RETURNING MATERIALS: MSU Place in book drop to remove this checkout from your record. FINES UBRMUES will be charged if book is returned ”- after the date stainped below. RHEOLOGICAL CHARACTERIZATION OF CROSSLINKED WAXY MAIZE STARCH SOLUTIONS UNDER LOW ACID ASEPTIC PROCESSING CONDITIONS USING TUBE VISCOMETRY TECHNIQUES BY Robert Vernon Dail A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Agricultural Engineering Department of Agricultural Engineering 1989 9 <1, / I v H ABSTRACT RHEOLOGICAL CHARACTERIZATION OF CROSSLINKED WAXY MAIZE STARCH SOLUTIONS UNDER LOW ACID ASEPTIC PROCESSING CONDITIONS USING TUBE VISCOMETRY TECHNIQUES by Robert Vernon Dail A rheological characterization of 1.82 and 2.72% (g dry starch/100g water) waxy maize starch solutions was performed at 121.1, 132.2, and 143.3°C using tube viscometry techniques. The data were fit with the power law model, and dilatant behavior was observed in 22 out of 23 experiments. The flow behavior index was observed to increase with concentration and decrease with temperature. Dilatancy and changes in the flow behavior index were explained in terms of the rigidity and volume fraction of the swollen granules combined with small shear stresses in the fluid due to the high temperatures and low shear rates. A parameter correlation analysis showed the rheological parameters to be nearly correlated with the flow behavior index being the dominant parameter. This made the observed behavior of the consistency coefficient difficult to interpret. The effect of dilatant flow behavior on residence time and heat transfer rates are discussed in regards to aseptic processing of both particulate and nonparticulate foods. A reexamination of whether aseptic processing is appropriate for foods with large particles is encouraged. ACKNOWLEDGEMENTS I would like to sincerely thank my major professor, Dr. James F. Steffe, for his support (both financial and moral) and interest in this project. I hope that we will be able to continue both a friendship and a working relationship long into the future. I would also like to express thanks to the guidance committee, Drs. Robert Ofoli, Ajit Srivastava, and Elaine Scott, for their time and help. Great appreciation goes to Dr. John Gerrish and Gary Connor for their help in resolving the instrumentation problems, which were considerable. The modification of the frequency board on the mass flow meter by Gary saved literally months of time. I also express appreciation to Dr. Dennis Gilliland (Department of Statistics) and Dr. James V. Beck (Department of Mechanical Engineering) for their help with the statistical analysis and parameter estimation problems, respectively. Thanks also to Messrs Kueck, Gyde, and Mata all now or formerly with the Dial Corporation for their support and encouragement. Thanks to the many friends (including Brian, Marc, iv Jill, Scott, Elaine, and Larry) who made the whole process enjoyable. The starch in this study was donated by National Starch and Chemical Corporation, and partial funding was provided by the Center for Aseptic Processing and Packaging Studies at North Carolina State University. The Dial Corporation donated the recorder/controller and lent us the air operated flow control valve used in this study. Finally, I reserve the most special thanks for the love and support of Betsy. TABLE OF CONTENTS page LIST OF TABLES ................................. x LIST OF FIGURES ................................ xii NOMENCLATURE ........................... ........ xiv CHAPTER 1. INTRODUCTION ........ .......... ....... l 1.1. Overview ...... ......... ..... . .......... ... 1 1.2. Objectives ..... ...... ..... .......... . ..... 8 CHAPTER 2. LITERATURE REVIEW ................... 9 2.1. Introduction ......................... ..... 9 2.1.1. Starch ............................. 9 2.1.2. Starch Gelatinization .............. 10 2.1.3. Starch Modification ................ 12 2.2. Starch Rheology ................... ...... .. 13 2.3. Summary 30 CHAPTER 3. ANALYTICAL METHODS IN TUBE VISCOMETRY 32 3.1. Introduction .............................. 32 3.2. Shear Stress and Shear Rate Calculations .. 32 3.3. Evaluation of Slip (Wall Effects) ......... 43 3.4. End Effects .................... ..... ...... 37 3.5. Laminar Flow Criteria ..................... 40 CHAPTER 4. MATERIALS AND METHODS ....... ..... ... 42 4.1. Description of the Tube Viscometer System . 42 4.2. Modification and Calibration of the Mass Flow Meter ....................... ......... 47 vi page 4.3. Pressure Transducer Calibration ............ 57 4.4. Description of Starch, Starch Preparation, and a Typical Experimental Run ....... ..... 61 4 O 5 0 Preliminary Tests \ O O O I O O I O O O O O O O O O O O O I 0 00000 67 4.5.1. The Test for Maximum Pressure Drop . 67 4.5.2. The Test for Time-dependency ....... 69 4.5.3. The Test for Slip (Wall Effects) ... 71 4.5.4. Starch Gelatinization Test ......... 74 4.6. Calculation of Flow Rates Required to Obtain DeSired Shear Rates 0 O O O O O O O O O O O O O O O O I O O O O O 76 4.7. Experimental Design ............ ...... ..... 77 CHANER 5. RESULTS ......OOOOOOOOOOOOOOO ........ 80 5.1. Determination of the Rheological Parameters from the Tube Viscometer Data ............. 80 5 O 2 O AnaIYSis Of variance 0 O O O O O O O O O O O O O O O O O O O O O 82 5.3. Rheograms ......OOOOOCOOOOOOOOOOOO000...... 95 5.4. Evaluation of Slip (Wall Effects) ......... 98 5.5. Parameter Correlation Analysis ............ 100 CHANER 6. DISCUSSION 0 O O O O O O O I O O O O O O O O O O O O O O O O O 111 6.1. Near Correlation of the Parameters: Implications for the Power Law Model and Effect on the Prediction of Hold Tube Velocity Profiles ................................... 111 6.2. Effect of Dilatancy on Hold Tube Velocity Profiles and its Implications for Aseptic ProceSSing 0.00.00.00.00...0.0.0.0... ...... 114 6.3. Response of the Flow Behavior Index to Changes in Concentration and Temperature and an Explanation for the Observation of Dilatancy .............................. 118 6.4. Use of Rheological Data in Aseptic Processing 123 vii page CHAPTER 7. SUMMARY AND CONCLUSIONS ............. 125 CHAPTER 8. SUGGESTIONS FOR FURTHER RESEARCH .... 128 APPENDIX A RHEOGRAMS .......................... 130 APPENDIX B RAW DATA AS COLLECTED BY THE DATA ACQUISITION SYSTEM: TEMPERATURE GOING IN AND COMING OUT OF THE TUBE VISCOMETER, PRESSURE TRANSDUCER OUTPUT, AND MASS FLOW METER OUTPUT .................. 147 APPENDIX C CALCULATED VALUES OF VOLUMETRIC FLOW RATE, PRESSURE DROP, SHEAR STRESS, SHEAR RATE, AND GENERALIZED AND CRITICAL REYNOLDS NUMBERS FOR EACH EXPERIMENT . 156 LIST OFREFERENCES ......OOOOOOOOOOOOO0.0.000... 167 viii LIST OF TABLES Table page 2.1 A summary of information from the pertinent works on starch rheology .... ................ 14 4.1 Parts list for the tube viscometer system (part numbers correspond to Figure 1.1) ..... 44 4.2 Gain switch settings for the mass flow meter 49 4.3 Frequency switch settings for the mass flow meter 0......00............OOOOOOOOOOOOOOO... 49 4.4 Final five readings from point calibration of the mass flow meter (lbm/min) ............... 49 4.5 Raw data points used to create the calibration curve for the mass flow meter (lbm/min) ..... 52 4.6 Mass flow meter calibration curve performance: meter indicated, predicted, and true mass flow rate 0.0..........OOOIOOOOOOOOOOO....... 55 4.7 The raw data points used to create the pressure transducer calibration curve ....... 59 4.8 Torque readings from the time-dependency test (Nm) 0............OOOOOOIOOOOOOO0.0.0.000... 72 4.9 Shear stress and shear rate values from 0.0212 m diameter tube viscometer .................. 73 4.10 Brookfield readings from the starch gelatinization test ......OOOOOOOOOOOOOO...O. 75 5.1 Values of consistency coefficient, K (Pa sn), and flow behavior index, n, from each individual block experiment ....... .......... 83 5.2 Analysis of variance table for the flow behavior index examining block and treatment effects O.....OOCIOOOOOOOOOOO....OOOOOOOOOOOO 84 ix Table page 5.3 Analysis of variance table for the consistency ~ coefficient examining block and treatment effects 0.00.00.00.000...0.00.00.00.00....... 84 5.4 Analysis of variance table for the flow behavior index examining treatment effects with block effects removed .................. 86 5.5 Analysis of variance table for the consistency coefficient examining treatment effects with block effects removed ....................... 86 5.6 Analysis of variance table examining temperature, concentration, and their interaction effects on the flow behavior index 87 5.7 Analysis of variance table examining temperature, concentration, and their interaction effects on the consistency coefficient ............................ ..... 87 5.8 Average values (treatment means) of consistency coefficient (K) and flow behavior index (n) for each treatment level (temperature/concentration combination) ..... 89 5.9 Flow behavior indices, consistency coefficients, and nonlinear coefficients of determination for each treatment level (temperature/concentration combination) where where block data has been pooled ............ 96 5.10 Nonlinear coefficients of determination for each of the individual block experiments .... 96 5.11 Values of the sensitivity coefficients (mi/s) and their ratios for various valugg of pfiessure drop (Pa) when n=1.0 and K=5.0*10 Pa 5 103 5.12 Values of the sensitivity coefficients (m3/s) and thier ratios for various valug§ of pfiessure 5 drop (Pa) when n=1.5 and K=5.0*10 Pa 103 6.1 Maximum values of flow behavior index for each temperature/concentration combination and the associated Umax/Uave ratios ................ 117 LIST OF FIGURES Figure page 1.1 A Typical System for Processing Viscous Liquid FOOd ......OOOOOOOOOOOO......OOOOOOOOOOOOOOO 4 3.1 Velocity Profile of a Power Law Fluid in a Pipe: without slip (a) - with slip (b) ..... 36 4.1 Diagram of Tube Viscometer System .......... 43 4.2 Mass Flow Meter Calibration Curve .......... 53 4.3a Standard Isolated Output as Received from Micromotion ................................ 56 4.3b Modified Board ........................ ..... 56 4.4 Pressure Transducer Calibration Curve ...... 60 4.5 Pictorial Diagram of Recorder/Controller Showing Location of Synchronizer Wheel and Sensitivity Adjustment ..................... 65 4.6 Experimental DeSign ......OOOOOOOOOOOOOOOOO. 79 5.1 Average Flow Behavior Index Values vs. Temperature ......OOOOOOOOOOOOOOOOO...... 90 5.2 Average Consistency Coefficient vs. Temperature ......OOOOOOCOOOOOOOOOOO00...... 91 5.3 Average Flow Behavior Index vs. Concentration .............................. 92 5.4 Average Consistency Coefficient vs. concentration ......OOOOOOOOOOOO00.000000... 93 5.5 Rheograms of 1.82% Starch at 121.1“C Through Viscometers of Different Diameters .......... 99 5.6 Sensitivity Coefficients Versus Pressure Drop forn=100 0............OOOOOOOOO0.0.0000...0 104 Figure 5.7 page Sensitivity Coefficients Versus Pressure Drop for n=105 ......0..........OOOOOOOOOOOOOOOOO 105 Consistency Coefficient Versus Flow Behavior Index .....COOOCOOOOOOOOOOOOO......OOOOOOOOO 107 A Diagram of Velocity Profiles for the Cases When n<1 (shear-thinning), n=1 (Newtonian), and n>1 (shear-thickening) ......... ........ 115 xii NOMENCLATURE a concentration (g/ml) = diameter (m) activation energy (Kcal/mole) = consistency coefficient (Pa s“) I." N t!) O 0 II = length (m) Le a entrance length (m) m.In a meter indicated mass flow rate (lbm/min) mt = true mass flow rate (lbm/min) n - flow behavior index (dimensionless) AP a pressure drop (Pa) Q a volumetric flow rate (mi/s) R a tube radius (m) or gas constant (Cal/mole) in Chapter Three r a radius of fluid core (m) r2 - coefficient of determination Re a generalized Reynolds number (dimensionless) ReN a Newtonian Reynolds number (dimensionless) t = arbitrary quantity T - temperature (°C) Tin - fluid temperature going into the tube viscometer (°C) T = fluid temperature leaving the tube viscometer (°C) out u = local fluid velocity (m/s) xiii uw = fluid velocity at wall (m/s) Uave - average fluid velocity (m/s), Chapter Six Umax - maximum local fluid velocity (m/s) Us a effective slip velocity (m/s) v 8 average fluid velocity (m/s), Chapter Three V a pressure transducer voltage output (mV) a a level of significance 5 a slip coefficient (m/(Pa s)) 4 a shear rate (8-1) x a circumference of circle divided by its diameter a a shear stress (Pa) a0 = yield stress (Pa) aw a wall shear stress (Pa) ,. w- 4,- d1 4’2 density (kg/m3) arbitrary quantity arbitrary parameter arbitrary parameter arbitrary parameter xiv CHAPTER ONE INTRODUCTION 1 . 1 . Overview In aseptic processing, also called high temperature short time (HTST) continuous processing, liquid food is rapidly heated to a temperature where undesirable microorganisms are destroyed at a rate much greater than the desirable chemical constitutents (vitamins, flavor and aroma components). The product is held at this temperature until commercial sterility is achieved, then rapidly cooled. Heating and cooling are achieved using some form of heat exchanger, and the product is held at the elevated sterilizing temperature for a relatively short period of time depending on the product and target microorganism involved. After cooling, the product is filled into a sterile container in a sterile environment (hence the term aseptic). Currently, there is renewed interest in the food industry in aseptic processing of liquid foodstuffs. There are a number of reasons for this interest. First, the 0.8. Food and Drug Administration (FDA) approved a petition by Erik Pak to use hydrogen peroxide as a sterilizing agent on 1 2 polyethylene food contact surfaces (FDA, 1981). Since that time, the FDA has approved the use of hydrogen peroxide as a sterilant of food contact surfaces for many other compounds (FDA, 1984a; FDA, 1985). Therefore, many of the packaging machines used in aseptic systems utilize plastic containers which are lightweight and/or microwavable. Some of the new packages provide the consumer the convenience of eating directly out of the container. Microwavable containers are important, from a marketing perspective, given the number of single households and the current and projected sales of microwave ovens in the United States. The lightweight containers also reduce shipping costs. Secondly, due to the difference in destruction kinetics between desirable chemical constituents and undesirable . microorganisms, the potential exists for a large improvement in product quality. Finally, many foods which are heat labile, such as wine containing sauces, can be commercially produced by aseptic processing but cannot be produced by conventional retorting methods. This enables food companies to get into new product areas. Some aseptically processed products enjoying commercial success in the United States are fruit juice drinks, tomato based sauces, applesauce, puddings, fruits, dairy products including cheese sauces, yogurt, milk, and smooth soups. The fruit, juice drinks, tomato based products, applesauce and yogurt have a pH of 4.6 or below (high acid or acidified foods). The microorganisms destroyed in the processing of these products are very heat labile; consequently, the thermal treatment these products receive is relatively mild. Milk, smooth soups, puddings and cheese sauces have a pH greater than 4.6 (low acid foods). The microorganism of concern in products with a pH greater than 4.6 is glostrigium botuligum which causes the fatal food poisoning known as botulism. This organism forms spores which have a high thermal resistance requiring a thermal treatment that is more severe than that given acid or acidified foods. Figure 1.1 shows a typical system for aseptically processing viscous liquid foods. The heat exchangers are scraped surface type which are superior for viscous liquid foods because they greatly reduce fouling. The product is held at the elevated sterilizing temperature by allowing it to flow through an insulated tube which is often called a hold tube. For products that contain suspended particulate matter, there is an energy transfer as heat from the liquid to the particles as the mixture flows through the hold tube. Therefore, the liquid phase cools as the particles are heated. For products that contain particulate matter, the particles must be sterilized by the time the mixture leaves the hold tube (USDA, 1984; Dignan, 1988). None of the commercially successful low acid liquid foods mentioned above contain discrete particulate matter. Liquid foods, with particulate matter, pose a special problem when it comes to developing thermal treatments. Smash! “.0 35¢me ugh-me ".0 was: >n mandamus.