(l+a)\"\\3 5 l l +aj / tfe. V l + a] ^ ' The value of a represents the ratio of bob radius to cup radius. The second term on the Chapter 2. LITERATURE REVIEW 8 left hand side of the equation may be ignored when the value of a is close to 1.0. (as in a narrow gap viscometer). Another condition stated that the ratio of (7j 1 a a JZ to 0 Shear Rate Figure 2.1: Model rheograms for Newtonian (1), Bingham (2) and Casson (3) flow be-havior. 2.3 R H E O M E T E R D E S C R I P T I O N 2.3.1 Brookfield Viscometer Brookfield viscometers are well known and have been widely used for viscosity mea-surement in industry for over forty-five years. This viscometer is relatively inexpensive, reliable and easy to use. As well, the availability of a wide variety of sample fixtures such as the small sample adapter and a narrower gap cup and bob geometry (UL fixtures), as well as cone and plate fixtures, make this instrument comparable to more expensive rheometers (Rosen and Foster, 1978; Smith, 1982; Brownsey, 1988). A synchronous induction-type motor transmits power through a gear drive assembly producing either four or eight specific rotational speeds, depending on the model. The HAT model, used in this investigation, has eight possible speeds and is recommended for high viscosity ma-terials like molten chocolate (Brookfield, 1985). The SC4-27/13R stainless steel bob and cup fixture is generally used along with a water jacketed small sample adapter allowing Chapter 2. LITERATURE REVIEW 12 for thermostatic control (Figure 2.2). The torque required to maintain a constant angular velocity of the immersed bob in the sample is measured via a calibrated spring which has been preset at the factory (Sequine, 1986). The bob has conical ends which helps to minimize error due to shear stresses occuring on the bottom and top of the bob (Howard, 1969; Powell, 1988). 2.3.2 Brabender Rheotron Viscometer The Brabender Rheotron viscometer has a much broader capability than the Brookfield viscometer. It can be used with both coaxial cylinder and cone and plate fixtures which are suitable for testing a variety of materials over a broad shear rate range (0.05 to 20,000 s _ 1 ) . There are 32 discrete operating speeds. Accurate speed control is accomplished through a d.c. servo-motor which is coupled, by magnetic clutches, to the gear box. The outer cylinder is rotated while the torque is measured at the bob (Figure 2.3). The torque measuring sensor features 3 interchangeable springs extending the shear stress range from approximately 0.25 to 105 Pa. This instrument can also be used with an optional speed programmer allowing for continuous shear in a linearly increasing and/or decreasing manner. 2.3.3 Carri-Med Controlled Stress Rheometer The first controlled stress rheometer was developed in the late 1960's by Davis, Deer and Warburton at the London School of Pharmacy (Davis et al., 1968). This prototype was later marketed as the Deer Variable Stress Rheometer which originally used turbines to support and apply a constant stress to the inner rotating cylinder of the coaxial cylinder fixture. Later, an induction drive motor replaced the air turbine. The Carri-Med controlled stress rheometer, in which Deer had been involved, is re-ferred to as a third generation instrument. It has a microprocessor-controlled induction 2.3. RHEOMETER DESCRIPTION 13 Figure 2.2: Schematic diagram of the Brookfield SC4-27/13R coaxial cylinder fixture and water jacket assembly (to scale). Chapter 2. LITERATURE REVIEW 14 Figure 2.3: Schematic diagram of the Brabender coaxial cylinder fixture A l (bob diameter is 54.0 mm, height is 80.0 mm and cup diameter is 56.0 mm) and water jacket (to scale). Chapter 2. LITERATURE REVIEW 15 drive motor system and can be used for a broad array of rheological tests. Although this instrument can be used manually, control through a microcomputer (either Apple or IBM) not only directs the machine but provides data logging and software for flow anal-ysis using the Casson, Bingham, Herschel-Bulkley and other models (Brownsey, 1988). Controlled stress rheometers differ from conventional controlled shear rate rheometers in two important ways. Firstly, in controlled stress testing, the sample may be sheared over a broader range continuously without having to change the torque measuring de-vice, or gear ratio, in order to increase or decrease speed. Secondly, the behavior and deformation of the sample at very low stresses can be studied (Cheng, 1986; Carri-Med, 1985). The Carri-Med narrow gap coaxial cylinder fixture, used in this investigation, is shown in Figure 2.4. This fixture is comparable to the one shown for the Brabender in that it features a hollow cavity in the bottom of the inner cylinder which traps a volume of air to help eliminate viscous drag by contact of the sample with the base of the bob. Standard equations for the calculation of shear stress and shear rate remain the same. Being a relatively new instrument, full use of the rheometer was limited by delays in developing comprehensive computer control and data analysis capablities (Brownsey, 1988). However, because controlled stress rheometers have now become so highly au-tomated, versatile and relatively straight forward to use, applied stress testing is being used more extensively in research today (Franck, 1985; Yoshimura et al., 1987; Barnes and Carnali, 1990). 2.4 STRESS RELAXATION METHOD Stress relaxation techniques have been used to determine the yield stress of a variety of food and non-food materials. This is a simple method and involves shearing the sample Chapter 2. LITERATURE REVIEW 16 Figure 2.4: Schematic diagram of the Carri-Med coaxial cylinder fixture, (bob diameter is 37.0 mm, height is 50.0 mm, and cup diameter is 41.5 mm), water jacket and Peltier plate (to scale). Chapter 2. LITERATURE REVIEW 17 at a low steady shear, then reducing the speed either gradually or suddenly and recording the decline in shear stress to an equilibrium value as a function of time (Michaels and Bolger, 1962; Tiu and Boger, 1974; Nguyen and Boger, 1983). Different test fixtures such as the parallel plate, bob and cup and cone and plate geometries have been used to measure residual stress (Patton, 1966; Tiu and Boger, 1974; Keentok, 1982). The equilibrium stress value can be graphically determined as described by Patton (1966) and the raw data converted to obtain plots of viscosity versus shear rate, or, shear stress versus shear rate. The shear stress-shear rate data can also be used to extrapolate to zero shear rate to estimate yield stress (Swartzel et al., 1980). Reproducibility of the stress relaxation method can sometimes be a problem. For greases (Keentok, 1982) and concentrated suspensions (Vocadlo and Charles, 1971; Nguyen and Boger,1983), slip between the sample and fixture surfaces can occur, thereby result-ing in inaccurate yield stress estimates. If long relaxation times are required, dense particles in the sample can settle out (Nguyen and Boger, 1983). Using fixtures made of different materials (Vocadlo and Charles, 1971) or different fixture geometries (Keentok, 1982) can result in significantly different yield stress values. As well, it can be difficult to distinguish between the effects of shear-thinning and time dependency (Smith, 1982). For example, residual stress measurements for mayonnaise were found to depend on the time of shear (Tiu and Boger, 1974). It is important, therefore, to repeat the relaxation test under several conditions. The use of different shear rates and shearing times has been recommended, before measuring the equilibrium stress after relaxation. (Barbosa-Canovas and Peleg, 1983; Nguyen and Boger, 1983). While stress relaxation may be inappropriate for some materials it has been used successfully for paints (Patton, 1966; Smith, 1982), guar gum and cornstarch dispersions (Lang and Rha, 1981), tomato puree and applesauce (Charm, 1963), and for moderately concentrated clay suspensions (Nguyen and Boger, 1983). Yield stress values were comparable to Chapter 2. LITERATURE REVIEW 18 those obtained using indirect extrapolation methods. 2.5 V A N E F I X T U R E M E T H O D The use of constitutive equations like Casson's to arrive at a yield stress value are empiri-cal and dependent on the model, the accuracy of the flow data and the type of rotational instrument used (Nguyen and Boger, 1983). Some research has been done using the vane fixture (Figure 2.5) as an alternative to the coaxial cylinder fixture in rotational viscometry. In soil mechanics, a simple vane technique has been widely used for many years to measure the shear strength of cohesive soils. Over the past decade researchers have adopted the vane method to measure the yield stress of clay suspensions, emulsions and greases (Keentok, 1982; Nguyen and Boger, 1983; 1985; James et al., 1987; Yoshimura, 1987). In food rheology, research by Tung et al. (1990) in which this author is involved, has used vane fixtures to test mayonnaise, salad dressing and chocolate melts. In recent studies, comparisons have been made between vane fixture methods and steady shearing flow extrapolation methods using flow models (Keentok, 1982; Nguyen and Boger 1983; Tung and Speers, 1986; James et al., 1987; Tung et a l , 1990). It has been suggested that when testing highly concentrated dispersions, the vane fixture method could provide a more accurate yield stress measurement over the conventional coaxial cylinder fixture method where slip effects on the surface of the cylinder can introduce significant error. 