1 RHEOLOGICAL PROPERTIES OF HIGH AND LOW CONCENTRATED ORANGE PULP By ELYSE MEREDITH PAYNE A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF M ASTER OF SCIENCE UNIVERSITY OF FLORIDA 2011
2 2011 Elyse Meredith Payne
3 To my parents, brother, and all my family and friends who helped, encouraged, and guided me through my pursuit of higher education.
4 ACKNOWLEDGMENTS I would like thank all who helped me through my academic career, including: my parents, brother, grandparents, family and friends for their relentless support. I would also like to thank my academic advisor Dr. Reyes for his suggestions, encouragement and supervision. I wou ld also like to thank my remaining graduate committee members, Dr. Yang and Dr. Ehsani for their valuable suggestions. Also a special thanks to my lab group John Henderson, Shelley Jones, Brittany Tomlin, Juan Fernando Munoz, Sabrina Terada, Dr. Giovanna I afelice, and Dr. Faraj Hijaz for all your help. I would also like to extend thanks to Dr. Paul Winniczuk of Sun Orchard for providing a pump, Dr. Wilbur Widmer of the USDA for providing a flowmeter, Mr. Thomas Fedderly of Coca Cola and Mr. Marcelo Bellarde of Citrosuco for providing orange pulp. Additionally I would like to extend my gratitude to Debra Abbott for instilling the love of science in me. Lastly, I would like to thank all the assistance provided to me from the University of Florida who without any of this could not have been possible.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 9 LIST OF ABBREVIATIONS ................................ ................................ ........................... 12 ABSTRACT ................................ ................................ ................................ ................... 15 CHAPTER 1 LITERATUERE REVIEW ................................ ................................ ........................ 17 Introduction ................................ ................................ ................................ ............. 17 Theoretical Background ................................ ................................ .......................... 18 Flow of Liquids ................................ ................................ ................................ 18 ................................ ................................ .................... 18 Flow regimes and velocity profiles ................................ ............................. 19 Principles of Rheology ................................ ................................ ............... 21 Methods of Determination ................................ ................................ ................ 24 Viscometers versus rheometers ................................ ................................ 24 Temperature effects ................................ ................................ ................... 30 Concentration effects ................................ ................................ ................. 31 Combined effect of concentrat ion and temperature ................................ ... 31 Wall slip ................................ ................................ ................................ ...... 32 Determination of slip coefficient by tube viscometry ................................ .. 3 3 Literature Review ................................ ................................ ................................ .... 37 Citrus Pulp Recovery ................................ ................................ ........................ 37 Rheology of Citrus Products ................................ ................................ ............. 37 Rheology of Difficult Foods ................................ ................................ ............... 40 Study Objectives ................................ ................................ ................................ ..... 44 2 RHEOLOGICAL DETERMINATION OF ORANGE PULP ................................ ....... 55 Introduction ................................ ................................ ................................ ............. 55 Materials and Methods ................................ ................................ ............................ 56 Materials ................................ ................................ ................................ ........... 56 Equipment and Instrumentation ................................ ................................ ........ 57 Methods ................................ ................................ ................................ ............ 57 Pulp preparation ................................ ................................ ......................... 57 Rheological characterization ................................ ................................ ...... 58 Results and Discussion ................................ ................................ ........................... 59 Conclus ion ................................ ................................ ................................ .............. 69
6 3 DETERMINATION OF PRESSURE DROP FOR ORANGE PULP ......................... 81 Introduction ................................ ................................ ................................ ............. 81 Materials and Methods ................................ ................................ ............................ 82 Materials ................................ ................................ ................................ ........... 82 Calculations ................................ ................................ ................................ ...... 84 Results and Discussion ................................ ................................ ........................... 86 Pressure Determination ................................ ................................ .................... 86 Flow Rate and Corrected Slip Coefficient Determination ................................ .. 91 Conclusions ................................ ................................ ................................ ............ 93 Overall Conclusions ................................ ................................ ................................ 94 Future Work ................................ ................................ ................................ ............ 94 APPENDIX: CAPILLARY VISCOMETRY ................................ ................................ .... 114 LIST OF REFERENCES ................................ ................................ ............................. 117 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 123
7 LIST OF TABLES Table page 1 1 Rheological methods for yield stress determination ................................ .......... 45 1 2 Power law parameters for FJOC. ................................ ................................ ....... 46 1 3 Power law parameters at different shear rate ranges for molasses .................... 46 1 4 Power law parameters and apparent viscosities at selected shear rates (s 1 ) 1 citrus pulp ................................ ................................ ........................ 46 1 5 Power law and Casson model characteristics for rheologically difficult fo ods. ... 47 1 6 Flow behavior index and consistency coefficient for homogenous and hetrerogenous Mexican sauces with a 40 mm cup and shear rate range of 10 100 s 1 ................................ ................................ ................................ .......... 48 1 7 Power law parameters for Cold Break tomato concentrate. ............................... 48 1 8 Power law parameters for Hot Break tomato concentrate. ................................ 48 1 9 Power law parameters for various fruit and vegetables. ................................ ..... 49 1 10 Approximate wall slip coefficient (mm/MPas) for tire tre ad compound found at different corrected wall shear stresses. ................................ .......................... 50 1 11 Corrected slip coefficients of four semi solid foods. ................................ ............ 50 1 12 Slip coefficients for a model coarse food suspension of green peas and aqueous sodium carboxy methylcellulose at selected temperatures. ................. 51 1 13 Summary of power law p arameters, activation energies, and slip coefficients for materials similar to citrus pulp. ................................ ................................ ...... 51 2 1 Average (n = 3) power law parameters, activation energies, and relative standard devia tion for different temperatures and concentrations of orange pulp. ................................ ................................ ................................ .................... 70 2 2 Power law parameters for various fruit and vegetables. ................................ ..... 71 2 3 Power law parameters and apparent viscosities at selected shear rates (s 1 ) 1 orange pulp. ................................ ................................ ................... 72 3 1 Average values of experimental and calculated pressure, measured and corrected flow rate for slippage, wall shear stress and corrected slip coefficie nt for orange pulp at 4 C and capillary diameter of 0.02291 m. ............ 96
8 3 2 Average values of experimental and calculated pressure, measured and corrected flow rate for slippage, wall shear stress and corrected slip coefficient for orange pulp at 10 C and capillary diameter of 0.02291 m. .......... 97 3 3 Average values of experimental and calculated pressure, measured and corrected flow rate for slippage, wall shear stress and corrected slip coefficient for orange pulp at 21 C and capillary diameter of 0.02291 m. .......... 98 3 4 Average values of experimental and calcula ted pressure, measured and corrected flow rate for slippage, wall shear stress and corrected slip coefficient for orange pulp at 30 C and capillary diameter of 0.02291 m. .......... 99 3 5 Averag e values of experimental and calculated pressure, measured and corrected flow rate for slippage, wall shear stress and corrected slip coefficient for orange pulp at 50 C and capillary diameter of 0.02291 m. ........ 100 3 6 Approximate flow rate and pressure drop for various fruit purees. ................... 101 3 7 Pressure drop of orange pulp for a capillary system of 49 mm inner diameter at d ifferent temperatures and flow rates. ................................ .......................... 101 3 8 Extrapolated pressure drop, flow rate without slippage, wall shear stress and corrected slipped coefficient at a measured flow rate of 2.1x 10 4 m3s 1 ......... 101
9 LIST OF FIGURES Figure page 1 1 Vane in cup spindle. ................................ ................................ ........................... 52 1 2 Roughened surface spindle. ................................ ................................ ............... 52 1 3 Schematic diagram of the tube viscometer used in this research. ...................... 53 1 4 Schematic diagram of the production of low and high concentration pulp. Modified from Braddock (1999). ................................ ................................ ......... 53 1 5 Schematic diagram of the production of citrus molasses. ................................ ... 54 2 1 Effect of shear rate on shear stress at ( 1 Valencia orange pulp. A) Shear rate 0 80 s 1 B) Region prior and immediately after slippage occurs. ................................ 73 2 2 Effect of shear rate on shear stress at ( 1 Valencia orange pulp. A) Shear rate 0 80 s 1 B) Region prior and immediately after slippage occurs. ................................ 74 2 3 Effect of shear rate on shear stress at ( ) 511 gL 1 1 gL 1 and (X) 775 gL 1 for 4 C for V alencia orange pulp. A) Shear rate 0 80 s 1 B) Region prior and immediately after slippage occurs. ................................ 75 2 4 Effect of shear rate on shear stress at ( ) 511 gL 1 1 gL 1 and (X) 775 gL 1 for 80 C for Valencia orange pulp. A) Shear rate 0 80 s 1 B) Region prior and immediately after slippage occurs. ................................ 76 2 5 Plot of ln( ) vs ln( ). The linear p ortion ( law applies. ................................ ................................ ................................ ......... 77 2 6 Apparent activation energy of consistency coefficient for each batch at low shear rates in the absence of slippage. ( .... 78 2 7 Effect of pasteurization on shear stress at selected shear rates at 4 C for 795.1 gL 1 orange pulp.( ....................... 79 2 8 Variation among batches of industrial and non industrial orange pulp at 4 C and 503 gL 1 ( ) Industrial Early Early mid orange pulp source 2 an .... 79 2 9 Vane geometry used with AR 2000 rheometer. ................................ .................. 80 3 1 Complete 1 inc h capillary system setup to measure the pressure drop and flow rate of orange pulp. ................................ ................................ ................... 102