- 89(- lflbdl g. mDOOm 050... mDOUm; UZfimuUOE— so”. Ewhm>m 45...: < . p. _. 550.“. 38; Oh g gt 838480: bi gd<> gut 80¢. Au When particulate containing foods are thermally processed by conventional retorting methods, the heat penetration rate into the can and the particle are determined by impaling the particle with a thermocouple, mounted in the center of the can, and monitoring the temperature during the process. An empirical temperature history is obtained which serves as a basis for calculating the required thermal process. In aseptic processing systems, the particles are being transported through the system by the liquid phase of the food. Therefore, the internal temperature of the particles cannot be measured by thermocouples, but must be mathematically estimated based on the temperature of the surrounding fluid. Recently, a British firm (Cross and Blackwell) introduced an aseptically processed low acid product containing discrete particulate matter (meat and vegetable pieces) into the European market. This product has not been introduced in the United States. Also, two U.S. firms have attempted to file low acid particulate processes with the U.S. Food and Drug Administration which have not been accepted for filing (Larkin, 1988). For a process to be accepted for filing with FDA, or for a process to be approved by USDA, a firm must satisfactorily show that the product does not present a public health hazard. For product sterilization, this includes data from inoculated pack studies. The FDA also requests that viscosity data be submitted if it is deemed critical to the delivery of the thermal process, asking that the product be characterized as Newtonian, pseudoplastic or dilatant (FDA, 1984b). The United States Department of Agriculture, Food Safety and Inspection Service, also states that flow properties of the formulated product may be included in the assessment of commercial sterility (USDA,1984). The FDA states that viscosity data may be taken from handbooks or technical literature, or it can be obtained by direct measurement (FDA, 1984b). A widely used thickener for low acid foods is crosslinked waxy maize starch. The extra crosslinking in these starches inhibits swelling of the starch granules at lower temperatures (Fennema, 1976; Hosney, 1986). Thus, liquid foods thickened with this material are better able to withstand the thermal abuse undergone by low acid foods. To date, no rheological data exists for crosslinked waxy maize starch in the low acid aseptic processing temperature range (121-143'C). Lack of this data is inhibiting progress in bringing aseptically processed low acid particulate foods to market in the United States, whether foreign or domestic. First, processors of low acid particulate foods are unable to provide rheological information to the U.S. regulatory agencies. Second, engineering design of required thermal processes is not possible without it. The data are required to determine velocity profiles in hold tubes, residence times and residence time distributions of suspended food particles, heat exchanger design, and to obtain heat transfer rates into particles being transported by the fluid. Producers of aseptically processed low acid nonparticulate foods that are starch thickened and that cannot provide rheological data to the regulatory agencies have been required to design hold tube length on the assumption that the flow behavior index is infinitely large (because starch thickened foods are suspected to be non- Newtonian), or establish the process with large inoculated pack studies (Stefanovic, 1988). Assuming the flow behavior index to be infinitely large results in the maximum fluid velocity in the hold tube being three times the bulk average velocity. This represents a worst case situation which results in overprocessing the product. Consequently, most producers of low acid nonparticulate starch thickened foods have established the thermal processes solely by inoculated pack studies (Stefanovic, 1988). The disadvantage in doing this is that any change in the system, such as hold tube diameter or speed of the mutator blades in the heat exchanger, etc., requires reestablishment of the thermal process by inoculated pack. This is quite labor intensive and time consuming. It is easily seen that a large benefit in process design flexibility can also be gained by producers of low acid, nonparticulate starch thickened foods by a rheological characterization of crosslinked waxy maize starch solutions. In summary, rheological characterization of crosslinked waxy maize starch solutions will aid in moving aseptic low acid particulate thermal processes through the approval or acceptance process at the U.S. regulatory agencies, enable engineering design of aseptic equipment and thermal processes, and provide greater process design flexibility for low acid nonparticulate foods already on the market. 1.2. Objectives The general objective of this research was to complete a rheological characterization of two crosslinked waxy maize starch solutions (1.82 and 2.72%, g dry starch/100g water) at three temperatures in the low acid aseptic processing temperature range (121, 132 and 143°C) using tube viscometry techniques. Specific objectives included building and instrumenting a tube viscometer that would prevent boiling of a test fluid heated above its boiling point and investigation of temperature, concentration, and their possible interaction effects on the rheological parameters. CHAPTER TWO LITERATURE REVIEW 2.1. Introduction It was mentioned in the introduction that modified waxy maize starches are widely used as a thickener for low acid foods that are either conventionally retorted or aseptically (HTST) processed. The mechanism by which starches thicken the water in which they are suspended has been well understood for years, and a description of this mechanism can be found in textbooks on food or starch chemistry (Hoseney, 1986; Whistler, et al., 1984; Fennema, 1976). In the following three sections, starch, starch gelatinization, and starch modification will be briefly reviewed prior to reviewing the literature on starch rheology. 2.1.1. Starch Starch is the primary means by which plants store energy. Most plant starches are composed of two polymer fractions: amylose and amylopectin. These polymers are polysaccharides composed of the monosaccharide glucose (Lehninger, 1973). Amylose is a linear molecule in which 9 10 the glucose residues are linked a-1,4 and has a molecular weight of approximately 250,000. Most of the linkages in amylopectin, a branched molecule, are also a-1,4; however, 4-6% of the linkages are a-1,6. The a-1,6 linkages cause the molecule to be branched instead of linear, and the molecules are very large with molecular weights as large as 100 million. Most plant starches are approximately 30% amylose with the remainder being amylopectin. However, the waxy starches are approximately 100% amylopectin, and there are hybrid plants that produce starches that are approximately 70% amylose (Hoseney, 1986). Plants store starch in granular form. The granules range in size from 2-150pm (Zobel, 1984). Waxy maize starch granules are approximately 15pm in diameter (Lineback, 1984). The granules possess a high degree of order as evidenced by the display of birefringence when viewed with polarized light. X—ray diffraction also shows the granules to be semi-crystalline which is thought to be due to the amylopectin. Approximately 30% of a granule is crystalline with the rest being amorphous (Hoseney, 1986). 2.1.2. Starch Gelatinization When starch granules are heated in the presence of water, they undergo morphological and chemical change. When the energy in the water becomes great enough to disrupt the hydrogen bonds between the starch molecules, the granule will swell and imbibe water causing an increase in 11 viscosity. This phenomena is called gelatinization and is accompanied by a loss of birefringence (Hoseney, 1986: Fennema, 1976) and a change in X-ray diffraction (Katz, 1928). The temperature at which gelatinization occurs depends on the plant source of the starch and whether or not the starch has been modified. For corn and waxy maize (a corn hybrid) starches which have not been modified (native starch), gelatinization starts to occur at approximately 62°C. Gelatinization is 50% complete at 67°C and 100% complete at 72°C (Lineback, 1984). Heating beyond this temperature range results in a continued increase in viscosity and is termed pasting. As a part of the gelatinization and pasting process, starch granules solubilize. In starches that contain amylose, the amylose fraction is the first to solubilize. This starts to happen early in the gelatinization process, and the solubilized amylose leaches out of the granule into the intergranular space. Christianson et al. (1982) showed that, for native corn starch, about 10% of the starch granule is solubilized at 70°C. Doublier (1987) states that most of the amylose in cereal starches (e.g. corn or wheat) does not solubilize until 80-90°C because internal lipids form insoluble complexes with amylose below 90°C. The solubilization of amylose leaves the granule composed primarily of amylopectin. However, the solubilization process is continuous, and the amylopectin can be made to solubilize with increasing temperature. Solubilization of 12 the amylopectin destroys the integrity of the granule with a subsequent loss of viscosity. The solubilization of amylopectin happens slowly (Zobel, 1984), and, even for native starches, complete loss of granular structure may not occur until a temperature of approximately 120°C (Hoseney, 1986). The increase in viscosity which occurs during pasting is thought to be due to hydrogen bonding of the solubilized amylose to two or more starch granules (Christianson, et al., 1982). 2.1.3. Starch Modification There are four primary types of starch modification: acid, crosslinking, oxidation, and substitution. The starch that will be used in this study is a crosslinked starch. Therefore, crosslinking will be reviewed here. Crosslinking is the forming of covalent bonds between two starch molecules to form a larger molecule (Hoseney, 1986). Crosslinking is performed primarily in two ways. First, a diester can be formed between the two molecules. This is usually done with phosphorous oxychloride (POC13). The second method is to form an ether bond between the molecules which is typically done using epichlorhhydrin (Hoseney, 1986). Other compounds used to a lesser extent to form covalent bonds between the molecules include acrolein, sodium trimetaphosphate, succinic anhydride, and adipic anhydride (Fennema, 1976). Crosslinking increases the gelatinization temperature 13 (Fennema, 1976) and causes starches to swell less, give a lower viscosity upon pasting, be less soluble, and not as subject to shear-thinning (Hoseney, 1986). 2.2. Starch Rheology Table 2.1 presents a summary of information from the pertinent works on starch rheology. Presented are the investigators, type of starch, type of viscometer, shear rate range, temperatures at which the rheological tests were conducted, length of time the starch was cooked, temperature at which the starch was cooked, and starch rheology. It can be seen that there are no rheological tests above 100°C. In fact, the only rheological testing on a liquid food that would normally boil at 100°C was that done by Bertsch and Cerf (1983) on milk and cream using a capillary rheometer. Despite there being no rheological testing on starch above 100°C, a review of the works listed in Table 2.1 is still deemed beneficial, because the explanation of flow phenomena at the lower temperatures may still be applicable at higher temperatures. Evans and Haisman (1979) performed a rheological characterization of corn, modified corn, potato, and tapioca starches. The modified corn starch was an acetylated waxy maize distarch adipate. 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The starches were cooked at 90'C until maximum viscosity was achieved. Rheological tests were conducted at 60‘C on concentrations up to 10%. The results showed that all solutions acted as shear- thinning, power-law fluids. They also found that the flow behavior index was a strong function of concentration with the flow behavior index increasing as the concentration was increased. Upon centrifuging, the starch pastes would separate into a clear supernatant and a semi-solid. They concluded from this that starch solutions were, in reality, particulate. The supernatant was found to have a low viscosity despite having a high solids content, and consequently, they suggest that (apart from intermolecular bonding that would cause bridging between granules by amylose) the supernatant contributes little to the rheology. Apparent viscosity was observed to increase with concentration with little effect on viscosity occurring until a critical concentration was achieved. To explain the observed rheological phenomena, the authors determined particle interaction by examining sedimentation rates and determined the volume that the swollen starch granules occupy by dye exclusion methods. The extent to which sedimentation rates are dependent on concentration is indicative of strength of particle interaction and the degree of aggregation of the particles. The volume of the swollen granules was deemed important because abrupt changes in rheological properties 17 had been observed for other systems (polymer microgels and polyacrylonitrile graft co-polymer solutions) at particular concentrations where the particles became close-packed. Results of the sedimentation test showed strong particle interaction. The close-packing point of corn and modified corn starch were determined to be 2.7 and 2.8%, respectively. Significant increases in apparent viscosity and the appearance of a yield stress were seen to occur at 3.3% for corn starch and 2.7% for modified corn starch. The authors concluded that the main factors effecting the rheology of gelatinized starch suspensions is intergranular interactions (e.g. hydrogen bonding), the volume fraction occupied by swollen granules, and the compressibility and deformability of the starch granules, since the pastes were still observed to be fluid even at concentrations greater than the close-packing point. The work reviewed above was performed on a fully pasted starch i.e., the starch was cooked until a maximum viscosity was achieved. Three works from the U.S. Department of Agriculture's Agricultural Research Service examined the effects of cooking time at cook temperatures throughout gelatinization and into the pasting range. In the first of these works, Bagley and Christianson (1982) characterized 7-25% (db) concentrations of native wheat starch cooked for 15, 30, 45, 60, and 75 minutes at 60, 65, 70 and 75°C. Rheological tests were performed on a Haake Rotovisco (concentric cylinder) viscometer at 60 and 23 °< sus coo int at she plc va] A1: of Oh: to co Vi 16 Vi CC as Pa ac th We Cc re 18 23°C covering a