UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Yield stress studies on molten chocolate Wilson, Laurie L. 1991

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1991_A6_7 W52.pdf [ 6.67MB ]
Metadata
JSON: 831-1.0098501.json
JSON-LD: 831-1.0098501-ld.json
RDF/XML (Pretty): 831-1.0098501-rdf.xml
RDF/JSON: 831-1.0098501-rdf.json
Turtle: 831-1.0098501-turtle.txt
N-Triples: 831-1.0098501-rdf-ntriples.txt
Original Record: 831-1.0098501-source.json
Full Text
831-1.0098501-fulltext.txt
Citation
831-1.0098501.ris

Full Text

YIELD STRESS STUDIES ON M O L T E N C H O C O L A T E by  Laurie L. Wilson B. Sc. (Biology) University of British Columbia, 1984  A THESIS S U B M I T T E D  IN P A R T I A L F U L F I L L M E N T  T H E REQUIREMENTS  FOR T H E D E G R E E  M A S T E R OF  OF  SCIENCE  in T H E F A C U L T Y OF G R A D U A T E STUDIES DEPARTMENT  OF FOOD SCIENCE  We accept this thesis as conforming to the required standard  T H E U N I V E R S I T Y O F BRITISH C O L U M B I A  August 1991 © Laurie L. Wilson, 1991  OF  In  presenting this  degree at the  thesis  in  University of  partial  fulfilment  of  of  department  this thesis for or  by  his  or  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  representatives.  an advanced  Library shall make it  agree that permission for extensive  scholarly purposes may be her  for  It  is  granted  by the  understood  that  head of copying  my 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  DE-6 (2/88)  iW^  > NftW  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, H I , 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 H A T 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 H M C , HSS and H2, but not sample H I . 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 H I 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  TABLE OF CONTENTS  , i  ABSTRACT  ii  LIST O F T A B L E S  vii  LIST O F F I G U R E S  xi  NOMENCLATURE  xiii  ACKNOWLEDGEMENT  xiv  1  INTRODUCTION  1  2  LITERATURE REVIEW  4  2.1  R H E O L O G I C A L P R O P E R T I E S 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 R O T A T I O N A L 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  VANE FIXTURE METHOD  18  2.5.1  18  Theory  iv  2.5.1 3  18  EXPERIMENTAL  22  3.1  CHOCOLATE SAMPLES  22  3.1.1  22  3.2  Product Description  CHEMICAL 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 4  Theory  DATA A N A L Y S E S  34  R E S U L T S A N D DISCUSSION  35  4.1  CHEMICAL ANALYSES  35  4.2  P A R T I C L E SIZE ANALYSIS  37  4.3  I N D I R E C T E S T I M A T I O N OF Y I E L D 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 v  57  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 H A T viscometer using the SC4-27/13R bob and cup fixture. .  4.7  Casson flow parameters for chocolate melts at 40° C obtained with the Brabender Rheotron using coaxial cylinder fixtures A l and A2  4.8  45  Analysis of variance for Casson yield stress obtained with the Brabender Rheotron using coaxial cylinder fixtures A l and A2  4.9  43  46  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 coaxial 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 recalculated 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 H I and H2 at 40°C for two run times obtained with the Carri-Med rheometer using coaxial cylinder 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 Relaxation 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 ) for chocolate samples at 40°C obtained with the -1  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 ) for chocolate sample HI at 40°C obtained with the _1  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 ) for chocolate sample H2 at 40°C obtained with the _1  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  2.2  11  Schematic diagram of the Brookfield SC4-27/13R coaxial cylinder fixture and water jacket assembly (to scale)  2.3  13  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)  2.4  14  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)  2.5  16  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 Brookfield H A T Viscometer using the SC4-27/13R bob and cup  4.8  fixture  Casson flow curves of chocolate samples at 40°C obtained with the Brabender Rheotron viscometer using coaxial cylinder fixture A l  4.9  42  48  Casson flow curves of chocolate samples at 40°C obtained with the Brabender Rheotron viscometer using coaxial cylinder fixture A2  xi  49  4.10 Casson flow curves of chocolate samples at 40°C obtained with the CarriMed 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 4.12 Plot of  2T /7r£> m  3  65  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. . . .  xn  72  NOMENCLATURE  a  Ratio of bob radius to cup radius, rj,/r .  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  Coefficient of determination.  2  c  n  Bob radius.  r  Cup radius.  T  Torque (vane fixture) (N-m).  T  Peak torque or maximum on start-up (N-m),  V  Apparent viscosity (Pa-s ).  c  -1  Casson viscosity (Pa-s ). -1  Vp  Bingham plastic viscosity (Pa-s ).  i  Shear rate ( s ) .  IN  Newtonian shear rate ( s ) .  n  Angular velocity (rad-s ).  7T  pi.  a  Shear stress (Pa).  0~ca  Casson shear stress (Pa).  -1  -1  -1  -1  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.  2  INTRODUCTION  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 agglomeration 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  LITERATURE REVIEW  2.1  RHEOLOGICAL 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 temperatures 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 + 7 / 7 J /  (2.1)  p  where a is the shear stress (Pa), a is the yield stress (Pa), T) is the the plastic viscosity y  v  (Pa- s ) , and j is the shear rate ( s ) . If the material is a true Bingham plastic, the -1  -1  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 , but there was -1  a pronounced curvature concave to the shear rate axis at shear rates under 15 s . Using _1  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 Tf ^f ca  (2.2)  Chapter 2. LITERATURE  REVIEW  7  where cr is the Casson yield stress (Pa) and rj is the Casson infinite shear viscosity ca  ca  (Pa-s ). Steiner (1958; 1962) found this model fitted the chocolate melt flow data more -1  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). A n equivalent 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 <T  /rj  ca  ca  must also  not exceed 10 if the term is to be omitted. This ratio is usually between 5 and 8 for most chocolates (Steiner, 1958; Sequine, 1986). Therefore the numerical value of this term is still less than 1.0 even when  a  is 0.5 and the  (T /rj ca  ca  ratio is as high as 10. When these  conditions are accounted for, the flow equation becomes:  In order to evaluate the Casson flow properties, (l ^a)^fo• may be plotted against J  (l+a)\/7 to obtain a straight line which may be extrapolated to zero shear rate. The Casson infinite shear viscosity is calculated from the slope and the Casson yield stress from the intercept. A modified Casson equation was suggested by Heimann and Fincke (1962a; b; c) as follows: *  2 / 3  = <d + ( ^ 7 ) /3  2 / 3  (2-5)  They stated that this model equation fitted flow data more accurately for many milk chocolates. Also, a more general flow equation was given,  ° = < + {viT m  (2.6)  where the exponent m was termed the flow index. Saunders (1968a) recommended that the optimum value of the flow index could be obtained by adjusting m by increments of 0.05 until the best fit to the flow data was achieved. He suggested that the value of m may be related to the structural characteristics of the chocolate and would not necessarily take on values of 0.5 or 2/3 as in the Casson or Heimann and Fincke models, respectively. However, in a collaborative study, values reported for the flow index, m, for samples tested, varied between laboratories (Steiner, 1972).  Chapter 2.  LITERATURE  9  REVIEW  The original Casson equation provided good approximations of the flow properties of most chocolates, and was therefore considered when there was a need to standardize the methodology. The Casson model became the provisional method of the International Office of Cocoa and Chocolate (OICC) in 1960, remained as such in an Office publication in 1970, and then was later accepted in its final form in 1973. The OICC protocol is widely used in research and in the European chocolate manufacturing industry (Malm 1967a; 1968; Banford et al., 1970; Chevalley, 1975; Niediek, 1980; 1981). In North America, the Casson model was slow to gain recognition over the years. Duck (1965) stated that the Casson parameters better defined the flow properties of chocolate as compared to using MacMichael viscosity which was the standard method of the American Association of Candy Technologists and the National Confectioners Association (Minifie, 1980). Duck detailed modifications made to a Brookfield viscometer and developed a nomograph for this instrument that would greatly simplify the determination for routine work. Howard (1969a; b) and Robbins (1979) outlined further changes made to the Brookfield H B T viscometer which could be used to measure both MacMichael viscosity and the Casson values. By 1986, a tentative methodology for the measurement of the Casson flow parameters was finalized by the National Confectioners Association (Sequine, 1986). The standard methodology is used mainly for quality control purposes and for research and development in the chocolate industry.  Relatively little activity  is evident in university or public sector laboratories, thus there is little published work on the flow properties of molten chocolate available in North America (Solstad, 1983; Zangger, 1984; Sequine, 1986). Recent studies on chocolate have included the development of a thermo-rheometry process where the flow properties of tempered chocolate masses have been measured (Kleinert, 1982a; b; c). In addition, the texture characteristics of solid chocolate have been described in terms of instrument parameters and in sensory studies (Tscheuschner  Chapter 2. LITERATURE  REVIEW  10  and Markov, 1986; Markov and Tscheuschner, 1989).  2.2  FUNDAMENTALS OF ROTATIONAL VISCOMETRY  In classical rotational viscometry, a rotating body is immersed into a fluid and the viscous drag.of the fluid exerting a opposing force is measured (Van Wazer et al., 1963). Rotational fixture designs include cone and plates, parallel plates and coaxial cylinders. For the coaxial cylinder fixture acting upon a Newtonian liquid, the shear rate is proportional to the rotational speed of the bob (or cup) and can be calculated from the dimensions of the fixture using the following equation(s): ™2  Air rpm 60  (2.7)  ri - rt  where 7^ is the Newtonian shear rate, Q is the angular velocity and r and c  are the  radius of the cup and bob, respectively. However, the assumption of Newtonian flow for non-Newtonian fluids can lead to appreciable error in calculated shear rates and should be corrected for. Shear stress can be calculated from the measured torque and the fixture dimensions as follows: M 1-KTlh  , (2.8) N  where M is the torque, 7*5 is the radius of the bob, and h is the height of the bob. Flow graphs may be constructed from the shear stress-shear rate data in order to assess the flow behavior of the material (Figure 1.1). A n ideal Newtonian (viscous) fluid is shown in curve 1. A Bingham plastic (curve 2) behaves as a solid until stressed beyond its yield value where a further increase in shear rate shows a proportional increase in shear stress. For a Casson material, after the yield point has been reached, the flow is nonlinear as shown in curve 3.  Chapter 2. LITERATURE REVIEW  11  3 2  0> (7j  1  a a  JZ  to  0  Shear Rate  Figure 2.1: Model rheograms for Newtonian (1), Bingham (2) and Casson (3) flow behavior. 