10 3 2 Screen shot of LabVIEW X front panel. ................................ ............................ 103 3 3 Measured pressure drops and standard deviations produced at flow rates with slippage at 4 C and selected concentration 1 1 1 1 ................................ ........... 104 3 4 Measured pressure drops and standard deviations produced at flow rates with slippage at 10 1 1 1 1 ................................ .......... 104 3 5 Measured pressure drops and standard deviations produced at flow rates with slippage at 21 1 1 1 1 ................................ ...... 105 3 6 Measured pressure drops and standard deviations produced at flow rates with slippage at 30 1 1 1 1 ................................ ...... 105 3 7 Measure d pressure drops and standard deviations produced at flow rates with slippage at 50 1 1 1 1 ................................ ........ 106 3 8 Measured pressure drops and standard deviations produced at flow rates 1 and selected temperature: 4 C (x) and 50 C ( ) .............. 107 3 9 Measured pressure drops and standard deviations produced at flow rates 1 and selected temperature: 4 C (x) and 50 C ( ) .............. 108 3 10 Measured pressure drops and standard deviations produced at flow rates 1 and selected temperature: 4 C C (x) and 50 C ( ) .............. 109 3 11 Measured pressure drops and standard deviations produced at flow rates 1 and s elected temperature: 4 C (x) and 50 C ( ) ............... 110 3 12 Experimental and calculated pressure drop of orange pulp at different flow rates for 4 C and ave rage concentrations. 1 1 ( 1 1 ...... 110 3 13 Experimental and calculated pressure drop of orange pulp at different flow rates for 50 C and average concentrations. 1 1 ( 1 1 ...... 111
11 3 14 Measured flow rate vs. slip coefficient for 50 C at selected concentrations: 1 1 1 1 .............................. 112 3 15 Corrected Slippage coeffecient at a constant flow rate of 2.1x10 4 m 3 1 at C ................................ ................................ ................................ .................... 113 A 1 1 ............ 114 A 2 tlet ( 1 collected in LabVIEW for replicate 3. ................................ ................................ ................... 115 A 3 Flow rate (m 3 1 1 for replicate 3. ............. 115 A 4 Measured pressure drops produced at flow rates with slippage at an average 1 and selected temperature for replicate 3: 4 C C (x) and 50 C ( ) ................................ .............. 116 A 5 Measured pressure drops produced at flow rates with slippage at 50 C and 1 1 1 1 ( ................................ ................................ ....................... 116
12 LIST OF ABBREVIATION S A Constant (s 1 ) B Constant c p Specific heat of the fluid (Jkg 1 K 1 ) D Pipe diameter (m) DS Dynamic stress/strain sweep E a Activation energy (kJmol 1 ) F riction factor FCOJ Frozen concentrated orange juice g Gravity (9.81 m/ s 2 ) g c for gravitational force (1 kg m/ (s 2 N ) k Rate Constant (s 1 ) for first order reactions K Consistency coefficient (Pas) Sudden contraction friction los s Sudden expansion friction loss Friction loss from fittings L Length of pipe (m) n Flow behavior index (unit less) ND No Data p m Pressure (Pa ) PME Pectin methyl estera se Volumetric flow rate (m 3 s 1 ) Measured volumetric flow rate (m 3 s 1 )
13 Flow rate without slip (m 3 s 1 ) r Pipe radius (cm) R Universal gas constant (Jmol 1 K 1 ) Re Reynold s number for Newtonian fluid Reynolds number for power law fluids in laminar flo w SR Steady rate sweep SS Steady stress sweep T Temperature in Kelvin Slip velocity (ms 1 ) V Volume (m 3 ) Velocity (ms 1 ) Velocity upstream from a sudden expansion (ms 1 ) Velocity downstream from a sudden contraction (ms 1 ) Mass flow rate (kgs 1 ) X Concentration (%w/w) z Elevation (m) Slip coefficient ( ) (m/ Pa s) Corrected Slip coefficient (m 2 / Pa s) Model parameters Shear rate (s 1 ) p e Entrance losses (psi) t Total pressure drop across capillary (psi)
14 v Viscous pressure drop across capillar y (psi) Viscosity (Pas) app Apparent viscosity (Pas) Pi Density (kg/ m 3 ) Shear stress (Pa) a Apparent shear stress at the wall (dynes/ cm 2 ) 0 Yield stress (Pa) w Apparent shear stress a the wall (Pa) Power (W)
15 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Master of Science RHEOLOGICAL PROPERTIES OF HIGH AND LOW CONCENTRAT ED ORANGE PULP By Elyse Me redith Payne December 2011 Chair: Jos I. Reyes De Corcuera Major: Food Science and Human Nutrition T A complete rheological characterization of orange pulp is needed for the design and optimization of pulp handling and processing equipment. Orange pulp is a difficult fluid to characterize because it displays slippage over a range of temperatures (4 to 80 C) and concentrations (~500 to ~850 g L 1 ). Orange pulp is a non Newtonian pse udoplastic fluid that can be modeled by the power law at very low shear rates Rheological determination showed that slippage takes place at shear rates between 2 and 4 s 1 Slippage was more pronounced at low temperatures and high concentrations and is a consequence of particle arrangement and resistance to flow. Slippage can be characterized by rotational rheology using a vane geometry. Both temperature and concentration did not have much effect on the flow behavior index ( n ) which ranged from 0.18 to 0.4 2. The consistency coefficient K was greatly affected by temperature and concentration. As the temperature increased K decreased, while as the concentration increased K increased from 47.9 to 233.6 Pa s n Along with the power law parameters, the activation energy of the consistency coefficient was determined. It ranged from 7.1 to 10.2 kJ mol 1 and as the concentration increased the activation
16 energy increased. Although similar in trend, the rheological behavior of orange pulp varied depending on source. T he second part of this study determined the effect of slippage on pressure drop and flow rate in capillary flow. The experimental pressure readings were consistently less than the calculated assuming no slippage for all studied temperatures and concentrati ons. As the measured flow rate increased the measured pressure drop increased and was a consequence of friction. Also as the concentration decreased the measured flow rate increased at every temperature because there was less resistance to flow. As the tem perature increased the measured flow rate also increased because at higher temperatures more molecular movement causes increased flow. The difference between the measured flow rate and the flow rate without slippage at the same pressure drop was related th rough a slippage coefficient. Generally as the measured flow rate increased the slippage coefficient increased.
17 CHAPTER 1 LITERATUERE R EVIEW Introduction Citrus fruits are grown or imported and enjoyed in most countries of the world. During the 2004/05 growing season, Brazil and the United States were the leading orange producers (39%); China (7%) and the European (17%) region accounted for a smaller portion. Over 36% of oranges produced in the wo rld were processed into juice. A significant 64% increase in world citrus production was seen from the 80 2004/05 season and Brazil gained dominance in citrus production and other regions troyed by frost and hurricanes (FAO, 2006) The Unit ed States 2009/10 season produced 134 million boxes valued at $2.88 billion with Florid a producing 65% of citrus crop (NASS, 2010) Since the improvements of transportat ion and packaging, larger production levels have been reached which have in turn lowered the cost of citrus fruits Sao Paulo, Brazil and Florida have retained their title as the flagship citrus capitals of the world; while new regional citrus markets like China, Spain, and Africa are expected to expand (Spreen, 2001) The world citrus belt falls between 20 N 40 N and 20 S 40 S latitudes. In this main growing region, the, seasons are defined with a combination of rainfall/droughts and where a relative humidity around 40 60% is the standard climate (FAO, 2001) In the 2007/08 dollars while the by products citrus pulp, molasses, and essential oils were sold for 136 million dollars (Rahmani & Hodges, 2009) Citrus pulp is an important by product that consists of ruptured juice sacs obtained by finishing (separating through a fin e mesh) pulpy juice. Citrus pulp market is increasi ng because the market for beverages
18 with pulpy mouth feel has increased in particular in Asia Therefore, larger amounts of pulp are handled and processed every season. However, the rheological properties of citrus pulp at different concentrations and temperature have not been reported, making it impossible to optimize pulp handling and pasteurization conditions. With this high economic value crop, complete rheological characterizations of citrus and citrus by products are imperative. The overall objective of this research is to characterize the rheological properties of citrus pulp at selected temperature s and pulp concentration s The reported properties are expected to be used by citrus pulp manufacturers, equipment manufacturers, process design engineers and by product end users to design and optimize flow systems. In this chapter fundamental theoretical background on flow of viscous liquids, rheology, and methods of rheological characterization; a litera ture review (1952 2010) of the citrus pulp processing and the most recent rheological properties of food pastes; as well as the specific objectives of this research are presented Theoretical Background Flow of Liquids quation tion is known as the conservation of energy for fluid flow (Smith, 2003) In an ideal system in the absence of friction it can be written as : (1 1) c is a real flowing system, frictional energy losses impact the energy balance. Major losses
19 are due to the friction of the liquid against the pipe (skin friction) while minor fric tion losses are due to fittings and sudden contractions and expansions in the system. The energy balance for a liquid flowing system can be expressed as (Equation 1 2): (1 2) Where f is the friction factor, L the pipe length, D the pipe diameter, is the coefficient for expansion, is the velocity after expansion, is the coefficient for contraction, is the velocity before contraction and is the coefficient for valves and fittings. To determine the power requirements (Equation 1 3) of a pump the work must be determined and then multiplied by the mass flow rate ( ) (Singh & Heldman, 2001) s equation is widely used in fluid dynamics. Several parameters for standard pipes are readily available such as dimensions and relative roughness. Other design terms like the velocity, friction factor and Reynolds number can be readily calculated. (1 3) Flow r egimes and v elocity p rofiles In order for fluids to flow in pipes, a pressure difference must be present (Wilhelm, Suter & Brusewitz, 2004) For in compressible fluids, such as in piping systems, the average fluid velocity for a particular point across the cross section of a pipe is a function of location. The fastest velocities are in the center of the stream while the slowest velocities are against the boundary layer near the pipe wall where, due to friction, velocity is practically null. There are two types of flow through pipes laminar and turbulent.