shear rate range of 1-1000 s-l. Starch suspensions were found to be shear-thickening for short cook times, shear-thinning for long cook times, and for intermediate cook times, were found to be shear-thickening at low shear rates (0<§<100 5.1) and shear-thinning at high shear rates (;zloo s-l). These results were presented in plots of apparent viscosity versus shear rate: actual values of the rheological parameters were not presented. Also, apparent viscosity was observed to increase with increasing concentration which agrees with the observations of Evans and Haisman (1979). Apparent viscosity was observed to increase with cook time, and the authors also found rapid increases in viscosity above certain concentrations, depending on temperature. At 60'C, the viscosity increased very rapidly with concentration above 16%. As the cooking temperature was raised, the rapid viscosity increases occurred at progressively lower concentrations. Explanation of the observed rheological phenomena was as follows: the authors first noted that shear-thickening (dilatancy) occurs in closely packed assemblages of solid particles for which system volume must increase to accommodate flow under shear. From this they concluded that the starch granules were rigid at the short cook times and were deformable at the long cook times. At the intermediate cook times, the granules were still fairly rigid and required greater stress to cause them to deform and for the 19 solution to appear shear-thinning. Greater shear stress occurred at the rheological test conducted at the lower temperature (23°C). Consequently, a solution that appeared to be dilatant at 60‘C might appear to be shear-thinning at 23°C. In summary, if the particles are not swollen enough to be readily deformed, or if the shear stress levels are too low to force the particles to deform, then dilatancy will be observed. Also, the extent of swelling and plasticization of the granules depends on cook time. As with the work of Evans and Haisman (1979), the observation that rapid increases in viscosity occur at certain threshold concentrations was explained in terms of the amount of granule swelling. However, because the cook times and temperatures were such that maximum viscosity was not achieved, a slightly different approach was used. Instead of directly determining the volume fraction of the swollen granules, the amount that the granules would swell if excess water was present was first determined (in a separate experiment) for each of the cook time/cook temperature combinations. For excess water to be present, the solutions had to be dilute (2-4%). The swollen gel from these experiments was weighed, and a variable, Q, was constructed which was grams of swollen gel/grams of dry starch used to make the gel. Then, instead of plotting apparent viscosity versus concentration, c, apparent viscosity was plotted against cQ. Since the concentration, c, has the units of grams of dry starch/grams starch 20 suspension, cQ has the units of grams of swollen gel/grams of starch suspension. Hence, when cQ<1, excess solvent exists between the particles, and when cQ>1, all of the solvent has been absorbed by the particles. In this way, the authors were able to unify their data. When cQ is less than one it is the volume fraction. Because swollen starch granules are both deformable and compressible, cQ can be greater than one, and the authors state that for values of cQ>1, the system is a "dough." The rapid increase in viscosity observed for certain threshold concentrations, depending on temperature, were found to occur at a cQ value of approximately 0.7. The authors reported difficulty in plotting the apparent viscosity versus Co for those cases where dilatancy occurred. They stated that the method should theoretically be usable for the shorter cook times (where dilatancy occurred), but the data were quite scattered. Lastly, it should be noted that at the cook temperatures used in the Bagley and Christianson (1982) work, little of the amylose was solubilized. Consequently, the rheological phenomena observed were free of the effects solubilized amylose. In a second work, Christianson et a1. (1982) performed a rheological characterization of native corn starch in conjunction with scanning electron microscopy of the starch granules to examine the morphological changes caused by cooking temperatures and times along with the effect of 21 shearing stresses applied to them. The emphasis was on presentation of the scanning electron micrographs, and the rheological findings were presented as examples of the type of flow that exist as a function of the starch morphology. Consequently, the experimental conditions for the rheological testing were not completely clear. However, the experimental conditions appear to be as follows: concentrations of native corn starch suspensions of 5-26% (db) were cooked for 15, 30, and 75 minutes at temperatures between and including 65-85°C. Rheological tests were performed on a Haake Rotovisco (concentric cylinder) viscometer at 60 and 23°C covering a shear rate range of 3- 500 5'1. Christianson et al. (1982) observed dilatancy for short cook times and shear-thinning behavior for long cook times. Either dilatancy or Newtonian behavior was observed for intermediate cook times at low shear rates. For the intermediate cook times, the dilatant or Newtonian behavior changed to shear-thinning behavior at shear rates above, 1. The same explanations for the approximately, 100 s- observed rheological phenomena were given for this work as were given for the Bagley and Christianson (1982) work; dilatancy occurs when the starch granules are rigid and closely packed, which occurs at short cook times. The rigidity of granules cooked for short times and at lower temperatures was supported by scanning electron micrographs, as was the plasticization and deformability of 22 granules cooked for long cook times or at higher temperatures. Two additional rheological observations were noteworthy: l.) The shear stress developed in the fluid is concentration dependent. The rheological effect of this is that a starch suspension which appears Newtonian or dilatant at a particular cook time and temperature at a particular concentration can appear shear-thinning at the same cook time and temperature but a higher concentration. The additional shear stress developed at the higher concentration causes the the starch granules to deform where they were too rigid to deform at the lower concentration. 2.) Cooking time has no effect on the extent of swelling. The viscosities are different at different cook times despite the amount of swelling being the same. The difference in viscosity is attributed to the degree of solubilization of amylose. The final work in rheological characterization of native corn starch by Christianson and Bagley (1983) considered 5-26% (db) concentrations of corn starch cooked at 65, 67, 70, 75, and 80°C for 15, 30, 45, and 75 minutes. Rheological tests were conducted on a Haake Rotovisco (concentric cylinder) viscometer at 60 and 23°C covering a 1 shear rate range of 3-500 5‘ . Results were the same as the previous two works where dilatancy appears for short cook times and intermediate cook times at low shear rates ({<150 s-l). Newtonian behavior was observed for 25% (water 23 limited) solution at 60°C over the shear rate range of 3-30 s-1. The apparent viscosity increased with concentration and the increase became very rapid when a threshold concentration was achieved. This was again explained in terms of the variable cQ. Apparent viscosity also was observed to decrease with temperature and increase with cooking time. Rheological data were presented in plots of apparent viscosity versus shear rate, concentration, or cQ. Actual values of the rheological parameters (n and K) were not presented. A notable observation made by the authors was that when the amount of swelling of the corn starch granules was equal to that of the wheat starch granules from the earlier work (Bagley and Christianson, 1982), the apparent viscosities were the same. Since the cook temperatures used were in the range where little solubilization of amylose takes place, the conclusion was that viscosity and other rheological behavior is due solely to the volume occupied by the starch granules. Consequently, as with wheat starch pastes, corn starch pastes increase in viscosity very rapidly for values of cQ greater than 0.7. It should finally be noted that, for the three works involving Bagley and Christianson above, the authors acknowledge that, in the rheological tests conducted at 60°C, the starch may have continued to paste contributing to the dilatancy observed. However, they discounted the effect on the results because the same behavior was seen to 24 occur for the same material at 23°C. Doublier (1981) performed a rheological characterization of wheat starch pastes where concentrations ranged from 0.3-8%. Rheological tests were conducted on two different Viscometers; a Rheomat 30 (concentric cylinder) was used for concentrations greater than 2.5%. Test temperatures were 25-70°C and covered a 1 shear rate range of 1-700 s- . A Low Shear 30 (concentric cylinder) was used for concentrations less than 2.5% and 1. All tests on this covered a shear rate range of 10-128 s- viscometer were done at 25°C. The starch was heated to 96°C and held for thirty minutes. It was then cooled to the temperature at which the test was being conducted. Part of the objective of this work was to examine the influence of heating rate and mixing speeds on rheological properties. For concentrations less 1.5% at 25°C, the author observed Newtonian behavior for shear rates less than 10 5-1; otherwise, shear-thinning behavior was observed. The majority of the tests for concentrations of 2.5-8% were done at 70°C and the consistency coefficient was observed to increase with concentration. The author derived the following expression for the consistency coefficient as a function of concentration: K=8.74*1o’7c3°88 ..........(2.1) where C is concentration in grams/milliliter. Other tests 25 conducted for concentrations of 2.5-8% at temperatures other than 70°C enabled a determination of temperature effects on the consistency coefficient using an Arrhenius relationship: K=Koexp[E/(RT)] ............(2.2) where Ko=1.51*10-4 kcal/mole. Pa, R=1.984 Cal/mole, and E=5.13 From the rheological tests at a shear rate of 1 s-l, the author was able to show that macromolecular entanglements (in this case, granule bridging by amylose) starts to occur at 0.5% which is also seen for certain types of polymers. At 1.5%, the rheology of the solution is transformed from one governed by macromolecular entanglements to that of a suspension governed by the volume fraction of the swollen granules. For higher shear rates and concentrations, the rheology was said to be primarily determined by the volume fraction of swollen granules. From the portion of the work where the effects of mixing and heating rates were examined, it was shown that rapid heating yields a higher consistency coefficient and that the amount of swelling was dependent on the heating rate. Greater swelling was seen to occur with rapid heating. Wong and Lelievre (1982) examined the behavior of 26 wheat starch pastes under steady shear conditions using concentrations of, approximately, 3.1-6.1%. The suspensions were cooked from 5-60 minutes at 85-95°C. Rheological tests were conducted at 30°C on a Ferranti-Shirley cone and plate viscometer covering a shear rate range of 0.4 - 4000 3.1. Part of the objective was to examine the effect of wheat variety on rheology. All of the suspensions were found to be shear-thinning for shear rates greater than 10 5.1. For shear rates less than 10 s-1 , a yield stress was seen to exist in all varieties except at the lowest concentrations. The close packing percentages were given for two of the varieties and were found to be 2.82% for Raven and 3.92% for Kamaru. Large increases in viscosity occurred when the concentration was approximately 0.7 of the close packing concentration. This agrees with the work of Bagley and Christianson (1982) and Christianson and Bagley (1983). Apparent viscosity was observed to increase with increasing concentration. The final conclusion was that the rheology of the wheat starch pastes are primarily governed by the volume the swollen particles would occupy if close-packed (with excess solvent present) and the size distribution of the particles. Colas (1986) performed the only rheological characterization of the type of starch used in this study: crosslinked waxy maize. Three waxy maize starches with different degrees of crosslinking were used in addition to 27 a native waxy maize which served as a control. The concentration used for all experiments was 3.3% (g dry starch/100g water), and the suspensions were heated to 95°C in 6.5 minutes. A Rheomat 30 (concentric cylinder) viscometer was used covering a shear rate range of 0-330 5-1. All tests were performed on pastes at 25°C. All pastes were found to be shear-thinning. The greater the degree of crosslinking, the less viscous the paste. This was explained by virtue of the fact that the greater the degree of crosslinking, the less the granules are able to swell. The consistency coefficient decreased with increased crosslinking while the flow behavior index was observed to increase. The increase in the flow behavior index as was attributed to the ability of the granules to resist deformation as crosslinking is increased. Lastly, the tendency toward a yield stress decreased with increased crosslinking, because the granules are less able to swell and imbibe water. Starch pastes at other concentrations were made to obtain other information. The consistency coefficient was observed to increase with increasing concentration which confirmed the observations made by Doublier (1981, 1987). The flow behavior index decreased with increasing concentration which contradicts the observation of Evans and Haisman (1979). The author also determined the concentration at which the starches would imbibe all of the available water (the close-packing concentration). It was 28 1.76% for native waxy maize and increased with the degree of crosslinking (2.60, 3.44, and 4.22%). The close-packing concentration for the native waxy maize is notably less than those seen by Christianson and Bagley (1982) for native corn starch. This may be due to lack of amylose in the starch granules or the difference in cook temperatures (the close-packing percentage decreases as the cook temperature increases). During the determination of the close-packing concentration, the author saw that very little starch had solubilized after being cooked at 90°C, particularly for the crosslinked starches. In fact, there was so little solubilization that the author states that the pastes can be treated as dispersions of swollen granules with no influence from solubilized starch. The final work on starch rheology to be reviewed is that by Doublier (1987) where the rheology of two cereal starches (wheat and maize) was compared to the rheology of two legume starches (faba bean and smooth pea). The effect ~of heating rate was also examined. The starches were cooked on two different viscoamylographs to 96°C. Concentrations of 5-10% were cooked on a Brabender viscoamylograph which heated the suspensions at a rate of l.5°C/minute. A 9% concentration of the starches was heated on an Ottawa Starch Viscometer which heated the suspensions at a rate of approximately 6°C/minute. Rheological tests were done on a Rheomat 30 (concentric cylinder) viscometer at 60°C covering a shear rate range of 0-660 s-l. 29 The legume starches were found to solubilize at lower temperatures than the cereal starches but yielded pastes of comparable consistency. For all of the starches, the heating rate was seen to greatly affect the amount of solubilization and the degree of swelling: the slower the heating rate, the less viscous the paste. The rheology of the pastes could be explained in terms of the solubilization and the degree of swelling: the rapid heating rate increased the consistency coefficient. Legume starches were more affected in this regard than were the cereal starches. In other words, the rheology of the legume starches is more sensitive to pasting conditions than cereal starches. All of the starches considered were shear- thinning, and the consistency coefficient was observed to increase with concentration which is consistent with all previous observations. The author finally sought to explain the rheology in terms of the amount of starch solubilized and the volume fraction and deformability of the swollen granules. It should lastly be noted that Hoseney (1986) states that shear-thinning is due to solubilized molecules orienting themselves in the direction of flow when a stress is applied to the fluid, and that the more soluble the starch, the more shear-thinning it is. This statement does not necessarily contradict the findings of Bagley and Christianson (1982) and Christianson and Bagley (1983), because their experiments were done on pastes where little 30 of the amylose was solubilized. However, the statement by Hoseney (1986) is incomplete because it does not account for the deformability of the starch granules. If orientation of the macromolecules in the continuous phase in the direction of flow enhances shear-thinning, one might speculate that starches containing amylose are more prone to exhibit slip, because molecular alignment would first occur in the boundary layer where the shear stress is highest. Also, waxy starches (which contain no amylose) might exhibit Newtonian or dilatant behavior until the temperature is high enough to solubilize amylopectin and soften the granule. 