2.5.1 Theory The vane method employed with constant speed instruments involves immersing the vane fixture into a cup containing the sample and slowly rotating the vane at a constant Chapter 2. LITERATURE REVIEW 19 rotational speed while measuring the torque response as a function of time. As the vane rotates, the material deforms elastically, with the torque increasing to a maximum value before dropping off to a lower equilibrium value. The presence of a peak torque on a torque-time curve is characteristic of materials possessing a yield stress. The shape of the torque-time curves may also be influenced by the nature of the instrumentation used. For example, with viscometers that have the torsion transducer in the drive system between the motor and vane fixture, the transducer compliance, fixture and sample inertia, and recording system characteristics may play a role in determining the appearance of the resulting curves. It has been demonstrated that the yielding of the material occurs along the cylindrical surface described by the rotating vane (as shown in Figure 2.5). The torque, T, is due to shearing of the sample on the cylindrical surface and two ends of the vane and is equal to: where D and H are the diameter and height of the vane respectively, aa is the shear stress on the cylindrical yielding surface and cre is the end shear stress which is unknown (Nguyen and Boger, 1985). To calculate yield stress from measured torque, it is assumed that the end shear stress is constant and equal to the shear stress on the curved shearing surface (Keentok, 1982; Nguyen and Boger, 1983). As well, the assumption is made that the material yields instantaneously along the cylindrical surface at the maximum torsional moment (Nguyen and Boger, 1983). Under these assumed conditions, the stress on the cylindrical and flat end surfaces described by the rotating vane is equal to the yield stress (ay) at the maximum torsional moment (T m ) and Equation 2.9 is reduced to, (2.10) Tm = TTOy D2H D3 Chapter 2. LITERATURE REVIEW 20 Nguyen and Boger (1983; 1985) concluded that the assumption of a uniform shear stress distribution over the end surfaces is valid for vanes of very small diameters (as D approachs 0). In practice, vanes have a finite diameter and there will then be some error made in calculating yield stress using Equation 2.10. The following equation, proposed by Nguyen and Boger (1983), can be used to approximate the error involved in making this assumption: M T D 3 [ F 1 1 , = ~ 2 ~ [~D + mTlsJ <2-U> where m is a constant describing the radial distribution function of 0.05) in a comparison of results from test samples. However, a 15 minute shearing period was included so that sample treatment was uniform and more closely related to pretest handling of samples used in the other methods. Spring A was used in the torque sensor of the instrument to provide greater sensitivity to the stress generated using the vane fixtures. Rotational speeds of 0.064, 0.120 and 0.224 were selected for the test procedure. The peak torque values were measured for duplicate samples using the five vane fixtures, randomized within each sample, and rotational Chapter 3. EXPERIMENTAL 34 speeds were randomized within each of the vane fixtures. The peak torque data were analyzed using the Single Vane Method and Multiple Vane Methods I and II as previously described. 3.5 D A T A A N A L Y S E S The yield stress and viscosity estimates obtained using Brabender Rheotron were ana-lyzed in a two-way analysis of variance (ANOVA) using a repeated-measures design to test for a significant difference between fixture types. This design was also used for the Carri-Med data obtained over consecutive runs as well as for the second data set where two different run times were used. Data sets analyzed using Vane Methods I and II were tested for equality of lines using a multiple regression analysis. Since there was no significant difference between regression lines, the data were pooled and a two-way analysis of variance (ANOVA) was used to test for a significant difference in rotational speeds used. Yield stress estimates obtained using the conventional vane method were analyzed using a split-plot design. A l l statistical procedures used (Steel and Torrie, 1960) were calculated using the B M D P program (Dixon, 1985) on the UBC Amdahl 5860 computer. Graphical presentation of the data was performed using the Tell-A-Graf graphics program also available on the U B C mainframe computer. Chapter 4 RESULTS AND DISCUSSION 4.1 CHEMICAL ANALYSES A proximate analysis, consisting of moisture, ash, fat and protein determinations, was carried out on each chocolate sample. An estimate of total carbohydrate was derived from the difference. Also, since it is known that chocolate has a high sugar content, the sucrose content of each sample was determined. A l l analyses were carried out to characterize the test material and provide some insight into the differences in flow properties observed between test samples. The compositions of the four chocolate samples are given in Table 4.3. The relative amounts of moisture, fat, protein and sucrose found in the test materials were similar to values reported in the literature for other dark and milk chocolate formulations. The moisture content was low for all samples tested, ranging from 0.92% for H2 to 1.84% for H M C . Previous studies have shown how the water content can influence viscosity and yield stress. Researchers found that viscosity did not vary significantly over a range of 0.6 - 1.1% moisture, whereas yield stress increased steadily as moisture content increased (ChevaUey, 1975). The ash content of the samples varied between 1.22% for HSS to 1.65% for HI and H M C ; H2 was slightly less at 1.54%. The higher ash values may be due to milk in the Hershey milk chocolate as well as in the other two. Although it is not known what ingredients were used in the manufacture of HI and H2, the light color and flavor of the 35 Chapter 4. RESULTS AND DISCUSSION 36 Table 4.3: Composition of the chocolate samples. Analysis Composition of Sample (%) H M C HSS HI H2 Moisture 1.84 1.22 1.67 0.917 Ash 1.65 1.22 1.65 1.54 Fat 31.8 30.8 30.1 32.1 Protein 6.75 4.91 6.99 6.44 Carbohydrate^ 58.1 61.9 59.5 59.1 Sucrose 49.7 52.1 50.1 50.0 J- [100 - (total of other components)] Chapter 4. RESULTS AND DISCUSSION 37 chocolate suggested the presence of milk. HSS was a semi-sweet chocolate and did not contain milk. Samples H2 and H M C contained the most fat at 32.1% and 31.8%, respectively. HSS contained 30.8%, which was approximately 1.0% less, and, HI contained 30.1% fat, a difference of 2.0% as compared to H2. Generally, the fat content of chocolate is in the range of 28 - 40% (Tscheuschner and Markov, 1986). An inexpensive chocolate may contain between 22 - 28% fat (Niediek, 1980). The protein content of chocolate is not high. Milk chocolate has a slightly higher protein content than dark chocolate due to the presence of milk protein. Of the four samples analyzed, HI had the highest protein content of 6.99%. H M C and H2 had slightly lower amounts at 6.75 and 6.44%, respectively. The semi-sweet chocolate, HSS contained approximately 2.0% less protein than the other samples at 4.91%. Total carbohydrate was estimated by the difference between 100 and the percent totals of the other components. Chocolate is a rich source of carbohydrate of which a large proportion is comprised of sucrose. The samples were found to contain, in increasing order, 49.7, 50.0, 50.1 and 52.0% sucrose for H M C , H2, HI and HSS, respectively. A multivariate analysis of variance (MANOVA), using the BMDP:4V statistical soft-ware program, was used to test for significant differences among samples. The samples differed significantly in chemical composition (Table 4.4), and the univariate statistics showed that each chemical analysis was significantly different between chocolate samples tested. 4.2 PARTICLE SIZE ANALYSIS A Coulter Counter Model TAII was used to analyze the particle size distribution in each of the four chocolate samples. The pooled mean particle size determined for each Chapter 4. RESULTS AND DISCUSSION Table 4.4: Multivariate analysis of variance for chemical composition. Variate df Mean Square F-Ratio Sample 15 0.5288E-05U' 46.63 ** Ash 3 0.1255 19.83 ** Error 7 0.0063 Moisture 3 0.4447 402.6 ** Error 7 0.0011 Fat 3 2.0856 7.010 * Error 7 0.2975 Protein 3 2.6088 49.06 ** Error 7 0.0532 Sucrose 3 3.7082 20.48 ** Error 7 0.1810 w - Wilks' lambda likelihood ratio statistic. * - significant at p<0.05 ** - significant at p<0.01 Chapter 4. RESULTS AND DISCUSSION Table 4.5: Range and mean sizes of particles in the chocolate samples. 39 Sample Pooled Mean (pm) Coefficient of Variation (%) Size Range (fim) H M C 6.98 6.93 2.5 - 80.5 HSS 5.73 2.22 2.5 - 80.5 HI 6.27 4.21 2.5 - 64.0 H2 7.15 11.01 2.5 - 80.5 chocolate is given in Table 4.5. Sample HSS had the smallest average particle size of 5.73 pm, followed by HI with a mean size of 6.27 pm and H M C and H2 with mean particle sizes of 6.98 and 7.15 pm, respectively. Figure 4.6 shows the percentage of particles at sizes ranging from 2.5 to 25.5 pm. Larger sized particles between the sizes of 25.5 and 80.5 pm accounted for less than 1% of the total population. Generally, for chocolate, the particle size of the sugar crystals ranges from 5 to 35 fim and the particle size of the cocoa solids from 15 to 20 pm (Tscheuschner and Markov, 1986). In this analysis, the greatest number of particles appeared to be in the range of 4.0 to 5.0 pm. Approximately 70 and 80% of the total population of particles, for samples HI and HSS, respectively, he within this size range. For samples H M C and H2 the numbers are lower at 60 and 65%, respectively and these samples have a broader particle size distribution. Overall, these results were similar to Coulter analysis data reported in the literature (Malm, 1967; Minifie, 1980). 60 50 40 c o CL O Q_ 30 2 0 H 10 Legend ra HMC HSS E a HI LZ3 H2 2.5 4 5 6.3 8 II 10.1 20.2 25.4 12.7 16 Particle Size (um) Figure 4.6: Distribution of sizes for particles contained in the chocolate samples 8 !=0 Co t3 CO O Cj co o o Chapter 4. RESULTS AND DISCUSSION 41 4.3 INDIRECT ESTIMATION OF YIELD STRESS 4.3.1 Brookfield Viscometer The Brookfield HAT viscometer was one of three rotational viscometers used in this investigation to determine the flow properties of the four chocolate samples. The samples were prepared and tested following the OICC methodology as described previously. The Casson equation was fitted to the shear stress-shear rate data and the appropriate non-Newtonian shear rate correction factor applied. The rheograms for each chocolate type are shown together in Figure 4.7 as the square root of shear stress vs the square root of shear rate. A good straight line fit would indicate that flow followed the Casson model, and in each case this was true with the exception of sample HI . The rheogram for sample HI showed a marked curvature towards the abscissa. The Casson flow parameters for each chocolate sample are fisted in Table 4.6. Yield stress values ranged, in order of increasing magnitude from 9.38 Pa for H M C , 9.59 Pa for HI , 10.6 Pa for H2, to 19.8 Pa for HSS. Correspondingly, Casson viscosity estimates were 10,010, 19,300, 4,500 and 5,270 mPa-s for H M C , HI , H2 and HSS, respectively The coefficients of variation for all samples tested were below 10%. Although the SC4-27/13R fixture is recommended for use with the Brookfield HAT viscometer for testing molten chocolate, the maximum shear rate obtainable was 17.0 s - 1 . This does not meet the maximum shear rate of 60 s - 1 recommended by the OICC. Also, the recommended bob to cup ratio (0.05) Table 4.13: Analysis of variance for Casson viscosity of chocolate samples at 40°C over consecutive runs obtained with