20 Laminar Flow Laminar flow occurs when the particles in the fluid move in parallel paths. The flui d can be both very viscous and/or have a low velocity. The laminar flow velocity profile takes on a parabolic shape and has a mean velocity about 50% of the maximum velocity and flow is stratified so that at constant flow rate the velocity at any particula r point is constant. In laminar flow, for a given length of pipe the pressure drop is proportional to the flow rate of the fluid (Smith, 2003) Turbulent Flow Turbulent flow can be described as flow with particles bouncing in all directions causing mixing and heat transfer (Smith, 2003; Wilhelm, Suter & Brusewitz, 2004) The turbulent flow takes on a plug shape and has a mean velocity approximately 82% of the maximum velocity (Smith, 2003) When turbulent flow occurs eddies form and velocity at any particular flow rate fluctuate s. In turbulent flow, the pressure drop increases with an increase in flow rate and follows an approximate squared relationship (Smith, 2003) Friction Factor The friction during flow varies with flow rates and surface roughness. The effect of skin friction forces is in part account ed for by a friction factor ( Equation 1 4). Depending on fluid classification, different friction factor equations are needed and because citrus pulp is a non Newtonian fluid flowing in laminar flow only this equation will be discussed (Singh & Heldman, 2001) (1 4) The friction factor can also be determined using a modified friction factor chart for power law fluids (McCabe, Smith & Harriott, 1985) Reynolds Number and Gener alized Number. Laminar and turbulent flows are determined through the use of the Reynolds number. Reynolds number is a
21 dimensionless number that indicates the turbulence in fluid flow (Smith, 2003) Reynolds number is calculated from the fluid properties and the type/size and geometry of the pipe or reservoir where the fluid is flowing. For a pipe with circular cross section, Reynolds number can be expressed as: (1 5) W h the fluid viscosity. The transition between laminar and turbulent flow is not well defined. For Newtonian fluids laminar flow occurs at Reynolds number of less than 2,000 2,300; while higher Reynolds values (3,000 and beyond) correlate to tu rbulent flow (Smith, 2003; Wilhelm, Suter & Brusewitz, 2004) For non Newtonian fluids a generalized Reynolds number can be used: (1 6) Where is used to denote a generalized Reynolds num ber and is based on the flow fluid velocity ( ) (Johnson 1999). The power law parameters n and K are calculated from the mathematical model dis cussed in the next section. Principles of Rheology Flow Behavior. Rheology can be defined as the science of deformation and flow of matter (Steffe, 1996) The flow behavior of a biological material can be broken down into categories. The two major subcategorie s are elastic and viscous. Elastic materials undergo irreversible deformation when stress is applied while viscous materials have reversible deformation when applied stress is removed. The viscous subcategory can
22 be further broken down into Newtonian and n on Newtonian. Newtonian fluids have a shear stress and shear force that is directly proportional to the rate of deformation (Kyereme, Hale & Farkas, 1999) She ar stress is defined as the stress component applied tangential to the plane on which the forces act. The unit of shear stress is the Pascal (Pa). Shear rate is defined as the velocity gradient established in a fluid as a result of an applied shear stress and has a unit of reciprocal seconds (s 1 ) (Bourne, 2002) Newtonian foods can be represented by simple liquids like coffee, milk and tea (Barb osa Canovas, 2005) The formula used to determine the viscosity of Newtonian fluids is (1 7) non Newtonian fluids is not constant but depends on shear rate (Kyereme, Hale & Farkas, 1999) app ) is commonly used to describe non Newtonian behavior because viscosity depends on the shear rate at which it is measured (Kyereme, Hale & Farkas, 1999) Non Newtonian foods include egg whites, tomato puree, mayonnaise, and concentrated fruit juices. Non Newtonian fluids can be subdivided into two subcategories: time independent and time dependent. The two major types of time independent fluids are shear thinning and shear thickening. Shear thinning or pseudoplastics have an apparent viscosity that decreases when the shear rate increases and can be represented by condensed milk, fruit purees, or mayonnaise (Sin gh & Heldman, 2001) During the increasing shearing, a continuous breakdown and
23 (Barbosa Canovas, 2005) Shear thickening or dilatent fluids have the opposite effect with respect to apparent viscosity. As the shear rate increases, the apparent viscosity also increases. Time dependent fluids are a function of shear rate and time. These types of fluids reach a constant apparent viscosity only after certain amount of time has elapsed after stress has been applied (Singh & Heldman, 2001) Time dependent fluids are either thixotropic or rheopectic. Thixotropic fluids behave in the same fashion as the pseudopla s tic fluid but the hallmark decrease in apparent viscosity becomes reversible when the stress is removed and the fluid is allowed to recover. Rheopectic fluids follow the behavior of shear thickening fluids and al so have reversible affects of the apparent viscosity when recovery was allowed (Bourne, 2002) Mathematical Models for Non Newtonian Fluids. Rheological properties of non Newtonian fluids can be measured through multiple models. Four common models used are the power law (Equation 1 8), Herschel Bulkley (Equation 1 9), Casson (Equation 1 10) and Modified Casson (Equation 1 11). In the absence of yield stress ( ), the power law is mainly used (Ozkanli, 2008) Yield stress is defined as the minimum shear stress required to initiate flow (Steffe, 1996) Determining the yield stress of structured fluids is necessary to predict product stability with reduced phase separation and sedimentation (1 8) where shear stress is n is the flow behavior index. The last three rheology models are used for foods that have a defined yield stress (Ozk anli, 2008)
24 Herschel Bulkley: (1 9) Casson: (1 10) Modified Casson: (1 11) Predicting the apparent viscosity of non Newtonian flow is complicated because it is affected by many parameters such as temperature, pressure, moisture content and solid concentration (Kyereme, Hale & Farkas, 1999; Ozkanli, 2008) The flow beh avior index (n) varies slightly with an increase in temperature; while the consistency coefficient (K) is severely affected by temperature changes (Kyereme, Hal e & Farkas, 1999) Depending on the type of fluid, the flow behavior index changes. For Newtonian fluids n is equal to one. For pseudopla s tic fluids, n is less than one and for dilatent fluids the n is greater than one (Singh & Heldman, 2001) Methods of Det ermination Viscometers versus r heometers Viscometers and rheometers are both instruments used to determine the viscosity of a material, while a rheometer can also determine the relationship between shear rate and shear stress. Capillary Viscometers The si mplest viscometers are the capillary or tube viscometers. This type of viscometer works either through gravitational forces, hydrostatic forces or pressurized gas/piston movement. The main operating principle behind tube viscometers is to measure the resul ting pressure drop from a flowing fluid viscosity. Glass capillary viscometers usually range from 0.1 mm to 4 mm in diameter while a typical pipe diameter is between 7 mm and a few feet (Rao & Steffe, 1997) The
25 glass capillary viscometers are used to determine viscosity through hydrostatic and gravitational forces and can be used for both Newtonian and Non Newtonian fluids. Both glass and pipe capillary viscometers can determine tim e independent fluid characteristics (Kr ess Rogers & Brimelow, 2001; Steffe, 1996) The other type of capillary viscometer is the high pressure viscometer. High pressure viscometers differ from glass and pipe viscometers by relying on compressed gas or piston movement to induce fluid flow throu gh pipes. The gas high pressure viscometer operates via constant pressure while the piston operates under a constant flow rate. High pressure gas viscometers are generally set up with capillary tubes ranging in size from 2.5 mm to 6 mm that are connected t o an intake and receiving reservoir. When the gas supply passes through the pressure regulator into the intake reservoir the pressure force created causes the fluid in the reservoir to pass through the capillary tubing into the receiving reservoir. The int ake reservoir is a cylindrical barrel with a fitted piston head that is used to force the liquid through the capillary tube to the receiving reservoir (Kress Rogers & Brimelow, 2001) Rotational Viscometers and Rheometers Rotational viscometers are c ommonly found in the food industry because many Newtonian and Non Newtonian fluids can be easily measured. The term viscosity only applies to Newtonian fluids while the apparent viscosity of non Newtonian fluids can be determined with a viscometer. The pri nciple of operation of rotational viscometers and rheometers is based on the viscous drag as a function of the speed of the rotating body in contact with the liquid. However, the rheological behavior of complex non homogeneous foods and other biological ma terials cannot be characterized by viscosity alone. A more advanced
26 detection method is need for more complex materials. Rheometers can be used to determine other rheological characteristics like the relationship between shear rate and shear stress. Depend ing on the characteristics of the fluid, different surface geometries have been used: Concentric Cylinder The first geometry that can be used in a rotational viscometer is the concentric cylinder/Cuvette. A circular bob is placed concentrically inside a cup that holds the sample fluid and is allowed to rotate while the torque is measured. When the shear rate is changed the resulting change in shear stress is seen and then the viscosity can be calculated (Fung & Matthews, 1991) C one and Plate The cone and plate viscometer can also be used to determine a materials viscosity. This type of viscometer is set up with a flat bottom plate that has a n inverted shallow angled (3 5 ) cone that rests just above the tip of the plate and has the ability to rotate at multiple angular velocities One advantage of the cone and plate viscometer is that a constant shear rate is observed at all points of the fluid when small conical angles are used which leads to a very useful measurement tool for n on Newtonian fluids. The shear stress is variable and dependent on cone diameter. If the diameter decreases, the shear stress will increase and the opposite will happen when the cone diameter increases. Another advantage of the cone and plate is that very small samples can be tested. In some cases, the viscosity of samples as small as 0.5 ml can be accurately measured. The one drawback of the cone and plate system is that the material being tested must have particles that are 10 times smaller than the size of the gap (Kress Rogers & Brimelow, 2001)
27 Parallel Plate The viscosity of a fluid can also be determined through the use of a parallel plate viscometer. The parallel plate viscometer has a similar design to the cone and plate geometry but instead of a cone a second flat plate is used and a variable gap can be accomplished. Due to the infinite gap size, a wide range of fluids and course materials can be tested. Even with the great flexibility of the parallel plates, multiple disadvantages occur. The first is the uneven shear rate distribution on the plates. The shear rate is zero at the center and reaches a maximum at the outer edge of plates. The second drawback is that slippage may occur (Kress Rogers & Brimelow, 2001) Vane Geometry The van e geometry can also be used with a rotational viscometer. The vane geometry consists of a rotating spindle with numerous blades protruding into the sample. The vane geometry is used to reduce or prevent wall slip. Rheometers have four modes of operation. The most common method is the ramp increase where either the shear rate or shear stress is steadily increased while the resultant stress or rate respectively is measured. The second method is the stepwise increase of shear rate or stress. The third mode is continuous operation at constant settings. In this mode, either the shear stress or shear rate is measured constantly over a period of time. The last method of operation is small amplitude oscillatory. In small amplitude oscillatory mode, small clockwise and counterclockwise angles are made measuring viscoelasticity with the geometry (Bourne, 2002) Rotational viscometers also have the ability to detect time dependency attributes. With the great range of geometries available, the rotational viscometer is the mos t widely used type of viscometer (Van Wazer, Lyons, Kim & Colewell, 1963)