2.3 2.3.1  R H E O M E T E R DESCRIPTION Brookfield Viscometer  Brookfield viscometers are well known and have been widely used for viscosity measurement 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 materials 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 10 Pa. This instrument can also be used with an 5  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 referred 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).  14 Chapter 2. LITERATURE  REVIEW  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 analysis 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 device, 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 automated, 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 M E T H O D  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  16 Chapter 2. LITERATURE  REVIEW  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  17  REVIEW  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; T i u 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 resulting 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  VANE FIXTURE METHOD  The use of constitutive equations like Casson's to arrive at a yield stress value are empirical 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, a is the shear a  stress on the cylindrical yielding surface and cr is the end shear stress which is unknown e  (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 (a ) at the y  maximum torsional moment ( T ) and Equation 2.9 is reduced to, m  DH 2  T  m  =  TTOy  D  3  (2.10)  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: T D  M  =  3  [ F  1  1  ,  ~ 2 ~ [~D mTlsJ  <->  +  2U  where m is a constant describing the radial distribution function of <x. When m = 0, e  Equation 2.11 becomes Equation 2.10. A second method proposed by Nguyen and Boger (1985) recommends using vane fixtures of varying lengths but which have the same diameter, therefore, the second term in Equation 2.9 is constant. The yield stress can then be calculated from the slope of the plot of peak torque versus vane height.  Chapter 2. LITERATURE  REVIEW  Figure 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).  Chapter 3  EXPERIMENTAL  3.1 3.1.1  CHOCOLATE SAMPLES Product Description  Two commercial chocolate samples, Hershey Milk Chocolate and Hershey Special Dark chocolate (Hershey Chocolate Company, Hershey, PA) and two 5 kg blocks of experimental chocolate products were obtained directly from the Hershey Chocolate Company for use in this study. Of the two commercial samples, one was a milk chocolate and the other was a semi-sweet type chocolate. The milk chocolate contained sugar, milk, cocoa butter, chocolate, soya lecithin and vanillin. The semi-sweet chocolate contained sugar, chocolate, cocoa butter, soya lecithin and natural flavor. The ingredient list for the block samples was not provided, and they were marked as simply Hershey-1 and Hershey-2 and are referred to as HI and H2 in this investigation. The commercial milk and semi-sweet products have been coded H M C and HSS, respectively.  3.2  CHEMICAL ANALYSES  The four chocolate products were analyzed for moisture, ash, crude protein, fat and sucrose content.  Prior to chemical analysis, composite chocolate samples were finely  grated and stored in airtight containers until used. Samples were tested in triplicate for each analysis.  22  Chapter 3.  3.2.1  23  EXPERIMENTAL  Moisture  Moisture was determined for each chocolate sample using a modified A O A C Method 13.002 for cacao products (AOAC, 1984). The samples (2 g) were weighed accurately into twelve predried, desiccator-cooled, weighed aluminum pans (60 mm diameter, 18 mm depth). The samples were placed in a vacuum oven at 100°C and 100 kPa for 12 hours. The samples were cooled in a desiccator containing silica gel, and then weighed. The samples were returned to the oven for an additional hour, cooled and reweighed. No change in weight was observed in the second drying period, thus the the loss in weight compared to the original sample weight was reported as percent moisture.  3.2.2  Ash  The ash content was determined using A O A C Method 13.005 for cacao products (AOAC, 1984). The ground chocolate samples (3 g) were accurately weighed into twelve 50 mL porcelain crucibles previously heated (lids included) to 600°C, cooled in a desiccator, and weighed. The samples were placed in the furnace and the temperature slowly brought to 600°C over a period of four hours. The samples were then ashed overnight, cooled in a desiccator for one hour and weighed. They were returned to the oven for an additional hour, cooled and reweighed.  The change in weight in the second high temperature  treatment was negligible, so the ash content of each sample was calculated from the final weight of ash in comparison with the initial sample weight.  3.2.3  Crude Protein  Protein analysis was carried out using a micro-Kjeldahl technique (Concon and Soltess, 1973).  Prepared samples were accurately weighed (0.10 g) into twelve clean 30 mL  Kjeldahl flasks. A catalyst, 2.3 g of a K S 0 - H g O mixture (190:4, w/w), was added, 2  4  Chapter 3.  24  EXPERIMENTAL  followed by 2.3 mL concentrated H 2 S O 4 . The samples were placed on heating elements and digested with periodic additions of small amounts of H 2 O 2 until all organic material had oxidized and the clear solution was refluxing halfway up the neck of the flask. The solutions were removed from the heat, cooled and diluted to 15 mL with distilled deionized water. A n aliquot of each solution was analyzed for nitrogen content using a Technicon Autoanalyzer (Technicon Industrial Systems, Tarrytown, N Y ) . Crude protein content was then calculated by multiplying nitrogen content by a factor of 6.25.  3.2.4 Fat The fat content was determined using a modified International Office of Cocoa and Chocolate - A O A C Method 13.032 for cacao products (AOAC, 1984). Prepared samples were accurately weighed (1 g) into twelve 250 mL beakers. To each beaker, 20 mL of boiling water was added slowly, while stirring, to give an homogeneous suspension. A n additional 25 mL of 8 M H C l was added, the beakers covered with watch glasses and the solutions gently boiled for 15 minutes. The digest was filtered through Whatman No. 542 filter paper. The beakers and watch glasses used were rinsed with water and the washings added back to each sample. The digest was washed until the filtrate was Cl-free as determined by adding a few drops of 0.1M A g N 0 . The samples, rolled up inside the wet 3  filter paper and placed inside Whatman cellulose extraction thimbles (22 x 80 mm), were then placed inside glass support thimbles and dried in covered beakers for 12 hours in a oven at 100°C. The digestion beakers, drying beakers and watch glasses were rinsed with petroleum ether and the washings poured through each thimble and collected in 100 mL Labconco extraction flasks. The flasks had been previously dryed for 1 h at 100°C, cooled in a desiccator and weighed prior to use. The thimbles, containing dried sample, and the extraction flasks were placed into the Goldfisch extractor (Labconco Corporation, Kansas  Chapter 3.  EXPERIMENTAL  25  City, MO). Additional petroleum ether was added to each flask to make up approximately 30 mL and the samples gently refluxed overnight to complete extraction. The flasks were removed from the extractor and placed in a fume hood until the solvent had been expelled. The flasks were then dried at 100°C for 2 hours, cooled in a desiccator and weighed. No change in weight was observed after an additional drying period of 1 hour and the fat content of each sample was calculated.  3.2.5  Sucrose  The sucrose content was determined using A O A C Method 13.054 for cacao products ( A O A C , 1984). This procedure was modified to accommodate a smaller sample size. As well, only a direct polarization was carried out. Prepared samples (5 g) were accurately weighed into twelve 250 mL Nalgene centrifuge bottles each containing 50 mL of petroleum ether. The bottles were capped, the samples mixed for 5 minutes and centrifuged for 10 minutes at 4,080 x g. The extraction was repeated and the bottles placed in a fume hood until the petroleum ether had been expelled. The defatted samples were mixed with 50 mL of water and the bottles immersed in a water bath set at 90°C. The bottles were removed from the bath, cooled and approximately 1 mL of basic P b ( O A c )  2  solution ( C P . Bakers Analyzed), with a specific gravity of 1.25, was added to complete precipitation. The samples were mixed thoroughly, centrifuged and the supernate decanted through filter paper (Whatman No. 4). Any excess Pb was precipitated out using K2C2O4  and the solutions filtered again. The pH of the twelve test solutions was mea-  sured and fell between pH 7.0 and 7.5. Each sample was then polarized in a 100 mm tube at 20°C at a wavelength of 589 nm using a Perkin-Elmer 141 polarimeter (Perkin-Elmer Corporation, Norwalk, C T ) . The sucrose content of the samples can be calculated from the measured degree of optical activity in the prepared solutions.  Chapter 3.  3.3  EXPERIMENTAL  26  PARTICLE SIZE ANALYSIS  The mean particle size and particle size distribution of the four chocolate samples were determined using a Coulter Counter Model TAII (Coulter Electronics Inc., Hialeah, F L ) An experimental procedure was developed following recommendations outlined by Robbins (1983). Robbins did not recommend defatting the samples prior to analysis. A n electrolyte solution of 5% ammonium thiocyanate (Fisher Certified A.C.S.) and absolute ethanol was prepared and clarified by centrifugation in 250 mL stainless steel cups at 4,080 x g for 30 minutes. Sample suspensions were made by mixing 0.15 g of sample in 20 mL electrolyte solution in new (dust free) Simport 20 mL dilution vials. One drop of Tween 20 was added to each vial to aid in breaking up aggregates of particles. The suspensions were sonicated for two minutes (Bransonic 220, Branson Instruments Co., Shelton, CO) prior to analysis in order to ensure complete dispersal of the sample in electrolyte. Samples were tested in duplicate and three runs were taken for each sample.  3.4  YIELD STRESS DETERMINATION  The flow properties of chocolate melts can be determined by either indirect or direct methods, as previously described. Using the indirect method, yield stress was estimated by fitting the Casson equation to shear stress-shear rate data and extrapolating to zero shear rate. Direct methods of measurement used were the Stress Relaxation Method, the Single Vane Method and Multiple Vane Method I and Method II.  3.4.1  Calibration  The calibration of each of the three rheometers used in this study was checked prior to use. The form factors, which relate torque to shear stress and rotational speed to shear rate, listed in the operation manuals, were verified using standard oils and recalculated  Chapter 3.  EXPERIMENTAL  27  if necessary. The Brookfield HAT viscometer (Brookfield Engineering Laboratories,  Stoughton,  M A ) was checked using two Brookfield viscosity standards consisting of silicone oil fluids of known viscosity at 25°C. The viscosity values obtained experimentally were in close agreement with that of the standard used. The Brabender Rheotron viscometer (C.W. Brabender Instruments Inc., South Hackensack, NJ) with coaxial cylinder fixtures A l and A2 was calibrated using a certified viscosity standard, S600, (Cannon Instrument Company, State College, PA) at 20°C using coaxial cylinder fixture A l . This instrument no longer conformed to the parameters given in the manual and the shear stress factors for springs A, B and C were recalculated. The method used included a correction factor for end effect. As well, the operating speeds on the Brabender were checked and found to differ from those printed on the control unit. These new speeds (rpm) were used in the calculation of new shear rate values for fixtures A l and A2. The Carri-Med Controlled Stress rheometer (Carri-Med Limited, Dorking, U K ) with coaxial cylinder fixture 5222 was calibrated using the Cannon standard oil, S600, at 20°C. The calibration, which included a correction for end effect, was calculated and applied to the stress factor. The instrument parameters are listed in Table 3.1. 