2.3. Summary Several observations, distilled from the works reviewed above, are summarized here. 1.) Gelatinized starch "solutions" are two phase and are comprised of a continuous phase containing solubilized macromolecules and dispersed phase comprised of swollen granules. The amount of dissolved macromolecules depends on the type of starch (waxy, legume or cereal, etc.) and the temperature at which it is cooked. The degree to which the granules are swollen depends on the cook temperature, the rate of heating, and whether the starch is crosslinked. 2.) Apart from the effects of the solubilized macromolecules, the rheology of starch suspensions depends on the volume fraction of the swollen granules and how 31 deformable they are. When the granules are deformable, shear-thinning behavior is usually observed for all concentrations. When the volume fraction reaches 0.7 there is a rapid increase in viscosity with further increases in concentration. If the granules are not deformable, and the concentration is such that the granules are near close packing, dilatancy will be observed. Increasing the shear stress by reducing the temperature of the suspension, or by increasing the concentration, may induce Newtonian or shear thinning behavior in a suspension that was previously dilatant. 3.) The consistency coefficient was always observed to increase with starch concentration. 4.) The flow behavior index is a function of concentration. 5.) In the one study where it was examined, the consistency coefficient was observed to decrease with temperature and was modeled with an Arrhenius relationship. CHAPTER THREE ANALYTICAL METHODS IN TUBE VISCOMETRY 3.1. Introduction The theory associated with tube viscometry has been well established for many years. In this chapter, the pertinent equations and their assumptions are presented for completeness and to serve as a reference for the rest of the text. 3.2. Shear Stress and Shear Rate Calculations. An expression for the shear stress acting on a fluid flowing through a tube can be obtained by performing a force balance on an arbitrary core of fluid, which yields: a=(APr)/(2L) .. ....... ......(3.1) This expression can also be obtained by performing a shell momentum balance (Bird et al., 1960). At the wall of the tube, i.e. at r=R, the shear stress is a maximum and is denoted aw' Therefore, the wall shear stress can be obtained by measuring the pressure drop, AP, over a length of tube, L, with a known radius, R. There are no 32 33 assumptions associated with this equation. The expression for the volumetric flow rate in a tube is: a Q=((1rR3)/aw3) fz2f(o)da ........ (3.2) O for any time-independent fluid. For viscometric flow in a pipe, f(a) is the fluid velocity gradient i.e., the shear rate and is a unique function which relates the shear rate to the shear stress (Whorlow, 1980). Rabinowitsch (1929) and Mooney (1931) manipulated this equation to obtain the shear rate explicitly: d(Q/«R°) du/dr=§=(3Q)/(«R3) + 0 ................. (3.3) This is the classic Rabinowitsch-Mooney equation (Bird et al., 1960: Whorlow, 1980). Several assumptions have to be met in the application of Equation 3.3: laminar flow, homogeneous and isotropic material, isothermal, steady state conditions, incompressible fluid, and no slip (the velocity of the fluid at the wall is zero). Slip is discussed in the following section. The derivative in Equation 3.3 is evaluated at values of wall shear stress that correspond to the volumetric flow rate, Q. Equation 3.3 is general, meaning that no particular fluid model was assumed in the derivation. Also, 34 Equation 3.3 is is most easily evaluated for fluids where plots of Q/(«R3) versus aw are nearly linear, which is common for fluids with Newtonian, Bingham, and power law behavior (Whorlow, 1980). Plots of shear stress versus shear rate are called rheograms, and there are many models available to describe the rheological properties exhibited in these plots. The Herschel-Bulkley model is very useful, because the Newtonian, Bingham, and power law models are all special cases of it. The Herschel-Bulkley model is: a = 1((4)n + co ........... (3.4) When n equals one the fluid is Bingham, when 0 equals 0 zero the fluid is power law, and when n equals one and co equals zero, the fluid is Newtonian. 3.3. Evaluation of Slip (Wall Effects). Slip is the phenomenon where the velocity of a fluid flowing under an applied stress appears not to be zero at the stationary wall containing the fluid. At a molecular level, slip never occurs, because the smoothest wall is sufficiently rough to prevent it. However, for suspensions and two phase systems, the portion of the fluid system having a viscosity less than the bulk viscosity may form a layer at the wall which acts as a lubricant for the main body of material causing slip. An example of a two phase 35 system is paper pulp where a thin layer of water forms at the wall. A second type of two phase system is frozen orange juice concentrate where liquid orange juice forms a layer at the wall. Figure 3.1 is a diagram of velocity profiles with and without slip. If slip is present, the flow rate is larger than it would be if slip was not present causing errors in shear rate calculations. To account for slip, the following modification to the expression for the volumetric flow rate in a tube is made (Whorlow, 1980): 0’ W Q=((«R3)/aw3)) f a2f(a)da + «Rzus ...(3.5) o where Us is the slip velocity (m/s) and is a function only of the wall shear stress. If a slip coefficient is defined as p=Us/aw, then the modified expression for the volumetric flow rate can be written as: Q/(«R30w)=,6/R + (l/aw‘) Jp‘zzfiama ...(3.6) 0 The slip coefficient, p, can be evaluated from tube viscometer measurements from tubes of the same length but different radii. Skelland (1967) and Darby (1976) have summarized the procedure which has become the standard for the determination of the slip coefficient. What is finally obtained is the slip coefficient as a function of the wall 36 3:3 :25 - .3 .....m 59.55 as... < z. 93.. BS 525.. < “6 3:2... >:oo._u> ...m 250: 1 1m WNW 1-03 T E 3v n63! ”if“ ~ /r T M\\ HULJLJLLJLAL T. :33: ans: 37 shear stress which is used to correct volumetric flow rates as follows: Q -,80w1rR2 .......(3.7) no slip = Qmeasured where the wall shear stress is that corresponding to the measured volumetric flow rate. The corrected volumetric flow rate values are then used in the Rabinowitsch-Mooney equation (Equation 3.3) to obtain shear rate values. It should be noted that the wall shear stress values should be corrected for excess pressure loss due to end effects, if they are a problem. End effects are discussed in the following section. 3.4. End Effects End effects are mechanical energy losses associated with flow transitions at the entrance and exit of the tube viscometer. At the end of the tube, part of the work done by the driving pressure is converted to the kinetic energy of the emerging stream (Whorlow, 1980). At the entrance of the tube, a certain length is required before the boundary layer, which starts developing at the entrance of the tube, converges on the center line and fully developed flow ensues. The length required for fully developed flow is called the entrance length. Static pressure drop along the entrance length is greater than that along an equal length of tube in the fully developed region 38 (Skelland, 1967). Consequently, placement of a pressure tap in the entrance length, or too close to the end of the tube, can result in erroneous pressure drop readings. In turn, this makes the calculated values of wall shear stress in error; Whorlow (1980) presents a method for correcting for the kinetic energy loss at the end of the tube. However, it is stated that, in practice, the correction is important only for low viscosity liquids at high flow rates. The criteria given is to compare pv2 to the total pressure drop. If small compared to the pressure drop, the correction can be neglected. The kinetic energy correction is more important for capillary (extrusion) viscometers where the force required to push a fluid through a capillary open to the atmosphere is recorded. For large tube viscometers where a pressure tap can be placed upstream from the end of the tube, the kinetic energy correction is not needed, because the streamlines are still parallel to the tube wall. The correction for entrance length effects is a more difficult problem. Theoretically, for a non-Newtonian power law fluid, the entrance length can be calculated if the rheological parameters are known. Skelland (1967) presents a review of the methods available to do this. These methods, however, are of little use in the characterization of an unknown fluid. Skelland (1967) also reviews an empirical method, developed by Bagley (1957), that 39 compensates for entrance length effects. In this method, pressure drop measurements are collected for various ratios of length over diameter for constant values of volumetric flow rate. The pressure drop is plotted against the length over diameter ratio yielding a fictitious length which is added to the "L" in Equation 3.1. The effect is to yield values of wall shear stress unaffected by entrance length. Alternatively, from the same plots, a correction to the pressure drop term can be obtained which achieves the same outcome. The correction is subtracted from the pressure drop term in Equation 3.1. Some experimental work has been completed examining entrance length effects. Yoo (1974) observed that for Newtonian and inelastic non-Newtonian fluids, pressure drop readings were unaffected beyond forty diameters from the entrance. For viscoelastic fluids, he observed that eighty diameters were required. Tung (1978) was able to confirm the observations of Yoo (1974) while observing that an entrance length of one-hundred diameters was required for certain solutions of Separan. Therefore, placement of the leading pressure tap greater than one-hundred diameters downstream from the entrance should eliminate entrance length effects on pressure drop readings. Finally, the analytical relationship for determining the entrance length for Newtonian fluids is given as a reference (Potter and Foss, 1982): 40 Le = 0.05750 Re ........... (3.3) N where Le is the entrance length, D is the diameter, and ReN is the Newtonian Reynolds number. 3.5. Laminar Flow Criteria The most general expressions for laminar flow criteria in non-Newtonian fluids are those developed by Hanks and Ricks (1974) for Herschel-Bulkley fluids. The Herschel- Bulkley model is general, and Bingham, Newtonian, and power-law fluids can all be considered a special case of it, as mentioned previously. Steffe and Morgan (1986) summarized the work of Hanks and Ricks (1974) in a paper on pipeline design and pump selection for non-Newtonian fluid foods. The critical Reynolds number for pipe flow of a power-law fluid is: Critical Re = ---------------------- .....(3.9) The generalized Reynolds number for a Herschel-Bulkley fluid and all of its special cases is: To determine the critical Reynolds number for fluids with a yield stress, calculation of the generalized 41 Hedstrom number is also required. This is covered by Steffe and Morgan (1986) and will not be presented here. The equations presented above will be used to determine if the laminar flow criterion, required.by the Rabinowitsch-Mooney equation (Equation 3.2), is met. CHAPTER FOUR MATERIALS AND METHODS 4.1. Description of the Tube Viscometer System. To perform a rheological characterization of crosslinked waxy maize starch solutions under low acid aseptic processing conditions, a viscometer system that allowed heating of the starch solution to 143°C, while simultaneously preventing boiling of the fluid, was required. This was achieved with a tube viscometer system. Figure 4.1 is a pictorial diagram of the tube viscometer system built for this purpose. Parts are listed in Table 4.1, with the part numbers corresponding to the label numbers in Figure 4.1. The system consisted of two Cherry Burrell Model UAS 50 vats (Cherry Burrell, Cedar Rapids, IA), a Waukesau Model 10 positive displacement pump (Abex Corp., Waukesau, WI), an air filled shock tube with a dial pressure gauge mounted on top, a Micro Motion Model DL100 mass flow meter (Micro Motion, Denver, CO), a concentric tube heat exchanger, and several tube viscometers of different diameters. The lines leading from the pressure taps in the tube viscometer to the pressure transducer are 0.95 centimeter in diameter, stainless steel 42 43 .2mhm>w «HES—onus man... to 2:050 Ut >°~— I 3| , =3. .—.¢ 559.”