2 8 Controlled stress and strain rheometers have the ability to have rapid step changes in stress and strain whi ch leads to a complete material characterization. In the controlled stress and strain modes, a complex range of rheological test can be performed. Such test can simulate spraying, mixing, leveling, extrusion, and sedimentation. A typical rheometer also inc ludes a temperature control unit that holds a sample at a specified temperature or allows for different temperature ranges to be tested. Rheometers have a wide dynamic range and control which leads to a more versatile piece of equipment. Some rheometers al so use a low friction air bearing system as opposed to the mechanical bearing which allows for accurate measurement of low viscous materials. Rheometers also perform at wider shear rate ranges (10 6 to10 5 s 1 ) that allow characterizing a wide range of flow conditions. Rheometers can determine yield stress, perform sweeps (frequency, time, and temperature) and have oscillatory movement. Typical rheometers operate through rotation, capillary, oscillation or combination action (Carrington, 2005) Yield Stress determination Both power law parameters were determined after the linearization of the measured shear stress and shear rate. The slope of the resulting equatio n is the flow behavior index while the exponent of the y intercept is the consistency coefficient. Determining the yield stress is important to structured fluids and helps give a better understand of product performance. The apparent yield stress is determ ined through the extrapolation of the equation of the relationship between shear stress and shear rate to zero. There are multiple ways to determine the apparent yield stress depending on the materials viscosity (Chen, 2006) The m ost common methods to determine the apparent
29 yield stress are the Steady Stress Sweep (SS), Steady Rate Sweep from High to Low Shear Rates (SR), and Dynamic Stress/Strain Sweep (DS) (Chen, 2006) (Table 1 1). The first method, stead y stress sweep, is a very common method to measure the yield stress for medium viscosity materials Low viscosity materials do not respond well to extremely slow increases in stress which may lead to false yield stress measurements. High viscosity semi soli d materials like grease or pastes often produce wall slip which reduces accuracy and reproducibility. With the correct viscosity material, an accurate yield stress measurement can be taken by a step wise increase of stress until the material starts to flow (Chen, 2006) Steady rate sweep method is another method to determine the yield stress. The SR method is optimal for low viscosity materials that have a low yield stress and can be easily damaged upon loading into the test geometry In this method, the shear rate is logarithmically decreased from high (10 s 1 to 100 s 1 ) to low rates (10 5 s 1 ). The yield stress is reached when the sample reaches a plateau and shear rate becomes independent. With this method, the yield stress can be measured to 4 x 10 4 Pa. An advantage of the SR method is that when the shearing takes place from high to low the sample history is eliminated (Chen, 2006) Dynamic stress/strain sweep is the preferred method to determine yield str ess for highly viscous materials but can work for all viscosities. In this type of test, small sinusoidal waves are applied and the stress/strain is measured in the linear region. In is a measure of energy dissipated as heat per cycle of deformation per unit volume
30 (Gunasekaran & Ak, 2000) T function of oscillation stress (Chen, 2006) The benefits of DS include a more reliable and sensitive measurement while not destroying the sample matrix (Ahmed, Ayad, Ramaswamy, Am & Shao, 2007; Gunasekaran & Ak, 2000) Also, the incidence of wall slip is decreased (Chen, 2006) Yield stress can also be referred to as the stress that must be e xerted to just move one fluid layer past another (Missaire, Qiu & Rao, 1990) In food engineering, it is critical to know if a fluid will flow over given shear stresses and time courses (Rao & Steffe, 1997) Tempera ture e ffects One of the most important factors affecting the behavior of a fluid is the temperature. In the food industry, a wide range of temperatures are encountered from freezing to 135 C in ultra high temperature pasteurization. Viscosity and the cons istency coefficient are greatly affected by temperature and the effect is most likely due to the interactions among molecules. For most liquids, viscosity of the consistency coefficient decrease with temperature. An Arrhenius type equation (Equation 1 12) is commonly used to describe such effects: (1 12) (1 13) where, A is a constant, E a is activation energy of flow, R is the gas constant, and T is the absolute temperature in Kelvin. T he viscosity of a sample wa s found to be most affected by temperature at the highest activation energy and concentration (Belibagli & Dalgic, 2007) Non Newtonian fluids like fruit pulps can be affected by temperature. As
31 the temperature increases the viscosity generally decreases. The Arrhenius like equation (Equation 1 12) can also describe the effect of temperat ure on non Newtonian fluids at a constant shear rate. The apparent viscosity decreases exponentially with temperature (Haminiuk, Sierakowski, Maciel, Vidal, Branco & Masson, 2006; Haminiuk, Sierakowski, Vidal & Masson, 2006) Concentration e ffects In genera l as concentration (in particular of soluble solids) increases the apparent viscosity increases. Insoluble solids have the greatest effect on apparent viscosity and power law parameters and are usually most pronounced at low temperatures (Nindo, Tang, Powers & Ta khar, 2007; Ozkanli, 2008) The effect of concentration on power law parameters n and K has been characterized empirically: (1 14) (1 15) where coefficients A and b are empirical constants and X is conc entration. As concentration increases n decreases while K increases. Combined effect of concentration and t emperature The combined effects of temperature and concentration can be expressed as: (1 16) (1 17) are empirical parameters (Velez Ruiz & Barbosa Canovas, 1998)
32 Wall s lip Slippage is a phenomenon that happens in multiphase liquids in which a thin layer of liquid of lower viscosity separate from the bulk is formed at the interface of the fluid (Barnes, 1995) In suspensions, the general belief is that a thin layer of fluids exists next to the test geometry (the wall) with the particles either not interacting with the wall or interacting weakly causing a slip (Barnes, 1995; Walls, Caines, Sanchez & Khan, 2003) If there is sufficient shear rate, the fluid next to the wall has a higher velocity when compared to what would be expected of the bulk material in the absence of slippage (Walls, Caines, Sanchez & Khan, 2003) For extreme cases of shear rate, the particle lean fluid near the wall flows, while the bulk material remains un deformed (Walls, Caines et al. 2003) Liqui ds that are concentrated solutions of high molecular weight polymers or suspensions, exhibit the greatest slip effects (Barnes, 1995) According to Barnes (1995), four conditions usually lea d to large and significant slip : large particles as the dispersed phase ; a large dependence of viscosity on the concentrati on of the dispersed phase, smooth walls and small flow dimensions ; usually low speeds or flow rates; walls and particles carrying like electrostatic charges and having the continuous phase electrically conductive. One of the most accepted methods of compen sating for wall slip is the use of vane in cup geometry (Figure 1 1) or the use of roughened surface (Figure 1 2). The effectiveness of the vane geometry to reduce wall slip greatly out weights the need to have a large sample volume. In the vane in cup met hod, a cylinder with multiple thin blades is placed in the sample and the shear stress is monitored versus the steady
33 rotation (Walls, Caines, Sanchez & Khan, 2003) An advantage with the vane geometry is that there is less sample disturbance which causes minimal st ructural damage to the sample prior to testing (Geraghty & Butler, 1999) The vane geometry also allows for the ing takes place between the blades of the geometry (Leongpoi & Allen, 1992) Most often the use of vane geometry is used to determine the yield stress of food dispersions because the wall slip of suspension is greatly reduced. In addition to using the vane to re duce slippage, geometries can be fabricated that are material specific and c an completely reduce slippage during measurement. Determination o f s lip c oefficient by t ube v iscometry For most fluids that display slippage such as citrus pulp, it is impossible to determine rheological parameters that are useful for the design of flow systems by using only a rotational rheometer. An alternative method has been proposed based on the use of pressurized tube viscometers (Figure 1 3). In order to have accurate tube viscometer results, the data must be corrected for entrance losses, pressure drop, and the slip according to Jastrzebski (1967) and Steffe (1996). There are seven steps used to correct the data: 1. Determine entrance correction for each radius. Entrance loss is the pressure drop required to cause the abrupt change in velocity and she ar strain distribution from a large tank to a small tube. The total pressure is the pressure drop necessary to maintain a viscous flow in the tube plus the pressure drop associate with the entrance effects and a small amount of kinetic energy loss. Entranc e losses can be calculated from (Jastrzebski, 1967) :
34 (1 18) t v e is t for at least three tubes of different lengths but the same diameter. Then the values o t are read for each tube length at a specific flow rate and plotted against Length/Radius for different tube lengths. This linear relationship can be extrapolated to the Length/Radius axis e is the intercept. The kinetic en ergy losses are caused by the difference in kinetic energy from the acceleration of the fluid in high pressure capillaries. Kinetic energy losses are small and difficult to distinguish from entrance pressure losses and it is considered reasonable to assume kinetic energy losses are accounted for in the entrance effect correction. The entrance length can also be neglected if long tubes are used and the proper placement of pressure transducer is done to ensure the entrance region has no effect on data (Steffe, 1996) 2. Correct pressure drop data. Entrance effects should be evaluated for each tube radius before the measured pressure drop can be corrected. 3. Calculate shear stress at the wall. The apparent shear stress at the wall is a function of tube radius, tube lengt h, and pressure difference. The shear stress is zero at center while the maximum is at the wall. The apparent shear stress at the wall is can be expressed as: (1 19)
35 Where p is pressure, r is the radius, and L is the pipe length (Jastrzebski, 1967; Steffe, 1996) 4. Determine slip coefficient. For a given pressure drop, slip manifests as the direct increase in flow rate through the tube when compared to the flow rate in the absence of slip (Jastrzebski, 1967) In theory, addition of an additional term to the flow rate term can be used to account for the difference: (1 20) Where Q ws is the flo w rate with out slip. When the shear stres w ) is constant the integral term is constant and a slip velocity can be added to account for the different values of flow rate measured (Q m ). The slip velocity is a function of shear stress at the wall and if no slippage occurs then the sli s =0) is zero: (1 21) Dividing equation 21 by w : and the new equation becomes (Equation 1 22): (1 22) and with further simplification equation 1 22 becomes (1 23) The slip coefficient is a function of the wall shear stress and the inverse of the tube c can be determined: (1 24)
36 Substituting the corre cted slip coefficient the flow rate becomes: (1 25) different radii. Data is plotted of Q m 3 w w From this plot values of Q m / 3 w ) at diffe w Q m 3 w w c with 1/r 2 The flow rate without slippage (Q ws ) is used in the Rabinowitsch Mooney equation. With t he slip coefficient or corrected slip coefficient the new volumetric flow rate becomes (Equation 1 26): (1 26) (1 27) C ( Equation 1 27) may only be useful for dense suspensions and purees but can be meanin gless if plug flow model should be used and not the traditional viscous flow model (Steffe, 1996) 5. Correct flow data with slip coefficient. 6. Calculate the shear rate (Equation 1 28) at the wall using the Rabinowitsch Mooney equation for power law fluids. Since concentrated suspensions display considerable slippage, Equation 1 28 may produce inaccurate data. The wall shear rate ( ) maximum can be estimated with