3.4.2  Sample Preparation  The chocolate samples were prepared for rheological testing as recommended by the International Office of Cocoa and Chocolate (OICC, 1973). Composite samples were cut into 5 gram pieces or smaller. Approximately 125 grams of each grated sample was placed in 300 mL beakers covered with foil and heated in an incubator oven set at 55°C. The chocolate was stirred by hand with a rubber tipped stirring rod at intervals using a stirring rate not exceeding 60 revolutions per minute until the chocolate had completely melted  Chapter 3.  EXPERIMENTAL  28  Table 3.1: Instrument parameters for the coaxial cylinder fixtures used.  Cylindrical Fixtures  Brookfield  SC4-27/13R  17.0  0.34  0.62  Brabender  A l , spring A B C  0.0198 0.1209 1.3016  2.985  0.964  A2, spring A B C  0.0231 0.1410 1.5182  1.033  0.893  5222  0.010  9.751  0.892  Carri-Med  Form Factors Shear Stress Shear Rate (Pa)  Bob/Cup Radius Ratio (a)  Instrument  and reached a temperature of 50° C as determined by a calibrated thermocouple. The thermocouple used was a Teflon-coated, Type J iron/constantan wire pair with a soldered junction and readout provided by a digital temperature indicator meter (C.W. Brabender Instruments, Inc., South Hackensack, NJ). The thermocouple and digital readout system was calibrated against an A S T M certified thermometer. The time taken in the oven for the sample to completely melt and reach a temperature of 50°C was determined to be between 15 and 25 minutes. All fixtures were preheated in the incubator for five minutes prior to testing. The spindle or vane fixture was then attached to the torsion head of the rheometer, and the sample gently poured into the cup and loaded into the instrument. Temperature in the sample was maintained at 40°C with a thermostatically controlled water supply circulating in a water jacket around the sample cup. The chocolate was brought to 40°C while shearing the sample at a rate between 5  Chapter 3.  EXPERIMENTAL  29  and 25 s . The sample temperature was monitored using the thermocouple. The time _1  required to reach 40° C was determined to be 15 minutes for the larger sample volume required by the Brabender Rheotron and 10 minutes for the smaller sample volume used with the Brookfield and Carri-Med rheometers.  3.4.3  Indirect Methods  The Casson Model equation was fitted to the experimental shear stress-shear rate data obtained from each of the three rheometers used in this investigation. Shear stress (cr, Pa) and shear rate (7, s~ ) values were calculated from the mean scale readings using the x  calibration data, form factors and rotational speeds. The appropriate non-Newtonian shear rate correction factor specific to the coaxial cylinder fixture used was appUed to each data set. Least squares linear regression was used to obtain the equation for the Casson model and related parameters for each set of flow data.  Brookfield Viscometer Flow measurements of each chocolate sample were made using the Brookfield H A T viscometer with the small sample adapter consisting of the SC4-13R water jacketted sample chamber or cup with the SC4-27 cylindrical bob. Scale readings were taken at 1.0, 2.5, 5, 10, 20 and 50 rpm using first the ascending, then descending order of speeds. These speeds represented a shear rate range of approximately 0.34 to 17.0 s . With the one -1  viscometer and fixture combination it was not possible to obtain readings for all speeds. For example, readings were off scale at 50 rpm for H M C and HSS and at both 20 and 50 rpm for H I . A total of twelve samples was tested in a random order.  Chapter 3.  EXPERIMENTAL  30  Brabender Rheotron Viscometer Two coaxial cylinder fixtures, A l and A2, of differing gap width were used with the Brabender Rheotron to evaluate the rheological behavior of the chocolate melts. Scale reading measurements were taken at eleven discrete speeds using the A l fixture and twelve discrete speeds using the A2 fixture, representing shear rate ranges of approximately 0.19 to 75.8 s  - 1  and 0.07 to 50.8 s , respectively. Using a stripchart recorder, _1  the torsion signal was monitored at each speed and readings were recorded when an equilibrium value was reached. Again, readings were taken in an ascending then descending order over the range of speeds used for each fixture. The twelve samples were tested in a random order using the A2 coaxial cylinder fixture first, followed by the A l coaxial cylinder fixture.  Carri-Med Controlled Stress Rheometer The Carri-Med Controlled Stress Rheometer was used with coaxial cylinder fixture 5222 to evaluate the flow properties of the four chocolate samples. Operation of the rheometer was controlled through a microcomputer interfaced to the instrument.  In preparation  for testing, the sample was loaded manually, and sheared at a low constant stress for 10 minutes while the temperature of the sample equilibrated prior to testing. The sample cup which was supported on a pneumatic ram, automatically rose to bring the sample up to surround the spindle which was attached to the drive motor, when the switch was turned on or when instructed through the computer.  This ram  action was found to be too abrupt, thereby forcing some of the sample to spill out of the cup and possibly introducing air bubbles into the sample. A satisfactory solution was found when the distance between the sample cup and the spindle was increased by adjusting the micrometer wheel on the lower ram assembly. Then, when the ram switch  Chapter 3.  EXPERIMENTAL  31  was activated, the sample cup rose and the spindle was immersed only part way into the sample. Turning the micrometer wheel, the cup was slowly moved up until the spindle was fully immersed in the sample. The bottom gap width was set to 1.5 mm before each test run. The spindle was rotated through a programmed loop of increasing and then decreasing stress for 10 minutes. This represented shear rate ranges of approximately 0 to 10 s , 0 _1  to 40 s , 0 to 20 s" and 0 to 50 s _1  1  _ 1  for H M C , HSS, H I and H2, respectively. Duplicate  samples were evaluated in random order with two consecutive runs taken for each sample. A second test was conducted in which the effect of run time was studied in relation to the yield stress measured. Two procedures consisting of run times of 12 and 30 minutes were used on triplicate samples of H2 and H I .  3.4.4  Direct Methods  Stress Relaxation Method The Brabender Rheotron with coaxial cylinder fixtures A l and A2 were used for direct measurement of yield stress using the stress relaxation method. The sample was brought to an equilibrium condition by shearing for a 30 minute period at 0.064 rpm. Not all samples required a 30 minute period to reach an equilibrium state, but this length of time was chosen because it represented the maximum amount of time required and all samples would be tested in the same manner. Two procedures for stress relaxation were used. In the first procedure, a single measurement was taken after shearing the samples for 10 minutes, turning off the drive motor, and recording the residual stress remaining in the sample using a stripchart recorder. When measurements recorded over a 10 to 15 minute period were virtually unchanged, these values were taken to represent the yield stress of the sample.  Chapter 3.  EXPERIMENTAL  32  The test samples in the second procedure were sheared at speeds of 0.064, 0.120 and 0.224 rpm for 10 minute intervals. The drive motor was then turned off and the residual stress remaining, after shearing at each rotational speed, was recorded using a stripchart recorder.  Again, measurements recorded over a 10 to 15 minute period  were virtually unchanged and these values were taken to represent the yield stress of the sample. Replicate samples were tested in a random order using the A2 fixture first and then the A l fixture. The speeds were randomized within each sample and fixture combination.  Vane Fixture Method Direct yield stress measurements can also be made using the vane fixture method (Nguyen and Boger, 1983). A series of 4-bladed vane fixtures was constructed for these experiments as shown in Figure 2.5 with dimensions as given in Table 3.2. Based on recommendations of Nguyen and Boger (1985) vane fixtures E , F and G were chosen for testing. In addition, two larger vanes, K and O, were used, although they did not meet all of the dimensional criteria described in the procedure outlined by Nguyen and Boger. A selected vane fixture was attached to the torque sensing unit of the Brabender Rheotron and the sample carefully loaded into the A-series cup (56 mm diameter). Once the sample had reached the equilibrium test temperature of 40°C, a constant speed was applied while the torsion signal during the start-up of rotation was recorded on a potentiometric stripchart. The maximum or peak torque recorded was converted to a stress value using the torsion spring constant and surface area within the sample sheared at the surface of a cylindrical volume described by the length and diameter of the vane fixture. This peak stress was taken as an estimate of the yield stress. Relaxation stresses in the sample were also recorded; however, residual readings were negligible using this type of fixture with the Brabender viscometer.  Chapter 3.  EXPERIMENTAL  33  Table 3.2: Vane fixture dimensions Vane Fixture  Vane Height (cm)  Vane Diameter (cm)  Ratio  E  4.0  1.5  2.6  F  4.0  2.0  2.0  G  4.0  2.5  1.6  K  5.5  2.5  2.2  0  7.0  2.5  2.8  H/D  Preliminary tests showed a dependence of the peak torque value measured on the rotational speed used. Torque values appeared to be relatively constant at very low speeds, but they increased significantly at tested speeds of between 0.849 and 8.36 rpm, probably due to inertial effects on sudden start-up. As well, another preliminary test was conducted in which the peak torque was measured immediately upon loading the sample and after shearing the sample for 15 minutes at 0.064 rpm. No significant difference was observed (p>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  DATA ANALYSES  The yield stress and viscosity estimates obtained using Brabender Rheotron were analyzed 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. All statistical procedures used (Steel and Torrie, 1960) were calculated using the B M D P program (Dixon, 1985) on the U B C 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 A N D DISCUSSION  4.1  CHEMICAL ANALYSES  A proximate analysis, consisting of moisture, ash, fat and protein determinations, was carried out on each chocolate sample. A n 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  36  Chapter 4. RESULTS AND DISCUSSION  Table 4.3: Composition of the chocolate samples.  Composition of Sample (%) HI HSS  H2  Analysis  HMC  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). A n 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 ( M A N O V A ) , using the B M D P : 4 V statistical software 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  Sample  15  Mean Square  F-Ratio  0.5288E-05 ' U  46.63  **  19.83  **  Ash Error  3 7  0.1255 0.0063  Moisture Error  3 7  0.4447 0.0011  Fat Error  3 7  2.0856 0.2975  Protein Error  3 7  2.6088 0.0532  49.06  **  Sucrose Error  3 7  3.7082 0.1810  20.48  **  w - Wilks' lambda likelihood ratio statistic. * - significant at p<0.05 ** - significant at p<0.01  402.6  **  7.010 *  39  Chapter 4. RESULTS AND DISCUSSION  Table 4.5: Range and mean sizes of particles in the chocolate samples.  