. sF) main 0.8618 8 0.1077 2.112 0.106 block 0.1351 3 0.0450 0.883 0.474 treatment 0.7445 5 0.1489 2.919 0.052 residual 0.7142 14 0.0510 Table 5.3. Analysis of variance table for the consistency coefficient examining block and treatment effects. sum of degrees of mean * prob source squares freedom square F (>F) main 1178.03 8 147.25 2 422 0.070 block 258.97 3 86.324 1.420 0.279 treatment 921.44 5 184.29 3.031 0.046 residual 851.25 14 60.80 85 values). In other words, the primary cause of changes in response are not due to unwanted experimental or systematic effects. Tables 5.4 and 5.5 are analysis of variance tables examining treatment effects without block effects (since they are not significant). These tables show that treatment effects are significant at a=0.05 for both the flow behavior index and the consistency coefficient when block effects are not included. Table 5.6 is an analysis of variance table examining the effects of temperature and concentration, along with possible interaction effects, on the flow behavior index. This table shows that the flow behavior index is significantly affected (at a=0.05) by changes in both the temperature and the concentration. Interaction effects are not significant (the probability of the F ratio being greater than F is eighty-six percent) which means that effects due to temperature or concentration change on the flow behavior index are additive. Therefore, the effect of temperature on the flow behavior index can be examined independently of concentration effects and vice versa. The table also shows that the flow behavior index is slightly more affected by changes in concentration than changes in temperature. The last analysis of variance table repeats the analysis performed in Table 5.6 using the consistency coefficient. These results are presented in Table 5.7 and 86 Table 5.4. Analysis of variance table for the flow behavior index examining treatment effects with block effects removed. sum of degrees of mean * prob source squares freedom square F (>F) main 0.7226 5 0.1453 2.909 0.045 treatment 0.7226 5 0.1453 2.909 0.045 residual 0.8494 17 0.0500 Table 5.5. Analysis of variance table for the consistency coefficient examining treatment effects with block effects removed. sum of degrees of mean prob source squares freedom square F (>F) main 919.06 5 183.81 2 815 0.050 treatment 919.06 5 183.81 2 815 0.050 residual 1110.2 17 63.307 87 Table 5.6. Analysis of variance table examining temperature, concentration, and their interaction effects on the flow behavior index. sum of degrees of mean * prob source squares freedom square F (>F) main 0.7116 3 0.2372 4.748 0.014 temperature 0.3802 2 0.1901 3.805 0.043 concentrate 0.2851 1 0.2851 5.707 0.029 interaction 0.0150 2 0.0075 0.150 0.861 residual 0.8494 17 0.0500 Table 5.7. Analysis of variance table examining temperature, concentration, and their interaction effects on the consistency coefficient. sum of degrees of mean * prob source squares freedom square F (>F) main 746.18 3 248.72 3 808 0.030 temperature 514.99 2 257.50 3.943 0.039 concentrate 187.11 1 187.11 2.865 0.109 interaction 172.87 2 86.437 1 324 0.292 residual 1110.2 17 65.307 88 shows that the consistency coefficient is significantly affected by changes in temperature (a=0.05). Effects caused by changes in concentration are nearly significant at a=0.1. It is concluded from these results that the consistency coefficient is a strong function of temperature and a weak function of concentration. Temperature/concentration interaction effects on the consistency coefficient are not significant since the probability of the F ratio being greater than F is approximately 29%. Therefore, the effects caused by temperature and concentration on the consistency coefficient are additive. Average values (treatment means) of the flow behavior index and the consistency coefficient are presented in Table 5.8 for each treatment level (temperature/concentration combination). An examination of Table 5.8, together with Figures 5.1-5.4, reveal the following: 1. Generally, the flow behavior index decreases as temperature increases. However, for a given concentration, there is little change in the flow behavior index until the temperature is increased to 143.3°C from 132.2°C (Figure 5.1). 2. The consistency coefficient generally increases as temperature increases. However, as with the 89 Table 5.8. Average values (treatment means) of consistency coefficient (K) and flow behavior index (n) for each experiment. . * y - ..... ffEffiTEEE .............. 3222 ........... Eeysf_i3-i---- 121.1°C, 1.82% starch 1.395 4.34 132.2°C, 1.82% starch 1.348 4.65 143.3°C, 1.82% starch 1.093 20.2 121.1°C, 2.72% starch 1.558 2.60 132.2°C, 2.72% starch 1.634 2.13 143.3°C, 2.72% starch 1.314 6.08 90 838383 .m> mm:_o> xOoE ._o_>or_mm 26E mooLm>< I Tm 6.39... Gov OLBEOQEOR mVP 0*: mm: 0MP mNF ONF PFLIFII—IFIRLIIPFFPFLLLLLIPIFPLLL O.—. IN._. I. 11 I0.— rm; 33 .183. Rand In 33 eegm RS; I 0. N xepuI JOIAoqeg MOB ‘u 91 Q: L b OLBOLOQEOH .m> moEo> EOEEOOO xocofificoo omoco>< I Nat. 6.59.1 Gov 9.38an8. 0*; mm. PLFbI-Irhi— bib P IP L-Lirbbhb om— MNF ON? L I4 33 seem Rana «I. 33 :83... Ram; I 06 was we... mos Toe was: vod— woe: 11.0.9 mos. wodm CNN (Us Dd) T70” 40910141303 AOUSISISUOQ 92 cozobcmocoo .m> mo:_o> xooE ..o_>ozmm 32... 600.624 I Om 939.1 3R5 cozobcmocoo 583m 0N 0d 0.9 _ L 0; IN; ...: To; End: mIm Tm; Pad... To 9:9 I 0. N xepul JOIAoqeg MOL-j ‘u 93 cozobcmocoo .m> mm:_o> meofmoo 3:066:00 mmocm>< I To 839.; “no.5 cozobcoocoo £0.65 QM MN O.N _ / oonfiti Tm oomdm: «In oowéwp I 06 Ted To... mod woe wed? Iode we: woe. no.3 ..odm .. Qua (us Dd) KoueiSIsuoo 1,0 L* TueIOIIIeoo 94 flow behavior index, there is little change until the temperature is increased to 143.3°C from 132.2°C (Figure 5.2). 3. The flow behavior index increases with concentration (Figure 5.3). 4. The consistency coefficient decreases with concentration (Figure 5.4). Figures 5.1 to 5.4 are a statistical tool often used in conjunction with analysis of variance (Neter et al., 1985), and other information can be obtained from them. For instance, the degree to which the lines are parallel in the figures is an indication of the degree of interaction (Neter, et al., 1985). The high degree of parallelism in Figures 5.1 and 5.3 indicates almost no interaction which is confirmed in Table 5.6 (P[F2F*]~0.86). In Figures 5.2 and 5.4, there is a divergence going from 132.2 to 143.3°C indicating some interaction effects. However, Table 5.7 revealed this to be insignificant (P[F2F*]~0.29). Figures 5.3 and 5.4 present the same information as Figures 5.1 and 5.2 except it is viewed in a different way. Figures 5.3 and 5.4 allow observation of concentration effects on the parameters for a given temperature whereas, in Figures 5.1 and 5.2, the effect of temperature on the parameters is observed for a given concentration. Concentration effects can still be seen in Figures 5.1 and 5.2: if there were no concentration effects, the lines would superimpose. 95 It is most easily seen in Figures 5.3 and 5.4 that the responses at 121.1 and 132.2°C are essentially the same. 5.3. Rheograms As mentioned previously, the insignificance of block effects allowed pooling of data and/or averaging of responses (K and n values). All of the analysis performed thus far has been with the average values of consistency coefficient and flow behavior index for each treatment level, i.e., treatment means. Another way of viewing the results is to pool the data from the four blocks and perform nonlinear regression to obtain the rheological parameters. There are several benefits in doing this. First, a comparison can be made between the parameters obtained from the pooled data and the treatment means. Second, it allows visual observation of the variation within a treatment level when plotted in a rheogram. Nonlinear regression was performed, and rheograms were created, with a commercially available statistical/plotting package called "Plotit" (Eisensmith, 1987). The pooled data parameters are presented in Table 5.9 along with the nonlinear coefficients of determination. A comparison with the treatment means presented in Table 5.8 shows that, with the exception of the consistency coefficient at 143.3°C and 1.82% starch, the values are nearly the same and follow the same trends. This is the expected result. The rheograms for the six experiments where the data have been pooled are 96 Table 5.9. Flow behavior indices, consistency coefficients, and nonlinear coefficients of determination for the six experiments (temperature/concentration combinations) where block data has been pooled. experiment n K*10‘ (Pa 3“) r2 121.1°C, 1.82% starch 1.444 2.87 0.973 132.2°C, 1.82% starch 1.389 3.49 0.978 143.3°C, 1.82% starch 1.111 12.01 0.871 121.1°C, 2.72% starch 1.477 1.71 0.955 132.2°C, 2.72% starch 1.556 1.69 0.911 143.3°C, 2.72% starch 1.222 7.38 0.988 Table 5.10. Nonlinear coefficients of determination for each of the individual block experiments. experiment block 1 block 2 block 3 block 4 T1C1 0.977 0.983 0.994 0.967 T2C1 0.981 0.958 0.983 0.996 T3C1 0.998 0.989 0.994 0.998 T1C2 0.988 0.957 0.968 0.986 T2C2 0.987 0.980 0.995 0.934 T3C2 failed 0.998 0.996 0.978 where: T1=121.1°C T2=132.2°C T3=143.3°C and C1=1.82% starch C2=2.72% starch 97 presented in Figures A7-A12 in Appendix A. The rheograms in Figures A7-A12 can be presented in ways that allow examination of temperature or concentration effects. Figures A13 and A14 show temperature effect for 1.82 and 2.72% starch, respectively. Note that rheograms allow observation of the combined effect of the flow behavior index and the consistency coefficient, since both are required to define a rheogram. For example, it was shown earlier that the flow behavior index decreases with temperature whereas the consistency coefficient increases. Therefore, for a given concentration, the rheogram for 143.3°C would be expected to be slightly elevated and not as steep as observed in Figures A13 and A14. Figures A15-A17 show concentration effects for 121.1, 132.2, and 143.3°C, respectively. As expected, the rheograms for 1.82% starch are slightly elevated and not as steep when compared to the 2.72% starch rheograms. However, the observational differences are not as great as one might expect, because the rheological parameters estimated from the pooled data are closer together in value than the treatment means. Finally, the rheograms of the individual block experiments (replications), for all six temperature/concentration combinations are presented in Figures Al-A6. These were done to allow observation of variation between blocks, provide a check on the rheological parameters estimated by the computer program 98 "Tubev," and obtain nonlinear coefficients of determination for each of the twenty-three individual experiments. The rheological parameters estimated by Plotit exactly matched those estimated by "Tubev." The nonlinear coefficients of determination are presented in Table 5.10. 5.4. Evaluation of Slip The standard evaluation for slip, as outlined in Chapter Three, could not be performed due to the inability of the heat exchanger to maintain fluid temperature at the higher flow rates required to cover the same shear rate range in the larger tube viscometer. Also, a smaller diameter tube viscometer could not be used, because the minimum pump speed provided a flow rate that yielded shear rate values that were too large. Consequently, the best that could be done was a qualitative evaluation. The rheogram for the test conducted in the larger tube viscometer is presented in Figure 5.5 along with the rheogram from the pooled data at 121.1°C and 1.82% starch. If slip is not present, the rheograms from the two different diameter viscometers should superimpose when they cover the same shear rates. It can be seen from Figure 5.5 that the overlap in shear rates is approximately seven reciprocal seconds. The flow behavior index and consistency coefficient for the larger diameter viscometer are 1.365 4 and 6.25*10- Pa 3“, respectively. These values are not the same as those for the pooled data from the smaller 99 m8 6820 280:5 Lo mLBOEoomS : 39:: 0:9 8 583m RN? .6 meeoooemImS 8%: Am\S Box .695 03 of of owe om: mm 00 0... ON _ . _ L _ . O Ememodnofi .05.. cofimemmm ---- Ememodnofi .3501 Soc D EnaPodnofi .95 663531 I Emmeodnofi .Esom Soc 0 00.0 joed Toad Tond 10.4.0 T T00.0 00.0 (Dd) SSSJlS .Ioqu 100 viscometer (Table 5.9). However, the values from the larger tube viscometer do fall within the variation between the block experiments that, together, comprise the rheogram for the smaller diameter viscometer (Table 5.1). Since slip was not expected to occur in these fluids, and the rheogram for the larger diameter viscometer falls within the block variation, the conclusion is drawn that slip is negligible. However, if a larger heat exchanger can be obtained, future research should include a quantitative evaluation of slip. 5.5. Parameter Correlation Analysis During the execution of the nonlinear regression analyses required to obtain the coefficients of determination (Tables 5.9 and 5.10), it was noticed that the parameter correlation matrix was yielding a value near one for the off diagonal elements. This indicates that the flow behavior index and consistency coefficient might be correlated. Evidence to support this can be seen in Table 5.8 and Figures 5.1-5.4: As the flow behavior index decreases with increasing temperature, the consistency coefficient increases (Figures 5.1 and 5.2). Also, as the flow behavior index increases with increasing concentration, the consistency coefficient decreases (Figures 5.3 and 5.4). If the parameters are correlated, then one of the parameters should be eliminated in favor of a simpler, one parameter model. In simpler terms, this 101 means that only one of the parameters (K or n) would be required to describe all changes in fluid behavior. To determine if the parameters are correlated, sensitivity coefficients were determined and plotted against an independent variable (Beck and Arnold, 1977). The sensitivity coefficients constructed for this purpose were: 49 19 (K) ax (Man An expression for the volumetric flow rate, Q, was obtained from an alternative version of the power law model: a = KI<<3n+1I/I4n)I*I<4QI/I«R3)II“ ..... (5.1) This version of the power law model was obtained by substituting an alternate form of the Rabinowitsch-Mooney equation for the velocity gradient. Equation 5.1 was then rearranged to solve the volumetric flow rate explicitly, and the derivatives were obtained from this expression. Either the volumetric flow rate or the pressure drop could have been chosen to construct the sensitivity coefficients. Volumetric flow rate was chosen because it was thought to have larger error associated with it. Also, the derivatives of the volumetric flow rate with respect to the parameters could both be obtained analytically. Derivatives were calculated for values of pressure drop 102 between 50 and 700 pascals which is the approximate range seen in the experiments. This was done for two values of the flow behavior index (n=1 and n=1.5) while the value of the consistency coefficient was held constant at 5.0410-5 n. These values are within the range seen in the Pa 3 experiments. Calculated values of the sensitivity coefficients are presented in Tables 5.11 and 5.12. The third column of these tables is the ratio of the sensitivity coefficients. Plots of the sensitivity coefficients versus pressure drop are presented in Figures 5.6 and 5.7. The ordinates in Figures 5.6 and 5.7 have been multiplied by negative one for convenience. If the sensitivity coefficients are found to be linearly dependent, then one would conclude that the parameters are correlated (Beck and Arnold, 1977). It can be seen in Tables 5.11 and 5.12 and Figures 5.6 and 5.7 that the sensitivity coefficients are not linearly dependent but are nearly so. Therefore, the conclusion is that both parameters are required to describe flow behavior, i.e., eliminating one by expressing it as a function of the other would result in a loss of information and a larger sum squared error. The near correlation of the parameters makes it impossible to unambiguously estimate the parameters and causes problems in the interpretation of their behavior. The reason for this is that the behavior of each parameter is influenced by the other. One of the objectives of this 103 Table 5.11. Values of the sensitivity coefficients (m3/s) and thier ratio for various values of pHessure drop (Pa) when n=1 and K=5.0*10 5 Pa s . AP K(aQ/aK)*106 n(aQ/an)*105 ratio 50 -1.391 -5.564 3.987 100 -2.782 -13.02 4.681 ° 150 -4.173 -21.21 5.083 200 -5.564 -29.90 5.374 250 -6.995 -38.91 5.595 300 -8.346 -48.23 5.779 400 -11.13 -67.51 6.066 500 -13.91 -87.49 6.290 600 -16.69 -108.0 6.472 700 -19.47 -129.0 6.626 Table 5.12. Values of the sensitivity coefficients (HP/s) and thier ratio for various valuessof pressure drop (Pa) when n=1.5 and K=5.0*10 Pa 5 . AP K(aQ/aK)*106 n(aQ/an)*106 ratio 50 -2.465 -9.801 3.976 100 -3.912 -18.21 4.655 150 -5.126 -25.95 5.062 200 -6.210 -33.23 5.351 250 -7.260 -40.17 5.575 300 -8.138 -46.84 5.756 400 -9.858 -59.57 6.043 500 -11.44 -7l.69 6.267 600 —12.92 -83.30 6.447 104 0;": Lou. coco crammed mameo> 3:22:80 bSEmcmmlmh 0.59... Aodv no.5 crammed DOD DON. 000 com 00.9V Don CON OD _. IP IP P lb L b + Ll L P I— b F IIP (S/EUJ) siueIoIIISOQ .