37 (1 28) 7. Construct a rheogram of shear stress versus shear rate. Literature Review Citrus Pulp Recovery Many concentrations of pulp can be produced from low (500 g/L ), to high (800 900 g/L) and may be packaged as aseptic or non aseptic fro zen product. Pulp production begins with the extraction of pulpy juice that is then passed through a hydrocyclone defect removal system where centrifugal force brings about the separation of pulpy juice and defects such as seeds, peel particles, or miss co lored pulp cells through density differences. Finally, the juice passes through a primary finisher where the pulp is brought to a concentration range of 500 g/L (Figure 1 4). The low concentration pulp can be pasteurized and packaged into drums and stored as aseptic chilled pulp. After the primary finisher and pasteurization, a secondary finisher is used to bring up the concentration to the high concentration range. Due to the finisher being considered a non aseptic process the concentrated pulp is then fil led in either in a box or drum and stored frozen (Braddock, 1999) A few high concentration pulp aseptic pasteurizers are manufactured but have not been optimized. Currently, small pipe diameters are used because of the heat transfer paramete rs of the viscous citrus pulp. The small pipe diameters used to fabricate the pasteurizers lead to high pressure drops which require a large and expensive pump. Rheology of Citrus Products The rheological properties of citrus products such as frozen conce ntrated orange juice (Tavares, Alcantara, Ta dini & Telis Romero, 2007; Vitali & Rao, 1984a, b) clarified
38 orange juice (Ibarz, Gonzalez & Esplugas, 1994) and molasses (Hendrickson & Kesterson, 1952; Togrul & Arslan, 2004) have been characterized while the rheological properties of h igh concentration citrus pulp are not well studied. Frozen concentrated orange juice (FCOJ) is produced in millions of metric tons every year. FCOJ is comprised of an average of 10% w/w pulp (Tavares, Alcantara, Tadini & Telis Romero, 2007) Concentrated orange juice is a non Newtonian, mild shear thinning fluid with ins ignificant yield stress and has been described with the power law (Table 1 2) (Vitali & Rao, 1984a, b) The concentrated orange juice samples in these studies ranged from a soluble solids content of 46 to 65 Brix and were tested at temperatures from 19 to 30 C (Vitali & Rao, 1984a, b) From these studies it was found that the rheological properties of orange juice were a function of pul p concentration. As the pulp concentration increased at a fixed temperature, the apparent viscosity and consistency coefficient increased (Vitali & Rao, 1984a, b) Tavares and others (2007) report ed that as the FCOJ soluble solids content increased the flow behavior index remained almost constant while the consistency coefficient increased. As temperature decreased the consistency coefficient of FCOJ increased (Tavares, Alcantara, Tadini & Telis Romero, 2007) The Vitali and Rao studies determined the power law p arameters for FJOC over a range of temperatures that included frozen to room temperatures. Ibarz, Gonzalez and Esplugas (1994) found that orange juice without pulp or clarified orange juice is a Newtonian fluid across a wide range of temperatures (5 to 70 C) and SSC concentrations (30.7 to 63.5 Brix). The activation energy increased from 4.23 to 9.59 kcal/mol as SSC concentration increased from 30.7 to 63.5 Brix. Viscosity
39 of clarified orange juice decreased with an increase in temperature for every conc entration (Ibarz, Gonzalez & Esplugas, 1994) Figure 1 5 shows the production of citrus molasses (Hendrickson & Kesterson, 1952, 1964) Hendrickson and Kesterson (1964) determined that citrus molasses viscosity increased with SSC from 60 to 84 Brix; while showing a decrease in viscosity as the temperature increased from 5 to 65 C. To rul and Arslan (1994) performed rheological studies on molasses not from citrus origin but harvested from a sugar factory. This study found that molasses had non Newtonian pseudoplasti c behavior that followed power law with a flow behavior index that ranged from 0.756 to 0.793 and a consistency coefficient that ranged from 19.51 to 9.23 (Pas n ) as the temperature ent viscosity decreased with increas ing temperature and shear rate ( Table 1 3) (Togrul & Arslan, 2004) In a preliminary study, Levati (2010) found that high concentration citrus pul p exhibits non Newtonian, pseudoplastic behavior and its apparent viscosity is dependent on temperature. As temperature increased from 11 to 50 C the consistency coefficient de creased from 97.31 to 50.84 (Pa s n ) while the flow behavior index increased fro m 0.08 to 0.15 (Levati 2010) (Table 1 4). In this study, slippage was not noted in the rheological characterization which could lead to incorrect reporting of power law parameters (Levati, 2010) Rheological characterization of most orange processing products and by products has been done while the characterization of citrus pulp is l acking. Once the pulp has been characterized, optimized pasteurizers and transport systems can be built from the properties determined.
40 Rheology of Heterogeneous and Complex Foods Determining the unique rheological properties of some foodstuffs is challen ging. The lack of reliable and accurate rheological data of semi solid foods is due to the limitations of wall slip and secondary flow. With these gaps, the design and selection of equipment is a trial and error process (Dervisoglu & Kokini, 1986) The most difficult foods on which to de termine rheological properties include gels, emulsions, semi liquids, soft foods, and spreadable foods (Sun & Gunasekaran, 2009b; Tabilo Munizaga & Barbosa C anovas, 2005) Understanding the rheological properties of gels is complicated by their structural matrix of small solids surrounded by liquids. Gels have the ability to form a solid but also retain some characteristics of the principle liquid (Tabilo Munizaga & Barbosa Cano vas, 2005) This dual behavior makes rheological characterization of gels a challenge. Emulsions like peanut butter, mayonnaise, margarine and chocolate are found throughout the food industry. Determining the rheological characteristics of emulsions is co mplicated because most emulsions experience damage when they are loaded into the test cup. Emulsions also display some degree of slippage. The type of emulsion (oil in water or water in oil) also affects the rheological properties. Water in oil emulsions t end to be higher in fat and have a self lubricating effect (Campanella & Peleg, 1987; Sun & Gunasekaran, 2009a) The best way to overcome the rheological characterization difficulties with emulsions is to use the vane geometry or a modified squeeze flow device (Sun & Gunasekaran, 2009a) Peanut butter is a pseudoplastic, time independent emulsion that exhibits severe slip and has a yield stre ss that becomes negligible wh en fitted to the power law ( Table 1 5 ) (Citerne, Carreau & Moan, 2001) Chocolate has rheological properties that are affected by particle size and level of
41 agitation. The International Office of Cocoa, Chocolate and Sugar Confectionary recommend the Casson Model to determine rheological pr operties. Both coarse gro und te have been characterized ( Table 1 5). For both types of milk chocolate, as the shear rate increased the apparent viscosity decreased (Karnjanolarn & McCarthy, 2006) Semi liquid like sauces, condiments, concentrates, and purees are difficult foods to characterize because these foods are complex (chemically/physically) which leads to the use of experimental models to predict th eir rheological properties (Krokida, Maroulis & Saravacos, 2001) Mexican sauces can be described as a multiphase dispersed systems with solid rigid particles, solid de formable particles and liquid deformable particles in a continue phase (usually water) A rheological study done on three homogeneous (fine particles less than 1 mm) and three heterogeneous (coarse particles greater than 1 mm) sauces with a vane geometry fo und that both types display slippage and were shear thinning fluids that could be modeled by the power law. The power law parameters for the homogeneous (barbecue, chipotle, and valentine) and heterogeneous (verde, taquera, and ranchera) Mexican sauces are presented in Table 1 6 (Martinez Padilla & Rivera Vargas, 2006) Tahin (tahini), a common sauce/condiment found in the Middle East, is made into a paste from ground de hulled dry roasted sesame seeds. The rheological properties were determined for tahin at a temper ature range of 30 to 75 C ( Table 1 5). It was found that as the temperature increased the consistency index decreased. The smaller the flow behavior index the greater the departure fro m Newtonian behavior. Tahin behaves as a pseudoplastic fluid with a viscosity that decreases as the temperature
42 increases and decreases as the shear rate increases from 0 to 70 rpm. When the tahin is heated molecular entanglement decreases and allows for a reduced molecular volume which in turn decreases the viscosity. The temperature sensitivity of tahin was determined with an Arrhenius type equation and found that it has an activation energy of 30.329 kJ/mol (Alpaslan & Hayta, 2002) Tomato concentrate, another non Newtonian pseudoplastic, power law semi solid liquid, can be produced as cold (below 70 C) or hot (85 90 C) break depending on the thermal treatment during concentration. One study determined the rheological properties for both cold and hot tomato concentrate at soluble solids content ranging from 5 to 28 Brix. Both power law characteristics can be found in Tables 1 7 and 1 8. For the cold break concentrate, the consistency coefficient increased as the soluble solids content increased from 5 to 25 Brix; while K decreased as the temperature increased at each soluble solids content. The flow behavior index ranged from 0.45 to 0.33. Hot break tomato concentrate had a flow behavior index range of 0.22 to 0.4. The consistency coefficient showed a general trend of increasing as the soluble solids content increased; while K decrease as the temperature increased for each soluble solids content. The activation energy was also calculated for both cold (16.99 MJ kgmol 1 ) and hot break concentrate (22.75 MJ kgmol 1 ). The activation energy was lower for cold break because the particles are aligned in a pattern which allowed for easier flow (Fito, Clemente & Sanz, 1983) Fruit a nd vegetable pulps are suspensions of high non soluble solids. The power law parameters of many types of pulps and purees can be found in Table 1 9. For pulpy products the flow behavior index was close to 0.5 while it was close to 1.0 for clear juices but decreased with concentration. The concentration of soluble and insoluble
43 solids content has a profound non linear effect on Newtonian viscosity along with the consistency coefficient and apparent viscosity of non Newtonian foods (Krokida, Maroulis & Saravacos, 2001) The literature review presented on the fruit and vegetable purees is very extensive for materials th at follow the power law parameter s but only a few report ed activation energ y none mention ed slippage in any of the purees. Dough also presents some rheological challenges. Dough is considered to be a soft solid food that has viscoelastic properties, a defined yield stress, and displays slippage (Sofou, Muliawan, Hatzikiriakos & Mitsoulis, 2008) The most unique feature about dough is that it develops its strength in stages which complicates determining its rheological properties. The early stages of dou gh are marked with little resistance to deformation because of the lack of gluten chains, while the later stages have fully developed gluten chains that create more elasticity in the dough (Zheng, Morgenstern Campanella & Larsen, 2000) Not only is the elasticity of the dough affected by the gluten development, the viscosity is also affected. The best method to test the rheological properties of dough would be to use extensional methods as opposed to the sta ndard shearing (Gras, Carpenter & Anderssen, 2000) In suspensions, slippage manifests as increased flow rate at the wall of the viscometer due to particle migration. Using the slip coefficient, corrected flow rate values can be calculated. Slip coefficient data of some common non food materials an d foods can be found in Tables 1 10, 1 11, and 1 12. Table 1 10 gives the slip coefficient for a rubber compound found in tire tread. Both the corrected slip coefficients and wall shear for foods rheologically similar to orange pulp can be found in Table 1 11. Table 1 12 is the slip coefficient equations and valid range of wall shear for a model suspension
44 of green peas and aqueous sodium carboxy methylcellulose. Slippage has a huge impact and if it is not accounted for the accuracy of the rheological data is severely affected. Peanut butter, cement paste, wood pulp suspensions and mayonnaise are materials that show slippage but no slip coefficient has been determined. Table 1 13 provides a summary of power law parameters, activation energies and slip coeff icients for foods that are rheologically similar to citrus pulp. Study Objectives The long term goal of this research is to optimize flow systems for high concentration citrus pulp The specific objective of this research was to characterize the rheologi cal properties of citrus pulps. Two studies were proposed: 1. Rheological characterization using a rotational rheometer 2. Determination of pressure drop by capillary viscometry It is expected that the results from this research will be used by processors, eng ineers and equipment manufactures to understand the relationship between pressure drop and rheological characteristics of high concentration citrus pulp which will allow the optimal design of flow systems for pulp.