Sample  Pooled Mean (pm)  Coefficient of Variation (%)  Size Range (fim)  HMC  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 H I 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  8  50  !=0 Co  40 t3  c o  CO  O  Cj co  Legend  30  ra HMC HSS E a HI  CL O Q_  LZ3  20H  o  H2  10  2.5  4  5  6.3  8  10.1  12.7  16  20.2  II  25.4  Particle Size (um) Figure 4.6: Distribution of sizes for particles contained in the chocolate samples  o  Chapter 4. RESULTS AND DISCUSSION  4.3  41  INDIRECT ESTIMATION OF YIELD STRESS  4.3.1  Brookfield Viscometer  The Brookfield H A T 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 nonNewtonian 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 H I . The rheogram for sample H I 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 H I , 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 , H I , 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 H A T viscometer for testing molten chocolate, the maximum shear rate obtainable was 17.0 s . This does not meet the maximum shear rate of 60 s -1  - 1  recommended by the OICC.  Also, the recommended bob to cup ratio (<x) is 0.65 or greater. This ratio is 0.62 for the Brookfield fixture. However, the Casson rheograms for 3 of the 4 samples tested were linear, indicating that this model applied to the data over the shear rate range tested using a coaxial cylinder fixture with a wider gap width. Sample H I was very viscous and a higher yield stress estimate was expected. At the lower shear rates, it is possible that this sample was not being sheared across the entire gap. As well, the sample could be  Chapter 4. RESULTS AND DISCUSSION  42  26  22  H  Figure 4.7: Casson flow curves of chocolate samples at 40°C obtained with the Brookfield H A T Viscometer using the SC4-27/13R bob and cup fixture.  Chapter 4. RESULTS  AND  DISCUSSION  43  Table 4.6: Casson flow parameters for chocolate melts at 40°C obtained with the Brookfield H A T viscometer using the SC4-27/13R bob and cup fixture.  Sample o"ca,  Coefficient of Determination, r  Casson Parameters •q , (mPa-s) (Pa)  9.38 (8.45)t  ca  10110 (3.68)  1.000  (n=5)  19.8 (4.53)  5270 (2.82)  0.999  (n=5)  HI  9.59 (6.57)  19300 (2.61)  0.970  (n=4)  H2  10.6 (1.47)  4510 (1.58)  1.000  (n=6)  HMC HSS  2  t- Coefficient of variation (%)  slipping at the fluid/fixture contact surfaces. Both would contribute to a lower apparent yield stress estimate. The National Confectioners Association (Sequine, 1986) recommended a minimum a ratio of 0.60 along with a minimum speed of 5 rpm (1.7 s~ ) at which to shear the sample, x  in that the conditions outlined by Steiner, for the correct use of the Casson equation, would be satisfied. If these guidelines were followed, only two data points could then be used to plot a rheogram for sample H I , at 5 and 10 rpm; readings were offscale at 20 and 50 rpm (see Appendix A ) . Data below 5 rpm, at 2.5 and 1.0 rpm, for the other samples showed no deviation from linearity and were included in the calculations for the Casson flow parameters.  Chapter 4. RESULTS AND DISCUSSION  4.3.2  44  Brabender Rheotron Viscometer  The steady shear Casson flow behavior of the chocolate samples was determined using the Brabender Rheotron viscometer and coaxial cylinder fixtures A l and A2. The flow parameters are listed in Table 4.7. These values were similar to those obtained using the Brookfield instrument, with the exception of sample H I . The yield values, in particular, were slightly higher for the Brabender viscometer tests, and were greater for the A l fixture as compared to those obtained using the A2 fixture, again with the exception of sample H I . Conversely, the viscosity values were lower for the A l fixture as compared to the A2 fixture for all samples. Coaxial cylinder fixture A l had a smaller gap width than fixture A2. The variation coefficients were below 10% for all samples tested except for the viscosity value measured for sample HI using the A2 fixture. Analysis of variance results in Tables 4.8 and 4.9 using the B M D P : 2 V program (for repeated measures) indicated that fixture and fixture x sample interaction significantly (p<0.01) influenced yield stress and viscosity values. The discrepancy in yield values between the two fixtures may be due to a combination of plug flow and/or wall slip. Slip effects were reported to occur in chocolate tested with coaxial cylinder fixtures (Steiner, 1962). Chocolate yield values measured using wide and narrow gap fixtures with a Haake Rotovisco viscometer were higher for the narrow gap fixture. Although Charm (1963) reported from unpublished data that there was no difference between fixtures of varying gap widths when measuring yield stress of chocolate, he did find differences for applesauce and tomato puree. In other fluid-like materials, problems due to slip when using coaxial cylinder fixtures have been widely reported in the literature (Cloud and Clark, 1985; Yoshimura and Prud'homme, 1988; Kiljanski, 1989; Qui and Rao, 1989). The gap width of the coaxial cylinder fixture, as well as the test material, may influence the magnitude of these effects.  Chapter 4. RESULTS AND DISCUSSION  45  Table 4.7: Casson flow parameters for chocolate melts at 40°C obtained with the Brabender Rheotron using coaxial cylinder fixtures A l and A2.  Sample  Fixture  Casson Parameters cr , (Pa) rjca, (mPa-s)  Coefficient of Determination, r  ca  HMC  Al A2  15.7 (8.10)t 12.3 (3.4.5)  7325 (1.71) 8770 (0.58)  0.997 0.998  (n=ll) (n=12)  HSS  Al A2  29.3 (0.82) 24.0 (2.24)  4486 (3.68) 4952 (1.64)  0.995 0.993  (n=ll) (n=12)  HI  Al A2  29.7 (3.18) 30.4 (7.11)  6171 (0.60) 8748 (12.2)  0.996 0.989  (n=ll) (n=12)  H2  Al A2  17.5 (8.18) 17.2 (4.44)  3942 (6.78) 4411 (5.52)  0.994 0.994  (n=ll) (n=12)  f - Coefficient of variation (%)  2  Chapter 4. RESULTS AND DISCUSSION  46  Table 4.8: Analysis of variance for Casson yield stress obtained with the Brabender Rheotron using coaxial cylinder fixtures A l and A2.  Source of Variation  df  Sample Error  3 8  Fixture Interaction Fixture x Sample Error  Mean Square  344.43 2.8238  F-Ratio  122.0  25.359  23.84 *  11.227 1.0637  10.55 *  significant at p<0.05  Table 4.9: Analysis of variance for viscosity obtained with the Brabender Rheotron using coaxial cylinder fixtures A l and A2.  Source of Variation  df  Mean Square  • F-Ratio  Sample Error  3 8  224.99E05 265.13E03  84.86 **  921.78E04  39.77 **  151.09E04 231.77E03  10.55 *  Fixture Interaction Fixture x Sample Error  * - significant at p<0.05  ** - significant at p<0.01  Chapter 4. RESULTS AND DISCUSSION  47  Table 4.10: Casson yield stress estimates for chocolate samples at 40°C recalculated over the Hnear portion of the rheograms obtained with the Brabender Rheotron using coaxial cylinder fixtures A l and A2.  Sample  Fixture  Yield Stress a , (Pa) ca  Coefficient of Determination, r  HMC  Al A2  16.0 (7.4.4.)t 12.9 (2.33)  0.997 0.998  (n==10) (n==10)  HSS  Al A2  30.1 (0.67) 25.6 (2.75)  0.994 0.995  (n==10) (n==10)  HI  Al A2  33.2 (1.90) 38.1 (2.48)  0.997 0.997  (n==9) (n==9)  H2  Al A2  18.0 (6.06) 17.2 (3.87)  0.994 0.993  (n==10) (n==10)  2  t - Coefficient of variation (%) The rheograms for steady shearing flow of chocolate melts produced using fixtures A l and A2 are shown in Figures 4.8 and 4.9. There was a marked curvature towards the x-axis at the lower shear rates. Apart from slip, the shape of the rheograms suggested that the sample was deforming, but had not yielded to the shearing force applied. This deviation from linearity occurred below approximate shear rates of 0.3 to 0.5 s samples tested using the A2 fixture and 0.4 to 0.7 s  _ 1  - 1  for  for samples using the A l fixture.  When these data points were removed and the Casson model fitted to the linear portion of the rheogram, higher yield stress estimates result (Table 4.10).  Figure 4.8: Casson flow curves of chocolate samples at 40° C obtained with the Brabender Rheotron viscometer using coaxial cylinder fixture A l .  Chapter 4. RESULTS AND DISCUSSION  49  Figure 4.9: Casson flow curves of chocolate samples at 40° C obtained with the Brabender Rheotron viscometer using coaxial c) linder fixture A2. r  Chapter 4. RESULTS AND DISCUSSION  4.3.3  50  Carri-Med Controlled Stress Rheometer  The Casson flow behavior of the chocolate melts was determined under controlled stress conditions using the Carri-Med rheometer. The mean Casson yield stress and viscosity estimates over two consecutive runs are listed in Table 4.11. The yield stress values did not vary significantly over consecutive runs (Table 4.12) but a significant difference was found for viscosity measurements (Table 4.13). The yield values were comparable to those estimated from steady shearing flow using the Brabender viscometer. The largest discrepancy in yield value was for sample H I . A mean yield value of 23.5 Pa for HI was measured using the Carri-Med as compared to 30.4 Pa obtained using the Brabender with the A2 fixture. The gap width of coaxial cylinder fixture 5222 used with the Carri-Med was the same as the A2 coaxial cylinder fixture. The Casson viscosity estimates were higher for all samples when measured using the Carri-Med rheometer.  This could be due to the testing procedure used.  For a  programmed run of 10 minutes, sample flow occurred over a narrower shear rate range in the Carri-Med rheometer as compared to the Brabender viscometer. The sample may not have thinned out as much as it could have had it been subjected to greater shear forces. The viscosity estimates obtained using the A l and A2 fixtures with the Brabender also resulted in higher values measured for the A2 fixture where the maximum shear rate obtainable was less than the A l fixture. The Casson equation fitted the steady shear flow data, obtained with the Brabender, more accurately than the controlled stress data obtained with the Carri-Med. This may be due to the greater capability of the Carri-Med to measure flow continuously, when interfaced to a computer, and the ability to measure flow (or deformation) at lower rates of shear. Judging by the curvature of the rheograms (Figure 4.10), the molten chocolate  Chapter 4. RESULTS AND DISCUSSION  51  Table 4.11: Casson flow parameters for chocolate samples at 40°C obtained with the Carri-Med rheometer using coaxial cylinder fixture 5222.  Sample  Run ^ca,  Casson Parameters 7] , (mPa-s ) (Pa) -1  ca  Coefficient of Determination, r  HMC  1 2  13.4 (12.1)t 11.3 (0.04)  11020 (7.74) 10500 (8.12)  0.964 0.995  (n=392) (n=392)  HSS  1 2  21.0 (1.90) 20.1 (2.06)  5600 (0.49) 5210 (4.04)  0.976 0.948  (n=388) (n=387)  HI  1 2  23.3 (1.43) 23.6 ( - )  11260 (1.16) 11390 ( - )  0.978 0.978  (n=388) (n=385)  H2  1 2  19.9 (5.36) 18.4 (7.00)  10160 (16.8) 10850 (17.4)  0.977 0.982  (n=388) (n=389)  f- Coefficient of variation (%)  2  Chapter 4. RESULTS AND DISCUSSION  52  Table 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 coaxial cylinder fixture 5222. Source of Variation  df  Mean Square  F-Ratio  Sample Error  3 3  75.410 0.8905  84.68 **  4.5881  1.57 ns  0.45082 2.9278  0.15 ns  Run Interaction Run x Sample Error  3 3  * - significant at p<0.01  ns - not significant (p>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  25.53 *  * - significant at p<0.05  504.57E02 448.85E02  ns - not significant (p>0.05)  1.12 ns  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 H I , 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, H I 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 distributed 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 rotational 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 H I 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 H I 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 o-ca, (Pa)  Coefficient of Determination, r  HMC  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)  2  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 (min)  Casson Yield o-ca, (Pa)  Coefficient of Determination, r  HI  12 30  29.1 (4.73)t 20.6 (8.83)  .983 .969  (n=386) (n=389)  H2  12 30  9.94 (2.34) 9.49 (3.10)  .995 .994  (n=381) (n=393)  2  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 Variation  df  Sample Error  3 4  686.89 3.6821  186.55 **  Run Time Interaction Run x Sample Error  1  59.981  182.87 **  1 4  48.410 0.32799  147.60 **  ** - significant at p<0.01  Mean Square  F-Ratio  Chapter 4. RESULTS AND DISCUSSION  4.4  STRESS R E L A X A T I O N  57  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 yaxis. 