(iIAIigsueg 105 0;": toe no.5 8:3de 95.55 3:23.080 szBCOmlka 6.59.1 non: doLQ mezwmmed 000 0mm 0mm 0mm. 0a.; 0mm 0mm 0m: 0 SIS cm fl. (S/ELLI) 340913144303 All/\IIISUSS 106 research was to examine the influence of temperature and concentration on the behavior of the rheological parameters, and it would seem that unambiguous estimates of the parameters would make the analysis of variance results, obtained earlier, meaningless. However, the fact that the parameters were shown to be significantly affected by changes in concentration and temperature suggests that one of the parameters is dominating the fluid behavior i.e., that one of the parameters is highly dependent on the other. An examination of Figures 5.6 and 5.7 reveals the flow behavior index to be the dominating parameter, because small perturbations in the flow behavior index cause larger changes in the volumetric flow rate than small perturbations in the consistency coefficient. Consequently, the behavior of the consistency coefficient is mostly determined by the behavior of the flow behavior index, and not by changes in concentration and temperature. Evidence of the near correlation of the parameters can be seen in Figure 5.8 where a plot of the consistency coefficient versus the flow behavior index is presented. An equation that fits this relationship well is K = exp[-4.534n-l.647] ..........(5.2) Using the first three values of the flow behavior index from Table 5.9 in the Equation 5.1 yields values of 4 4 4 n 2.76*1o' , 3.55*1o' , and 12.50*1o' Pa s for the 107 xooE 63930 307.. momco> EEOCCOOQ >oc3m_mc00Im.m 6.39.1 xooE ._o_>o:om so: 0N MN —.N 0.— hé m... 04 ...F 0.0 50 0.0 b —I b b b n .— h b n — h F p L E _IpL O O G O 8 a w r S 5...... m. o I: w. .. 0 oo nA I0N O .x. I. O .. 0 m. .V H... Tom D. a . 0 1| .2 ....m o - S on {w 108 consistency coefficient, respectively. These values compare favorably to the estimated values in the table of 2.87*10- 4 4 4 n , 3.49*1o“ , and 12.01*1o' Pa 8 , respectively. However, not all of the changes in the consistency coefficient can be predicted by the flow behavior index, because the parameters are not absolutely correlated, i.e., some of the variation is due to the changes in temperature and concentration. For this reason, it is inappropriate to incorporate Equation 5.1 into the power law model to create a new, one parameter model. Another way of examining the degree to which the flow behavior index is dominating the fluid behavior is to fit the data with the following model: a = Koexp[-4.534n-l.647]7n ......(5.3) The exponential term is a "parameter" that is completely dependent on the flow behavior index. This term will also be recognized as the approximate representation for the consistency coefficient given above. Therefore, the parameter Ko will represent the amount of information in the consistency coefficient not attributable to the flow behavior index. An estimated value of one for Ko would indicate that the consistency coefficient is completely dependent on the flow behavior index, and a large value would indicate that the consistency coefficient is dominating the fluid behavior. The data in Table C4 of 109 Appendix C was arbitrarily chosen, and the parameters in Equation 5.1 were estimated using Gauss minimization (Beck and Arnold, 1977). The estimated value of K0 was 1.028 indicating that the consistency coefficient is highly dependent on the flow behavior index and that the fluid behavior is almost entirely described by the flow behavior index. The final indicator of the dominance of the flow behavior index, and of the reliability of the estimates of this parameter, can be seen in the standard error of the estimates. The standard error of the estimated values of the flow behavior index were always less than 10% of the estimated value, whereas, the standard errors of the estimated values of the consistency coefficient could be 1000% of the estimated value. Part of the large standard errors associated with the consistency coefficient can be attributed to the lowest shear rates in these experiments being 40 s-l, i.e., if lower shear rates could have been obtained, the standard errors would have been smaller. The main point is that the small standard errors of the estimates associated with the flow behavior index indicate that the estimates are reliable and that the analysis of variance on this parameter is meaningful. The influence of the flow behavior index on the consistency coefficient makes the analysis of variance performed with the consistency coefficient meaningless. This is due to the consistency coefficient being influenced 110 by the flow behavior index in an inverse way, i.e., if the flow behavior index is significantly affected by changes in concentration or temperature, the consistency coefficient is likely to be significantly affected, but in an inverse way. Figures 5.1-5.4 together with Tables 5.6 and 5.7 reveal this to be the case. The fact that the consistency coefficient is only weakly affected by concentration, while the flow behavior index is strongly affected, is probably due to correlation not being absolute. CHAPTER SIX DISCUSSION 6.1. Near Correlation of the Parameters: Effect on the Prediction of Hold Tube Velocity Profiles and Implications for the Power Law Model Near correlation of the parameters in this study might have been avoided if the sensitivity coefficients in Chapter Five were investigated beforehand. However, to do this requires knowledge of the parameter values which were not available. Near correlation may have also been avoided if a broader range of volumetric flow rate (and consequently, shear rate) had been used. This would have been difficult to achieve because of the laminar flow requirement of the Rabinowitsch-Mooney equation. Also, broadening the shear rate range beyond that seen in aseptic processing may have made the results useless. The laminar flow restraint of the Rabinowitsch-Mooney equation (Eq. 3.3) raises the question as to whether it is possible to achieve a broad enough flow range to reduce the degree of correlation between the parameters. An inverse relationship between the flow behavior index and the consistency coefficient has also been seen in other studies 111 112 (Ford, 1984: Vercruysse, 1987: Salas-Valerio, 1988: Doublier, 1981) which raises a suspicion that some degree of correlation between the parameters existed in these studies. Note that these studies used different materials and/or different rheometers than used in the current work, and a broader shear rate range was covered. If it is true that it is not possible to reduce the degree of correlation between the parameters due to laminar flow constraints on flow rate, then serious questions can be raised about the appropriateness of the power law model for liquid foods, if physical significance is to be given to the parameters. A method for dealing with nearly correlated parameters is to combine them into a new parameter which, in effect, creates a new model. This is different than eliminating a parameter, because both parameters define the value of the new parameter. Therefore, no information is lost. As an example, consider a model of the form: 4 s ¢1¢2t ................ (6.1) If ¢1 and ¢2 are nearly correlated, then a new parameter can be introduced such that ¢ = ¢ This new parameter 1¢2° will yield the same value of W for a given value of t, and no information is lost (Beck and Arnold, 1977). A way of combining the parameters of this study is to define a new parameter: 113 where c is the median value of the ratio of the sensitivity coefficients (Beck, 1989). However, how this new parameter could be used to express the relationship between the stress and rate of deformation tensors is not clear. A question that remains is whether the inability to unambiguously estimate the parameters due to the near correlation has any effect on predicting velocity profiles in hold tubes. It will be seen in the following section that the design of hold tube lengths is dependent only on the flow behavior index when the hold tube length is designed on the basis of the fastest moving fluid or food particle. Since the estimates of the flow behavior index have been shown to be reliable, the values obtained in this study can be used for engineering design of hold tube lengths based on the fastest moving fluid or food particle. The consistency coefficient has been shown to be primarily dependent on the flow behavior index: therefore, it has lost most of it physical significance. However, it is still useful in predicting the relationship between pressure drop and flow rate (witness the high values of the coefficient of determination in Table 5.10) and consequently, hold tube velocity profiles. The conclusion is that the values of consistency coefficient determined in this study have no physical significance by themselves, but they can be used 114 with the values of flow behavior index for engineering design purposes. This allows the hold tube to be treated as a laminar flow reactor, i.e., microbial lethality can be integrated across the hold tube, if that method of hold tube design is preferred. 6.2. Effect of Dilatancy on Hold Tube Velocity Profiles and its Implications for Aseptic Processing Shear-thickening behavior results in the velocity differential between the fastest and slowest moving fluid stream to be greater than if the material was shear- thinning. Mathematically, for laminar flow of power law fluids in tubes: U =[(3n+l)/(n+l)]U max ave therefore If n=infinity Umax=3'OOUave If n=2 Umax=2'33Uave If n=1 Umax=2'00Uave If n=0.5 Umax=l'67UaVe If n=0 Umax=Uave Figure 6.1 is a diagram of velocity profiles for the cases when n<0.5 (shear-thinning), n=1 (Newtonian), and n>1 (shear-thickening). Since the starch solutions in this study were shear-thickening, hold tubes must be designed so that the velocity of the fastest moving fluid stream is 115 .2 A 5 62.55:: 53:... 0 oz< .= u 5 2523252 8 . .3 v 5 62.22:: 53:... 2 62.26:... as: 35 525.. < mo 33:9... >532, Enos—2.5.5... «.0 $50.“— 116 greater than twice the bulk average velocity. It was mentioned in the introduction that the microorganism of concern in the thermal processing of low acid foods is glostridium botulinum. This requires that hold tubes be designed based on the worst case value of the flow behavior index for each temperature/concentration combination, i.e., the treatment mean flow behavior index values in Table 5.8 should not be used for hold tube design. Instead, the largest value of the flow behavior index for each temperature/concentration combination should be used (see Table 5.1). Table 6.1 presents the largest value of flow behavior index for each temperature/concentration combination along with the ratio of U It can be seen from this table that the max/Uave’ largest value of flow behavior index from any of the U ratio of experiments is 2.076 which results in a Umax/ ave 2.35. Note that these results are only good for the conditions of these tests: producers of low acid foods should perform their own rheological characterization if processing conditions are different. Examples of different processing conditions that would affect the results here would be a change in pH, addition of salts, sugars, or hydrocolloids, and markedly different heat exchanger residence times. For processors of low acid foods containing particulate matter, dilatant flow behavior has several implications. First, the fluid next to the particles will 117 Table 6.1. Maximum values of flow behavior index for each temperature/concentration combination and the associated V ax/Vave ratios m ...... ff??fi§f§f-----_------fas§------------YsssCYexs--_--- 121.1°C, 2% starch 1.612 2.23 132.2°C, 2% starch 1.461 2.19 143.3°C, 2% starch 1.443 2.18 121.1°C, 3% starch 1.861 2.30 132.2°C, 3% starch 2.076 2.35 143.3°C, 3% starch 1.466 2.19 118 be more viscous than the bulk fluid due to the velocity gradient in the boundary layer of the particle. This will have the effect of decreasing heat transfer rates, because the more viscous fluid will act as an insulator. On the positive side, form drag on the particle should be increased which will aid in keeping the particle suspended and moving with the fluid. Dilatant behavior will also result in greater overprocessing of the fluid phase than if the starch solutions were shear-thinning, because the differential between the fastest moving particle and the slowest fluid stream is greater. Since heat is being transferred from the fluid to the particle, i.e., the fluid is acting as a heat transfer medium, it is dubious that producers of foods that contain large particles will gain much in the way of product quality. Given the other problems that exist in developing thermal processes for particulate containing foods, producers may want to reexamine whether aseptic processing is appropriate for foods containing large particles. 6.3. Response of the Flow Behavior Index to Changes in Concentration and Temperature and an Explanation for the Observation of Dilatancy It was seen in Chapter Five that the flow behavior index increased with concentration and decreased with temperature. The fact that the flow behavior index increases with concentration is in agreement with the 119 results of Evans and Haisman (1979) but in disagreement with the results of Colas (1986). The observation of the flow behavior index increasing with concentration and decreasing with temperature can be explained with the same logic used by Bagley and Christianson (1982), Christianson et a1. (1982), and Christianson and Bagley (1983) for starch pastes at lower temperatures: increasing the concentration causes the granules to become more closely packed and will increase the flow behavior index if the granules are still somewhat rigid. They observed rigidity in the starch granules for low cook temperatures where all of the granules have not gelatinized and/or short cook times. In this system, the starch is cooked in the heat exchanger, and the cook time is the residence time in the heat exchanger. If the fluid is assumed Newtonian and an average density value is used, an estimate of the average residence time can be obtained. Doing this shows that the minimum residence time is approximately 0.284 minutes (17 seconds) and the maximum residence time is approximately 2.41 minutes (144 seconds). With such short cook times, it may be that little of the amylopectin is solubilized, and the granules are still rigid. Colas (1986) showed that the close-packing concentration for unmodified waxy maize was 1.76% and was 2.60% (g dry starch/100 g water) for the most lightly crosslinked waxy maize. Starch concentrations used in this study are within, or exceed, this range. In 120 light of this, if the granules in the solutions of this study were still rigid, it is reasonable to expect the flow behavior index to increase with concentration. This, combined with the fact that the high temperatures and low shear rates of this study caused the shear stresses in the fluid to be very small, also serves as a reasonable explanation for the observation of dilatancy. Other factors may have also contributed to dilatancy. First, starch continued to cook (paste) during the residence time in the tube viscometer. If continued pasting affected the solutions at the slower flow rates causing the granules to be significantly less rigid than those at higher flow/shear rates, an apparent dilatancy would be caused. Whether this significantly affected the results is questionable, because the average residence time in the tube viscometer is approximately the same as that for the heat exchanger. Second, despite the hold tube being insulated, temperature losses were experienced. Losses depended on the temperature of the solution and on the flow rate. At 121.1°C, the loss was 2-2.5°C: for 132.2°C, 2-3°C: and for 143.3°C, the loss was 3.5-4°C. Changes in the viscosity of starch pastes upon cooling at these temperatures is mostly due to increased interaction between starch molecules and an increase in viscosity of the continuous phase (water). For water, the decrease in viscosity going from 147 to 127 °C is 1.7=Ir10-5 Pa 5 (Incropera and Dewitt, 1985). Apparent viscosities of the 121 starch solutions in this study are all on the order of 10-3 Pa 5. Therefore, the viscosity change in the continuous phase is negligible. The effect of increased interaction between starch molecules at these temperatures is unknown. However, it is difficult to imagine that it is significant at such high temperatures. It is acknowledged that both ongoing pasting and temperature losses may have contributed to an apparent dilatancy. Overall though, it is felt that the observation of dilatancy is best attributed to the mechanism described above. Finally, it should be noted that slip is not a reasonable explanation for the observation of dilatancy, because not accounting for slip causes a fluid to appear more shear thinning than it is in reality. The observation that the flow behavior index decreased with increasing temperature might be expected, because increasing temperature would cause a more rapid disruption of the hydrogen bonds within the starch granules. In this case, granules would gelatinize quickly allowing more time for the solubilization of amylopectin and softening of the granule. Then, following the logic of Bagley and Christianson (1982), the granules would be more likely to deform under stress, decreasing the flow behavior index. Also, if significant amounts of solubilization have taken place, and shear stress causes the solubilized molecules to align in the direction of flow, then a decrease in the flow behavior index would be expected according to Hoseney (1986). 