45 Table 1 1. Rheological methods for yiel d stress determination (Chen, 2006) Method Advantages Disadvantages Steady Stress Sweep Stress or torque is logarithmically increased until material begins to flow and the yield point is determined Mainly used for medium viscosi ty materials Challenge for low and high viscosity suspension materials due to the slow incremental added stress Wall slip could lead to inaccurate measurement Steady Rate Sweep Shear rate is logarithmically decreased from high (100 s 1 ) to low (10 5 s 1 ) and yield point is reached when the stress of the sample becomes independent of the rate Is ideal for low viscosity suspensions When sweeping from high to low all loading history is removed Good reproducibility Challenge for medium and high viscosit y materials Dynamic Stress/Strain Sweep Sinusoidal waves are used and the strain/strain is measured in the linear region with the additions of frequency Works with all types of materials but works best with high viscosity materials Ca n be performed on both stress/strain controlled rheometers Wall slippage is minimized with proper geometry Good reproducibility
46 Table 1 2. Power law parameters for FJOC. Material Sample K n Temperature 1.FJOC 65.1 Brix (7.1% pulp) 19 to 30 C (Ns n /m 2 ) 29.16 0.91 0.71 0.75 65.1 Brix (4.6% pulp) 19 to 30 C 27.63 0.95 0.78 0.71 2.FJOC 65.04 Brix 16 to 0 C (Pas n ) 105.58 34.04 0.55 0.52 58.56 Brix 14 to 0 C 21.52 10.38 0.54 46.56 Brix 8 to 0 C 3.02 2.04 0.5 7 0.58 1. (Vitali & Rao, 1984a, b) 2. (Tavares, Alcantara, Tadini & Telis Romero, 2007) Table 1 3. Power law parameters at different shear rate ranges for molasses (Togrul & Arslan, 2004) Concentration (Brix) Temperature C N K (Pas n ) 1 ) 81.46 45 0.756 19.51 1.33 11.7 50 0.777 18.24 1.30 11.3 55 0.776 15.81 1.30 16.2 60 0.793 9.23 1.27 15.9 Table 1 4. Power law parameters and apparent viscosities at selected shear rates (s 1 ) 1 citrus pulp (Levati, 2010) Temperature C n K (Pas n ) 1 app 10 app 100 app 11 0.082 97.31 97.31 11.767 1.423 25 0.114 67.286 67.286 8.744 1.136 38 0.137 53.226 53.226 7.296 1 50 0.152 50.836 50.836 7.211 1.023
47 Table 1 5. Power law and Casson model characteristics for rheologically difficult foods. Material Temperature C n K (Pas n ) 0CA (Pa) app (Pas) 1 ) 1.Peanut Butter 23 0.57 250.85 No Data 57.6 No Data 2.Coarse Ground Milk Chocolate 40 No Data No Data 67.286 3.73 0 50 2.Fine Ground Milk Chocolate 40 No Data No Data 34.8 11 0 50 3.Tahin 30 40 50 60 65 75 0.58 0.58 0.58 0.48 0.51 0.58 19.9 19.4 16. 3 14.7 10.2 6.79 No Data No Data No Data 4.Ketchup 25 45 65 95 0.27 0.29 0.29 0.25 18.7 16.0 11.3 7.45 No Data No Data 10 560 4.Minced Fish Paste 3 6 0.91 8.55 No Data No Data 7 238 4.Mayonnaise 25 0.55 0.54 0.60 0.59 6.4 6.6 4.2 4.7 No Data No Data 3 0 1300 30 1300 40 1100 40 1100 4.Mustard 25 0.39 0.39 0.34 0.28 18.5 19.1 27.0 33.0 No Data No Data 30 1300 30 1300 40 1100 40 1100 4.Marshmallow Cream 25 0.379 563.10 No Data No Data No Data 4.Apple Butter 25 0.145 222.90 No Data No Data No Data 4.St ick Butter 25 0.085 199.28 No Data No Data No Data 5.Blueberry Pie Filling 20 0.43 6.08 No Data No Data No Data 5.Creamed Corn 23 80 0.35 0.26 23.8 20.4 No Data No Data No Data 5.Chunky Salsa 23 80 0.20 0.28 30.8 10.9 No Data No Data No Data 1. (Singh, Castell Perez & Moreira, 2000) 2. (Karnjanolarn & McCarthy, 2006) 3. (Alpaslan & Hayta, 2002) 4. (Kokini, 1992) 5. (Steffe & Daubert, 2006)
48 Table 1 6. Flow behavior index and consistency coefficient for homogenous and hetrerogenous Mexican sauces with a 40 mm cup and shear rate range of 10 100 s 1 Mexican Sauce n K (Pas n ) Homogeneous Barbecue 0.33 16.52 Chipotle 0.21 5.83 Valentia 0.28 3.53 Heterogeneous Verde 0.47 3.78 Taquera 0.33 15.26 Ranchera 0.45 5.13 Table 1 7. Power law parameters for Cold Break tomato concentrate (Fito, Clemente & Sanz, 1983) Temperature C Concentration ( Brix) n K (N s n m 2 ) 15 5 25 0.43 0.34 0.45 29.32 20 5 25 0.43 0.34 0.38 27.46 30 5 25 0.38 0.34 0.56 25.94 40 5 25 0.44 0.33 0.27 23.03 50 5 25 0.41 0.35 0.40 19.41 60 5 25 0.43 0.33 0.26 17.86 70 5 25 0.45 0.34 0.12 15.08 Table 1 8. Power law parameters for Hot Break tomato concentrate (Fito, Clemente & Sanz, 1983) Temperature C Concentration ( Brix) n K (N s n m 2 ) 15 10 28 0.28 0.40 6.98 76.90 20 10 28 0.29 0.37 7.00 81.25 30 10 28 0.25 0.36 7.24 76.69 40 10 28 0.27 0.37 6.03 86.82 50 10 28 0.26 0.38 4.84 67.74 60 10 28 0.22 0.37 4.75 87.60 70 10 28 0.24 0.35 4.49 43.55
49 Table 1 9. Power law para meters for various fruit and vegetables (Krokida, Maroulis & Saravacos, 2001) Material Temperature C Concentration (% solids) Shear Rate (s 1 ) n K (Pas n ) Apple 25 .0 18.2 100 2000 0.4 20.2 29.2 63.2 5 50 1.0 0.2 29.6 52.8 100 2000 0.9 40.1 82.0 8.1 5 50 0.3 9.0 27.0 8.1 100 2000 0.3 12.7 30.0 8.09 5 50 0.3 11.6 Apricot 27.0 1.9 5 50 0.3 167.5 30.0 5.3 5 50 0.3 6.8 27.0 6.3 5 50 0.4 7.2 Currant blac k 32.5 49.9 N D 1 0.0 Guava 24.0 15.4 100 10000 0.8 5.3 23.4 10.3 100 10000 0.5 3.9 Mango 25.0 16.0 20 250 0.3 12.3 25.0 17.0 20 250 0.3 27.8 50.0 18.7 20 250 0.4 4.3 25.0 16.0 20 250 0.3 10.0 Navel 1.5 65.1 ND 0.7 9.2 orange 7.5 39.9 0 500 0.8 0.4 36.4 28.8 100 600 0.8 0.4 0.9 65.1 100 500 0.7 16.5 Peach 27.0 2.8 5 50 0.4 85.6 26.9 54.9 50 700 1.0 0.1 30.0 7.6 5 50 0.3 7.2 Pear 26.4 36.1 1 2000 0.4 81.4 26.3 60.3 100 1000 1.0 0.2 55.4 28.8 0.1 2600 0.5 10.4 27.0 14.6 100 2000 0.4 5.3 Pineapple 7.5 41.1 0 500 0.8 0.8 37.5 21.7 100 600 0.9 0.1 Raspberry 30.0 27.7 3 2000 0.9 0.5 Tamarind 24.0 21.8 3 1300 0.8 0.0 46.9 35.7 10 400 0.7 1.2 Tomato 25.0 21.1 4 576 0.3 91.6 40.7 18.7 ND 0.3 19.7 55.6 15.5 500 800 0.4 3.9 57.3 30.0 500 800 0.4 13.4 20.0 8.1 0 10 0.4 5.7 33.6 24.7 4 576 0.4 98.6 Valencia orange 7.5 42.5 0 500 0.7 1.0
50 Table 1 10. Approximate wall slip coefficient (mm/MPas) for tire tread compound found at different corrected wall shear stresses (Karrabi, Ghoreishy & Bakhshandeh, 2004) Temperature C Corrected Wall Shear Stress for Different Rubbers (MPa) 0.6 0.9 1.1 80 225 290 340 100 235 295 330 120 190 260 300 Table 1 11. Corrected slip coefficients of four semi solid foods (Kokini & Dervisoglu, 1990) Food Corrected Slip Coefficients m 2 (Pas) 1 Wall S hear Stress (Pa) Apple Sauce 0.025 150 0.022 136 0.019 123 0.016 109 0.013 95 0.010 81 0.0076 68 0.0051 54 0.003 40 Ketchup 0.0420 200 0.0350 181 0.0290 163 0.0230 144 0.0180 125 0.0130 107 0.0093 88 0.0060 69 0.0034 5 0 Mustard 0.037 200 0.032 181 0.028 163 0.024 144 0.019 125 0.015 107 0.011 88 0.0077 69 0.0046 50 Tomato Paste 0.0065 750 0.005 688 0.0037 625 0.0026 563 0.0018 500 0.00115 438 0.0007 375 0.00038 313 0.00018 250
51 Table 1 12. Slip coefficients for a model coarse food suspension of green peas and aqueous sodium carboxy methylcellulose at selected temperatures (Chakrabandhu & Singh, 2005) Temperature C Slip Coefficient Equation m(Pas) 1 Wall Shear Stress (Pa) 85 80.84 124.73 110 22.51 57.52 135 19.41 29.10 Table 1 13. Summary of power law parameters, activation energies, and slip coefficients for materials similar to citrus pulp. Material n K (Pas n ) E a kJmol 1 C m 2 (Pas) 1 Paste/Concentrate Peanut butter 0.57 250.85 ND ND Creamed corn 0.26 0.35 20.4 23.8 ND ND Tomato paste 0.22 0.45 0.12 87.60 16.99 22.75 0.00018 0.0065 Apple sauce 0.3 1.0 0.2 40.1 No Data 0.0051 0.010 Mango pulp 1 0.16 0.19 27.41 31. 85 8.9 11.8 ND Arac pulp 2 0.17 0.25 13.52 32.66 11.03 ND Citrus pulp with slip 0.082 0.152 50.836 97.31 ND ND Liquids Mexican sauces 0.21 0.47 3.53 16.52 ND ND Tahin 0.48 0.58 6.79 19.9 30.3 ND FJOC 3 0.52 0.58 2.04 105.58 6.6 3 ND Ketchup 0.25 0 .29 7.45 18.7 ND 0.0034 0.042 Mustard 0.28 0.39 18.5 33.0 ND 0.0046 0.037 1. (Khandari, Gill & Sodhi, 2002) 2. (Haminiuk, Sierakowski, Vidal & Masson, 2006) 3. (Crandall, Chen & Carter, 1982)
52 Figure 1 1. Vane in cup spindle Figure 1 2. R oughen ed surface spindle
53 Figure 1 3. Schematic diagram of the tube viscometer used in this research Figure 1 4. Schematic diagram of the production of low and high concentration pulp. Modified from Braddock (1999).