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 Relaxation Method and the Brabender viscometer with coaxial cylinder fixtures A l and A2.  Method  Cylindrical Fixture  Yield St]cess (Pa) HI HSS  HMC  Single measurement  A2 Al  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 Al  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)  H2  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 estimated 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 measured. 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  V A N E FIXTURE M E T H O D  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: cT = 2 T / [ 7 r / J ( t f + D/3)]  (4.12)  2  y  m  where D and H are the diameter and height of the vane fixture, T  m  is the maximum  torque measured and a is the calculated yield value. Table 4.18 shows the yield stress y  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 Speed (rpm)  E  HMC  0.064 0.120 0.224  31.3 32.8 33.4  30.4 32.9 32.7  29.9 30.2 31.8  HSS  0.064 0.120 0.224  39.7 42.8 44.5  35.6 37.0 39.2  HI  0.064 0.120 0.224  70.5 68.8 71.9  H2  0.064 0.120 0.224  29.0 30.9 31.9  Yield Stress (Pa) F G K  0  Coefficient of Variation (%)  31.5 33.0 32.4  29.0 30.0 31.1  3.98 5.45 3.56  36.8 38.8 40.4  38.5 39.7 40.0  44.8 44.3 47.6  8.63 7.71 8.70  109 107 109  68.0 65.4 66.9  66.5 65.3 66.5  61.1 63.5 65.1  23.45 23.23 22.71  29.5 31.2 32.1  30.7 30.4 31.7  32.4 36.2 35.6  31.4 31.8 34.9  6.72 8.57 6.92  Chapter 4. RESULTS AND DISCUSSION  61  A split plot analysis was carried out to determine if there were any significant differences between vane fixtures as well as rotational speeds. The results of the analysis of variance using the B M D P : 2 V 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 relatively 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 H I 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  - significant at p<0.05  46.829 14 8 56  2.8797 2.2798 1.4043  ** - significant at p<0.01  33.35 ** 2.05 * 1.62 ns  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  HMC  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)  2  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, cr = a^/rpm + a y  yo  (4-13)  Yield stress (o~ ) values estimated by this procedure (Figure 4.11) would presumably be yo  independent of rotational speed employed. The values are listed in Table 4.20. Vane F data for sample H I 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  90  75  Legend 60  o  H M C  •  H S S  o  HI  v H2 45  H  30  150.0  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  4.5.2  66  Multiple Vane Method I  This method utilized Equation 2.11 as described previously in Chapter 2. By plotting 2T /ir D as a function of the vane length to diameter ratio (H/D), the yield stress can 3  m  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 w ith H / D varying from 1.6 to 2.8. A linear regression test for equality of T  lines using the B M D P : 1 R 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 H I 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 Speed (rpm)  Yield Stress cj , (Pa)  m  Coefficient of Determination, r n=10  HMC  0.064 0.120 0.224  29.5 31.2 32.1  -0.60 -0.37 -0.10  0.947 0.906 0.959  HSS  0.064 0.120 0.224  55.2 54.8 59.4  -5.49 -6.08 -5.56  0.937 0.950 0.931  HI  0.064 0.120 0.224  34.0 40.8 44.4  -2.70 -2.58 -2.53  0.125 0.175 0.197  H2  0.064 0.120 0.224  30.1 32.3 37.0  -0.32 +0.16 +9.41  0.848 0.793 0.871  y  2  Chapter 4.  RESULTS AND DISCUSSION  68  o o  Legend o o o  o HMC • HSS  o o  o H1  v H2  • a  •  a  B  •  0.5  1.5  H/D  2.5  3.5  Figure 4.12: Plot of 2T /7rI> versus H / D (Method I) for estimating yield stress of chocolate samples at 40°C using vane fixtures E , F, G , K and 0. 3  m  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 Variation  df  Sample Speed Error  3 2 6  Mean Square  625.29 42.389 7.4041  F-Ratio  84.45 * 5.73 *  * - 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 B M D P : 2 V 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  4.5.3  70  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- = 2slope/TrD y  2  (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 H I , 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 H I , 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 Speed (rpm)  Yield Stress cjy, (Pa)  Coefficient of Determination, r n=6  HMC  0.064 0.120 0.224  27.5 29.6 30.1  0.946 0.916 0.973  HSS  0.064 0.120 0.224  57.7 53.3 59.3  0.967 0.954 0.944  HI  0.064 0.120 0.224  50.0 60.3 62.2  0.911 0.927 0.932  H2  0.064 0.120 0.224  32.4 34.1 40.2  0.956 0.871 0.957  2  Figure 4.13: Plot of peak torque versus vane height (Method II) for estimating yield stress of chocolate samples at 40°C using vanefixturesG, 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 Variation  df  Mean Square  F-Ratio  Sample Speed Error  3 2 6  636.89 37.392 11.622  54.80 ** 3.22 ns  ** - 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 H I . 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 conditions. 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 distinguishing 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, H I , 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 H I 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 H I . 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 H I , and, thereby, some error in calculating the yield value resulted. Also, sample H I 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 H I , 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 investigated. 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 values on sudden start-up obtained with the Brabender viscometer. Using the Single Vane Method, single point measurements were made at three different rotational speeds. A n 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 significant 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 H I . 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.  If further investigation of the  vane methods proves satisfactory, this method of estimating the yield stress of molten chocolate could be used for quality control purposes.  LITERATURE CITED  [1] Abbink, J . 1984. Shelflife of compounded chocolate. Confect. Manuf. and Market. 21(10):16. [2] A O A C . 1984. Official Methods of Analysis. 14th ed. Association of Official Analytical Chemists. Washington. D C . [3] Balmaceda, E., Huang, F. and Rlia, O K . 1973. Rheological properties of hydrocolloids. J . Food Sci. 38:1169. [4] Banford, H.F., Gardiner, K . J . , Howat, G.R. and Thomson, A . F . 1970. The use of polyglycerol polyricinoleate in chocolate. Confect. Prod. 36:359. [5] Barbosa-Canovas, G . V . and Peleg, M . 1983. Flow parameters of selected commercial semi-liquid food products. J . Text. Stud. 14:213. [6] Brookfield Engineering Laboratories Stoughton, M A .  Inc. 1985. When Viscosity is Measured.  [7] Brownsey, G . J . 1988. Commercial rotational instruments. In Rheological Measurement, A . A . Collyer and D.W. Clegg (Eds.) p. 405. Elsevier Applied Science PubUshers Ltd., London, U K . [8] Carri-Med Ltd. Instruction Handbook for the Carri-Med ControUed Stress Rheometer. Dorking, U K . [9] Casson, N . 1959. A flow equation for pigmented-oil suspensions of the printing ink type. In Rheology of Disperse Systems, O C . MiU (Ed.) p. 82. Pergamon Press, New York, N Y . [10] Charm, S.E. 1963. The direct determination of shear stress-shear rate behavior of foods in the presence of a yield stress. J . Food Sci. 28(1):107. [11] Cheng, D . C - H . 1978. On Bingham plastic fluids: theory and practice. Br. Soc. Rlieol. Bull. 21:60. [12] Cheng, D . C - H . 1986. Yield Stress: A time dependent property and how to measure it. Rheol. Acta. 25:542. [13] Chevalley, J . 1975. Rheology of chocolate. J . Text. Stud. 6:177. 79  LITERATURE  CITED  80  [14] Cloud, J . E . and Clark, P.E. 1985. Alternatives to the power-law fluid model for cross-linked fluids. Soc. Petrol. Eng. J. 25:935. [15] Cockinos, C. 1985. Developments in chocolate manufacturing. Manuf. Confect. 65(2)55. [16] Concon, J . M . and Soltess, D. 1973. Rapid micro-Kjeldahl digestion of cereal grains and other biological materials. Analytical Biochem. 53:35. [17] C.W. Brabender Instruments Inc. The Brabender Rheotron Instruction Manual. South Hackensack, N J . [18] Darby, R. 1985. Couette viscometer data reduction for materials with a yield stress. J. Rheol. 29(4):369. [19] Davis, S.S., Deer, J.J. and Warburton, B. 1968. A concentric cylinder air turbine viscometer. J . Sci. Instr. 1:933. [20] De Kee, D., Turcotte, G. and Fildey, K . 1980. New method for the determination of yield stress. J. Text. Stud. 10:281. [21] Dervisoglu, M . and Kokini, J . L . 1986. Steady shear rheology and fluid mechanics of four semi-solid foods. J . Food Sci. 51(3):541. [22] Dixon, W . J . 1985. B M D P Statistical Software. University of California Press, Berkeley, C A . [23] Duck, W . N . 1965. A rapid method for calculation of Casson flow values of chocolate. Manuf. Confect. 45(5):33. [24] Elliott, J . H . and Ganz, A . J . 1977. Salad dressings - preliminary rheological characterization. J . Text. Stud. 8:359. [25] Elliott, J . H . and Green, G . E . 1972. Modification of food characteristics with cellulose hydro colloids. II. The modified Bingham body - a useful rheological model. J . Text. Stud. 3:194. [26] Franck, A.J.P. 1985. A rheometer for characterizing polymer melts and suspensions in shear creep and recovery experiments. J . Rheol. 29(6):833. [27] Hanks, R . W . 1983. Couette viscometry of Casson fluids. J . Rheol. 27(1):1. [28] Heathcock, J.F. 1985. Characterization of milk proteins in confectioner}' products. Food Microstructure. 4(1):17.  LITERATURE  CITED  81  [29] Heimann. W . and Fincke, A . 1962a. Rheometry of chocolate - the flow equation of Casson and its application to rheometry of chocolate. Z Lebensm. Untersuch. Forsch. 117:93. [30] Heimann, W . and Fincke, A . 1962b. Measuring the flow limits and their calculation from the Casson equation. Z Lebensm. Untersuch. Forsch. 117:225. [31] Heimann, W . and Fincke, A . 1962c. Application of a modified Casson equation to milk chocolates and cocoa pastes. Z. Lebensm. Untersuch. Forsch. 117:297. [32] Heimann, W . and Fincke, A . 1962d. Temperature dependence of the flow behavior of molten chocolate. Z. Lebensm. Untersuch. Forsch. 117:301. [33] Howard, D . W . 1969a. Adapted instrument measures Casson values. Candy Ind. 133(8):21. [34] Howard, D . W . 1969b. Brookfield develops reliable measurement of chocolate viscosity. Manuf. Confect. 49(10):48. [35] Hunter, R . J . and Nicol, S.K. 1968. The dependence of plastic flow behavior of clay suspensions on surface properties. J . Colloid, and Interface Sci. 28(2):250. [36] James. A . E . , Williams, D.J.A. and Williams, P.R. 1987. Direct measurement of static yield properties of cohesive suspensions. Rheol. Acta. 26(5):437. [37] Kaletunc-Gencer, G. and Peleg, M . 1984. Digitizer aided determination of yield stress in semi-liquid foods. J . Food Sci. 49(6):1620. [38] Keentok, M . 1982. The measurement of the yield stress of liquids. Rheol. Acta. 21:325. [39] Kiljanski, T. 1989. A method for correction of the wall-slip effect in a Couette rheometer. Rheol. Acta. 28:61. [40] Kleinert, J . 