Carri-Med rheometer using coaxial cylinder fixture 5222. Source of Variation df Mean Square F-Ratio Sample Error 267.45E05 496.82E04 5.38 Run Interaction Run x Sample Error 114.59E04 504.57E02 448.85E02 25.53 * 1.12 ns * - significant at p<0.05 ns - not significant (p>0.05) Chapter 4. RESULTS AND DISCUSSION 53 was deforming and/or slipping rather than flowing at apparent shear rates below 0.5 s _ 1 . Also, at these low shear rates, it was likely that plug flow was occurring. No flow could be detected below approximately 3.9 Pa for HI , 6.0 Pa for H M C and HSS and 8.5 Pa for H2. The lowest shear rate values measured were 0.05, 0.04, 0.03 and 0.06 s _ 1 for samples H M C , HSS, HI and H2, respectively. Casson yield stress estimates recalculated over the linear portion of the rheograms were higher (Table 4.14). The linear Casson model cannot accurately describe the flow of chocolate over the entire shear rate ranges used in either the Brabender or Carri-Med instruments. The ranges in viscosity and yield stress values obtained using different viscometers were comparable to published results (Steiner, 1958). As well, in collaborative studies (Steiner, 1972; Prentice and Huber, 1981) where standard chocolate samples were dis-tributed among different laboratories and tested with different rotational instruments (using coaxial cylinder fixtures), the coefficient of variation in measured yield values was as high as 23%. The variation coefficients for yield values, obtained with the three rota-tional instruments used in this investigation, were 20.8, 18.5, 40.2 and 23.3% for H M C , HSS, HI and H2, respectively. A second experiment was conducted using samples HI and H2 and estimating yield values from data measured over a 12 and 30 minute programmed run. The yield estimates are listed in Table 4.15 and an analysis of variance (Table 4.16) indicated that there was a significant difference in yield values measured over these two run times and a significant run x sample interaction. The yield values for sample HI were significanlty lower when the sample was sheared for 30 minutes as compared to the yield values obtained when the sample was sheared for 12 minutes. It is apparent that the Casson flow parameters for chocolate using the Casson flow equation depend on the accuracy of the measured flow data and the rotational instrument used. As well, the use of model equations, to estimate yield stress, may not be very Figure 4.10: Casson flow curves of chocolate samples at 40° C obtained with the Carri-Med rheometer using coaxial cylinder fixture 5222. Chapter 4. RESULTS AND DISCUSSION 55 Table 4.14: Mean Casson yield stress estimates for chocolate samples at 40°C recalculated over the linear portion of the rheograms obtained with the Carri-Med rheometer using coaxial cylinder fixture 5222. Sample Yield Stress Coefficient of o-ca, (Pa) Determination, r 2 H M C 13.9 (H.4)t 0.993 (n=360) HSS 23.8 (3.87) 0.983 (n=358) HI 32.0 (1.44) 0.993 (n=340) H2 23.7 (9.76) 0.991 (n=349) f - Coefficient of variation (%) representative of the true physical yield property of the sample (Nguyen and Boger, 1983; Rao and Cooley, 1983). Chapter 4. RESULTS AND DISCUSSION 56 Table 4.15: Casson yield stress estimates for chocolate samples HI and H2 at 40°C for two run times obtained with the Carri-Med rheometer using coaxial cylinder fixture 5222. Sample Run Time Casson Yield Coefficient of (min) o-ca, (Pa) Determination, r 2 HI 12 29.1 (4.73)t .983 (n=386) 30 20.6 (8.83) .969 (n=389) H2 12 9.94 (2.34) .995 (n=381) 30 9.49 (3.10) .994 (n=393) t - Coefficient of variation (%) Table 4.16: Analysis of variance for Casson yield stress of chocolate samples at 40°C for two run times obtained with the Carri-Med rheometer using coaxial cylinder fixture 5222. Source of df Mean Square F-Ratio Variation Sample 3 686.89 186.55 ** Error 4 3.6821 Run Time 1 59.981 182.87 ** Interaction Run x Sample 1 48.410 147.60 ** Error 4 0.32799 ** - significant at p<0.01 Chapter 4. RESULTS AND DISCUSSION 57 4.4 STRESS RELAXATION METHOD The results obtained with the stress relaxation methods are given in Table 4.17. Residual stress remaining in the material after shearing was stopped provided direct experimental evidence that a yield stress was present in the time frame of the experiment (Tiu and Boger, 1974). The small yield stress values obtained could be interpreted two ways. Firstly, these values could be thought to represent the true yield stress of the samples tested. The flow curves obtained using both the Brabender and Carri-Med rheometers showed a marked curvature towards the abscissa. Since a straight line was fitted to the curved data, the intercept could be higher than if a smooth curve were to be drawn and extended to the y-axis. Accordingly, the calculated yield value of the material could therefore occur at much higher shear stresses than if the values were obtained by curvilinear extrapolation. A second interpretation, is that the low values measured were an artifact of the experiment and do not provide a meaningful estimate of the yield stress of the samples. It is noteworthy that accuracy was not greatly improved in that, in general, coefficients of variation were higher for direct estimation of yield stress by the Stress Relaxation Method as compared to the indirect method of extrapolating flow data to zero shear rate. As well, although this residual stress method was simple, there was no great time savings in conducting this experiment. The samples had to be pre-sheared for a longer period of time (30 minutes) in order to reach an equilibrium state and, as well, several rotational speeds and relaxation periods were performed. When this procedure was shortened by using only one rotational speed, greater variation in the data was observed as shown in Table 4.17. As well, yield values were higher for the single point measurements as compared to multiple measurements made at three rotational speeds. It may be that the values measured were dependent on both shear rate and/or the test procedure used. Chapter 4. RESULTS AND DISCUSSION 58 Table 4.17: Yield stress estimates for chocolate samples at 40°C using the Stress Re-laxation Method and the Brabender viscometer with coaxial cylinder fixtures A l and A2. Method Cylindrical Yield St] cess (Pa) Fixture H M C HSS HI H2 Single measurement A2 A l 4.42 (17.3)t 4.23 (22.7) 4.09 (21.0) 4.31 (7.45) 11.1 (6.48) 15.8 (28.0) 5.43 (11.1) 6.04 (28.1) Multiple measurements A2 A l 1.74 (21.5) 2.38 (15.0) 2.85 (14.9) 4.49 (11.0) 8.59 (8.07) 9.16 (16.3) 2.53 (10.3) 3.80 (10.2) t- Coefficient of variation (%) Robinson-Lang and Rha, 1981, and Nguyen and Boger, 1983, found this method to be acceptable for the measurement of yield stress in low and moderately concentrated clay suspensions. However, Nguyen and Boger (1983) found that in highly concentrated suspensions (greater than 60% solids by weight) slip effects and a nonuniform shear distribution contributed to poor reproducibility. As well, low recorded yield stress values for wheat starch dispersions following stress relaxation were reportedly due to slip effects (Navickis and Bagley, 1983). Chocolate melts are highly concentrated dispersions and it is possible that slip effects were occuring, resulting in lower recorded yield values. In a collaborative study (Prentice and Huber, 1983) in which yield stress was esti-mated using the Casson equation, one laboratory, using cone and plate fixtures, allowed the sample to relax after each measurement. The residual stress or yield stress fell to a steady value independent of shear rate, but noted that the measured values were also Chapter 4. RESULTS AND DISCUSSION 59 lower in magnitude than yield values obtained by extrapolation of Casson steady flow data to zero shear rate. Apart from possible slip effects, another problem in using this method is that the structure of the test material is disrupted before yield stress is mea-sured. Stress relaxation may be an appropriate method for measuring the yield stress of molten chocolate in cases where structure of a sheared sample is important. 4.5 VANE FIXTURE METHOD The vane fixture method was found to be applicable for direct determination of the yield stress of the four chocolate samples tested. The five vane fixtures, E, F, G, K and 0 were used to measure start-up torque overshoot values from which were derived estimates of the yield stress of the molten chocolate test samples. Yield stress was estimated from the raw data using three different analyses; the Single Vane Method (Keentok, 1982; Nguyen and Boger, 1983) and Multiple Vane Methods I and II (Nguyen and Boger, 1985). 4.5.1 Single Vane Method Peak torque values were obtained by measuring the maximum torque at the start-up of vane rotation after the 15 minute pre-shear period. Low rotational speeds of 0.064, 0.120 and 0.224 rpm were used and single measurements were taken using each vane fixture. Yield stress estimates were obtained from the following relationship: cTy = 2T m / [7r / J 2 ( t f+ D/3)] (4.12) where D and H are the diameter and height of the vane fixture, T m is the maximum torque measured and ay is the calculated yield value. Table 4.18 shows the yield stress estimates determined for the four chocolate samples using single measurements taken from each vane fixture at three different speeds. Chapter 4. RESULTS AND DISCUSSION 60 Table 4.18: Yield stress estimates for chocolate samples at 40°C using the Single Vane Method. Sample Rotational Yield Stress (Pa) Coefficient of Speed E F G K 0 Variation (%) (rpm) H M C 0.064 31.3 30.4 29.9 31.5 29.0 3.98 0.120 32.8 32.9 30.2 33.0 30.0 5.45 0.224 33.4 32.7 31.8 32.4 31.1 3.56 HSS 0.064 39.7 35.6 36.8 38.5 44.8 8.63 0.120 42.8 37.0 38.8 39.7 44.3 7.71 0.224 44.5 39.2 40.4 40.0 47.6 8.70 HI 0.064 70.5 109 68.0 66.5 61.1 23.45 0.120 68.8 107 65.4 65.3 63.5 23.23 0.224 71.9 109 66.9 66.5 65.1 22.71 H2 0.064 29.0 29.5 30.7 32.4 31.4 6.72 0.120 30.9 31.2 30.4 36.2 31.8 8.57 0.224 31.9 32.1 31.7 35.6 34.9 6.92 Chapter 4. RESULTS AND DISCUSSION 61 A split plot analysis was carried out to determine if there were any significant dif-ferences between vane fixtures as well as rotational speeds. The results of the analysis of variance using the BMDP:2V statistical software are given in Table 4.19. As shown, the rotational speeds (rpm) used had a significant (p<0.01) influence on the yield stress values obtained. In concentrated clay suspensions, yield values measured using vane fixtures were rel-atively constant over rotational speeds ranging from 0.1 to 8.0 rpm, but increased at speeds greater than 8.0 rpm (Nguyen and Boger, 1983). In prehminary testing, peak torque values measured using the vanes increased significantly when