54 Figure 1 5. Schematic diagram of the production of citrus molasses.
55 CHAPTER 2 RHEOLOGICAL DETERMINATION OF ORANGE PULP Introduction During the 2004/05 growing season, Brazil and the United States were the leading orange producers (39%), while China (7%) and the European (17%) region accounted for a less significant portion. In the 2004 /05 growing season over 36% of the oranges produced were processed and a total of 64% growth in world orange production was seen fr (FAO, 2006) processed into juice or juice products totaling 3,303.6 million dollars while the by products : orange pulp, molasses, and essential oils were sold for 136 million doll ars (Rahmani & Hodges, 2009) In the last few years an interest of citrus flavored beverages with mouth feel supplied by pu lp has i ncreased, in particular in Asia This trend has created a new market for intact pulp cells that retain their flavor and structure through processing and shipping. Post fruit extraction, defect removal and primary finishing, the concentrati on of pul p is approximately 500 gL 1 which is deemed low concentration and can be pasteurized. To continue to remove juice from the pulp a second non aseptic finisher is employed to bring the concentration of pulp to 800 900 gL 1 which is deemed high concentratio n This second concentration stage is necessary to reduce shipping and storage costs, but leaves a problem of sterility. High concentration pulp must be stored frozen in boxes or barrels. A few high concentration pulp aseptic pasteurizers are manufactured but have not been optimized. Currently, small pipe diameters are used to favor heat transfer to the pulp that flows under laminar regime because of its very large
56 apparent viscosity The small pipe diameters used to fabricate the pasteurizers lead to high pressure drop which in turn, results in high capital and operating pumping costs Knowledge of the rheological properties of high concentration pulp is needed for optimal design of processing equipment such as pasteurizers and flow systems. The rheologica l characterization of many types of paste like foods including fruit pulps and purees have been performed. Apple pulp, mango puree, and banana puree were all described using the power law (Krokida, Maroulis & Saravacos, 2001) Tomato paste (Fito, Clemente & Sanz, 1983) and peanut butter (Singh, Castell Perez & Moreira, 2000) have also been characterized. In a recent study, Levati (2010) f ound that high concentration orange pulp exhibit ed non Newtonian, pseudoplastic behavior but shear stress vs shear rate curves were noisy decreasing the reliability of the determination s of apparent consistency coefficient and flow index. The objective o f this study was to characterize the rheological properties of orange pulp at selected concentrations across a range of temperatures found under industrial processing conditions. M aterials and Methods Materials Early 1 ) sa mples donated by the Coca Cola Company (Auburndale, FL), Early 1 ) samples were donated by Citrosuco Company (Lake Wales, FL) and Valencia orange citrus pulp 1 ) produced at the Citrus Research and Education Center (CREC) pilot plant (Lake Alfred, FL) were used for this study. Sodium benzoate was purchased from Fisher Scientific (Waltham, MA).
57 Equipment and Instrumentation An industrial juice extractor, FMC 10 79 (Lakeland, FL) with pre finisher #2 was used in conju nction with a FMC screw finisher (Model 35, FMC Corporation, Hoopeston, Illinois) at 50 psi with a J.U. 5 2 No. 20 mesh screen to produce high concentration pulp at the CREC pilot plant. Instrument Contro used for the rheological characterization of the pulp. Methods Pulp p reparation Concentration determination. Initial pulp concentration was determined with a Quick Fiber apparatus (Philadelphi a, PA) and the FMC, FoodTech Procedure for Citrus Products Analysis. Approximately 500 mL of pulp was weighed into a 20 mesh screen and placed on the Quick Fiber apparatus. After 2 min of mechanical shaking, the screen and pulp were weighed. Pulp concentra tion was calculated as using Equation 2 1. (2 1) Pulp concentration. Orange pulp with an initial concentration of ~500 g.L 1 was concentrated using a Quick Fiber apparatus (Philadelphia, PA) and the FMC, FoodTech Procedure for Citrus Products Analysis. Approximately 500 mL of pulp was weighed into a 20 mesh screen and placed on the Quick Fiber apparatus. After 50 seconds of mechanical shaking, the screen and pulp were weighed. Pulp concentration was calculated with Equation 2 1. Approximately 4000 mL of ~ 800 g.L 1 orange pulp was prepared Concentration was adjusted by adding back pulp free single strength orange juice until the correct concentration was achieved. Concentration conformation was
58 performed by the same procedure us ed to determine initial pulp concentration After determining that the C itrosuco sample was high concentration dilutions were made with pulp free single strength orange juice to ~ 500 600 and 650 g.L 1 Just as before, the concentration was confirmed. Th e average concentrations of the samples were 503 8, 597 11, 643 6, and 795 1 The large standard deviations in concentrations are due to the variability in pulp source and also the large quantity in which the samples were prepared. Sodium be nzoate was added at 0.05% to act as a preservative and anti mold agent. Rheological c haracterization Prior to any rheological characterization, samples were placed in a water bath model Isotemp 3016S from Fisher Scientific (Waltham, MA) to equilibrate t he sample at the selected temperature of 4, 20, 37.5, 57.5, or 80 C. These temperatures were selected because they fall within the range typically encountered during thermal processing or cold storage in the citrus industry. Preliminary experiments perfor med using concentric cylinder and hatched parallel plate geometries found a sudden decrease in apparent viscosity caused by slippage. Using a vane geometry minimized slippage between the geometry surface and the sample because the orange pulp was able to yield between the blades of the vane (Figure 2 9) After setting the normal force to zero and setting the gap to 4000 m, approximately 35 mL of orange pulp was placed in the water jacketed cup and the 10.7 cm tall, 1.4 cm radius four blade vane was plac ed at the assigned gap. The rheometer was set for continuous shear rate ramp control and to measure shear stress. Three shear rate ranges were selected: from 0 to 1 s 1 for 3 min with 60 points 0 to 10 s 1 for 6 min with 120 points or 0 to 80 s 1 for 6 min with 120 points. Each pulp batch was
59 analyzed separately. Rheological determinations were carried out in a block design with pulp batch and temperature blocks, and randomized by pulp concentration. Temperature was blocked to reduce experimental time assoc iated with sample thermal equilibration. Pulp was also blocked based on availability from industrial donors A nalytical replicates were performed for each batch and the mean of shear stress and shear rate was reported The effect of shear rate on shear str ess was best fitted to power law after evaluating Herschel Bulkley, Casson, and Modified Casson models as well Linear regression was used for model fit ting C onsistency coefficient and flow behavior index were determined. Standard errors were calculated f rom linear regression. The effect of temperature on the consistency coefficient was determined using an Arrhenius like approach. The apparent activation energy was determined from the linear regression of ln K vs. 1/T plot. Linear regression parameters and s tandard errors were calculated using Microsoft Excel regression analysis tool Results and Discussion The effect of shear rate on shear stress at the highest pulp concentration of this 1 between 4 and 80 C for Valencia orange pulp can be seen in Figure 2 1. Shear stress increased up to 256.3 Pa as shear rate increased up to 3.3 s 1 at 4 C. At 21 C, shear stress increased to 212.5 Pa as shear rate increased to 2.6 s 1 The same trend was seen at 37.5 C. Shear stress increased to 167.7 Pa as shear rate increased to 2.2 s 1 At 4, 21, and 37.5 C a sharp increase in shear stress as shear rate increased was followed by immediate sharp decrease at shear rates above approximately 2 s 1 indicated slippage. At the higher temperatures of 57.5 and 80 C, slippage was less pronounced but observed as the rapid leveling off of shear stress as shear rate increased. At 57.5 C, shear stress increased to 141.3 Pa as shear rate
60 increased to 3.2 s 1 At 80 C, shear stress increased to 130.5 Pa as shear rate increased to 2.9 s 1 In contrast, Figure 2 2 shows the effect of shear rate on shear stress at the lowest pulp concentration 1 between 4 and 80 C fo r Valencia orange pulp. For all temperatures below 57.5 C a sharp peak in shear stress was seen at shear rates between 2.2 and 2.9 s 1 then followed by slippage. At 4 C, shear stress increased to 90.5 Pa as shear rate increased to 2.2 s 1 At 21 C, shea r stress increased to 79.8 Pa as shear rate increased to 2.9 s 1 At 37.5 C, shear stress increased to 70.1 Pa as shear rate increased to 2.9 s 1 At 57.5 C, shear stress increased to 65.5 Pa as shear rate increased to 2.6 s 1 At 80 C a distinct decrea se in shear stress was not observed but slippage was indicated by the rapid leveling off of shear stress at a higher shear rate. At 80 C, shear stress peaked at 41.2 Pa as shear rate increased to 3.2 s 1 A t all temperature s shear stress increased with pu lp concentration as shown in Figures 2 1 and 2 2. It can be hypothesized that the higher the concentration the more particles present which in turn creates more particle interlocking and therefore a higher shear stress (Nindo, Tang, Powers & Takhar, 2007) S lippage has been reported in multiphase systems and is a direct effect of the displacement of the dispersed phase away from the solid system boundaries leaving a low viscosity thin liquid layer that acts as a lubricant that cause the material to slip Slip page comes from the combination of steric, hydrodynamic, viscoelastic, chemical and gravitational forces on the dispersed phase that is adjacent to the solid boundary. Slippage starts at different shear rates but for suspensions in which the dispersed phas e consist mostly of large particles, slippage is greatest at low shear rates (Barnes,