1976. Rheology of chocolate. In Rheology and Texture in Food Quality, J . M . deMan, P.W. Voisey, V . F . Rasper and D . W . Stanley (Eds.) p.445. AVI Publishing Co. Inc., Westport, C T . [41] Kleinert, J . 1982a. Cyclo-TRG measurements I. Rev. C h o c , Confect. and Bakery. ' 7(2):4. [42] Kleinert, J . 1982b. Cyclo-TRG measurements II. Rev. C h o c , Confect. and Bakery. 7(2):4.  [43] Kleinert, J . 1982c. Cyclo-TRG measurements III. Rev. Choc, Confect. and Bakery. 7(3):3.  LITERATURE  CITED  82  Krieger, I . M . 1968. Shear rate in the couette viscometer. Trans. Soc. Rlieol. 12:5. Kuster, W . 1985. Efficient use of five-roll refiner in producing chocolates and other fatty mixtures. Manuf. Confect. 65(6):55. Lang, E.R. and Rha C . K . 1981. Determination of the yield stress of hydrocolloid dispersions. J . Text. Stud. 12:47. Levine, L. 1987. A n introduction to the measurement of viscosity. Viscous Products, p. 14. Malm, M . 1967a. Interrelation between Casson values and other properties of chocolate. Manuf. Confect. 47(5):63. Malm, M . 1967b. More refining raises chocolate yield value. Candy Ind. 129(8):21. Malm, M . 1968. Inter-relations between Casson values and other properties of sweet and milk chocolate. Confect. Manuf. Market. 5(2):22. Markov, E. and Tscheuschner, H.D. 1989. Instrumental texture studies n chocolate: IV. Comparison between instrumental and sensory texture studies. J . Text. Stud. 20:151. Minifie, B. (Ed.). 1980. Chocolate, Cocoa and Confectionery. AVI Publishing Co. Inc., Westport, C T . Motz, R . J . 1964. Notes on viscometry. Rev. Intern. Chocolat. 19:198. Navickis, L . L . and Bagley, E . B . 1983. Yield stresses in concentrated dispersions of closely packed, deformable gel particles. J . Rheol. 27(6):519. Nguyen, Q.D. and Boger, D . V . 1983. Yield stress measurement for concentrated suspensions. J . Rheol. 27(4):321. Nguyen, Q.D. and Boger, D.V. 1985. Direct yield stress measurement with the vane method. J . Rheol. 29(3):335. Niediek, I.E.A. 1980. The characterisation of the flow properties of melted chocolated masses. Rev. Choc, Confect. and Bakery. 5(3):3. Niediek, I.E.A. 1981. The characterisation of the flow properties of melted chocolated masses II. Rev. Choc, Confect. and Bakery. 6(2):3. Office International du Cacao et du Chocolate. 1970. 1973. Viscosity of Chocolate determination of Casson yield value and Casson plastic viscosity. Int. Choc. Review. 28(9):223.  LITERATURE  83  CITED  [60] Paredes, M . D . C . , Rao, M . A . and Bourne, M . C . 1989. Rheological characterization of salad dressings 2: Effect of storage. J . Text. Stud. 20:235. [61] Patton, T . C . 1966. A new method for the viscosity measurement of paint in the settling, sagging, leveling and penetration shear rate range of .001 to 1.0 reciprocal seconds using a cone/plate spring relaxation technique. J . Paint Technol. 38(502):656. [62] Prentice, J . H . and Huber, D. 1981. Results of the colaborative study on measuring rheological properties of foodstuffs. In Physical Properties of Foods, R. Jowitt, F. Esher, B . Hallstrom, H.F.Th. Meffert, W.E.I. Spiess and G. Vos (Eds.) p. 123. Applied Science Publishers, London, U K . [63] Qiu, C . G . and Rao, M . A . 1989. Effect of dispersed phase on the slip coefficient of apple sauce in a concentric cylinder viscometer. J . Text. Stud. 20:57. [64] Rao, M . A . and Coolej , H.J. 1983. Applicability of flow models with yield for tomato concentrates. J . Food Process Eng. 6:159. r  [65] Reade, M . G . 1985. Cooling processes - the natural rate of solidification of chocolate. Manuf. Confect. 65(1 ):59. [66] Robbins, J . W . 1979. A quick, reliable method for measuring yield value, plastic viscosity and MacMichael viscosity of chocolate. Manuf. Confect. 59(5):38. [67] Robbins, J . W . 1983. Methods for measuring particle size distribution of chocolate products. Candy Ind. 148(7):39. [68] Rosen, M . R . and Foster, W . W . 1978. Approximate rheological characterization of Casson fluids - Template method for the Brookfield Synchro-lectric viscometers. J . Coatings Technol. 50(643):39. [69] Rostagno, W., Chevalley, J . and Viret, D. 1974. Rheological properties of chocolate. First International Congress on Cocoa and Chocolate Research. 174. [70] Rostagno, W . 1974. Rheological properties of chocolate. Dechema-monographien. 77:283. [71] Saunders, P.R. 1968a. The flow properties of chocolate in relation to structure. Brit. Food. Manuf. Ind. Res. Assoc. Techn. Circ. No. 387. [72] Sequine, E.S. 1986. Instrument review: Brookfield. Manuf. Confect. 66(1):49. [73] Smith, R . E . 1982. Brookfield viscometers for determination of low-shear viscosity and leveling behavior. J . Coatings Technol. 54(694):21.  LITERATURE  CITED  84  [74] Solstad, 0. 1983. Viscosity properties of chocolate. Manuf. Confect. 63(8):41. Sommer, K . 1974. On the flow behavior of chocolate masses. First Intern. Cong, on Cocoa and Chocolate Res., Munich, May 8-10, p.181. Steel, R.G.D. and Torrie, J . H . 1960. Principles and Procedures of Statistics. Mcgraw-Hill Book Co. Inc., New York, N Y . Steiner, E . H . 1958. A new rheological relationship to express the flow properties of melted chocolate. Brit. Food. Manuf. Ind. Res. Assoc. 13(7):290. Steiner, E . H . 1962. An investigation into the validity of the Casson relationship for melted chocolate at low rates of shear and at various temperatures. Brit. Food. Manuf. Ind. Res. Assoc. 17:150. Steiner, E . H . 1972. Melted chocolate: 52(9):24.  Measuring its viscosity. Manuf. Confect.  Swartzel, K . R . , Hamann, D . D . and Hansen, A.P. 1980. Rheological modelling of U H T milk gels using a cone and plate creep-relaxation test. J . Food Process. Eng. 161. Tiu.^ C. and Boger, D.V. 1974. Complete rheological characterization of timedependent food products. J . Text. Stud. 5:329. Tscheuschner, H.D. and Markov, E . 1986. Instrumental texture studies on chocolate: I. Methods of measurement and texture characteristics. J . Text. Stud. 17:37. Tscheuschner, H.D. and Wunsche, D. 1979. Rheological properties of chocolate masses and the influence of some factors. Ch. 3. In Food Texture and Rheology, P. Sherman (Ed.), p. 355. Academic Press, London, U K . Tung, M . A . , Speers, R . A . , Britt, I.J., Owen, S.R. and Wilson, L . L . 1990. Yield stress characterization of structured foods. In Engineering and Food: Volume 1. Phj'sical Properties and Process Control, W.E.L. Spiess and H . Schubert (Eds.) p. 79. Elsevier Applied Science, London, U K . Tung, M . A . and Speers, R . A . 1986. Development of Yield Stress Measurement Methodology. Final Report. DSS File No. 01SG.97702-R-5-0679, prepared for Defence Research Establishment Suffield, Ralston, A B . Van Wazer, J.R., Lyons J.W., K i m K . Y . and Colwell, R . E . 1963. Viscosity and Flow Measurement - A Laboratory Handbook of Rheology. John Wiley and Sons Inc., New York, N Y .  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 comparison 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 Rate (s") 1  0.340 0.850 1.70 3.40 6.80 17.0  HMC  HSS  HI  H2  asc  dsc  asc  dsc  asc  dsc  asc  dsc  33.0 49.2 67.0 96.3 146  28.5 42.6 59.8 89.4 144  46.9 60.5 74.0 95.6 132  43.8 57.1 71.8 93.6 130  36.0 70.8 99.6 138  35.0 66.0 94.8 133  28.2 36.7 46.9 63.3 94.5 164  27.2 35.7 45.6 61.3 89.1 163  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 A l and spring C for steady shear tests at ascending (asc) and descending (dsc) shear rate. Shear Rate (s ) 1  0.191 0.358 0.669 1.30 2.54 5.00 10.0 25.0 24.2 40.3 75.8  HI  HSS  HMC  H2  asc  dsc  asc  dsc  asc  dsc  asc  dsc  28.9 36.4 43.2 50.8 69.0 103 175 305 286 492 787  23.0 30.8 37.7 48.6 67.7 101 170 287 266 451 744  39.9 50.8 58.8 67.7 82.7 106 157 243 231 369 607  34.7 46.6 55.5 65.5 78.5 102 152 235 225 361 594  37.1 44.3 56.6 75.9 97.6 135 198 321 308 488 742  36.7 43.8 55.8 74.2 96.1 133 194 303 286 449 720  25.4 34.3 39.0 47.1 58.6 77.4 113 194 178 306 490  22.3 31.9 35.8 44.0 54.9 72.5 106 180 167 285 479  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 Rate (a") 1  0.066 0.124 0.231 0.448 0.877 1.73 3.46 8.63 8.38 13.9 26.2 50.8  HMC  HSS  HI  H2  asc  dsc  asc  dsc  asc  dsc  asc  18.5 25.6 31.4 35.9 45.3 59.2 89.1 147 138 231 379 635  14.2 21.8 27.3 33.7 42.0 58.4 87.5 141 136 217 345 605  27.3 39.2 44.3 52.1 58.7 71.1 93.1 127 123 184 282 463  23.0 34.4 39.7 49.1 55.7 68.1 89.8 123 120 178 274 440  27.6 36.7 51.4 69.3 85.8 107 149 219 208 328 463 701  28.6 38.0 51.9 67.6 80.0 103 139 199 193 289 433 671  22.5 29.9 34.2 37.7 43.3 52.4 70.1 102 98.2 154 238 396  dsc 20.2 28.1 32.1 35.9 41.5 50.6 67.6 96.0 92.9 142 225 384  Appendix A. LISTING OF EXPERIMENTAL  FLOW DATA  Table A.28: Shear rate data (s ) obtained for the chocolate samples at 40°C using the Carri-Med rheometer and coaxial cylinderfixture5222 for controlled stress tests at ascending (asc) and descending (dsc) shear stress. 1  Shear Stress (Pa) 1.926 3.852 5.778 7.704 9.630 11.55 13.48 15.40 17.33 19.26 21.18 23.11 25.03 26.96 28.89 30.81 32.74 34.66 36.59 38.52 40.44 42.37 44.29 46.22 48.15 50.07 52.00 53.92 55.85 57.78 59.70 61.63 63.55 65.48 67.41  HMC asc  0.0409 0.0502 0.0653 0.0887 0.0887 0.1124 0.1331 0.1566 0.1725 0.1955 0.2150 0.2396 0.2615 0.2896 0.3190 0.3502 0.3802 0.4158 0.4592 0.5040 0.5577 0.6162 0.6766 0.7539 0.8187 0.8945 0.9983 1.044 1.183 1.279 1.385 1.484  dsc 0.0370 0.0409 0.0672 0.0916 0.1098 0.1287 0.1506 0.1669 0.1862 0.2089 0.2386 0.2652 0.2983 0.3332 0.3741 0.4214 0.4748 0.5228 0.5796 0.6593 0.7322 0.8163 0.9003 0.9894 1.081 1.181 1.288 1.379 1.498 1.620 1.723 1.835 1.916 2.059  HSS asc  0.0464 0.0487 0.0660 0.0858 0.0782 0.0939 0.1062 0.1184 2.571 0.1494 0.1689 0.1930 0.2157 0.2362 0.2691 0.3005 0.3337 0.3771 0.4297 0.4858 0.5503 0.6242 0.7021 0.7852 0.8967 1.004 1.116 1.248 1.377 1.524  HI dsc  asc  H2 dsc  asc  0.0292  0.0341  0.0097 0.0585  0.0546 0.0624 0.0766 0.0838 0.0950 0.1121 0.1272 0.1423 0.1587 0.1811 0.2006 0.2259 0.2596 0.2991 0.3451 0.4027 0.4655 0.5423 0.6283 0.7317 0.8462 0.9554 1.089 1.217 1.346 1.516 1.677 1.825 1.998 2.166 2.336  0.0609 0.0276 0.0448 0.0600 0.0721 0.0835 0.0945 0.1092 0.1221 0.1433 0.1550 0.1807 0.1943 0.2122 0.2307 0.2509 0.2739 0.2951 0.3120 0.3377 0.3584 0.3805 0.3698 0.4316 0.4579 0.4914 0.5196 0.5447 0.5749 0.5970 0.6230  0.0819 0.1033 0.1009 0.1186 0.1394 0.1599 0.1742 0.1907 0.2083 0.2307 0.2528 0.2756 0.2986 0.3185 0.3522 0.3744 0.3987 0.4211 0.4536 0.4846 0.5158 0.5430 0.5772 0.6070 0.5599 0.6769 0.7253 0.7588 0.7975  0.0624 0.0526 0.0438 0.0465 0.0746 2.133 0.0975 0.1075 0.1219 0.1431 0.1584 0.1840 0.1984 0.2203 0.2369 0.2554 0.2854 0.3125 0.3383 0.3622 0.3919 0.4239 0.4526 0.4797 0.5228 0.5574 0.6118 0.6600 0.7056 0.7595 0.8192 0.8865  dsc 0.0390 0.0646 0.0890 0.1105 0.1293 0.1456 0.1589 0.1618 0.1963 0.2154 0.2392 0.2678 0.2925 0.3233 0.3490 0.3809 0.4225 0.4608 0.5076 0.5557 0.6097 0.6659 0.7215 0.8044 0.8631 0.9262 1.021 1.091 1.173 1.252 1.347 continued..  