rotational speeds greater than 0.8 rpm were used. Also, when measuring the yield point of a material, it would be better to use very low speeds. For these reasons, low speeds were used in the test procedure, but still lower speeds may be necessary for optimal results; however, the Brabender viscometer is not capable of applying slower speeds. Nguyen and Boger also recommended that the diameter of the cup and the depth of the suspension in the cup be at least twice as large as the diameter and height of the vane in order to minimize boundary effects. In this investigation, vanes E, F and G, which had vane blade heights of 4.0 cm, were chosen according to these criteria. In addition, vanes K and O, which had vane blade heights of 5.5 and 7.0 cm, respectively, were used although the depth of the molten chocolate in the cup was not twice that of the height of the immersed vane. However, no significant difference was found for the different sized vanes used. The material itself may govern what the limiting dimensions of the vane(s) and cup fixtures might be. The coefficients of variation for yield values measured using the five vane fixtures were below 10% for samples H M C , HSS and H2 (Table 4.18). The high variation in results for sample HI is due to high peak torque values measured using vane F. In an attempt to eliminate the effect of start-up speed on the estimated value of the Chapter 4. RESULTS AND DISCUSSION 62 Table 4.19: Split plot analysis of variance for estimates of yield stress in chocolate samples at 40°C using the Single Vane Method. Source of Variation df Mean Square F-Ratio Sample Vane Error 7 4 28 548.13E01 418.32 267.76 20.47 ** 1.57 ns Speed Interactions Speed x Sample Speed x Vane Error 14 8 56 46.829 2.8797 2.2798 1.4043 33.35 ** 2.05 * 1.62 ns - significant at p<0.05 ** - significant at p<0.01 ns - not significant (p>0.05) Chapter 4. RESULTS AND DISCUSSION 63 Table 4.20: Yield stress estimates for chocolate samples at 40°C from extrapolating mean yield stress values for vanes at three start-up speeds to zero rpm. Sample Rotational Speed (rpm) Mean Yield Stress (Pa) Extrapolated Yield Stress (Pa) Standard Error Estimate of Y Coefficient of Determination r 2 H M C 0.064 0.120 0.224 30.4 31.8 32.3 28.6 1.46 0.213 (n=30) HSS 0.064 0.120 0.224 39.1 40.5 42.3 35.4 3.52 0.132 (n=30) HI 0.064 0.120 0.224 66.5 65.7 67.6 64.7 5.61 0.008 (n=24) H2 0.064 0.120 0.224 30.6 32.1 33.2 27.7 2.48 0.166 (n=30) yield point, the yield stress was calculated by extrapolation of data gathered at finite rotational speeds, back to zero rpm (Tung et al., 1990). The data were successfully fitted by the following equation, cry = a^/rpm + ayo (4-13) Yield stress (o~yo) values estimated by this procedure (Figure 4.11) would presumably be independent of rotational speed employed. The values are listed in Table 4.20. Vane F data for sample HI were omitted in this analysis. The standard error estimates reflect the accuracy of the yield values obtained for the chocolate samples using this method. Chapter 4. RESULTS AND DISCUSSION 64 Yield stress values calculated at zero rpm were slightly lower than the mean yield values obtained at 0.064, 0.120 and 0.224 rpm. Chapter 4. RESULTS AND DISCUSSION 65 9 0 75 6 0 Legend o H M C • H S S o H I v H2 45 H 3 0 15-0 . 0 0 .2 VRPM 0.4 0 .6 Figure 4.11: Yield stress estimated at zero rpm for the chocolate samples at 40°C using mean yield values obtained from the five vane fixtures. Chapter 4. RESULTS AND DISCUSSION 66 4.5.2 Multiple Vane Method I This method utilized Equation 2.11 as described previously in Chapter 2. By plotting 2Tm/ir D3 as a function of the vane length to diameter ratio (H/D), the yield stress can be determined directly from the slope of the graph. The vane fixture data were analyzed according to this method using vanes E, F, G, K and 0 wTith H / D varying from 1.6 to 2.8. A linear regression test for equality of lines using the BMDP:1R statistical computer program showed there was no significant difference (p>0.05) between duplicates tested. The duplicates were pooled and the data plotted for each chocolate sample at each of the three rotational speeds used. The results obtained from the analysis are listed in Table 4.21. For chocolate samples H M C , HSS and H2, the linearity of plots in Figure 4.12 confirms the validity of this method for the set of vane fixtures used. However, this analysis was not adequate for calculating the yield value of HI as shown by the plotted data in Figure 4.12 for this sample. It appears that measurements obtained using vanes E and F were responsible for the scatter in the plotted data. When these data points were removed the recalculated yield values were 49.9, 60.4 and 62.2 Pa for speeds of 0.064, 0.120 and 0.224 rpm, respectively, which compared more closely with the single point measurements. These vanes were the smallest in both diameter and height of the series of vanes used in this investigation. It may be that small vanes should not be used to test highly viscous chocolate melts. Table 4.21 also lists the values for ra, an empirical parameter describing the stress distribution at either end of the vane fixture and should vary little about zero. The m values for samples HI and HSS, as well as the ra value obtained at the highest test speed for sample H2, were large, and therefore, some error in calculating the yield values would result. In fact, the yield values obtained for these samples do not compare with yield Chapter 4. RESULTS AND DISCUSSION 67 Table 4.21: Yield stress estimates for chocolate samples at 40°C using Method I for analyzing vane fixture data. Sample Rotational Yield Stress Coefficient of Speed cjy, (Pa) m Determination, r 2 (rpm) n=10 H M C 0.064 29.5 -0.60 0.947 0.120 31.2 -0.37 0.906 0.224 32.1 -0.10 0.959 HSS 0.064 55.2 -5.49 0.937 0.120 54.8 -6.08 0.950 0.224 59.4 -5.56 0.931 HI 0.064 34.0 -2.70 0.125 0.120 40.8 -2.58 0.175 0.224 44.4 -2.53 0.197 H2 0.064 30.1 -0.32 0.848 0.120 32.3 +0.16 0.793 0.224 37.0 +9.41 0.871 Chapter 4. RESULTS AND DISCUSSION 68 o o Legend o HMC • HSS o H1 v H2 • B a • o o o • a o o 0 . 5 1.5 2.5 H/D 3 . 5 Figure 4.12: Plot of 2Tm/7rI>3 versus H / D (Method I) for estimating yield stress of chocolate samples at 40°C using vane fixtures E, F, G, K and 0. Chapter 4. RESULTS AND DISCUSSION 69 Table 4.22: Analysis of variance in yield stress estimates derived at various rotational speeds in chocolate samples at 40° C using multiple vane fixture data analyzed by Method I. Source of df Mean Square F-Ratio Variation Sample 3 625.29 84.45 * Speed 2 42.389 5.73 * Error 6 7.4041 * - significant at p<0.05 values estimated using the Single Vane Method. For chocolate samples H M C and H2 (at the two lower speeds), m ranged from -0.60 to -0.10 and the corresponding yield values were comparable to those obtained using single vane measurements. A uniform shear stress distribution over the end surfaces of the vane fixture was confirmed experimentally for clay suspensions (Nguyen and Boger, 1985; James et al., 1987), but could not be confirmed for two of the four chocolate samples tested in this investigation, thus, some error in estimating the yield value for these samples could result. In order to test for possible differences between rotational speeds, a two-way analysis of variance (ANOVA) was conducted using the BMDP:2V statistical software. Analysis of variance results in Table 4.22 indicated that rotational speed significantly affected the derived yield stress, but this effect was only marginally significant (p=0.0407). Chapter 4. RESULTS AND DISCUSSION 70 4.5.3 Multiple Vane Method II Experimental data for vane fixtures, G, K and 0 were analyzed using the second method proposed by Nguyen and Boger (1985). These vanes had a diameter of 2.5 cm and ranged in height from 4.0 to 5.5 and 7.0 cm for fixtures G, K and 0 , respectively. By using a series of vane fixtures which have the same diameter but different heights, the shear stress distribution at either end of the vane fixture did not have to be considered. The yield stress was then estimated from the slope of the peak torque versus vane fixture height function using the following equation: o-y = 2slope/TrD2 (4.14) A linear relationship was found between the peak torque and vane fixture height (Figure 4.13) for each of the samples tested. This supports the validity of assumptions made in analyzing the vane fixture data by Method II. Yield stress values derived by this procedure are listed in Table 4.23. For graphical purposes, data from the duplicate measurements were pooled as well as the peak torque data obtained over the three rotational speeds used. A test for equality of lines showed there were no significant differences (p>0.05) between duplicates. The effect of start-up speed was analyzed in a two-way analysis of variance and showed no significant difference (p>0.05, Table 4.24). Yield values estimated for samples H M C and H2 were comparable among the three vane methods used. For sample HSS, Methods I and II gave comparable estimates for yield stress, but these values were not comparable with the single point measurements. For sample HI, the yield values were somewhat similar between the Single Vane Method and Method II, but were much lower when Method I was used. For HSS and HI, the m values would indicate that the Method I analysis and, therefore, the torque balance equation used to estimate yield stress for single point measurements for these samples Chapter 4. RESULTS AND DISCUSSION 71 Table 4.23: Yield stress estimates for chocolate samples at 40°C using Method II for analyzing vane fixture data. Sample Rotational Yield Stress Coefficient of Speed cjy, (Pa) Determination, r 2 (rpm) n=6 H M C 0.064 27.5 0.946 0.120 29.6 0.916 0.224 30.1 0.973 HSS 0.064 57.7 0.967 0.120 53.3 0.954 0.224 59.3 0.944 HI 0.064 50.0 0.911 0.120 60.3 0.927 0.224 62.2 0.932 H2 0.064 32.4 0.956 0.120 34.1 0.871 0.224 40.2 0.957 Figure 4.13: Plot of peak torque versus vane height (Method II) for estimating yield stress of chocolate samples at 40°C using vane fixtures G, K and 0. Chapter 4. RESULTS AND DISCUSSION 73 Table 4.24: Analysis of variance for yield stress estimates derived at various rotational speeds for chocolate samples at 40° C using multiple vane fixture data analyzed by Method II. Source of df Mean Square F-Ratio Variation Sample 3 636.89 54.80 ** Speed 2 37.392 3.22 ns Error 6 11.622 ** - significant at p<0.01 ns - not significant (p>0.05) would result in some error. HI and HSS had the highest yield stress values of the four test samples and, therefore, it is possible that larger vane fixtures would be more suitable for testing very thick samples. For example, vane E and F