122 The temperature dependence of the flow behavior index (and consequently the consistency coefficient in this work) has several implications for aseptic processing. First, for processors of particulate foods where there is cooling of the liquid phase as the particles are being heated, the rheology of the suspending solution will be changing as the temperature of the solution changes. In turn, the velocity profile and residence time of the fastest moving particle will be changing. This effect becomes greater as the percentage of particles is increased. If the change in fluid temperature is known as a function of hold tube length, it is possible to recalculate the velocity profile along the length of the hold tube. An alternative approach, that is microbiologically conservative, would be to design the hold tube on the basis of constant rheological properties using the highest value of the flow behavior index, i.e., the value corresponding to the temperature at the end of the hold tube. This would result in some overprocessing. The flow behavior of the starch used in this study (National 465) is more sensitive to temperature change between 132 and 143°C. Hence, overprocessing caused by assuming constant rheological properties in the hold tube is minimal if hold tube temperature is between 121 and 132°C. A second implication of the temperature dependence of the flow behavior index is that the differential between the fastest and slowest fluid stream is minimized for 123 higher temperatures, since the flow behavior index generally decreases with temperature (Table 6.1). This means that processors should obtain higher quality product from processing at the higher temperatures. The concentration dependence of the flow behavior index (n increases with increasing concentration) indicates that higher quality product will be obtained with the lower starch concentration, since this will minimize the differential between the fastest and slowest fluid stream. For the material in this study, the highest quality product will be obtained for product formulated with the lower starch concentration which is processed at higher temperature. This is particularly true for nonparticulate foods or foods with small rapidly heating particles. In foods that contain large, slow heating particles (e.g., meat pieces) the quality gained by minimizing the differential between the fastest and slowest fluid streams by processing at higher temperatures will be lost to the extra time at the high temperature required to sterilize the particles. 6.4. Use of Rheological Data in Aseptic Processes FDA (1984b) states, with regard to using rheological data in an actual process, that "consistency must be controlled during processing and records of the measurements must be kept." To do this will require some kind of on-line viscometer, i.e., the ability to measure 124 pressure drop of the fluid flowing through the hold tube. The design of such an instrument would be challenging, because it would need to be done in a way that would preclude the entry of bacteria into the system. Differential pressure transducers are not flow through, and it is undesirable to expose the diaphrams of the transducer to the temperature seen in aseptic processing of low acid foods. Therefore, some kind of sanitary pressure tap using a flexible diaphram might be appropriate. If such a pressure tap could be designed, producers of aseptic processing equipment could incorporate them directly in to the hold tubes during manufacturing. Control of flow rate is a critical process parameter in aseptic processing, since it determines the residence time in the hold tube. To evaluate the rheology of non- Newtonian fluids requires varying the flow rate so that the derivative term in the Rabinowitsch-Mooney equation (Eq. 3.3) can be evaluated. Consequently, it is not possible to determine the rheology on-line: instead, it must be determined beforehand. The velocity profile in the hold tube can then be determined by simply measuring the pressure drop in the hold tube, and the volumetric flow rate. CHAPTER SEVEN SUMMARY AND CONCLUSIONS A rheological characterization of two waxy maize starch solutions (1.82 and 2.72% db) was completed under the following conditions: Temperature Shear Rate Range 121.1°C 4o - 155 s"1 132.2°C 4o - 135 s’1 143.3°C 4o - 100 s"1 The solutions were found to be shear thickening (dilatant) in 22 out of 23 experiments. The dilatancy was explained in terms of the rigidity and volume fraction of the swollen starch granules combined with exceedingly small shear stresses in the fluid due to the high temperatures and low shear rates. Due to the experimental conditions (the pressure and temperatures of the tests), the volume fraction occupied by the granules could not be verified. Instead, close-packing concentrations for crosslinked waxy maize starches were taken from the published literature. Contributions to dilatancy from ongoing pasting and 125 126 temperature loss were acknowledged but thought to be minor compared to the volume fraction effect. Analysis of variance showed the flow behavior index to be significantly affected by changes in both temperature and concentration: increasing with concentration and decreasing with temperature. The analysis also showed the consistency coefficient to be significantly affected by changes in temperature but only marginally affected by changes in concentration. The consistency coefficient acted in a manner inverse to the flow behavior index. The construction of sensitivity coefficients showed the two power law fluid parameters to be nearly correlated with the flow behavior index being the dominant parameter. This effectively made the observed behavior (and the analysis of variance) of the consistency coefficient difficult to interpret, because most (not all) of its behavior was determined by the flow behavior index. Because the correlation is not absolute, the sum of squares function has a unique minimum, and the estimated values of the parameters are unique. Therefore, the consistency coefficient could not be expressed as a function of the flow behavior index to reduce the relationship between the stress tensor and the rate Of deformation tensor to a one parameter model. The effect of dilatancy on power law fluid velocity profiles is to increase the differential between the fastest and slowest fluid stream. For low acid foods that 127 contain discrete particles, this will cause overprocessing of the fluid phase since the between the fastest moving particle and the stream is greater than if the carrier fluid thinning. A dilatant fluid will also act as because of shear-thickening in the boundary greater differential slowest fluid was shear- an insulator layer of the particle. Consequently, food producers are encouraged to reexamine whether aseptic processing is appropriate for foods containing large particles. For producers of nonparticulate foods, it was shown that (for the material considered in this study) the highest quality product will be obtained for foods with lower starch concentrations that are processed at higher temperatures due to the flow behavior index. depression of CHAPTER EIGHT SUGGESTIONS FOR FURTHER RESEARCH 1. If the explanation given for dilatancy is correct, then Newtonian or shear-thinning behavior should be induced if the concentration is increased due to the increased shear stress. Confirming this would validate the explanation given for dilatancy and substantiate the reasoning of Bagley and Christianson (1982), etc., for starch at these temperatures. 2. If a heat exchanger were placed in the system after the tube viscometer, it may be possible to cool the starch below the atmospheric boiling point so that the volume fraction of the starch granules can be determined. Knowing the volume fraction as a function of temperature and concentration would be useful in the interpretation of the rheological results. This system would also allow determination of the amount of solubilized amylopectin which may also be useful in interpreting rheological results. 128 129 3. Now that rheological parameters exist for National 465 starch under the conditions of this study, it is possible to verify the theoretical equations of Hanks and Ricks (1974) for laminar-turbulent transition by measuring pressure drop as a function of flow rate. This information would be very useful to producers of aseptically processed non-particulate foods in designing thermal processes based on turbulent flow regime. Large gains in product quality should be realized because holds tube lengths could be shortened by one-half to one-third. 4. The parameters in this study were nearly correlated and acted inversely to one another. The inverse behavior of the parameters has been observed in other studies using different rheometers and materials which raises the suspicion of near correlated or correlated parameters in these studies. The reason for this may be due to the limitation of the flow rate range caused by laminar flow requirements. This raises questions about the value of the power law model for liquid foods. An investigation into the value of a one parameter model that contains a fixed "consistency constant" might be useful. 5. A quantitative evaluation of slip should be performed. APPENDICES APPENDIX A RHEOGRAMS 130 85% . mm; 6.29 so 358% m. _.< .. 2 Sam: Am\ 3 flow. Loozm on; 00— on? m— — no mm. mm on \\\\\\\Q . ..\ .. . x ..s. .98 ImNd on: 5.39.09. .4 x3 I. . 858 3% .4 ...a . 05. 5.8808 .n x... II I090 .. 358 3% .n x... a . ....m as. 53339. .N x... ..-..- ....v 353 Boo .N x... o r010 or: c3323.. .— x3 I. U .. 358 32. .. ..s o 00.0 (od) 588.113 Joaqs 131 at .OoN. NMP #0 meOECO 655. N04 xm :4 I N< 0.59.“. Am\ 0 Box 52% mm? 00— mp F 00 ms. 00 mm I LI r b L b L h L h s _ b no.0 “.me .. xvmwwfi... WEN} Tm: 0 ImNd 2.: 5.3202 .14 x3 I- 1 352. 8% .... .3 o 2... 3.39.09. .n 33 II 10nd ...x. 352. 2% .n 3.... a . x a m... on: 5.30.59. .N :3 ..-... o 352. Boo .N 0.... o 1.3.0 on: 5.30.52 ... x3 I 352. 9.8 .. .3 o 00.0 (0:!) 888.118 .IDSLIS 132 mm; 65% . mm... .992; .5 ESE... x... __< I 2 2:9... Am\ 5 Bow. Lomsm 00— 009 mp P 00 mm mm mm .. ........LI.W 00.0 ISMLE .. 1.3.0 «a ImN.0 2... 5.3808 J. 0.3 I... . 35.. 38 ... .... o 2.... 5.3808 .n .3 II I000 352. 3% .... .3 a . 2... 5.3808 .N x3 350a Bop .N :3 o T010 2... 5.3808 .— x3 I .. 352. 38 .. ..s o 00.0 (Dd) 859.113 100.5 133 141.1..1 I. :83 . N: data? 5 8.55.3 xu __< I 4< 830.“. Am\ C Eom 59.0 0: 00 F 0m? 0w — 00 05 00 00 . . . . . R . . . . . _ _.I 0 0.0 10.0 S u. .. m. 43.0 m. 2... 5.3808 .4 x3 I- a n... 352. 38 .4 .3 . .4. 2... 5.3808 .n 4.3 II 100.0 S x . 352. Soc .0 x3 4 T \I \\\\\o 2... 5.3808 .N 4.3 ..-..- moo xxx... .. .....2. 38 .N .... a 34... ( \ 2... 5.3808 .F 4.... I . Q m 3500 Duct ... x3 0 00.0 134 0\. — £830 . NBN 6&3. .5 38E... X. .2 I 2 .59.. Am\ C 33... 58.0 00F 00w 0— F 00 0h 00 00 b L I _ . b R — . L F _ L no.0 I0F.0 \ r0N.0 H \x..... 0:: 5.3808 .4 x3 I. - V. a £52. 38 .4 3.... 4 xxx 2.: 5.3808 .0 in II I000 . 352. 28 .... 3.... 4 . xx 2... 5.3808 .N 4.... ---- 3.5a Soc .N 4.3 o I000 44 0:: 5.3808 ... x3 I .. 3...... 3% .. ...... o (od) SSSJlS Joeqs 135 0hr .83 . «RN .o.m.n4. .5 388.... 0. __< I 9. 85...... IIP 00— IF In Am\ 3 Bow. 59.0 00— 0: 00 0x. 00 p F F 0 p L Ir 2.... 5.3808 ..4 4.... 352. 38 .4 ...s 0.... 5.3808 .0 .3 352. 38 .n .... 2... 5.3808 .N in 352. 38 .u .... (od) SSSJiS Joaqs 136 :83 Ram... .93. 6.8 860.. 0NP 00F _ b Am\ C Boy. .685 0%— 0: R p 00 R I .2 859.. ac... 5.3803. II 350.. 200 O (0d) 888.05, .0qu 137 :83 3...... down. .28 8.8.. I m... 8:9... Am\ C 83. 50:0 0: 00 P 00V. 0 w P 00 0x. 00 00 L L R 0:... 5.3808". I 8303 Son. 0 I-I _ . b p F I mo.o (Dd) 888.118 .0qu 138 665 xmm; don: ”Boo Boom .. 2 835 Am\ C 3an Lomcm m5 m2 mm? 0%? F mm mm Wm mm . _ r b _ p h p b cc: coimeoom ...... 3501 Soc 0 (0:!) 333.113 .10qu 139 :8on RN: .oLS 66o Boon. .. 02 83: nu— P Am\ 5 30m Lomzm mm. mmp n: no an on L L _ _ . _ _ b . _ L L 0:3 :6inQO 11. m 3501 300 O (Dd) 339.113 Joeqs 140 £55 §§ .994 ”38 8.81 I :< 8%: mhp b mmp L Am\ C 30m .695 mm. 0.: mm mm mm b — n h n — b D b 0 0:3 coimemmm II 350m 300 o (0:!) seems Joeqs 141 665 Nu: don: ”88 8.08 .. m2 8%: Am\C 301 Lomzm mhp r mm— L P mmp h m: r L mm L on mm PrbbL mm on: co_mmo..oom ...I ESOQ Soc 0 no.0 Impd 1mN.o Tmnd Im¢.o r mmd (Dd) 533.113 Joeqs 142 686 NS; .385 838883 .. m2 95mm mm." Am\ C 30m 395 m on no on L 3.3., . 9.: _ xi 3. _ . 30.0 44. \...\.n.& V. 4‘ \\.).YI ‘d 4.: 2.x 9 $3 <\< .h\\ .-o .- .D\MU\\\ ImN O . ~ \ 0:: 5:30.63. can: ...... Tmnd a. 0.»: q 1. an m. as... coimoamm 9N2 ....-- 0 OoNnP D Tm¢.0 o 25 co_mmo..oom ULNF ..I. T 00—N— O Jmnd (0d) 333.14g Joeqs 143 68% Na? .625 838882 .. i< 2%: whp Am\ 5 Box 82m on, or P mm mm mm mm + L b '— L h . — n b .‘1 no.0 . 5.1.4.... .... D D . .51”. .m T ...o . a. co. . r? o 5 \.\ r o. ,. . . 39.? Kg 0.. ... 0% a . u 25 533.53.. can: ll Fond . 9n: 4 3 cc: cofimeuom ooNnP -....- O‘an D IW¢.O a 0:3 co_mmo._mom 0.5. II .. um. 0:3 0 no.0 (0:!) 333.145 .10qu 144 our? Jomtm cozobcmocoo I m2 939.. Am\ 3 8?. 62m mhw mm. on. a: no an on on b b F P n — F P L — F — O OH \ _jmo.o Av.10 O r ram—HO ImNd [find 0:3 coincboM :EBw NNNN ....-- . 1!? 53% km: a 19.0 .mx 0:: 5330501 50.5.5 Nmmé .11 - m. m. 50.65 Raw; 0 (0d) 339.115 .10qu 145 0&2 08:0 8:828:00 1 m? 2:9: Am\ 5 89m 92m mhF new _ L on? _ P mp F mm mm mm L B b L L b b L 0:: 533.60.. 283m Rand --.... 223m Rand 0 on: c2389.. 5830 Run; II 5830 Run; 0 (Dd) 339.145 109143 146 9%.: .3th 350.3330 1. 5.4 839.. Am\ a 80m .83 mm; mm? mm; cc: 333..QO no.3m NNmN ..-..- £9.05 Rand 0 2.3 333.31 3.65 Run; 11. 3.05 Run; 0 m .2 no m3 3 mm (0d) 339.115 .10qu APPENDIX B RAW DATA AS COLLECTED BY THE DATA ACQUISITION SYSTEM: TEMPERATURE GOING IN AND COMING OUT OF THE TUBE VISCOMETER, PRESSURE TRANSDUCER OUTPUT, AND MASS FLOW METER OUTPUT 147 Table 81. Block 1, 121.1°C, 1.82% starch T. T t transducer output flow meter output (°&P (°8?