Appendix A. LISTING OF EXPERIMENTAL  FLOW  DATA  91  Table A.28 continued. Shear Stress (Pa)  HMC  HSS  HI  H2  asc  dsc  asc  dsc  asc  dsc  asc  dsc  69.33 71.26 73.18 75.11 77.04 78.96 80.89 82.81 84.74 86.67 88.59 90.52 92.44 94.37 96.30 98.22 100.1 102.0 104.0 105.9 107.8 109.7 111.7 113.6 115.5 117.4 119.4 121.3 123.2 125.1 127.1 129.0 130.9 132.8 134.8 136.7 138.6  1.590 1.694 1.795 1.918 2.030 2.126 2.224 2.339 2.475 2.576 2.677 2.795 2.887 3.004 3.103 3.208 3.311 3.418 3.531 3.601 3.764 3.873 4.003 4.067 4.222 4.336 4.459 4.576 4.697 4.837 4.945 5.074 5.196 5.292 5.440 5.527 5.675  2.193 2.303 2.426 2.562 2.682 2.612 2.909 3.031 3.165 3.297 3.409 3.507 3.638 3.763 3.902 4.022 4.141 4.285 4.412 4.512 4.640 4.785 4.926 5.029 4.965 5.281 5.434 5.549 5.691 5.848 5.945 6.074 6.215 6.333 6.483 6.595 6.710  1.659 1.820 1.975 2.129 2.293 2.443 2.597 2.778 2.948 3.085 3.228 3.378 3.515 3.669 3.819 3.987 4.176 4.328 4.514 4.677 4.840 5.027 5.201 5.373 5.563 5.735 5.917 6.101 6.273 6.475 6.649 6.853 7.021 7.270 7.449 7.625 7.829  2.497 2.684 2.875 3.041 3.262 3.424 3.600 3.825 3.997 4.202 4.398 4.588 4.786 4.983 5.225 5.410 5.634 5.851 6.061 6.273 6.481 6.681 6.921 7.112 7.354 7.586 7.796 8.017 8.218 8.450 8.660 8.924 9.124 9.393 9.603 9.800 10.02  0.6649 0.4686 0.3714 0.7608 0.8229 0.8609 0.8943 0.9386 0.9984 1.046 1.092 1.143 1.206 1.256 1.325 1.354 1.454 1.530 1.589 1.651 1.732 1.827 1.901 1.976 2.081 2.153 2.245 2.337 2.417 2.478 2.587 2.686 2.766 2.751 2.969 3.066 3.135  0.8460 0.9025 0.9476 0.9971 1.057 1.006 0.9177 1.223 1.286 1.358 1.426 1.495 1.579 1.634 1.357 1.808 1.880 1.968 2.047 1.775 2.221 2.370 2.411 2.490 2.574 2.670 2.761 2.835 2.957 3.051 3.146 3.243 3.352 3.449 3.030 3.662 3.807  0.9587 1.038 1.110 1.203 1.276 1.373 1.465 1.543 1.633 1.741 1.838 1.926 2.026 2.135 2.236 2.339 2.455 2.554 2.647 2.758 2.868 2.981 3.063 3.193 3.310 3.400 3.532 3.662 3.778 3.912 4.023 4.139 4.292 4.393 4.529 4.649 4.751  1.450 1.539 1.631 1.731 1.829 1.937 2.023 1.463 2.244 2.078 1.894 1.873 2.858 2.976 3.111 3.228 3.350 3.503 3.593 3.727 3.875 4.004 4.123 4.265 4.389 4.463 4.633 4.808 4.922 5.079 5.198 5.297 5.457 5.579 5.742 5.872 5.989  :  continued..  Appendix A. LISTING  OF EXPERIMENTAL  FLOW  DATA  92  Table A.28 continued. Shear Stress (Pa)  HMC  HSS  asc  dsc  asc  140.5 142.5 144.4 146.3 148.3 150.2 152.1 154.0 156.0 157.9 159.8 161.7 163.7 165.6 167.5 169.4 171.4 173.3 175.2 177.1 179.1 181.0 182.9 184.8 186.8 188.7 190.6 192.6 194.5 196.4 198.3 200.3 202.2 204.1 206.0 208.0 209.9  5.820 5.925 6.041 6.197 6.292 6.401 6.533 6.632 6.749 6.800 6.966 7.106 7.226 7.376 7.456 7.600 7.692 7.862 7.930 8.013 8.172 8.284 8.467 8.535 8.610 8.816 8.989 9.094 9.176 9.369 9.443 9.543 9.745 9.851 9.955 10.15 10.25  6.865 7.013 6.573 7.266 7.413 7.535 7.652 7.672 7.916 7.997 8.174 8.327 8.356 8.607 8.077 8.872 8.948 9.151 9.226 9.346 9.531 9.601 9.779 9.916 9.949 10.16 10.34 10.47 10.56 10.77 10.83 11.00 11.14 11.26 11.38 11.52 11.46  8.049 8.230 8.401 8.657 8.850 9.063 9.245 9.434 9.626 9.795 10.09 10.36 10.50 10.78 10.92 11.22 11.36 11.63 11.75 11.90 12.18 12.30 12.64 12.81 13.10 13.29 13.60 13.76 13.91 14.19 14.44 14.62 14.95 15.13 15.27 15.63 15.83  HI dsc  10.27 10.47 10.69 10.98 11.21 11.43 11.67 11.91 12.13 12.26 12.58 12.90 13.04 13.31 13.50 13.80 14.02 14.31 14.46 14.57 14.95 15.10 15.44 15.57 15.90 16.09 16.47 16.60 16.76 17.16 17.31 17.50 17.84 18.00 18.19 18.55 18.77  H2  asc  dsc  asc  dsc  3.255 3.357 3.415 3.533 3.634 3.700 3.788 3.807 3.968 4.059 4.203 4.291 4.435 4.603 3.912 4.916 5.000 5.157 5.242 5.302 5.459 5.518 5.626 5.115 5.801 5.944 6.089 6.123 5.715 6.325 6.407 6.320 6.633 6.715 5.674 6.928 6.995  3.870 3.965 4.045 4.183 4.263 4.420 4.500 4.574 4.690 4.371 4.913 4.962 5.111 4.218 5.346 5.454 5.578 5.718 5.793 5.810 6.012 6.134 6.252 6.306 6.409 6.041 6.096 6.852 6.881 6.794 7.156 7.169 7.417 7.505 7.575 7.014 7.841  4.903 5.052 5.158 5.299 5.448 5.572 5.689 5.827 5.943 6.045 6.191 6.303 6.431 6.562 6.705 6.848 6.527 7.100 7.216 7.294 7.445 7.554 7.721 7.782 7.890 8.066 8.249 8.364 8.440 8.388 8.753 8.847 9.026 9.126 9.232 9.413 9.572  6.002 6.300 6.439 6.591 6.726 6.866 7.008 7.098 6.986 7.354 7.543 7.639 7.819 7.966 8.120 7.457 8.420 8.604 8.693 8.784 8.951 8.362 9.305 9.467 8.616 9.698 9.867 8.918 9.034 9.227 9.310 9.385 8.572 9.719 9.774 10.02 10.12 continued.  Appendix A. LISTING OF EXPERIMENTAL  FLOW  DATA  93  Table A.28 continued. Shear Stress (Pa)  HMC  HSS  HI  asc  dsc  asc  dsc  211.8 213.7 215.7 217.6 219.5 221.4 223.4 225.3 227.2 229.1 231.1 233.0 234.9 236.8 238.8 240.7 242.6 244.6 246.5 248.4 250.3 252.3 254.2 256.1 258.0 260.0 261.9 263.8 265.7 267.7 269.6 271.5 273.4 275.4 277.3 279.2 281.1  10.35 10.54 10.62 10.78 10.92 11.07 11.17 11.29 11.47 11.61 11.63 11.83 11.99 11.96 12.34 12.42 11.92 12.72 12.77 12.96 13.12 13.37 13.34 13.46 13.66 13.81 13.87 14.08 14.29 14.15 14.56 14.64 14.77 14.78 14.94 15.23 15.12  11.76 11.94 12.05 12.19 12.42 12.49 12.64 12.78 12.86 13.01 13.13 12.44 13.45 13.54 13.78 13.87 13.96 14.12 14.09 14.41 14.56 14.54 14.75 14.85 15.16 15.24 15.32 15.49 15.54 15.54 15.91 16.00 16.15 16.26 16.38 16.46 16.72  16.08 16.36 16.55 16.64 17.06 17.22 17.47 17.81 18.02 18.21 18.43 18.63 18.97 19.18 19.59 19.82 20.01 20.21 20.42 20.83 21.06 21.27 21.43 21.71 22.10 22.33 22.56 22.77 23.22 23.43 23.66 23.90 24.15 24.35 24.61 25.03 25.26  19.03 19.27 19.48 19.68 20.02 20.22 20.40 20.77 20.98 21.16 21.36 21.53 21.93 22.10 22.49 22.71 22.86 23.12 23.27 23.70 23.90 24.05 24.30 24.48 24.91 25.08 25.28 25.49 25.89 26.11 26.32 26.52 26.74 26.92 27.15 27.57 27.76  H2  asc  dsc  asc  dsc  7.083 7.153 7.355 7.406 7.574 7.685 7.775 7.973 8.065 8.156 8.284 8.303 8.618 8.669 8.750 8.929 9.076 9.208 9.309 9.442 9.582 9.708 9.768 9.853 10.06 10.20 10.28 10.38 10.59 10.73 10.81 10.68 10.97 11.20 11.28 11.47 11.60  6.842 8.051 8.213 8.251 8.467 8.490 8.706 8.864 8.940 9.029 7.130 9.279 9.374 9.506 9.582 9.854 9.912 10.02 10.10 9.463 10.44 10.52 10.65 10.73 10.94 11.05 9.364 11.22 11.41 11.36 11.73 11.82 11.90 11.78 12.13 10.62 12.40  9.637 9.760 9.945 10.06 10.27 10.42 10.48 10.73 10.84 10.96 11.05 11.16 11.44 11.52 11.65 11.79 11.95 12.12 12.17 12.45 12.55 12.29 12.82 12.94 13.16 13.26 13.42 13.52 13.72 13.86 14.05 14.15 14.37 14.40 14.62 14.83 14.89  10.18 10.28 10.52 10.64 9.989 10.96 11.03 11.26 11.30 11.44 11.55 11.69 11.86 11.93 11.97 12.28 12.41 12.52 12.67 12.92 13.00 13.08 13.25 11.86 13.58 13.67 13.66 13.84 14.08 13.86 14.33 14.48 14.59 14.67 14.85 15.05 15.19 continued..  Appendix A. LISTING OF EXPERIMENTAL  FLOW DATA  94  Table A.28 continued. Shear Stress (Pa)  HMC  HSS  HI  H2  asc  dsc  asc  dsc  asc  dsc  asc  dsc  283.1 285.0 286.9 288.9 290.8 292.7 294.6 296.6 298.5 300.4 302.3 304.3 306.2 308.1 310.0 312.0 313.9 315.8 317.7 319.7 321.6 323.5 325.4 327.4 329.3 331.2 333.1 335.1 337.0 338.9 340.9 342.8 344.7 346.6 348.6 350.5 352.4  15.52 15.60 15.77 16.04 15.80 16.29 16.37 16.56 16.69 16.80 16.23 16.89 17.20 16.87 17.46 17.65 17.93 18.03 18.16 18.31 18.44 18.70 18.90 19.00 19.13 19.20 19.37 19.25 19.76 19.90 20.01 20.04 20.33 19.94 20.68 20.33 20.92  16.84 16.99 17.05 17.33 17.45 17.57 17.70 17.79 17.93 18.02 18.14 18.23 18.40 18.35 18.63 18.75 19.04 18.94 19.28 19.33 19.49 19.71 19.88 20.02 20.14 20.23 20.38 20.49 18.53 21.88 20.62 21.00 20.64 21.29 21.37 21.45 21.56  25.53 25.68 26.02 26.42 26.65 26.90 27.07 27.38 27.62 27.80 28.08 28.36 28.58 28.82 29.04 29.47 29.81 30.04 30.31 30.47 30.77 31.29 31.56 31.80 32.03 32.16 32.50 32.86 33.19 33.43 33.62 33.81 34.05 34.44 34.67 35.00 35.21  28.00 28.19 28.40 28.86 29.04 29.24 29.45 29.66 29.91 30.16 30.32 30.49 30.72 31.00 31.17 31.61 31.84 32.06 32.26 32.41 32.64 33.10 33.37 33.59 33.74 33.93 34.17 34.35 34.63 34.88 35.11 35.28 35.44 35.64 35.95 36.17 36.38  11.62 11.80 11.99 12.00 12.06 11.59 12.50 12.61 12.74 12.85 12.93 13.10 13.21 11.56 13.39 13.62 11.95 13.94 14.06 14.17 14.28 14.46 14.60 14.77 15.01 15.13 15.21 15.39 15.43 15.62 15.79 15.89 16.15 16.13 16.27 15.48 16.58  12.57 12.71 12.78 12.93 11.28 13.25 13.34 13.40 13.62 13.59 13.44 13.93 14.00 14.21 14.30 14.53 14.68 14.73 14.91 15.00 15.06 15.13 15.39 15.61 15.67 15.80 15.91 16.05 16.19 16.36 16.35 16.60 16.62 16.71 16.92 16.97 17.21  15.06 15.18 15.30 15.48 15.69 15.86 16.04 16.23 16.11 16.47 16.59 16.72 16.93 17.07 17.16 17.41 17.56 17.71 17.93 19.24 18.21 18.36 18.54 18.80 18.90 19.01 19.21 19.43 18.86 19.78 19.92 20.15 20.22 19.64 20.57 20.73 20.87  15.32 15.44 15.51 15.72 15.86 15.99 16.08 16.28 16.36 16.52 16.57 16.69 16.83 16.92 17.08 17.26 17.37 17.43 17.69 17.78 17.94 18.09 18.14 18.43 18.48 17.34 18.75 18.91 19.00 19.19 19.30 19.43 19.46 19.08 19.61 19.81 19.97 continued.  Appendix A. LISTING OF EXPERIMENTAL  FLOW  DATA  Table A.28 continued. Shear Stress (Pa)  asc  dsc  asc  dsc  asc  dsc  asc  dsc  354.3 356.3 358.2 360.1 362.0 364.0 365.9 367.8 369.7 371.7 373.6 375.5 377.4 379.4 381.3 383.2 385.2  21.21 21.39 21.54 21.70 21.85 21.75 21.49 22.26 22.51 22.64 22.47 22.98 23.08 23.29 23.40 23.61 23.77  21.74 21.96 21.58 22.25 22.31 22.44 22.59 22.20 22.85 22.94 23.08 23.18 23.00 23.47 23.59 23.58 23.81  35.65 35.93 36.24 36.57 36.84 37.15 37.48 37.67 38.00 38.27 38.51 38.74 38.99 39.22 39.58 39.84 40.07  36.79 36.94 37.15 37.37 37.60 37.81 38.04 38.27 38.52 38.70 38.85 39.04 39.25 39.53 39.70 39.90 40.12  16.74 16.94 17.14 17.37 17.24 17.51 17.69 17.97 18.02 18.20 18.28 16.67 18.64 18.80 18.98 19.11 19.28  16.34 17.38 17.71 17.82 17.83 17.94 18.03 18.22 16.28 18.47 18.48 18.69 18.71 18.88 19.10 19.24 19.25  21.14 21.30 21.58 21.70 21.88 22.07 22.19 22.41 22.56 22.71 22.88 23.02 23.24 23.46 23.61 23.78 24.00  20.09 20.30 20.41 20.50 20.69 20.84 20.94 21.07 21.20 21.34 21.40 21.57 21.64 21.71 21.85 21.90 22.13  HMC  HI  HSS  H2  s  Appendix A. LISTING OF EXPERIMENTAL  96  FLOW DATA  Table A.29: Shear rate data (s ) 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. 1  30 min run  12 min run Shear Stress (Pa) 12.11 14.53 16.95 19.38 21.80 24.22 26.64 29.06 31.48 33.91 36.33 38.75 41.17 43.59 46.02 48.44 50.86 53.28 55.70 58.13 60.55 62.97 65.39 67.81 70.24 72.66 75.08 77.50 79.92 82.35 84.77  Shear rate ' (s-) asc dsc 1  0.0507 0.0493 0.0644 0.1034 0.0937 0.1165 0.1412 0.1601 0.1805 0.2046 0.2261 0.2472 0.2742 0.3009 0.3243 0.3523 0.3822 0.4147 0.4473 0.4798 0.5065 0.5367 0.5696 0.6005 0.6386 0.6698 0.7040  0.0673 0.0683 0.0904 0.1096 0.1259 0.1513 0.1740 0.1997 0.2267 0.2531 0.2804 0.3149 0.3458 0.3757 0.4089 0.4473 0.4840 0.5218 0.5628 0.6008 0.6434 0.6897 0.7326 0.7837 0.8373 0.8881 0.9496 1.011 1.073 1.145 1.218  Shear Stress (Pa) 5.813 8.720 10.17 11.63 13.08 14.53 15.98 17.44 18.89 20.34 21.80 23.25 24.70 26.16 27.61 29.06 30.52 31.97 33.42 34.88 36.33 37.78 39.24 40.69 42.14 43.59 45.05 46.50 47.95 49.41 50.86  Shear rate IV ) 1  asc  0.0161 0.0312 0.0307 0.0290 0.0468 0.0426 0.0514 0.0615 0.0748 0.0862 0.0992 0.1106 0.1220 0.1350 0.1513 0.1653 0.1802 0.1958 0.2111 0.2297 0.2437 0.2583 0.2723 0.2853 0.2986 0.3155 0.3295 0.3412 0.3556  dsc 0.0166 0.0322 0.0335 0.0452 0.0537 0.0641 0.0777 0.0917 0.1057 0.1204 0.1353 0.1493 0.1646 0.1783 0.1939 0.2082 0.2277 0.2375 0.2521 0.2658 0.2807 0.2941 0.3087 0.3240 0.3370 0.3520 0.3679 0.3832 0.3972 0.4229 0.4392  continued.  Appendix A. LISTING OF EXPERIMENTAL  97  FLOW DATA  Table A.29 continued. 12 min run Shear Stress (Pa) 87.19 89.61 92.03 94.45 96.88 99.30 101.7 104.1 106.6 109.0 111.4 113.8 116.3 118.7 121.1 123.5 125.9 128.4 130.8 133.2 135.6 138.0 140.5 142.9 145.3 147.7 150.2 152.6 155.0 157.4 159.8 162.3 164.7 167.1  30 min run  Shear rate (s-) asc dsc 1  0.7446 0.7879 0.8393 0.8917 0.9362 0.9935 1.048 1.113 1.177 1.251 1.335 1.414 1.490 1.592 1.693 1.794 1.907 2.020 2.129 2.254 2.383 2.501 2.612 2.739 2.865 3.009 3.155 3.285 3.407 3.550 3.681 3.807 3.937 4.068  1.299 1.384 1.464 1.565 1.651 1.748 1.841 1.947 2.049 2.157 2.257 2.374 2.491 2.602 2.724 2.842 2.961 3.086 3.221 3.344 3.465 3.599 3.719 3.872 4.003 4.132 4.270 4.400 4.527 4.665 4.809 5.027 5.104 5.268  Shear Stress (Pa) 52.31 53.77 55.22 56.67 58.13 59.58 61.03 62.49 63.94 65.39 66.84 68.30 69.75 71.20 72.66 74.11 75.56 77.02 78.47 79.92 81.38 82.83 84.28 85.74 87.19 88.64 90.10 91.55 93.00 94.45 95.91 97.36 98.81 100.3  Shear rate (s-) asc dsc 1  0.3725 0.3865 0.4017 0.4203 0.4352 0.4512 0.4678 0.4821 0.5000 0.5156 0.5293 0.5426 0.5592 0.5794 0.6002 0.6187 0.6392 0.6578 0.6795 0.7036 0.7225 0.7443 0.7703 0.7970 0.8243 0.8487 0.8777 0.9027 0.9323 0.9635 0.9941 1.032 1.068 1.107  0.4613 0.4779 0.4951 0.5127 0.5306 0.5442 0.5673 0.5829 0.5992 0.6155 0.6421 0.6581 0.6861 0.7241 0.7687 0.7999 0.8354 0.8744 0.9089 0.9447 0.9824 1.016 1.058 1.096 1.139 1.181 1.225 1.270 1.316 1.365 1.419 1.469 1.520 1.576  continued.  Appendix A. LISTING OF EXPERIMENTAL  98  FLOW DATA  Table A.29 continued. 