data, using the Method I analysis, appear to be responsible for the variability found in the yield values measured for HI. This sample proved difficult to characterize using both indirect and direct methods. However, a better estimate of the yield stress value may be made using a vane fixture rather than a coaxial cylinder fixture where slip effects can cause significant error. In cases where single point measurements are questionable, Method II could be used to verify the yield estimates where data are obtained using at least a minimum of three vane fixtures. In general, yield stress values obtained using the vane methods were 1.5 to 2.5 times higher than the Casson yield stress estimates. Higher yield values obtained using the vane methods as compared to yield values obtained using the Casson model equation have been reported by other researchers (Keentok, 1982; James et al., 1987; Tung et al., 1990). As well, other direct methods used to measure the yield stress of starch suspensions, butter Chapter 4. RESULTS AND DISCUSSION 74 and mayonnaise have resulted in higher comparative yield values than those determined by indirect methods (Elliot and Green, 1972; Elliot and Ganz, 1977; Navickis and Bagley, 1983). It has been suggested that the discrepancy in the yield values measured using both direct and indirect methods may reflect the way in which the yield point was measured. For example, measurements using the vane fixture are made under virtually static condi-tions. When model equations are used to estimate the yield stress, the equation is fitted to shear stress-shear rate flow data measured over a range of shear rates. Researchers have used the terms static yield stress and dynamic yield stress as a means of distinguish-ing between values measured under these two conditions (Cheng, 1978; Keentok, 1982; Cheng, 1986). Chapter 5 CONCLUSIONS This study investigated several methodologies that could be used to estimate the yield stress of molten chocolate. The conventional method used is the OICC method, based on obtaining steady flow viscometric data and extrapolating the fitted model to zero shear rate. The accuracy of this method was checked using flow data obtained with three different rotational instruments. In addition, four alternative methods were used to measure the yield stress value directly. The chocolate test samples included two types of commercial chocolate samples and two experimental chocolate samples; all were obtained from the Hershey Chocolate Company. The composition of the samples was determined by proximate and sucrose analyses. As well, the mean particle size and distribution of sizes contained in the samples was determined. A multivariate analysis of variance indicated a significant difference (p<0.01) in composition among samples tested for ash, moisture, protein, carbohydrate and sucrose content, and a significant difference (p<0.05) for fat content. The mean particle sizes were found to be 5.73, 6.27, 6.98 and 7.15 /xm for samples HSS, HI , H M C and H2, respectively. The largest population of particles was found to be in the size range of 4.0 to 5.0 fim. The yield stress of four chocolate samples at 40°C was measured indirectly using the Casson flow model and directly using the Stress Relaxation Method, the Single Vane Method and Multiple Vane Methods I and II. The Casson flow model was fitted to shear stress-shear rate data to obtain an estimate of the yield value by extrapolation. Flow data 75 Chapter 5. CONCLUSIONS 76 were obtained with the Brookfield HAT viscometer, the Brabender Rheotron viscometer and the Carri-Med Controlled Stress Rheometer. Mean Casson yield stress values for the four chocolate samples ranged from 9.38 to 15.7 Pa for H M C , from 19.8 to 29.3 Pa for HSS, from 9.59 to 30.4 Pa for HI and from 10.6 to 19.9 Pa for H2 as determined using the three instruments. Samples HI and HSS had the highest yield stress values as well as the highest concentration of small particles of the four chocolates tested. Coefficients of variation for yield values from flow data obtained from the three different instruments were approximately 20% for samples H M C , HSS, and H2 and 40% for sample HI. The Casson flow model fitted the flow data for chocolate samples H M C , HSS and H2 obtained from the Brookfield viscometer. However, a deviation from linearity was apparent when this model equation was fitted to the flow data for HI , and, thereby, some error in calculating the yield value resulted. Also, sample HI was very thick and it was possible that slippage took place within the annular gap, which would lead to a lower estimate of yield stress than was expected. Deviation from linearity below approximately 0.5 s - 1 was apparent when the Casson equation was fitted to the flow data obtained with both the Brabender and Carri-Med instruments. The Casson equation did not accurately describe the flow-properties of the molten chocolate samples over the shear rate range tested, therefore, it was difficult to estimate the exact yield point of the sample. Yield values obtained from recalculation over the linear data points were higher. Further uncertainty was contributed by the fact that yield and viscosity values determined from flow data obtained with the Brabender using two coaxial cylinder fixtures of different gap widths were significantly different (p<0.05). Also, there was a significant fixture by sample effect (p<0.05). Using the Carri-Med rheometer, viscosity estimated from consecutive flow runs were significantly different (p<0.05). In a second experiment, where samples HI and H2 were sheared over two different run times of 12 and 30 minutes, resulted in significantly Chapter 5. CONCLUSIONS 77 different yield values measured for sample HI , and a significant run by sample interaction (p<0.01). The observed variability in the Casson flow parameters over the three different instruments used lends some uncertainty as to the accuracy of this method. Alternative methods of measuring the yield stress of molten chocolate were investi-gated. Yield values measured using the Stress Relaxation Method were very low and were believed to be an artifact of the measuring fixture and instrument. Low yield values have been reported by other researchers when testing very thick fluids by this method. However, residual stress measurements could be used to study the structural recovery of materials that have undergone shear. The direct measurement of yield stress using vane fixtures was also investigated. A series of five vane fixtures of varying dimensions was used to measure peak torque val-ues on sudden start-up obtained with the Brabender viscometer. Using the Single Vane Method, single point measurements were made at three different rotational speeds. An analysis of variance indicated a significant difference (p<0.01) in yield values measured using speeds of 0.064, 0.120 and 0.224 rpm. The speed by sample interaction was also sig-nificant at the p<0.05 level. There was no significant difference in yield values measured using different vane fixtures. The speed effect was marginally significant (p<0.04) when the peak torque data were analyzed using Method I, but was not a significant factor in Method II. Method I appeared to give valid estimates of the yield values for chocolate samples H M C , HSS and H2, but not for sample HI . As well, the values for the constant, m, used in this analysis, were large for samples HSS and HI and, therefore, the assumption of a uniform shear stress distribution over the ends of the vane was not valid. It is recommended that Multiple Vane Method II be used instead of Method I because it is not necessary to make any assumptions as to the nature of the stress distribution over the ends of the vane. Method II required more time to calculate a yield value than did the Single Vane Chapter 5. CONCLUSIONS 78 Method, but considerably less time was required to estimate yield stress by these methods as compared to the conventional OICC method using the Casson flow model. As well, the use of vane fixtures offers several other advantages. Problems with sample slip were not apparent, the immersion of the vane into the sample is far less disruptive than when using cylindrical fixtures and the level of precision required when using narrow gap coaxial cylinder fixtures is not necessary with vane fixtures. The disadvantage of using vane fixtures was that more sample volume was required for testing. As well, a viscosity estimate cannot be obtained because, under steady shear conditions, the flow about the vane blades would be difficult to characterize. The vane methods appear to provide an accurate assessment of the yield value of molten chocolate. Although values are 1.5 to 2.5 times higher than the Casson yield stress values, this may be explained by the differences in which the yield point was measured. It has been suggested by other researchers that the terminology for the yield stress value be further clarified to include the terms, static yield stress and dynamic yield stress where yield is measured under static conditions or measured from steady shearing flow. Further investigation of the vane method is recommended. The speed effect evidenced with the Brabender viscometer may not be evident in other constant shear rotational instruments where the inertial effects of the fixture and torque measuring system may differ. Also, the speed effect would be eliminated if a controlled stress rheometer was used. Additional vane fixtures might also be used to best determine the types and sizes of fixtures most suitable for testing molten chocolate. 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Final Report. DSS File No. 01SG.97702-R-5-0679, prepared for De-fence Research Establishment Suffield, Ralston, A B . Van Wazer, J.R., Lyons J.W., Kim K . Y . and Colwell, R.E. 1963. Viscosity and Flow Measurement - A Laboratory Handbook of Rheology. John Wiley and Sons Inc., New York, NY. LITERATURE CITED 85 [87] Vocadlo, J.J. and Charles, M.E . 1971. Measurement of yield stress of fluid-like viscoplastic substances. Can. J . Chem. Eng. 49:576. [88] Wildemuth, C.R. and Williams, M.C. 1985. A new interpretation of viscosity and yield stress in dense slurries: coal and other irregular particles. Rheol. Acta. 24:75. [89] Yoshimura, A.S., Prud'homme, R.K. , Princen, H .M. and Kiss. A.D. 1987. A com-parison of techniques for measuring yield stresses. J . Rheol. 31(8):699. [90] Yoshimura, A. and Prud'homme, R.K. 1988. Wall slip corrections for couette and parallel disk viscometers. J . Rheol. 32(1 ):53. [91] Zangger, R. 1984. Rheometry of chocolate melts. Alimenta. 