‘ (millivolts) (lbs/min) 120.6 118.9 1189 3.952 121.5 118.8 1182 3.800 121.9 119.3 1129 2.857 121.2 119.7 1122 2.739 121.0 120.1 1071 1.340 121 3 119.2 1070 1.309 Table 82. Block 1, 132.2°C, 1.82% starch T. T t transducer output flow meter output (°é? (°é’)‘1 (millivolts) (lbs/min) 131.7 129.4 1176 3.861 131.7 129.7 1176 3.833 132.8 130.0 1122 2.688 132.9 130.3 1114 2.643 132.7 129.9 1109 2.500 131.6 130.1 1077 1.587 131.1 129.4 1081 1.615 132.5 128.5 1071 1.361 133.0 129.0 1071 1.337 Table 83. Block 1, 143.3°C, 1.82% starch T. T ut transducer output flow meter output (°éP (°éb (millivolts) (lbs/min) 143.7 140.9 1086 1.791 144.2 140.6 1084 1.728 143.6 139.8 1075 1.444 144.1 139.5 1073 1.394 142.8 140.1 1063 1.114 1.062 148 Table B4. Block 1, 121.1°C, 2.72% starch T. T t transducer output flow meter output ('13? ('8)“ (millivolts) (lbs/min) 121.2 118.7 1185 3.841 121.5 119.2 1179 3.767 121.8 119.5 1173 3.678 121.0 118.0 1127 2.938 121.5 118.9 1124 2.997 121.4 119.1 1106 2.619 121.9 119.1 1101 2.557 121.3 119.4 1091 2.245 121.3 119.2 1090 2.236 121.4 118.9 1072 1.780 121.5 118.9 1068 1.755 121.0 119.0 1054 1.339 121.9 118.2 1047 1.287 121.4 118.4 1026 0.863 120.6 118.0 1037 0.796 Table B5. Block 1, 132.2°C, 2.72% starch T. T t transducer output flow meter output (°&P (°8)“ (millivolts) (lbs/min) 132.8 129.1 1127 3.181 132.3 130.4 1150 3.510 132.6 130.2 1146 3.422 131.2 130.1 1112 2.945 131.7 129.1 1115 2.947 132.1 129.3 1112 2.903 132.3 129.2 1102 2.571 132.1 129.4 1086 2.431 133.0 128.3 1068 2.049 133.2 129.7 1050 1.813 132.7 129.6 1043 1.722 132.4 129.5 1035 1.169 132.4 129.4 1039 1.154 Table B6. Block 1, 143.3°C, 2.72% starch - experiment failed 149 Table B7. Block 2, 121.1°C, 1.82% starch T. T t transducer output flow meter output (°0P (°é31 (millivolts) (lbs/min) 120.9 119.3 1217 4.347 120.7 119.7 1200 4.077 120.5 119.1 1201 4.070 120.9 119.5 1167 3.636 121.4 119.3 1164 3.577 120.8 119.4 1130 2.925 121.5 119.0 1126 2.837 121.2 119.3 1086 1.948 121.2 118.9 1085 1.965 121.1 119.0 1060 1.240 Table B8. Block 2, 132.2°C, 1.82% starch T. T ut transducer output flow meter output (110? (°8) (millivolts) (lbs/min) 132.2 129.3 1183 4.050 132.6 130.0 1180 3.983 132.4 129.8 1093 2.451 132.6 129.6 1091 2.318 132.6 130.0 1068 1.681 132.1 129.8 1068 1.657 132.1 129.4 1052 1.158 132.7 129.1 1050 1.092 132.1 128.4 1040 0.710 132.0 128.3 1039 0.648 Table B9. Block 2, 143.3°C, 1.82% starch T. T ut transducer output flow meter output (°éP (°8) (millivolts) (lbs/min) 143.6 139.2 1102 2.165 144.2 139.8 1103 2.106 144.3 140.4 1081 1.645 143.6 140.3 1077 1.460 143.2 139.5 1056 0.926 150 Table 810. Block 2, 121.1°C, 2.72% starch T. T t transducer output flow meter output (°éI‘ (°8)“ (millivolts) (lbs/min) 121.6 120.2 1223 4 030 120.7 120.3 1219 3.980 121.3 120.8 1136 3 044 122.1 120.8 1130 3.004 120.8 119.9 1087 2.391 121.4 119.5 1092 2.334 121.1 119.6 1062 1.715 121.1 119.1 1063 1.609 Table 811. Block 2, 132.2°C, 2.72% starch T. T t transducer output flow meter output (°éf‘ (165’)u (millivolts) (lbs/min) 131.9 130.2 1138 2.762 131.4 130.1 1137 2.768 133.0 129.8 1095 2.187 132.5 130.3 1090 2.171 132.3 130.4 1072 1 819 132.8 129.9 1072 1.786 132.7 129.5 1058 1 493 Table B12. Block 2, 143.3°C, 2.72% starch T. T ut transducer output flow meter output (°&P (°8) (millivolts) (lbs/min) 143.3 139.7 1106 2.632 143.1 140.1 1105 2.610 143.9 140.1 1070 1.707 143.6 140.0 1068 1 647 143.3 140.0 1050 1.088 143.3 139.8 1045 1 005 144.0 138.2 1032 0.584 144.3 138.1 1033 0 535 151 Table B13. Block 3, 121.1°C, 1.82% starch T T t transducer output flow meter output (°é? (°é?‘ (millivolts) (lbs/min) 121.1 119.2 1164 3.785 121.0 119.3 1164 3.778 121.9 119.2 1132 3.042 121.7 119.8 1105 2.930 121.7 119.6 1077 2.136 122.0 119.3 1072 2.094 121.8 119.1 1025 1.119 120.8 118.5 1033 1.077 Table 814. Block 3, 132.2°C, 1.82% starch transducer output flow meter output (°é? (nfiPt (millivolts) (lbs/min) 132.2 129.4 1185 4.041 132.3 130.0 1185 4.006 131.8 130.2 1122 2.991 131.7 129.7 1118 2.894 132.6 129.5 1098 2.482 133.1 130.0 1075 1.909 132.9 130.0 1073 1.879 132.4 129.6 1053 1.304 132.7 127.3 1048 1.228 131.5 128.2 1043 0.983 131.5 128.2 1042 0.947 Table B15. Block 3, 143.3°C, 1.82% starch T T ut transducer output flow meter output (°0P (°é5 (millivolts) (lbs/min) 143.2 139.5 1082 2.105 143.9 139.4 1079 2.046 143.8 140.2 1060 1.430 143.9 139.9 1059 1.384 143.7 139.7 1054 1.281 142.9 139.7 1054 1.277 143.4 138.8 1037 0.676 143.5 138.5 1037 0.610 152 Table B16. Block 3, 121.1°C, 2.72% starch T. T t transducer output flow meter output (‘0?’ ('631 (millivolts) (lbs/min) 121.3 119.0 1232 4.506 121.5 119.5 1230 4.471 120.4 119.6 1134 3 005 121.1 119.4 1128 2.880 121.3 119.3 1099 2.258 121.6 119.5 1094 2.069 121.1 119.2 1072 1.571 121.3 119.0 1067 1.454 121.1 118.3 1060 1.175 121.8 118.0 1058 1.095 120.8 118.1 1051 0.872 121.2 118.0 1048 0.815 Table B17. Block 3, 132.2°C, 2.72% starch T. T ut transducer output flow meter output (°éP' (‘65 (millivolts) (lbs/min) 133.0 129.8 1128 2.916 132.5 130.4 1111 2.585 132.9 130.4 1110 2.638 132.8 130.4 1094 2.268 131.9 130.5 1089 2.185 132.6 129.8 1067 1.677 133.1 129.6 1065 1.616 132.8 129.7 1056 1 329 132.0 129.4 1047 1.019 132.0 129.1 1045 1 060 132.1 128.3 1038 0.897 132.5 128.1 1035 0.840 Table B18. Block 3, 143.3°C, 2.72% starch T. T ut transducer output flow meter output («81‘ (°8) (millivolts) (lbs/min) 142.9 139.6 1091 2.223 142.9 139.6 1090 2.178 144.0 139.9 1061 1 496 143.3 139.8 1057 1.455 143.6 139.7 1038 0.969 143.8 139.4 1036 1.001 143.8 138.8 1031 0 754 153 Table 819. Block 4, 121.1°C, 1.82% starch T. T ut transducer output flow meter output (°éP (H?) (millivolts) (lbs/min) 121.3 119.4 1198 4.242 121.3 119.6 1196 4.241 121.1 119.4 1161 3.685 121.2 119.4 1159 3.664 121.2 119.4 1134 3.277 121.2 119.3 1132 3.173 121.0 118.8 1117 2.935 120.8 119.0 1124 3.016 121.3 119.2 1057 1.329 120.8 118.7 1056 1.327 121.6 118.5 1042 0.756 122.1 118.1 1041 0.741 Table B20. Block 4, 132.2°C, 1.82% starch T. T ut transducer output flow meter output (‘18:? (°8) (millivolts) (lbs/min) 132.4 129.9 1190 4.198 132.7 130.4 1186 4.139 131.8 129.8 1156 3.729 131.9 129.8 1161 3.711 132.7 129.5 1093 2.417 132.8 130.0 1091 2.367 133.2 130.0 1068 1.826 132.2 129.5 1065 1.746 ‘F3‘:?.':__'TI¢ 154 Table 821. Block 4, 143.3°C, 1.82% starch T. T ut transducer output flow meter output (1103‘ (°8) (millivolts) (lbs/min) 143.3 139.8 1116 3.075 143.8 140.3 1112 2.976 142.9 139.6 1089 2.489 143.1 139.9 1087 2.448 144.0 140.2 1072 2.097 143.8 140.5 1069 2.015 143 2 140.1 1055 1.672 143.9 139.8 1054 1.609 143.2 139.7 1044 1.377 143.8 139.1 1042 1.307 143.9 139.2 1035 1.074 143.9 138.9 1033 1.038 143.7 138.7 1030 0.784 143.3 138.2 1029 0.787 Table B22. Block 4, 121.1°C, 2.72% starch T. T t transducer output flow meter output ( ‘18:? ( °81u (millivolts) (lbs/min) 121.4 119.0 1205 4.209 121.8 119.5 1200 4.154 121.6 119.8 1198 4.097 122 0 120.0 1160 3.579 121.6 120.0 1140 3.292 121.8 120.2 1135 3.192 120.9 119.4 1096 2.630 120.4 119.2 1094 2.472 121.8 119.1 1046 1.383 121.9 119.0 1047 1.282 155 Table B23. Block 4, 132.2°C, 2.72% starch T. T ut transducer output flow meter output (°éi‘ (°8) (millivolts) (lbs/min) 131.6 130.4 1215 4.021 131.9 129.7 1209 3.942 132.4 130.4 1134 2.982 132.7 130.2 1128 2.905 132.7 130.0 1102 2.459 131.3 130.1 1101 2.451 132.2 129.3 1103 2.483 131.9 129.8 1071 1.929 132.6 130.0 1064 1.735 132.9 129.1 1036 0.732 132.3 128.8 1035 0.761 Table 824. Block 4, 143.3°C, 2.72% starch T. T ut transducer output flow meter output (‘0? (‘65 (millivolts) (lbs/min) 143.4 138.4 1078 1.907 143.7 140.7 1059 1.529 143.9 140.3 1056 1.542 143.1 137.7 1049 1.235 143.7 138.3 1047 1.222 143.7 139.4 1037 1.096 APPENDIX C CALCULATED VALUES OF VOLUMETRIC FLOW RATE, PRESSURE DROP, SHEAR STRESS, SHEAR RATE, AND GENERALIZED AND CRITICAL REYNOLDS NUMBERS FOR EACH EXPERIMENT 156 Table C1. Block 1, 121.1°C, 1.82% starch Q 5 AP 0 7 Re (m?/s)*10 (Pa) (Pa) (1/5) 3.485 630.50 0.436 154.21 1280 3.363 606.97 0.420 150.65 2.610 428.84 0.297 125.28 2.516 405.31 0.280 121.50 1.398 233.90 0.162 73.42 1.373 230.54 0.159 72.28 pH=7.28 Critical Re=1948 Table C2. Block 1, 132.2°C, 1.82% starch Q 5 AP 0 7 Re (mi/S)*10 (Pa) (Pa) (1/5) 3.444 586.80 0.406 155.56 1344 3.422 586.80 0.406 154.74 2.498 405.31 0.280 122.11 2.462 378.42 0.262 120.26 2.347 361.62 0.250 115.55 1.610 254.07 0.176 83.53 1.633 267.51 0.185 85.13 1.428 233.90 0.162 75.53 1.409 233.90 0.162 74.82 pH= not taken Critical Re=1969 Table C3. Block 1, 143.3°C, 1.82% starch Critical Re=2203 Q 5 AP 0 1 Re (m3/S)*10 (Pa) (Pa) (1/5) 1.795 284.31 0.197 93.91 756 1.743 277.59 0.192 91.20 1.512 247.34 0.171 79.20 1.471 240.62 0.166 76.94 1.243 207.01 0.143 64.86 1.200 207.01 0.143 63.26 pH=7.31 157 Table C4. Block 1, 121.1°C, 2.72% starch Critical Re=1787 Q 5 AP 0 1 Re (ms/81*10 (Pa) (Pa) (l/s) 3.396 617.05 0.427 149.16 1283 3.337 596.89 0.413 147.23 3.266 576.72 0.399 144.79 2.675 422.12 0.292 122.05 2.722 412.03 0.285 123.62 2.420 351.53 0.243 110.90 2.370 334.73 0.232 108.52 2.121 301.12 0.208 98.06 2.114 297.76 0.206 97.67 1.750 237.26 0.164 81.47 1.730 223.82 0.155 80.06 1.397 176.76 0.122 65.07 1.356 153.24 0.106 62.12 1.017 82.65 0.057 44.64 0.963 119.63 0.083 45.28 pH=7.37 Critical Re=1859 Table C5. Block 1, 132.2°C, 2.72% starch Q 5 AP 0 ‘1 Re (ma/5,410 (Pa) (Pa) (1/5) 2.896 422.12 0.292 127.63 1309 3.161 499.42 0.345 137.55 3.090 485.97 0.366 134.97 2.706 371.70 0.257 119.93 2.707 381.78 0.264 120.13 2.672 371.70 0.257 118.66 2.404 338.09 0.234 108.00 2.291 284.31 0.197 102.28 1.983 223.82 0.155 88.46 1.793 163.32 0.133 78.36 1.719 139.79 0.097 74.25 1.273 112.90 0.078 55.95 1.261 126.35 0.087 56.35 pH=7.82 158 Table C6. Block 1, 143.3°C, 2.72% starch - experiment failed Table C7. Block2, 121.1°C, 1.82% starch Q 5 AP 0 1 Re (m3/s)*10 (Pa) (Pa) (l/s) 3.800 724.61 0.501 165.74 1340 3.585 667.47 0.462 159.30 3.579 670.83 0.464 159.00 3.232 556.56 0.385 147.52 3.185 546.47 0.378 145.78 2.664 432.20 0.299 125.21 2.594 418.75 0.290 122.31 1.884 284.31 0.197 91.11 1.897 280.95 0.194 91.43 1.318 196.93 0.136 65.16 pH=7.35 Critical Re=1891 Table C8. Block 2, 132.2°C, 1.82% starch Q 5 AP 0 4 Re (ms/SWIG (Pa) (Pa) (1/8) 3.597 610.33 0.422 150.71 1425 3.543 600.25 0.415 149.49 2.307 307.84 0.213 110.75 2.200 301.12 0.208 106.57 1.686 223.82 0.155 84.14 1.667 223.82 0.155 83.44 1.264 170.04 0.118 64.90 1.211 163.32 0.133 62.14 0.903 129.71 0.090 48.15 0.853 126.35 0.087 45.99 pH=7.65 Critical Re=1940 Table C9. Block 2, 2.100 2.052 1.676 1.525 1.089 1.001 pH=8.44 Critical Re=2061 Table C10. Block pH=8.31 Critical Re=1719 Table C11. Block pH=7.78 Critical Re=1654 338.09 341.45 267.51 254.07 183.48 183.48 2, 121.1°C, 744.77 731.33 452.36 432.20 287.68 304.48 203.65 207.01 166.68 2, 132.2°C, 459.09 455.73 314.56 297.76 237.26 237.26 190.21 159 143.3°C, 1.82% starch 101.04 99.25 84.18 78.13 58.50 55.22 2.72% starch 144.58 143.81 123.12 121.87 100.86 99.71 77.32 74.31 66.54 2.72% starch 107.78 108.11 93.47 92.92 81.43 80.42 70.13 160 Table C12. Block 2, 143.3°C, 2.72% starch pH=8.15 Critical Re=2036 Table C13. Block pH=7.57 Critical Re=1807 351.53 348.17 230.54 223.82 163.32 146.51 102.82 106.18 3, 121.1°C, 596.89 546.47 546.47 438.92 348.17 254.07 237.26 79.29 106.18 96.10 117.79 117.00 83.86 81.25 60.53 56.72 40.30 39.10 1.82% starch 157.43 149.87 149.68 125.76 119.62 92.01 89.92 51.47 52.02 47.14 161 Table C14. Block 3, 132.2°C, 1.82% starch Critical Re=2081 Q 5 AP 0 7 Re (ma/SWIG (Pa) (Pa) (1/8) 3.589 617.05 0.427 156.51 1399 3.561 617.05 0.427 155.46 2.743 405.31 0.280 126.70 2.664 391.87 0.271 123.52 2.332 324.65 0.225 109.42 1.870 247.34 0.171 88.96 1.846 240.62 0.166 87.72 1.382 173.40 0.120 66.44 1.321 156.60 0.108 63.01 1.123 139.79 0.097 54.41 1.094 136.43 0.094 53.08 pH=7.75 Critical Re=1903 Table C15. Block 3, 143.3°C, 1.82% starch Q 5 AP 0 § Re (ma/S) *10 (Pa) (Pa) (1/8) 2.051 270.87 0.187 99.18 1038 2.003 260.79 0.180 97.05 1.500 196.93 0.136 75.25 1.463 193.57 0.134 73.66 1.379 176.76 0.122 69.45 1.376 176.76 0.122 69.33 0.886 119.63 0.083 46.56 0.832 119.63 0.083 44.53 pH=7.44 Table C16. Block pH=7.57 Critical Re=1944 Table C17. Block pH=7.54 Critical Re=1926 162 3, 121.1°C, 2.72% starch 775.02 768.30 445.64 425.58 328.01 311.20 237.26 220.46 196.93 190.21 166.68 156.60 3, 132.2°C, 425.48 368.34 364.98 311.20 294.40 220.46 213.73 183.48 153.24 146.51 122.99 112.90 168.00 167.29 128.93 124.83 103.37 97.05 78.50 73.98 64.17 61.33 53.05 50.61 2.72% starch 121.83 111.30 112.85 100.49 97.47 79.13 76.96 66.66 55.49 56.28 49.78 47.33 Table C18. Block pH=8.17 Critical Re=1912 Table C19. Block pH=7.79 Critical Re=1956 163 3, 143.3°C, 2.72% starch 301.12 297.76 200.29 186.85 122.99 116.26 99.46 99.46 4, 121.1°C, 660.75 654.02 536.39 529.67 445.64 438.92 388.51 412.03 186.85 183.48 136.43 133.07 1.82% starch 159.77 160.10 147.51 147.04 136.09 132.97 125.31 128.08 68.85 68.58 48.05 47.33 164 Table C20. Block 4, 132.2°C, 1.82% starch Q 5 AP 0 Re (mi/51*10 (Pa) (Pa) (l/s) 3.716 633.86 0.438 164.74 1455 3.668 620.41 0.429 163.08 3.338 519.58 0.359 150.79 3.323 536.39 0.371 150.35 2.280 307.84 0.213 105.96 2.239 301.12 0.208 104.14 1.803 223.82 0.155 84.00 1.739 213.73 0.148 81.03 1.139 119.63 0.083 52.46 pH=8.19 Critical Re=1869 Table C21. Block4, 143.3°C, 1.82% starch Critical Re=1877 Q 5 AP 0 7 Re (m§/s)*10 (Pa) (Pa) (1/5) 2.842 385.14 0.266 127.42 1388 2.761 371.70 0.257 124.31 2.364 294.40 0.204 108.10 2.331 287.68 0.199 106.68 2.044 237.26 0.164 94.11 1.977 227.18 0.157 91.16 1.698 180.12 0.125 78.27 1.646 176.76 0.122 76.13 1.457 143.15 0.099 66.92 1.400 136.43 0.094 64.33 1.210 112.90 0.078 55.51 1.181 106.18 0.073 52.90 0.974 86.02 0.060 44.53 0.976 82.65 0.057 44.37 pH=7.63 165 Table C22. Block 4, 121.1°C, 2.72% starch Q 5 AP 0 Re (HP/81*10 (Pa) (Pa) (l/s) 3.690 684.27 0.473 157.75 1337 3.646 667.47 0.462 156.60 3.601 660.75 0.457 155.10 3.187 533.03 0.369 141.60 2.957 465.81 0.322 132.90 2.878 449.00 0.311 129.80 2.429 317.92 0.220 110.15 2.302 311.20 0.215 105.18 1.432 149.87 0.104 64.83 1.352 153.24 0.106 62.06 0.916 75.57 0.052 40.43 pH=7.4l Critical Re=1815 Table C23. Block 4, 132.2°C, 2.72% starch Critical Re=1869 Q 5 AP 0 1 Re (m3/s)*10 (Pa) (Pa) (l/s) 3.573 717.88 0.497 146.41 1254 3.509 697.72 0.483 145.25 2.735 445.64 0.308 123.91 2.673 425.48 0.294 121.58 2.314 338.09 0.234 107.04 2.307 334.73 0.232 106.70 2.333 341.45 0.236 107.83 1.886 233.90. 0.162 87.45 1.730 210.37 0.146 80.47 0.921 116.26 0.080 44.40 0.944 112.90 0.078 45.03 pH=8.22 166 Table C24. Block 4, 143.3°C, 2.72% starch Q 5 AP 0 1 Re (mi/s)*10 (Pa) (Pa) (l/s) 1.889 257.43 0.178 87.92 923 1.581 193.57 0.134 70.98 1.592 183.48 0.127 70.60 1.341 159.96 0.111 59.46 1.331 153.24 0.106 58.60 1.228 119.63 0.083 52.43 1.191 109.54 0.076 50.39 pH=7.57 Critical Re=1867 LIST OF REFERENCES LIST OF REFERENCES Bagley, E.B. 1957. End corrections in the capillary flow of polyethylene. J. Appl Phys. 28: 624-7 Bagley, E.B. and Christianson, D.D. 1982. Swelling capacity of starch and its relationship to suspension viscosity - effect of cooking time, temperature, and concentration. J. Texture Studies. 13: 115-26 Beck, J.V. 1989. Personal communication. Michigan State University, East Lansing, MI. Beck, J.V. and Arnold, K.J. 1977. "Parameter Estimation in Engineering and Science," John Wiley and Sons, New York, NY. Bertsch, A.J. and Cerf, 0. 1983. Dynamic viscosities of milk and cream from 70 to 135°C. J. Dairy Research 50: 193-200 Bird, R.B., Stewart, W.E. and Lightfoot, E.N. 1960. 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[In Advances in Heat Transfer, Vol. 15, Academic Press, New York, NY.] Zobel, H.F. 1984. Gelatinization of starch and mechanical properties of starch pastes. Ch. 9. In "Starch Chemistry and Technology," Whistler, R.L. BeMiller, J.N. and Paschall, E.F. (Eds.). p. 285. Academic Press, Inc., Orlando, FL. HICHIGRN S TRTE UNIV. LIBRARIES ll I11I111111111111111111 6616 3129300577