12 min run Shear Stress Q?a) 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  30 min run  Shear rate (s") asc dsc 1  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  Shear Stress 0?a)  Shear rate (s ) asc dsc  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  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  99  Table A.29 continued. 12 min run  30 min run  Shear Stress (Pa)  asc  dsc  Shear Stress (Pa)  251.9 254.3 256.7 259.1 261.6 264.0 266.4 268.8 271.3 273.7 276.1 278.5 280.9 283.4 285.8 288.2 290.6 293.1 295.5 297.9 300.3 302.7 305.2 307.6 310.0 312.4 314.8 317.3 319.7 322.1 324.5 327.0 329.4 331.8  8.761 8.918 9.126 9.266 9.385 9.543 9.635 9.800 9.942 10.04 10.27 10.42 10.55 10.74 10.86 11.03 11.23 11.39 11.55 11.67 11.87 12.02 12.18 12.35 12.52 12.69 12.80 13.03 13.16 13.29 13.52 13.60 13.72 13.85  10.62 10.82 10.97 11.14 11.29 11.44 11.66 11.77 11.99 12.16 12.30 • 12.46 12.66 12.81 13.00 13.16 13.36 13.47 13.67 13.83 13.98 14.20 14.37 14.45 14.65 14.86 14.95 15.20 15.38 15.52 15.74 15.85 16.07 16.20  151.1 152.6 154.0 155.5 156.9 158.4 159.8 161.3 162.8 164.2 165.7 167.1 168.6 170.0 171.5 172.9 174.4 175.8 177.3 178.7 180.2 181.6 183.1 184.6 186.0 187.5 188.9 190.4 191.8 193.3 194.7 196.2 197.6 199.1  Shear rate  Shear rate (s-) asc dsc 1  3.127 3.184 3.258 3.329 3.424 3.468 3.529 3.603 3.664 3.726 3.819 3.884 3.947 4.007 4.050 4.103 4.164 4.251 4.344 4.412 4.455 4.533 4.601 4.685 4.742 4.805 4.865 4.937 4.999 5.076 5.173 5.186 5.253 5.365  3.828 3.881 3.960 4.024 4.088 4.144 4.210 4.271 4.382 4.440 4.522 4.595 4.651 4.715 4.798 4.892 4.973 5.041 5.080 5.164 5.236 5.298 5.364 5.434 5.492 5.570 5.624 5.726 5.819 5.837 5.908 6.031 6.121 6.116  continued..  100  Appendix A. LISTING OF EXPERIMENTAL FLOW DATA Table A.29 continued. 12 min run Shear Stress (Pa) 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  30 min run  Shear rate (s ) asc dsc 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  Shear Stress (Pa) 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  Shear rate (s") asc dsc 1  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  101  Table A.29 continued. 12 min run Shear Stress (Pa) 416.6 419.0 421.4 423.8 426.3 428.7 431.1 433.5 435.9 438.4 440.8 443.2 445.6 448.1 450.5 452.9 455.3 457.7 460.2 462.6 465.0 467.4 469.9 472.3 474.7 477.1 479.5 482.0 484.4  30 min run  Shear rate (s-) asc dsc 1  20.78 20.89 21.21 21.33 21.45 21.65 21.83 22.01 22.12 22.33 22.54 22.71 22.92 23.07 23.15 23.21 23.49 23.62 23.86 24.05 24.01 24.36 24.36 24.76 24.80 25.12 25.30 25.56 25.87  22.16 22.19 22.30 22.25 22.39 22.58 22.95 23.21 23.24 23.41 23.64 23.80 23.83 23.85 23.92 24.05 24.27 24.39 24.45 24.74 24.90 24.88 25.11 25.61 25.62 25.59 25.53 25.76 25.89  Shear Stress (Pa) 249.9 251.4 252.8 254.3 255.8 257.2 258.7 260.1 261.6 263.0 264.5 265.9 267.4 268.8 270.3 271.7 273.2 274.6 276.1 277.6 279.0 280.5 281.9 283.4 284.8 286.3 287.7 289.2 290.6  Shear rate (s-) asc dsc 1  8.163 8.317 5.561 8.452 8.540 8.653 8.761 8.834 8.921 9.010 9.023 9.170 9.205 9.348 9.437 9.540 9.663 9.787 9.881 9.981 10.07 10.12 10.20 10.29 10.40 10.54 10.66 10.73 10.76  8.758 8.839 8.908 9.030 9.117 9.195 9.304 9.375 9.380 9.503 9.507 9.649 9.704 9.819 9.909 9.979 10.08 10.18 10.26 10.25 10.34 10.42 10.52 10.62 10.70 10.79 10.81 10.89 10.89  Appendix A. LISTING OF EXPERIMENTAL  FLOW DATA  102  Table A.30: Shear rate data (s ) 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. 1  12 min run Shear Stress (Pa) 2.880 3.840 5.760 6.720 7.680 8.640 9.600 10.56 11.52 12.48 13.44 14.40 15.36 16.32 17.28 18.24 19.20 20.16 21.12 22.08 23.04 24.00 24.96 25.92 26.88 27.84 28.80 29.76 30.72 31.68 32.64  30 min run  Shear rate (s ) asc dsc 1  0.0196 0.0235 0.0304 0.0647 0.0376 0.0524 0.0510 0.0583 0.0666 0.0728 0.0853 0.1034 0.1169 0.1294 0.1548 0.1839 0.2127 0.2502 0.2960 0.3479 0.4096 0.4880 0.5713 0.6657 0.7742 0.9104 1.003 1.133 1.265  0.0368 0.0441 0.0405 0.0549 0.0598 0.0666 0.0745 0.0848 0.1019 0.1241 0.1509 0.1797 0.2296 0.2858 0.3593 0.4384 0.5250 0.6256 0.7249 0.8314 0.9447 1.061 1.174 1.302 1.431 1.561 1.695  Shear Stress (Pa) 2.880 4.320 5.760 7.200 8.640 10.08 11.52 12.96 14.40 15.84 17.28 18.72 20.16 21.60 23.04 24.48 25.92 27.36 28.80 30.24 31.68 33.12 34.56 36.00 37.44 38.88 40.32 41.76 43.20 44.64 46.08  Shear rate (s ) asc dsc 1  0.0147 0.0294 0.0284 0.0412 0.0490 0.0598 0.0679 0.0846 0.1049 0.1287 0.1650 0.2163 0.2822 0.3747 0.4893 0.6324 0.7928 0.9607 1.141 1.324 1.513 1.705 1.904 2.088 2.305 2.532 2.718 2.952  0.0255 0.2650 0.0338 0.0399 0.0477 0.0529 0.0611 0.0722 0.0885 0.1153 0.1669 0.2434 0.3489 0.4711 0.6233 0.7863 0.9692 1.156 1.348 1.554 1.768 1.981 2.205 2.440 2.647 2.907 3.162 3.383 3.663 3.919 4.146  continued.  Appendix A. LISTING OF EXPERIMENTAL  103  FLOW DATA  Table A.30 continued. 12 min run Shear Stress (Pa) 33.60 34.56 35.52 36.48 37.44 38.40 39.36 40.32 41.28 42.24 43.20 44.16 45.12 46.08 47.04 48.00 48.96 49.92 50.88 51.84 52.80 53.76 54.72 55.68 56.64 57.60 58.56 59.52 60.48 61.44 62.40 63.36 64.32 65.28  30 min run  Shear rate (s ) asc dsc 1  1.403 1.551 1.691 1.820 1.946 2.073 2.197 2.331 2.472 2.625 2.786 2.912 3.067 3.227 3.386 3.523 3.659 3.790 3.922 4.079 4.199 4.333 4.511 4.676 4.817 5.010 5.160 5.349 5.503 5.654 5.848 5.990 6.118 6.306  1.831 1.969 2.103 2.254 2.382 2.534 2.695 2.843 3.011 3.144 3.302 3.458 3.623 3.768 3.933 4.086 4.249 4.436 4.571 4.726 4.911 5.079 5.237 5.426 5.587 5.776 5.927 6.085 6.291 6.458 6.611 6.819 6.963 7.153  Shear Stress (Pa)  asc  47.52 48.96 50.40 51.84 53.28 54.72 56.16 57.60 59.04 60.48 61.92 63.36 64.80 66.24 67.68 69.12 70.56 72.00 73.44 74.88 76.32 77.76 79.20 80.64 82.08 83.52 84.96 86.40 87.84 89.28 90.72 92.16 93.60 95.04  3.176 3.379 3.585 3.836 4.047 4.294 4.524 4.763 4.992 5.223 5.490 5.705 5.934 6.230 6.483 6.726 6.980 7.228 7.492 7.736 8.010 8.245 8.518 8.780 9.018 9.275 9.559 9.795 10.05 10.31 10.63 10.88 11.16 11.40  Shear rate (S") 1  dsc 4.392 4.692 4.923 5.204 5.478 5.762 6.003 6.285 6.588 6.836 7.095 7.400 7.727 7.989 8.289 8.537 8.859 9.149 9.422 9.705 9.996 10.31 10.57 10.87 11.13 11.42 11.73 12.00 12.34 12.63 12.93 13.21 13.52 13.83 continued.  Appendix A. LISTING  OF EXPERIMENTAL  FLOW DATA  104  Table A.30 continued. 12 min run Shear Stress (Pa)  asc  66.24 67.20 68.16 69.12 70.08 71.04 72.00 72.96 73.92 74.88 75.84 76.80 77.76 78.72 79.68 80.64 81.60 82.56 83.52 84.48 85.44 86.40 87.36 88.32 89.28 90.24 91.20 92.16 93.12 94.08 95.04 96.00 96.96 97.92 98.88  6.425 6.594 6.764 6.943 7.110 7.277 7.408 7.550 7.719 7.912 8.075 8.253 8.402 8.597 8.745 8.924 9.057 9.236 9.424 9.616 9.758 9.931 10.11 10.28 10.44 10.65 10.84 11.00 11.15 11.35 11.52 11.71 11.86 12.05 12.25  30 min run  Shear rate (V )  dsc  Shear Stress (Pa)  7.325 7.511 7.684 7.875 8.016 8.211 8.393 8.559 8.743 8.934 9.111 9.331 9.454 9.637 9.807 9.981 10.20 10.36 10.52 10.73 10.89 11.07 11.27 11.47 11.64 11.83 11.97 12.16 12.36 12.56 12.69 12.93 13.09 13.27 13.49  96.48 97.92 99.36 100.8 102.2 103.7 105.1 106.6 108.0 109.4 110.9 112.3 113.8 115.2 116.6 118.1 119.5 121.0 122.4 123.8 125.3 126.7 128.2 129.6 131.0 132.5 133.9 135.4 136.8 138.2 139.7 141.1 142.6 144.0 145.4  1  Shear rate (s- ) asc dsc 1  11.69 11.97 12.26 12.52 12.80 13.05 13.29 13.60 13.86 14.15 14.46 14.71 15.03 15.31 15.59 15.88 16.15 16.46 16.72 17.02 17.35 17.64 17.87 18.19 18.46 18.79 19.05 19.39 19.64 19.95 20.25 20.55 20.81 21.14 21.41  14.13 14.40 .14.73 '15.02 15.26 15.61 15.89 16.21 16.55 16.81 17.14 17.42 17.76 18.05 18.33 18.66 18.98 19.30 19.59 19.86 20.18 20.55 20.78 21.13 21.42 21.76 22.03 22.37 22.66 22.98 23.24 23.64 23.86 24.16 24.52 continued.  Appendix A. LISTING OF EXPERIMENTAL  FLOW DATA  105  Table A.30 continued. 12 min run Shear Stress (Pa) 99.84 100.8 101.8 102.7 103.7 104.6 105.6 106.6 107.5 108.5 109.4 110.4 111.4 112.3 113.3 114.2 115.2 116.2 117.1 118.1 119.0 120.0 121.0 121.9 122.9 123.8 124.8 125.8 126.7 127.7 128.6 129.6 130.6 131.5 132.5  30 min run  Shear rate (s") asc dsc 1  12.40 12.58 12.79 12.95 13.16 13.29 13.55 13.69 13.84 14.05 14.24 14.45 14.62 14.78 14.97 15.18 15:39 15.54 15.73 15.93 16.12 16.30 16.49 16.70 16.89 17.09 17.24 17.47 17.67 17.82 18.01 18.25 18.38 18.64 18.78  13.63 13.85 14.04 14.19 14.43 14.58 14.77 14.92 15.15 15.30 15.52 15.68 15.86 16.05 16.25 16.43 16.64 16.81 16.99 17.17 17.36 17.58 17.75 17.89 18.11 18.32 18.50 18.64 18.87 19.04 19.21 19.39 19.60 19.80 19.94  Shear Stress (Pa) 146.9 148.3 149.8 151.2 152.6 154.1 155.5 157.0 158.4 159.8 161.3 162.7 164.2 165.6 167.0 168.5 169.9 171.4 172.8 174.2 175.7 177.1 178.6 180.0 181.4 182.9 184.3 185.8 187.2 188.6 190.1 191.5 193.0 194.4 195.8  Shear rate (s- ) asc dsc 1  21.69 22.05 22.31 22.65 22.94 23.20 23.56 23.83 24.02 24.37 24.66 25.00 25.35 25.61 25.91 26.27 26.54 26.90 27.25 27.53 27.82 28.19 28.38 28.69 28.98 29.38 29.65 30.00 30.22 30.52 30.89 31.30 31.63 31.73 32.08  24.81 25.16 25.42 25.73 26.06 26.33 26.53 26.91 27.19 27.52 27.89 28.17 28.45 28.80 29.08 29.43 29.80 30.08 30.38 30.77 30.93 31.21 31.50 31.89 32.16 32.55 32.74 33.02 33.42 33.80 34.09 34.19 34.58 34.97 35.28 continued.  Appendix A. LISTING OF EXPERIMENTAL  FLOW DATA  106  Table A.30 continued. 12 min run Shear Stress (Pa) 133.4 134.4 135.4 136.3 137.3 138.2 139.2 140.2 141.1 142.1 143.0 144.0 145.0 145.9 146.9 147.8 148.8 149.8 150.7 151.7 152.6 153.6 154.6 155.5 156.5 157.4 158.4 159.4 160.3 161.3 162.2 163.2 164.2 165.1 166.1  30 min run  Shear rate (s-) dsc asc 1  19.01 19.15 19.40 19.58 19.81 19.98 20.16 20.37 20.59 20.76 20.94 21.22 21.35 21.57 21.79 21.97 22.19 22.37 22.55 22.75 22.96 23.16 23.32 23.59 23.73 23.89 24.06 24.27 24.50 24.77 24.95 25.08 25.32 25.56 25.85  20.17 20.32 20.54 20.71 20.86 21.08 21.28 21.40 21.60 21.81 21.96 22.17 22.38 22.62 22.85 23.01 23.20 23.34 23.60 23.91 24.27 24.59 24.70 24.88 25.04 25.16 25.41 25.70 25.84 25.92 26.14 26.43 26.64 26.72 26.89  Shear Stress (Pa) 197.3 198.7 200.2 201.6 203.0 204.5 205.9 207.4 208.8 210.2 211.7 213.1 214.6 216.0 217.4 218.9 220.3 221.8 223.2 224.6 226.1 227.5 229.0 230.4 231.8 233.3 234.7 236.2 237.6 239.0 240.5 241.9 243.4 244.8 246.2  Shear rate (a") asc dsc 1  32.52 32.84 33.02 33.46 33.73 34.05 34.38 . 34.66 35.02 35.33 35.67 35.91 36.24 36.61 36.94 37.20 37.59 37.95 38.19 38.61 38.95 39.20 39.54 39.77 40.09 40.42 40.75 41.12 41.46 41.82 42.15 42.42 42.87 43.12 43.49  35.46 35.87 36.16 36.46 36.77 37.05 37.35 37.69 37.98 38.25 38.48 38.90 39.19 39.40 39.80 40.11 40.30 40.72 41.16 41.24 41.54 41.76 42.06 42.37 42.69 43.01 43.35 43.67 44.00 44.18 44.57 44.81 45.17 45.37 45.76 continued.  Appendix A. LISTING OF EXPERIMENTAL  FLOW DATA  107  Table A.30 continued. 12 min run Shear Stress (Pa)  asc  167.0 168.0 169.0 169.9 170.9 171.8 172.8 173.8 174.7 175.7 176.6 177.6 178.6 179.5 180.5 181.4 182.4 183.4 184.3 185.3 186.2 187.2 188.2 189.1 190.1 191.0 192.0  25.93 26.14 26.40 26.66 26.77 26.93 27.24 27.51 27.68 27.80 28.08 28.09 28.38 28.66 28.93 29.02 29.23 29.50 29.77 29.88 30.10 30.32 30.42 30.72 30.95 31.18 31.37  30 min run  Shear rate CV ) 1  dsc  27.15 27.40 27.46 27.61 27.91 28.16 28.29 28.34 28.62 28.66 28.88 29.14 29.39 29.48 29.63 29.88 30.15 30.19 30.36 30.52 30.60 30.89 31.14 31.32 31.49 31.65 31.61  Shear Stress (Pa) 247.7 249.1 250.6 252.0 253.4 254.9 256.3 257.8 259.2 260.6 262.1 263.5 265.0 266.4 267.8 269.3 270.7 272.2 273.6 275.0 276.5 277.9 279.4 280.8 282.2 283.7 285.1 286.6 288.0  Shear rate (s-) dsc asc 1  43.73 44.19 44.34 44.82 45.08 45.43 45.81 46.17 46.53 46.82 47.17 47.53 47.72 48.09 48.40 48.79 49.11 49.55 49.84 50.19 50.59 50.63 51.26 51.56 51.82 52.14 52.73 52.93 53.00  45.87 46.31 46.52 46.83 47.15 47.53 47.79 48.05 48.32 48.66 48.76 49.23 49.33 49.75 49.93 50.38 50.57 50.85 51.22 51.34 51.77 51.86 52.30 52.53 52.92 53.15 53.14 53.63 53.64  Appendix A. LISTING OF EXPERIMENTAL  108  FLOW DATA  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 (rpm)  Peak Torque on Vane (Nm x 10") 3  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  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0098501/manifest

Comment

Related Items