23(1):13. Appendix A LISTING OF EXPERIMENTAL FLOW DATA 86 Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.25: Shear stress data (Pa) for chocolate samples at 40°C obtained with the the Brookfield HAT viscometer using coaxial cylinder fixture SC4-27/13R for steady shear tests at ascending (asc) and descending (dsc) shear rate. Shear HMC HSS HI H2 Rate (s\"1) asc dsc asc dsc asc dsc asc dsc 0.340 33.0 28.5 46.9 0.850 49.2 42.6 60.5 1.70 67.0 59.8 74.0 3.40 96.3 89.4 95.6 6.80 146 144 132 17.0 43.8 36.0 35.0 28.2 27.2 57.1 70.8 66.0 36.7 35.7 71.8 99.6 94.8 46.9 45.6 93.6 138 133 63.3 61.3 130 94.5 89.1 164 163 Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.26: Shear stress data (Pa) for chocolate samples at 40°C obtained with the Brabender Rheotron viscometer using coaxial cylinder fixture Al and spring C for steady shear tests at ascending (asc) and descending (dsc) shear rate. Shear HMC HSS HI H2 Rate (s1) asc dsc asc dsc asc dsc asc dsc 0.191 28.9 23.0 39.9 34.7 37.1 36.7 25.4 22.3 0.358 36.4 30.8 50.8 46.6 44.3 43.8 34.3 31.9 0.669 43.2 37.7 58.8 55.5 56.6 55.8 39.0 35.8 1.30 50.8 48.6 67.7 65.5 75.9 74.2 47.1 44.0 2.54 69.0 67.7 82.7 78.5 97.6 96.1 58.6 54.9 5.00 103 101 106 102 135 133 77.4 72.5 10.0 175 170 157 152 198 194 113 106 25.0 305 287 243 235 321 303 194 180 24.2 286 266 231 225 308 286 178 167 40.3 492 451 369 361 488 449 306 285 75.8 787 744 607 594 742 720 490 479 Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.27: Shear stress data (Pa) for chocolate samples at 40°C obtained with the Brabender Rheotron viscometer using coaxial cylinder fixture A2 and spring C for steady shear tests at ascending (asc) and descending (dsc) shear rate. Shear HMC HSS HI H2 Rate (a\"1) asc dsc asc dsc asc dsc asc dsc 0.066 18.5 14.2 27.3 23.0 27.6 28.6 22.5 20.2 0.124 25.6 21.8 39.2 34.4 36.7 38.0 29.9 28.1 0.231 31.4 27.3 44.3 39.7 51.4 51.9 34.2 32.1 0.448 35.9 33.7 52.1 49.1 69.3 67.6 37.7 35.9 0.877 45.3 42.0 58.7 55.7 85.8 80.0 43.3 41.5 1.73 59.2 58.4 71.1 68.1 107 103 52.4 50.6 3.46 89.1 87.5 93.1 89.8 149 139 70.1 67.6 8.63 147 141 127 123 219 199 102 96.0 8.38 138 136 123 120 208 193 98.2 92.9 13.9 231 217 184 178 328 289 154 142 26.2 379 345 282 274 463 433 238 225 50.8 635 605 463 440 701 671 396 384 Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.28: Shear rate data (s1) obtained for the chocolate samples at 40°C using the Carri-Med rheometer and coaxial cylinder fixture 5222 for controlled stress tests at ascending (asc) and descending (dsc) shear stress. Shear HMC HSS HI H2 Stress (Pa) asc dsc asc dsc asc dsc asc dsc 1.926 3.852 0.0370 5.778 0.0409 7.704 0.0409 0.0672 9.630 0.0502 0.0916 11.55 0.0653 0.1098 13.48 0.0887 0.1287 15.40 0.0887 0.1506 17.33 0.1124 0.1669 19.26 0.1331 0.1862 21.18 0.1566 0.2089 23.11 0.1725 0.2386 25.03 0.1955 0.2652 26.96 0.2150 0.2983 28.89 0.2396 0.3332 30.81 0.2615 0.3741 32.74 0.2896 0.4214 34.66 0.3190 0.4748 36.59 0.3502 0.5228 38.52 0.3802 0.5796 40.44 0.4158 0.6593 42.37 0.4592 0.7322 44.29 0.5040 0.8163 46.22 0.5577 0.9003 48.15 0.6162 0.9894 50.07 0.6766 1.081 52.00 0.7539 1.181 53.92 0.8187 1.288 55.85 0.8945 1.379 57.78 0.9983 1.498 59.70 1.044 1.620 61.63 1.183 1.723 63.55 1.279 1.835 65.48 1.385 1.916 67.41 1.484 2.059 0.0292 0.0546 0.0464 0.0624 0.0276 0.0487 0.0766 0.0448 0.0660 0.0838 0.0600 0.0858 0.0950 0.0721 0.0782 0.1121 0.0835 0.0939 0.1272 0.0945 0.1062 0.1423 0.1092 0.1184 0.1587 0.1221 2.571 0.1811 0.1433 0.1494 0.2006 0.1550 0.1689 0.2259 0.1807 0.1930 0.2596 0.1943 0.2157 0.2991 0.2122 0.2362 0.3451 0.2307 0.2691 0.4027 0.2509 0.3005 0.4655 0.2739 0.3337 0.5423 0.2951 0.3771 0.6283 0.3120 0.4297 0.7317 0.3377 0.4858 0.8462 0.3584 0.5503 0.9554 0.3805 0.6242 1.089 0.3698 0.7021 1.217 0.4316 0.7852 1.346 0.4579 0.8967 1.516 0.4914 1.004 1.677 0.5196 1.116 1.825 0.5447 1.248 1.998 0.5749 1.377 2.166 0.5970 1.524 2.336 0.6230 0.0097 0.0341 0.0585 0.0390 0.0624 0.0609 0.0526 0.0646 0.0438 0.0819 0.0465 0.0890 0.1033 0.0746 0.1105 0.1009 2.133 0.1293 0.1186 0.0975 0.1456 0.1394 0.1075 0.1589 0.1599 0.1219 0.1618 0.1742 0.1431 0.1963 0.1907 0.1584 0.2154 0.2083 0.1840 0.2392 0.2307 0.1984 0.2678 0.2528 0.2203 0.2925 0.2756 0.2369 0.3233 0.2986 0.2554 0.3490 0.3185 0.2854 0.3809 0.3522 0.3125 0.4225 0.3744 0.3383 0.4608 0.3987 0.3622 0.5076 0.4211 0.3919 0.5557 0.4536 0.4239 0.6097 0.4846 0.4526 0.6659 0.5158 0.4797 0.7215 0.5430 0.5228 0.8044 0.5772 0.5574 0.8631 0.6070 0.6118 0.9262 0.5599 0.6600 1.021 0.6769 0.7056 1.091 0.7253 0.7595 1.173 0.7588 0.8192 1.252 0.7975 0.8865 1.347 continued.. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.28 continued. 91 Shear HMC HSS HI H2 Stress : (Pa) asc dsc asc dsc asc dsc asc dsc 69.33 1.590 2.193 71.26 1.694 2.303 73.18 1.795 2.426 75.11 1.918 2.562 77.04 2.030 2.682 78.96 2.126 2.612 80.89 2.224 2.909 82.81 2.339 3.031 84.74 2.475 3.165 86.67 2.576 3.297 88.59 2.677 3.409 90.52 2.795 3.507 92.44 2.887 3.638 94.37 3.004 3.763 96.30 3.103 3.902 98.22 3.208 4.022 100.1 3.311 4.141 102.0 3.418 4.285 104.0 3.531 4.412 105.9 3.601 4.512 107.8 3.764 4.640 109.7 3.873 4.785 111.7 4.003 4.926 113.6 4.067 5.029 115.5 4.222 4.965 117.4 4.336 5.281 119.4 4.459 5.434 121.3 4.576 5.549 123.2 4.697 5.691 125.1 4.837 5.848 127.1 4.945 5.945 129.0 5.074 6.074 130.9 5.196 6.215 132.8 5.292 6.333 134.8 5.440 6.483 136.7 5.527 6.595 138.6 5.675 6.710 1.659 2.497 0.6649 1.820 2.684 0.4686 1.975 2.875 0.3714 2.129 3.041 0.7608 2.293 3.262 0.8229 2.443 3.424 0.8609 2.597 3.600 0.8943 2.778 3.825 0.9386 2.948 3.997 0.9984 3.085 4.202 1.046 3.228 4.398 1.092 3.378 4.588 1.143 3.515 4.786 1.206 3.669 4.983 1.256 3.819 5.225 1.325 3.987 5.410 1.354 4.176 5.634 1.454 4.328 5.851 1.530 4.514 6.061 1.589 4.677 6.273 1.651 4.840 6.481 1.732 5.027 6.681 1.827 5.201 6.921 1.901 5.373 7.112 1.976 5.563 7.354 2.081 5.735 7.586 2.153 5.917 7.796 2.245 6.101 8.017 2.337 6.273 8.218 2.417 6.475 8.450 2.478 6.649 8.660 2.587 6.853 8.924 2.686 7.021 9.124 2.766 7.270 9.393 2.751 7.449 9.603 2.969 7.625 9.800 3.066 7.829 10.02 3.135 0.8460 0.9587 1.450 0.9025 1.038 1.539 0.9476 1.110 1.631 0.9971 1.203 1.731 1.057 1.276 1.829 1.006 1.373 1.937 0.9177 1.465 2.023 1.223 1.543 1.463 1.286 1.633 2.244 1.358 1.741 2.078 1.426 1.838 1.894 1.495 1.926 1.873 1.579 2.026 2.858 1.634 2.135 2.976 1.357 2.236 3.111 1.808 2.339 3.228 1.880 2.455 3.350 1.968 2.554 3.503 2.047 2.647 3.593 1.775 2.758 3.727 2.221 2.868 3.875 2.370 2.981 4.004 2.411 3.063 4.123 2.490 3.193 4.265 2.574 3.310 4.389 2.670 3.400 4.463 2.761 3.532 4.633 2.835 3.662 4.808 2.957 3.778 4.922 3.051 3.912 5.079 3.146 4.023 5.198 3.243 4.139 5.297 3.352 4.292 5.457 3.449 4.393 5.579 3.030 4.529 5.742 3.662 4.649 5.872 3.807 4.751 5.989 continued.. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.28 continued. 92 Shear HMC HSS HI H2 Stress (Pa) asc dsc asc dsc asc dsc asc dsc 140.5 5.820 6.865 142.5 5.925 7.013 144.4 6.041 6.573 146.3 6.197 7.266 148.3 6.292 7.413 150.2 6.401 7.535 152.1 6.533 7.652 154.0 6.632 7.672 156.0 6.749 7.916 157.9 6.800 7.997 159.8 6.966 8.174 161.7 7.106 8.327 163.7 7.226 8.356 165.6 7.376 8.607 167.5 7.456 8.077 169.4 7.600 8.872 171.4 7.692 8.948 173.3 7.862 9.151 175.2 7.930 9.226 177.1 8.013 9.346 179.1 8.172 9.531 181.0 8.284 9.601 182.9 8.467 9.779 184.8 8.535 9.916 186.8 8.610 9.949 188.7 8.816 10.16 190.6 8.989 10.34 192.6 9.094 10.47 194.5 9.176 10.56 196.4 9.369 10.77 198.3 9.443 10.83 200.3 9.543 11.00 202.2 9.745 11.14 204.1 9.851 11.26 206.0 9.955 11.38 208.0 10.15 11.52 209.9 10.25 11.46 8.049 10.27 3.255 8.230 10.47 3.357 8.401 10.69 3.415 8.657 10.98 3.533 8.850 11.21 3.634 9.063 11.43 3.700 9.245 11.67 3.788 9.434 11.91 3.807 9.626 12.13 3.968 9.795 12.26 4.059 10.09 12.58 4.203 10.36 12.90 4.291 10.50 13.04 4.435 10.78 13.31 4.603 10.92 13.50 3.912 11.22 13.80 4.916 11.36 14.02 5.000 11.63 14.31 5.157 11.75 14.46 5.242 11.90 14.57 5.302 12.18 14.95 5.459 12.30 15.10 5.518 12.64 15.44 5.626 12.81 15.57 5.115 13.10 15.90 5.801 13.29 16.09 5.944 13.60 16.47 6.089 13.76 16.60 6.123 13.91 16.76 5.715 14.19 17.16 6.325 14.44 17.31 6.407 14.62 17.50 6.320 14.95 17.84 6.633 15.13 18.00 6.715 15.27 18.19 5.674 15.63 18.55 6.928 15.83 18.77 6.995 3.870 4.903 6.002 3.965 5.052 6.300 4.045 5.158 6.439 4.183 5.299 6.591 4.263 5.448 6.726 4.420 5.572 6.866 4.500 5.689 7.008 4.574 5.827 7.098 4.690 5.943 6.986 4.371 6.045 7.354 4.913 6.191 7.543 4.962 6.303 7.639 5.111 6.431 7.819 4.218 6.562 7.966 5.346 6.705 8.120 5.454 6.848 7.457 5.578 6.527 8.420 5.718 7.100 8.604 5.793 7.216 8.693 5.810 7.294 8.784 6.012 7.445 8.951 6.134 7.554 8.362 6.252 7.721 9.305 6.306 7.782 9.467 6.409 7.890 8.616 6.041 8.066 9.698 6.096 8.249 9.867 6.852 8.364 8.918 6.881 8.440 9.034 6.794 8.388 9.227 7.156 8.753 9.310 7.169 8.847 9.385 7.417 9.026 8.572 7.505 9.126 9.719 7.575 9.232 9.774 7.014 9.413 10.02 7.841 9.572 10.12 continued. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.28 continued. 93 Shear HMC HSS HI H2 Stress (Pa) asc dsc asc dsc asc dsc asc dsc 211.8 10.35 11.76 213.7 10.54 11.94 215.7 10.62 12.05 217.6 10.78 12.19 219.5 10.92 12.42 221.4 11.07 12.49 223.4 11.17 12.64 225.3 11.29 12.78 227.2 11.47 12.86 229.1 11.61 13.01 231.1 11.63 13.13 233.0 11.83 12.44 234.9 11.99 13.45 236.8 11.96 13.54 238.8 12.34 13.78 240.7 12.42 13.87 242.6 11.92 13.96 244.6 12.72 14.12 246.5 12.77 14.09 248.4 12.96 14.41 250.3 13.12 14.56 252.3 13.37 14.54 254.2 13.34 14.75 256.1 13.46 14.85 258.0 13.66 15.16 260.0 13.81 15.24 261.9 13.87 15.32 263.8 14.08 15.49 265.7 14.29 15.54 267.7 14.15 15.54 269.6 14.56 15.91 271.5 14.64 16.00 273.4 14.77 16.15 275.4 14.78 16.26 277.3 14.94 16.38 279.2 15.23 16.46 281.1 15.12 16.72 16.08 19.03 7.083 16.36 19.27 7.153 16.55 19.48 7.355 16.64 19.68 7.406 17.06 20.02 7.574 17.22 20.22 7.685 17.47 20.40 7.775 17.81 20.77 7.973 18.02 20.98 8.065 18.21 21.16 8.156 18.43 21.36 8.284 18.63 21.53 8.303 18.97 21.93 8.618 19.18 22.10 8.669 19.59 22.49 8.750 19.82 22.71 8.929 20.01 22.86 9.076 20.21 23.12 9.208 20.42 23.27 9.309 20.83 23.70 9.442 21.06 23.90 9.582 21.27 24.05 9.708 21.43 24.30 9.768 21.71 24.48 9.853 22.10 24.91 10.06 22.33 25.08 10.20 22.56 25.28 10.28 22.77 25.49 10.38 23.22 25.89 10.59 23.43 26.11 10.73 23.66 26.32 10.81 23.90 26.52 10.68 24.15 26.74 10.97 24.35 26.92 11.20 24.61 27.15 11.28 25.03 27.57 11.47 25.26 27.76 11.60 6.842 9.637 10.18 8.051 9.760 10.28 8.213 9.945 10.52 8.251 10.06 10.64 8.467 10.27 9.989 8.490 10.42 10.96 8.706 10.48 11.03 8.864 10.73 11.26 8.940 10.84 11.30 9.029 10.96 11.44 7.130 11.05 11.55 9.279 11.16 11.69 9.374 11.44 11.86 9.506 11.52 11.93 9.582 11.65 11.97 9.854 11.79 12.28 9.912 11.95 12.41 10.02 12.12 12.52 10.10 12.17 12.67 9.463 12.45 12.92 10.44 12.55 13.00 10.52 12.29 13.08 10.65 12.82 13.25 10.73 12.94 11.86 10.94 13.16 13.58 11.05 13.26 13.67 9.364 13.42 13.66 11.22 13.52 13.84 11.41 13.72 14.08 11.36 13.86 13.86 11.73 14.05 14.33 11.82 14.15 14.48 11.90 14.37 14.59 11.78 14.40 14.67 12.13 14.62 14.85 10.62 14.83 15.05 12.40 14.89 15.19 continued.. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.28 continued. 94 Shear HMC HSS HI H2 Stress (Pa) asc dsc asc dsc asc dsc asc dsc 283.1 15.52 16.84 285.0 15.60 16.99 286.9 15.77 17.05 288.9 16.04 17.33 290.8 15.80 17.45 292.7 16.29 17.57 294.6 16.37 17.70 296.6 16.56 17.79 298.5 16.69 17.93 300.4 16.80 18.02 302.3 16.23 18.14 304.3 16.89 18.23 306.2 17.20 18.40 308.1 16.87 18.35 310.0 17.46 18.63 312.0 17.65 18.75 313.9 17.93 19.04 315.8 18.03 18.94 317.7 18.16 19.28 319.7 18.31 19.33 321.6 18.44 19.49 323.5 18.70 19.71 325.4 18.90 19.88 327.4 19.00 20.02 329.3 19.13 20.14 331.2 19.20 20.23 333.1 19.37 20.38 335.1 19.25 20.49 337.0 19.76 18.53 338.9 19.90 21.88 340.9 20.01 20.62 342.8 20.04 21.00 344.7 20.33 20.64 346.6 19.94 21.29 348.6 20.68 21.37 350.5 20.33 21.45 352.4 20.92 21.56 25.53 28.00 11.62 25.68 28.19 11.80 26.02 28.40 11.99 26.42 28.86 12.00 26.65 29.04 12.06 26.90 29.24 11.59 27.07 29.45 12.50 27.38 29.66 12.61 27.62 29.91 12.74 27.80 30.16 12.85 28.08 30.32 12.93 28.36 30.49 13.10 28.58 30.72 13.21 28.82 31.00 11.56 29.04 31.17 13.39 29.47 31.61 13.62 29.81 31.84 11.95 30.04 32.06 13.94 30.31 32.26 14.06 30.47 32.41 14.17 30.77 32.64 14.28 31.29 33.10 14.46 31.56 33.37 14.60 31.80 33.59 14.77 32.03 33.74 15.01 32.16 33.93 15.13 32.50 34.17 15.21 32.86 34.35 15.39 33.19 34.63 15.43 33.43 34.88 15.62 33.62 35.11 15.79 33.81 35.28 15.89 34.05 35.44 16.15 34.44 35.64 16.13 34.67 35.95 16.27 35.00 36.17 15.48 35.21 36.38 16.58 12.57 15.06 15.32 12.71 15.18 15.44 12.78 15.30 15.51 12.93 15.48 15.72 11.28 15.69 15.86 13.25 15.86 15.99 13.34 16.04 16.08 13.40 16.23 16.28 13.62 16.11 16.36 13.59 16.47 16.52 13.44 16.59 16.57 13.93 16.72 16.69 14.00 16.93 16.83 14.21 17.07 16.92 14.30 17.16 17.08 14.53 17.41 17.26 14.68 17.56 17.37 14.73 17.71 17.43 14.91 17.93 17.69 15.00 19.24 17.78 15.06 18.21 17.94 15.13 18.36 18.09 15.39 18.54 18.14 15.61 18.80 18.43 15.67 18.90 18.48 15.80 19.01 17.34 15.91 19.21 18.75 16.05 19.43 18.91 16.19 18.86 19.00 16.36 19.78 19.19 16.35 19.92 19.30 16.60 20.15 19.43 16.62 20.22 19.46 16.71 19.64 19.08 16.92 20.57 19.61 16.97 20.73 19.81 17.21 20.87 19.97 continued. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.28 continued. Shear HMC HSS HI H2 Stress s (Pa) asc dsc asc dsc asc dsc asc dsc 354.3 21.21 21.74 35.65 36.79 16.74 16.34 21.14 20.09 356.3 21.39 21.96 35.93 36.94 16.94 17.38 21.30 20.30 358.2 21.54 21.58 36.24 37.15 17.14 17.71 21.58 20.41 360.1 21.70 22.25 36.57 37.37 17.37 17.82 21.70 20.50 362.0 21.85 22.31 36.84 37.60 17.24 17.83 21.88 20.69 364.0 21.75 22.44 37.15 37.81 17.51 17.94 22.07 20.84 365.9 21.49 22.59 37.48 38.04 17.69 18.03 22.19 20.94 367.8 22.26 22.20 37.67 38.27 17.97 18.22 22.41 21.07 369.7 22.51 22.85 38.00 38.52 18.02 16.28 22.56 21.20 371.7 22.64 22.94 38.27 38.70 18.20 18.47 22.71 21.34 373.6 22.47 23.08 38.51 38.85 18.28 18.48 22.88 21.40 375.5 22.98 23.18 38.74 39.04 16.67 18.69 23.02 21.57 377.4 23.08 23.00 38.99 39.25 18.64 18.71 23.24 21.64 379.4 23.29 23.47 39.22 39.53 18.80 18.88 23.46 21.71 381.3 23.40 23.59 39.58 39.70 18.98 19.10 23.61 21.85 383.2 23.61 23.58 39.84 39.90 19.11 19.24 23.78 21.90 385.2 23.77 23.81 40.07 40.12 19.28 19.25 24.00 22.13 Appendix A. LISTING OF EXPERIMENTAL FLOW DATA 96 Table A.29: Shear rate data (s1) for chocolate sample HI at 40°C obtained with the Carri-Med rheometer and coaxial cylinder fixture 5222 for controlled stress tests at ascending (asc) and descending (dsc) shear stress for 12 and 30 minute run times. 12 min run 30 min run Shear Shear rate Shear Shear rate Stress ' (s-1) Stress IV1) (Pa) asc dsc (Pa) asc dsc 12.11 0.0673 5.813 0.0166 14.53 0.0683 8.720 0.0322 16.95 0.0904 10.17 0.0161 0.0335 19.38 0.1096 11.63 0.0312 0.0452 21.80 0.0507 0.1259 13.08 0.0307 0.0537 24.22 0.0493 0.1513 14.53 0.0290 0.0641 26.64 0.0644 0.1740 15.98 0.0468 0.0777 29.06 0.1034 0.1997 17.44 0.0426 0.0917 31.48 0.0937 0.2267 18.89 0.0514 0.1057 33.91 0.1165 0.2531 20.34 0.0615 0.1204 36.33 0.1412 0.2804 21.80 0.0748 0.1353 38.75 0.1601 0.3149 23.25 0.0862 0.1493 41.17 0.1805 0.3458 24.70 0.0992 0.1646 43.59 0.2046 0.3757 26.16 0.1106 0.1783 46.02 0.2261 0.4089 27.61 0.1220 0.1939 48.44 0.2472 0.4473 29.06 0.1350 0.2082 50.86 0.2742 0.4840 30.52 0.1513 0.2277 53.28 0.3009 0.5218 31.97 0.1653 0.2375 55.70 0.3243 0.5628 33.42 0.1802 0.2521 58.13 0.3523 0.6008 34.88 0.1958 0.2658 60.55 0.3822 0.6434 36.33 0.2111 0.2807 62.97 0.4147 0.6897 37.78 0.2297 0.2941 65.39 0.4473 0.7326 39.24 0.2437 0.3087 67.81 0.4798 0.7837 40.69 0.2583 0.3240 70.24 0.5065 0.8373 42.14 0.2723 0.3370 72.66 0.5367 0.8881 43.59 0.2853 0.3520 75.08 0.5696 0.9496 45.05 0.2986 0.3679 77.50 0.6005 1.011 46.50 0.3155 0.3832 79.92 0.6386 1.073 47.95 0.3295 0.3972 82.35 0.6698 1.145 49.41 0.3412 0.4229 84.77 0.7040 1.218 50.86 0.3556 0.4392 continued. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA 97 Table A.29 continued. 12 min run 30 min run Shear Shear rate Shear Shear rate Stress (s-1) Stress (s-1) (Pa) asc dsc (Pa) asc dsc 87.19 0.7446 1.299 52.31 0.3725 0.4613 89.61 0.7879 1.384 53.77 0.3865 0.4779 92.03 0.8393 1.464 55.22 0.4017 0.4951 94.45 0.8917 1.565 56.67 0.4203 0.5127 96.88 0.9362 1.651 58.13 0.4352 0.5306 99.30 0.9935 1.748 59.58 0.4512 0.5442 101.7 1.048 1.841 61.03 0.4678 0.5673 104.1 1.113 1.947 62.49 0.4821 0.5829 106.6 1.177 2.049 63.94 0.5000 0.5992 109.0 1.251 2.157 65.39 0.5156 0.6155 111.4 1.335 2.257 66.84 0.5293 0.6421 113.8 1.414 2.374 68.30 0.5426 0.6581 116.3 1.490 2.491 69.75 0.5592 0.6861 118.7 1.592 2.602 71.20 0.5794 0.7241 121.1 1.693 2.724 72.66 0.6002 0.7687 123.5 1.794 2.842 74.11 0.6187 0.7999 125.9 1.907 2.961 75.56 0.6392 0.8354 128.4 2.020 3.086 77.02 0.6578 0.8744 130.8 2.129 3.221 78.47 0.6795 0.9089 133.2 2.254 3.344 79.92 0.7036 0.9447 135.6 2.383 3.465 81.38 0.7225 0.9824 138.0 2.501 3.599 82.83 0.7443 1.016 140.5 2.612 3.719 84.28 0.7703 1.058 142.9 2.739 3.872 85.74 0.7970 1.096 145.3 2.865 4.003 87.19 0.8243 1.139 147.7 3.009 4.132 88.64 0.8487 1.181 150.2 3.155 4.270 90.10 0.8777 1.225 152.6 3.285 4.400 91.55 0.9027 1.270 155.0 3.407 4.527 93.00 0.9323 1.316 157.4 3.550 4.665 94.45 0.9635 1.365 159.8 3.681 4.809 95.91 0.9941 1.419 162.3 3.807 5.027 97.36 1.032 1.469 164.7 3.937 5.104 98.81 1.068 1.520 167.1 4.068 5.268 100.3 1.107 1.576 continued. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.29 continued. 98 12 min run 30 min run Shear Shear rate Shear Shear rate Stress (s\"1) Stress (s-1) Q?a) asc dsc 0?a) asc dsc 169.5 172.0 174.4 176.8 179.2 181.6 184.1 186.5 188.9 191.3 193.8 196.2 198.6 201.0 203.4 205.9 208.3 210.7 213.1 215.6 218.0 220.4 222.8 225.2 227.7 230.1 232.5 234.9 237.3 239.8 242.2 244.6 247.0 249.5 4.223 4.362 4.478 4.584 4.726 4.869 5.059 5.297 5.539 5.638 5.683 5.727 5.819 5.992 6.123 6.223 6.304 6.408 6.533 6.698 6.804 6.947 7.068 7.255 7.397 7.558 7.698 7.785 7.962 8.114 8.244 8.348 8.530 8.685 5.390 5.517 5.684 5.806 5.970 6.141 6.278 6.384 6.560 6.730 6.836 7.029 7.193 7.335 7.476 7.629 7.758 7.948 8.100 8.249 8.386 8.596 8.724 8.888 9.089 9.172 9.340 9.483 9.663 9.810 10.00 10.16 10.29 10.42 101.7 103.2 104.6 106.1 107.5 109.0 110.4 111.9 113.3 114.8 116.3 117.7 119.2 120.6 122.1 123.5 125.0 126.4 127.9 129.3 130.8 132.2 133.7 135.1 136.6 138.0 139.5 141.0 142.4 143.9 145.3 146.8 148.2 149.7 1.144 1.189 1.240 1.282 1.322 1.374 1.423 1.478 1.524 1.597 1.659 1.721 1.779 1.834 1.897 1.959 2.022 2.086 2.139 2.202 2.269 2.343 2.415 2.469 2.536 2.595 2.654 2.702 2.753 2.816 2.892 2.961 3.028 3.093 1.623 1.673 1.723 1.782 1.838 1.903 1.956 2.021 2.084 2.149 2.213 2.276 2.340 2.407 2.471 2.540 2.595 2.663 2.732 2.793 2.871 2.929 3.002 3.067 3.139 3.205 3.269 3.339 3.402 3.475 3.535 3.623 3.674 3.766 continued. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.29 continued. 99 12 min run 30 min run Shear Shear rate Shear Shear rate Stress Stress (s-1) (Pa) asc dsc (Pa) asc dsc 251.9 8.761 10.62 151.1 3.127 3.828 254.3 8.918 10.82 152.6 3.184 3.881 256.7 9.126 10.97 154.0 3.258 3.960 259.1 9.266 11.14 155.5 3.329 4.024 261.6 9.385 11.29 156.9 3.424 4.088 264.0 9.543 11.44 158.4 3.468 4.144 266.4 9.635 11.66 159.8 3.529 4.210 268.8 9.800 11.77 161.3 3.603 4.271 271.3 9.942 11.99 162.8 3.664 4.382 273.7 10.04 12.16 164.2 3.726 4.440 276.1 10.27 12.30 165.7 3.819 4.522 278.5 10.42 • 12.46 167.1 3.884 4.595 280.9 10.55 12.66 168.6 3.947 4.651 283.4 10.74 12.81 170.0 4.007 4.715 285.8 10.86 13.00 171.5 4.050 4.798 288.2 11.03 13.16 172.9 4.103 4.892 290.6 11.23 13.36 174.4 4.164 4.973 293.1 11.39 13.47 175.8 4.251 5.041 295.5 11.55 13.67 177.3 4.344 5.080 297.9 11.67 13.83 178.7 4.412 5.164 300.3 11.87 13.98 180.2 4.455 5.236 302.7 12.02 14.20 181.6 4.533 5.298 305.2 12.18 14.37 183.1 4.601 5.364 307.6 12.35 14.45 184.6 4.685 5.434 310.0 12.52 14.65 186.0 4.742 5.492 312.4 12.69 14.86 187.5 4.805 5.570 314.8 12.80 14.95 188.9 4.865 5.624 317.3 13.03 15.20 190.4 4.937 5.726 319.7 13.16 15.38 191.8 4.999 5.819 322.1 13.29 15.52 193.3 5.076 5.837 324.5 13.52 15.74 194.7 5.173 5.908 327.0 13.60 15.85 196.2 5.186 6.031 329.4 13.72 16.07 197.6 5.253 6.121 331.8 13.85 16.20 199.1 5.365 6.116 continued.. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.29 continued. 100 12 min run 30 min run Shear Shear rate Shear Shear rate Stress (s1) Stress (s\"1) (Pa) asc dsc (Pa) asc dsc 334.2 336.6 339.1 341.5 343.9 346.3 348.8 351.2 353.6 356.0 358.4 360.9 363.3 365.7 368.1 370.6 373.0 375.4 377.8 380.2 382.7 385.1 387.5 389.9 392.4 394.8 397.2 399.6 402.0 404.5 406.9 409.3 411.7 414.1 14.15 14.26 14.37 14.72 14.76 15.01 15.21 15.36 15.57 15.82 16.03 16.73 16.35 16.61 16.78 17.02 17.18 17.38 17.52 17.76 17.96 18.09 18.39 18.49 18.73 18.96 19.22 19.34 19.55 19.82 19.95 20.21 20.42 20.62 16.38 16.63 16.75 16.93 17.07 17.24 17.35 17.54 17.81 17.89 18.13 18.26 18.41 18.63 18.73 18.87 18.98 19.21 19.33 19.52 19.62 19.80 19.99 20.06 20.38 20.40 20.61 20.89 21.06 21.22 21.55 21.66 21.89 21.90 200.5 202.0 203.4 204.9 206.3 207.8 209.3 210.7 212.2 213.6 215.1 216.5 218.0 219.4 220.9 222.3 223.8 225.2 226.7 228.1 229.6 231.1 232.5 234.0 235.4 236.9 238.3 239.8 241.2 242.7 244.1 245.6 247.0 248.5 5.466 5.458 5.581 5.661 5.756 5.770 5.905 6.002 6.033 6.138 6.250 6.240 6.346 6.461 6.438 6.572 6.663 6.690 6.814 6.930 6.965 7.092 7.148 7.246 7.324 7.433 7.507 7.589 7.657 7.736 7.836 7.926 8.011 8.125 6.254 6.312 6.422 6.428 6.531 6.615 6.652 6.738 6.844 6.825 6.972 7.085 7.072 7.197 7.284 7.301 7.409 7.501 7.541 7.635 7.673 7.755 7.838 7.925 8.013 8.089 8.189 8.264 8.355 8.428 8.472 8.591 8.601 8.722 continued. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.29 continued. 101 12 min run 30 min run Shear Shear rate Shear Shear rate Stress (s-1) Stress (s-1) (Pa) asc dsc (Pa) asc dsc 416.6 20.78 22.16 249.9 8.163 8.758 419.0 20.89 22.19 251.4 8.317 8.839 421.4 21.21 22.30 252.8 5.561 8.908 423.8 21.33 22.25 254.3 8.452 9.030 426.3 21.45 22.39 255.8 8.540 9.117 428.7 21.65 22.58 257.2 8.653 9.195 431.1 21.83 22.95 258.7 8.761 9.304 433.5 22.01 23.21 260.1 8.834 9.375 435.9 22.12 23.24 261.6 8.921 9.380 438.4 22.33 23.41 263.0 9.010 9.503 440.8 22.54 23.64 264.5 9.023 9.507 443.2 22.71 23.80 265.9 9.170 9.649 445.6 22.92 23.83 267.4 9.205 9.704 448.1 23.07 23.85 268.8 9.348 9.819 450.5 23.15 23.92 270.3 9.437 9.909 452.9 23.21 24.05 271.7 9.540 9.979 455.3 23.49 24.27 273.2 9.663 10.08 457.7 23.62 24.39 274.6 9.787 10.18 460.2 23.86 24.45 276.1 9.881 10.26 462.6 24.05 24.74 277.6 9.981 10.25 465.0 24.01 24.90 279.0 10.07 10.34 467.4 24.36 24.88 280.5 10.12 10.42 469.9 24.36 25.11 281.9 10.20 10.52 472.3 24.76 25.61 283.4 10.29 10.62 474.7 24.80 25.62 284.8 10.40 10.70 477.1 25.12 25.59 286.3 10.54 10.79 479.5 25.30 25.53 287.7 10.66 10.81 482.0 25.56 25.76 289.2 10.73 10.89 484.4 25.87 25.89 290.6 10.76 10.89 Appendix A. LISTING OF EXPERIMENTAL FLOW DATA 102 Table A.30: Shear rate data (s1) for chocolate sample H2 at 40°C obtained with the Carri-Med rheometer and coaxial cylinder fixture 5222 for controlled stress tests at ascending (asc) and descending (dsc) shear stress for 12 and 30 minute run times. 12 min run 30 min run Shear Shear rate Shear Shear rate Stress (s1) Stress (s1) (Pa) asc dsc (Pa) asc dsc 2.880 0.0196 2.880 0.0255 3.840 0.0235 4.320 0.2650 5.760 0.0304 5.760 0.0338 6.720 0.0647 7.200 0.0147 0.0399 7.680 0.0368 8.640 0.0294 0.0477 8.640 0.0376 0.0441 10.08 0.0284 0.0529 9.600 0.0405 11.52 0.0412 0.0611 10.56 0.0524 0.0549 12.96 0.0490 0.0722 11.52 0.0510 0.0598 14.40 0.0598 0.0885 12.48 0.0583 0.0666 15.84 0.0679 0.1153 13.44 0.0666 0.0745 17.28 0.0846 0.1669 14.40 0.0728 0.0848 18.72 0.1049 0.2434 15.36 0.0853 0.1019 20.16 0.1287 0.3489 16.32 0.1034 0.1241 21.60 0.1650 0.4711 17.28 0.1169 0.1509 23.04 0.2163 0.6233 18.24 0.1294 0.1797 24.48 0.2822 0.7863 19.20 0.1548 0.2296 25.92 0.3747 0.9692 20.16 0.1839 0.2858 27.36 0.4893 1.156 21.12 0.2127 0.3593 28.80 0.6324 1.348 22.08 0.2502 0.4384 30.24 0.7928 1.554 23.04 0.2960 0.5250 31.68 0.9607 1.768 24.00 0.3479 0.6256 33.12 1.141 1.981 24.96 0.4096 0.7249 34.56 1.324 2.205 25.92 0.4880 0.8314 36.00 1.513 2.440 26.88 0.5713 0.9447 37.44 1.705 2.647 27.84 0.6657 1.061 38.88 1.904 2.907 28.80 0.7742 1.174 40.32 2.088 3.162 29.76 0.9104 1.302 41.76 2.305 3.383 30.72 1.003 1.431 43.20 2.532 3.663 31.68 1.133 1.561 44.64 2.718 3.919 32.64 1.265 1.695 46.08 2.952 4.146 continued. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.30 continued. 103 12 min run 30 min run Shear Shear rate Shear Shear rate Stress (s1) Stress (S\"1) (Pa) asc dsc (Pa) asc dsc 33.60 1.403 1.831 47.52 3.176 4.392 34.56 1.551 1.969 48.96 3.379 4.692 35.52 1.691 2.103 50.40 3.585 4.923 36.48 1.820 2.254 51.84 3.836 5.204 37.44 1.946 2.382 53.28 4.047 5.478 38.40 2.073 2.534 54.72 4.294 5.762 39.36 2.197 2.695 56.16 4.524 6.003 40.32 2.331 2.843 57.60 4.763 6.285 41.28 2.472 3.011 59.04 4.992 6.588 42.24 2.625 3.144 60.48 5.223 6.836 43.20 2.786 3.302 61.92 5.490 7.095 44.16 2.912 3.458 63.36 5.705 7.400 45.12 3.067 3.623 64.80 5.934 7.727 46.08 3.227 3.768 66.24 6.230 7.989 47.04 3.386 3.933 67.68 6.483 8.289 48.00 3.523 4.086 69.12 6.726 8.537 48.96 3.659 4.249 70.56 6.980 8.859 49.92 3.790 4.436 72.00 7.228 9.149 50.88 3.922 4.571 73.44 7.492 9.422 51.84 4.079 4.726 74.88 7.736 9.705 52.80 4.199 4.911 76.32 8.010 9.996 53.76 4.333 5.079 77.76 8.245 10.31 54.72 4.511 5.237 79.20 8.518 10.57 55.68 4.676 5.426 80.64 8.780 10.87 56.64 4.817 5.587 82.08 9.018 11.13 57.60 5.010 5.776 83.52 9.275 11.42 58.56 5.160 5.927 84.96 9.559 11.73 59.52 5.349 6.085 86.40 9.795 12.00 60.48 5.503 6.291 87.84 10.05 12.34 61.44 5.654 6.458 89.28 10.31 12.63 62.40 5.848 6.611 90.72 10.63 12.93 63.36 5.990 6.819 92.16 10.88 13.21 64.32 6.118 6.963 93.60 11.16 13.52 65.28 6.306 7.153 95.04 11.40 13.83 continued. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA 104 Table A.30 continued. 12 min run 30 min run Shear Shear rate Shear Shear rate Stress (V1) Stress (s-1) (Pa) asc dsc (Pa) asc dsc 66.24 6.425 7.325 96.48 11.69 14.13 67.20 6.594 7.511 97.92 11.97 14.40 68.16 6.764 7.684 99.36 12.26 .14.73 69.12 6.943 7.875 100.8 12.52 '15.02 70.08 7.110 8.016 102.2 12.80 15.26 71.04 7.277 8.211 103.7 13.05 15.61 72.00 7.408 8.393 105.1 13.29 15.89 72.96 7.550 8.559 106.6 13.60 16.21 73.92 7.719 8.743 108.0 13.86 16.55 74.88 7.912 8.934 109.4 14.15 16.81 75.84 8.075 9.111 110.9 14.46 17.14 76.80 8.253 9.331 112.3 14.71 17.42 77.76 8.402 9.454 113.8 15.03 17.76 78.72 8.597 9.637 115.2 15.31 18.05 79.68 8.745 9.807 116.6 15.59 18.33 80.64 8.924 9.981 118.1 15.88 18.66 81.60 9.057 10.20 119.5 16.15 18.98 82.56 9.236 10.36 121.0 16.46 19.30 83.52 9.424 10.52 122.4 16.72 19.59 84.48 9.616 10.73 123.8 17.02 19.86 85.44 9.758 10.89 125.3 17.35 20.18 86.40 9.931 11.07 126.7 17.64 20.55 87.36 10.11 11.27 128.2 17.87 20.78 88.32 10.28 11.47 129.6 18.19 21.13 89.28 10.44 11.64 131.0 18.46 21.42 90.24 10.65 11.83 132.5 18.79 21.76 91.20 10.84 11.97 133.9 19.05 22.03 92.16 11.00 12.16 135.4 19.39 22.37 93.12 11.15 12.36 136.8 19.64 22.66 94.08 11.35 12.56 138.2 19.95 22.98 95.04 11.52 12.69 139.7 20.25 23.24 96.00 11.71 12.93 141.1 20.55 23.64 96.96 11.86 13.09 142.6 20.81 23.86 97.92 12.05 13.27 144.0 21.14 24.16 98.88 12.25 13.49 145.4 21.41 24.52 continued. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA 105 Table A.30 continued. 12 min run 30 min run Shear Shear rate Shear Shear rate Stress (s\"1) Stress (s-1) (Pa) asc dsc (Pa) asc dsc 99.84 12.40 13.63 146.9 21.69 24.81 100.8 12.58 13.85 148.3 22.05 25.16 101.8 12.79 14.04 149.8 22.31 25.42 102.7 12.95 14.19 151.2 22.65 25.73 103.7 13.16 14.43 152.6 22.94 26.06 104.6 13.29 14.58 154.1 23.20 26.33 105.6 13.55 14.77 155.5 23.56 26.53 106.6 13.69 14.92 157.0 23.83 26.91 107.5 13.84 15.15 158.4 24.02 27.19 108.5 14.05 15.30 159.8 24.37 27.52 109.4 14.24 15.52 161.3 24.66 27.89 110.4 14.45 15.68 162.7 25.00 28.17 111.4 14.62 15.86 164.2 25.35 28.45 112.3 14.78 16.05 165.6 25.61 28.80 113.3 14.97 16.25 167.0 25.91 29.08 114.2 15.18 16.43 168.5 26.27 29.43 115.2 15:39 16.64 169.9 26.54 29.80 116.2 15.54 16.81 171.4 26.90 30.08 117.1 15.73 16.99 172.8 27.25 30.38 118.1 15.93 17.17 174.2 27.53 30.77 119.0 16.12 17.36 175.7 27.82 30.93 120.0 16.30 17.58 177.1 28.19 31.21 121.0 16.49 17.75 178.6 28.38 31.50 121.9 16.70 17.89 180.0 28.69 31.89 122.9 16.89 18.11 181.4 28.98 32.16 123.8 17.09 18.32 182.9 29.38 32.55 124.8 17.24 18.50 184.3 29.65 32.74 125.8 17.47 18.64 185.8 30.00 33.02 126.7 17.67 18.87 187.2 30.22 33.42 127.7 17.82 19.04 188.6 30.52 33.80 128.6 18.01 19.21 190.1 30.89 34.09 129.6 18.25 19.39 191.5 31.30 34.19 130.6 18.38 19.60 193.0 31.63 34.58 131.5 18.64 19.80 194.4 31.73 34.97 132.5 18.78 19.94 195.8 32.08 35.28 continued. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.30 continued. 106 12 min run 30 min run Shear Shear rate Shear Shear rate Stress (s-1) Stress (a\"1) (Pa) asc dsc (Pa) asc dsc 133.4 19.01 20.17 197.3 32.52 35.46 134.4 19.15 20.32 198.7 32.84 35.87 135.4 19.40 20.54 200.2 33.02 36.16 136.3 19.58 20.71 201.6 33.46 36.46 137.3 19.81 20.86 203.0 33.73 36.77 138.2 19.98 21.08 204.5 34.05 37.05 139.2 20.16 21.28 205.9 34.38 37.35 140.2 20.37 21.40 207.4 . 34.66 37.69 141.1 20.59 21.60 208.8 35.02 37.98 142.1 20.76 21.81 210.2 35.33 38.25 143.0 20.94 21.96 211.7 35.67 38.48 144.0 21.22 22.17 213.1 35.91 38.90 145.0 21.35 22.38 214.6 36.24 39.19 145.9 21.57 22.62 216.0 36.61 39.40 146.9 21.79 22.85 217.4 36.94 39.80 147.8 21.97 23.01 218.9 37.20 40.11 148.8 22.19 23.20 220.3 37.59 40.30 149.8 22.37 23.34 221.8 37.95 40.72 150.7 22.55 23.60 223.2 38.19 41.16 151.7 22.75 23.91 224.6 38.61 41.24 152.6 22.96 24.27 226.1 38.95 41.54 153.6 23.16 24.59 227.5 39.20 41.76 154.6 23.32 24.70 229.0 39.54 42.06 155.5 23.59 24.88 230.4 39.77 42.37 156.5 23.73 25.04 231.8 40.09 42.69 157.4 23.89 25.16 233.3 40.42 43.01 158.4 24.06 25.41 234.7 40.75 43.35 159.4 24.27 25.70 236.2 41.12 43.67 160.3 24.50 25.84 237.6 41.46 44.00 161.3 24.77 25.92 239.0 41.82 44.18 162.2 24.95 26.14 240.5 42.15 44.57 163.2 25.08 26.43 241.9 42.42 44.81 164.2 25.32 26.64 243.4 42.87 45.17 165.1 25.56 26.72 244.8 43.12 45.37 166.1 25.85 26.89 246.2 43.49 45.76 continued. Appendix A. LISTING OF EXPERIMENTAL FLOW DATA 107 Table A.30 continued. 12 min run 30 min run Shear Shear rate Shear Shear rate Stress CV1) Stress (s-1) (Pa) asc dsc (Pa) asc dsc 167.0 25.93 27.15 247.7 43.73 45.87 168.0 26.14 27.40 249.1 44.19 46.31 169.0 26.40 27.46 250.6 44.34 46.52 169.9 26.66 27.61 252.0 44.82 46.83 170.9 26.77 27.91 253.4 45.08 47.15 171.8 26.93 28.16 254.9 45.43 47.53 172.8 27.24 28.29 256.3 45.81 47.79 173.8 27.51 28.34 257.8 46.17 48.05 174.7 27.68 28.62 259.2 46.53 48.32 175.7 27.80 28.66 260.6 46.82 48.66 176.6 28.08 28.88 262.1 47.17 48.76 177.6 28.09 29.14 263.5 47.53 49.23 178.6 28.38 29.39 265.0 47.72 49.33 179.5 28.66 29.48 266.4 48.09 49.75 180.5 28.93 29.63 267.8 48.40 49.93 181.4 29.02 29.88 269.3 48.79 50.38 182.4 29.23 30.15 270.7 49.11 50.57 183.4 29.50 30.19 272.2 49.55 50.85 184.3 29.77 30.36 273.6 49.84 51.22 185.3 29.88 30.52 275.0 50.19 51.34 186.2 30.10 30.60 276.5 50.59 51.77 187.2 30.32 30.89 277.9 50.63 51.86 188.2 30.42 31.14 279.4 51.26 52.30 189.1 30.72 31.32 280.8 51.56 52.53 190.1 30.95 31.49 282.2 51.82 52.92 191.0 31.18 31.65 283.7 52.14 53.15 192.0 31.37 31.61 285.1 52.73 53.14 286.6 52.93 53.63 288.0 53.00 53.64 Appendix A. LISTING OF EXPERIMENTAL FLOW DATA 108 Table A.31: Peak torque values for chocolate samples at 40°C using different sized vanes with the Brabender Rheotron viscometer with the A cup and spring A. Sample Speed Peak Torque on Vane (Nm x 10\"3) (rpm) E F G K O HMC 0.064 0.120 0.224 0.4971 0.5224 0.5315 0.8925 0.9633 0.9578 1.420 1.431 1.508 1.959 2.050 2.014 2.231 2.304 2.395 HSS 0.064 0.120 0.224 0.6313 0.6803 0.7075 1.045 1.083 1.148 1.747 1.839 1.916 2.395 2.467 2.485 3.447 3.410 3.664 HI 0.064 0.120 0.224 1.121 1,094 1.143 3.193 3.138 3.193 3.229 3,102 3.175 4.136 4.063 4.316 4.698 4.880 5.007 H2 0.064 0.120 0.224 0.4608 0.4916 0.5079 0.8653 0.9143 0.9415 1.148 1.442 1.502 2.014 2.249 2.213 2.413 2.449 2.685 "@en ; edm:hasType "Thesis/Dissertation"@en ; edm:isShownAt "10.14288/1.0098501"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Food Science"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "Yield stress studies on molten chocolate"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/29792"@en .