61 1995) Slippage has been reported for food emulsions like peanut butter, mayonnaise and suspensions like tomato concentrate or other emulsions like cement. Slippage interference with true rheological characterization can be gre atly reduced by using a vane geometry or roughened surfaces (Sun & Gunasekaran, 2009a, b) One study performed on cement paste using both a vane and concentric cylinder geometry showed that with the vane geometry the true maximum shear stress ca n be determined and was approximately 150 Pa higher when compared to the concentric cylinder maximum shear stress (Saak, Jennings & Shah, 2001) Extrapolati on of our experimental results indicate that the yield stress was practically zero supporting the use of the power law model to describe our experimental data The reliability of yield stress mea surements is dependent on the method of determination and the sensitivity of the instrument. Because the instrument used to determine the yield stress was very sensitive, accurate yield stress measurements were determined. Figures 2 3 and 2 4 illustrate t he effect of shear rate on shear stress of Valencia orange pulp at different concentrations. 1 shear stress increased to 231.4 Pa as shear rate increased to 1.9 s 1 1 shear stress increased to 166.9 Pa as shear ra te increased to 1.9 s 1 1 shear stress increased to 159 Pa as shear rate increased to 2.9 s 1 1 shear stress increased to 90.5 Pa as shear rate increased to 2.2 s 1 Figure 2 4 describes the effect of shear rate o n shear stress at different concentrations at 80 C. At 1 shear stress increased to 40.4 Pa as shear rate increased to 2.5 s 1 At 585 1 shear stress increased to 61.0 Pa as shear rate increased to 2.6 s 1 1
62 shear stress increase d to 78.3 Pa as shear rate increased to 2.9 s 1 1 shear stress increased to 130.5 Pa as shear rate increased to 2.9 s 1 When comparing 1 at the extreme temperatures (4 and 80 C), 4 C had a more distinct peak with slippage ta king place at a slower shear rate. Both figures show the same trend that the higher the concentration the higher the shear stress at any given shear rate This trend is most likely due to the increased particle interlocking that caused more resistance to f low and therefore a higher shear stress. In agreement, as the soluble solid content of blueberry puree (without slippage) increased from 10 to 25 Brix at 25 C the shear stress increased from approximately 12 to 150 Pa (Nindo, Tang, Powers & Takhar, 2007) T he power law model was used to determine consistency coefficient (K) and flow behavior index (n) at selected concentrations and temperature s, at shear rates below the shear rate at which slippage occurs. At an average concentration 1 n value s ranged from 0.18 to 0.42 with the lowest n value at the hottest temperature of 80 C while the highest n was at 4 C. 1 the flow behavior index ranged from 0.22 to 0.41. Like 503 1 pulp the lowest n was at the highest temperature while the highest n was at 37.5 C. The flow behavior index ranged from 0.22 to 0.40 at an average 1 In the same fashion as the previous two concentrations the lowest n value was at the hottest temperature How ever, the highest n was at 20 C. 1 showed the same trends as the lowest two concentrations. The n 1 ranged from 0.21 to 0.39. A flow behavior index of less than one defines the fluid as non Newtonian pseudoplastic fluid (Steffe,
63 1996) T emperature and concentration did not have a large effect on the flow behavior index. There are two general trends in the effects of temperature and concentration of the consistency coefficient data but with a few inconsisten cies. First, as the concentration increased fr 1 the consistency coefficient increased. Second, as the temperature increased from 4 to 80 C the consistency coefficient 1 the K ranged from 33.0 to 70.0 Pa s n 1 K ranged from 59.9 to 123.5 Pa s n whi 1 it ranged from 74.9 to 137.2 Pa s n At the 1 the consistency coefficient ranged from 112.3 to 233.6 Pa s n Both temperature and concentration had an effect on K. The decrease in K can be explained because as t he temperature increased from 4 to 80 C greater intermolecular distances (thermal expansion) existed which created a decrease resistance to flow and therefor e, a decrease in K or a decrease in apparent viscosity (Haminiuk, Sierakowski, Maciel, Vidal, Branco & Masson, 2006; Haminiuk, Sierakowski, Vidal & Masson, 2006) Similarly, the increase in K from the increase in concentration of solid particles in suspension can be attributed to the greater resistance to flow Figure 2 8 shows the large variation among the orange pulp samples where two batches were from industry and one was produced in house. The variation among the samples can be explained by factors such as the type of finisher used to produce the pulp, different processing methods/conditions or the v ariety of orange. Orange pulp is a biological material in wi th inherent variation in size, shape, and length of the juice sac. A second place where the variation could account for the large difference between the power law parameters could be the type of e xtractor used. Either the Brown or the FMC extractor
64 would have been used. The Brown extractor reams the fruit at different pressures which could affect the quality of intact pulp sacs; the higher the pressure the more significant the pulp damage and the l ess accurate rheological characterization. In comparison, the FMC extractor works on the principle of squeezing the juice out of the fruit with a strainer tube attached to the extractor cup. The quality of pulp is dependent of the tube orifice size; the bi gger the tube slots the less pulp damage. Finishing of the pulp could also account for the variation in the data. There are two types of finishers paddle and screw finisher. Paddle finishers work at different speeds (rpm) and with adjustable paddle pitches At a higher rpm, more pulp separation will take place. Also depending on screen size the dryness of the pulp will vary. The screw finisher works by turning a screw and forcing the pulpy juice against a pressurized discharge. The higher the pressure (tigh t/hard finish) the more dry pulp is produced. Just as the paddle finisher, different size screens can be used to adjust the quality of the pulp produced. Just like extraction, true rheological characterization should be done with high quality pulp. Dependi ng on the type of finisher and extractor different qualities of intact pulp cells can be produced. At each different orange processing plant a different extractor and/or finisher was used to produce the samples which could have lead to some of the variatio n in the data. Sodium benzoate was added at such a small level (0.05%) that its effect on the results of the rotational rheometry analysis was negligible Mango pulp (20 Brix) ranging in temperature from 30 70 C had a flow behavior index range of 0.16 to 0.19 and a consistency coefficient range of 27.41 to 31.85 (Pa s n ) measured at a shear rate of 0 to 13 s 1 (Khandari, Gill & Sodhi, 2002) Appl e pulp at 25 C has a K value of 65.03 Pa s n and a flow behavior index of 0.084 (Kokini, 1992) All
65 three fruit pulps have flow behavior indexes below 1.0 with orange pulp being the highest and the apple pulp being the most pseudopla s tic. When comparing the consistency coefficient for these three fruit pulps, the consistency coefficient was the same magnitude except for the orange pulp at the highest concentration. The variability in flow beh avior index of orange pulp was greater than for other fruit purees and pastes because of the larger and more heterogeneous, variable size distribution of pulp particles. P ower law parameters for o ther fruit paste s can be found in Table 2 2. When comparin g to an earlier report for high concentrated orange (Levati, 2010) pulp (Table 2 3), both studies had flow behavior indexes below 1.0 The Levati study flow behavior index ranged from 0.082 to 0.152 while the n value ranged from 0.18 to 0.42 in this study. T he consistency coefficient values were much lower in Levati (2010) 50.83 97.31 Pa s n while 47.93 233.6 Pa s n in this study This difference in K can be attributed to the use of the shear rate range of 0 1300 s 1 by Levati (2010) that did not account for slippage occurring, as mentioned earlier at shear rate ar ound 2 s 1 Other foods with complex rheology have been modeled by the power law Tomato concentrates flow behavior index ranged from 0.24 to 0.44 while the K ranged from 0.12 to 86.82 (Pa s n ) for a temperature range of 15 70 C (Fito, Clemente & Sanz, 1983) In the study performed by Fito, Clemente et al. (1983), no slippage was reported. Peanut butter is an emulsion that displayed slippage and has a flow behavior index of 0.57 and a consistency coefficient of 250.85 Pa s n at a shear rate of 38.3 s 1 (Citerne, Ca rreau & Moan, 2001; Singh, Castell Perez & Moreira, 2000) P eanut butter, slippage occurred at a shear rate of 38.3 s 1 higher than for orange pulp (~4 s 1 ) This difference explains in
66 part the obvious difference between these two materials. According t o Barnes (1995), concentrated suspensions with large di spersed phase have slippage at low shear rates. T he apparent activation energy (E a ) for the effect of temperature on K was calculated as: (2 2 ) Where R is the gas constant A is a constant and T is th e absolute temperature Figure 2 5 shows the linearization of both shear stress and shear rate. The linear portion of the graph was determined and the slope and intercept were calculated. Linearization of power law: (2 3 ) Since two analytical replicates were done, both replicates were averaged to determine the power law parameters for that shear rate, concentration, and temperature combination. For all data, the linear portion always occurred at shear ra tes below 4 s 1 Only the data for shear rates 0 to 10 s 1 were considered because the all data points before slippage fell within that range Shear rates above 10 s 1 slippage occurred while shear rates in the range of 0 1 s 1 gave a pseudo Newtonian flui d that does not accurately describe orange pulp. Table 2 1 shows the average power law parameters at different concentrations and temperatures. Figure 2 6 shows the activation energies calculated from Table 2 1 for all studied pulp concentrations. For b atc h 1 generally E a increased from 3.2 to 10.7 kJmol 1 1 where the apparent activation energy was 7.8 kJmol 1 The apparent activation energy for batch 2 first increased from 7.3 to 9.6 kJmol 1 then decreased to 6.2 kJmol 1 at 644 1 and increased to 8.0 kJmol 1 1 Batch 3 had a n approximately constant
67 apparent activation energy of 10.6 kJmol 1 then increased to 11.7 kJmol 1 1 (Figure 2 6) At an average concentration of 1 the apparent activation energy ranged from 3.2 to 10.7 kJmol 1 while the standard error ranged from 71.7 5.4. The activation energy ranged from 8.9 to 10.5 kJmol 1 with a standard error range of 6.8 0.9 for an average concentration of 1 At an average 1 the activation energy range was 6.2 to 10.6 kJmol 1 and a standard error range of 5.1 to 3.7. At a n average 1 the activation energy range was 8.0 to 11.6 kJmol 1 with a standar d error range of 8.7 6.8 As the average concentra tion 1 1 the average activation energy increased from 7.1 to 10.2 kJmol 1 1 where the apparent activation decreased The higher the apparent E a the greater the effect of temperature on K which is especi ally seen at higher concentrations (Ozkanli, 2008; Steffe, 1996) Comparing the apparent activation energies of the consistency coefficient to other fruit pulps, orange pulp is of similar magnitude. The consistency coefficient for mango pulp has an apparent activat ion energy range of 8.9 to 11. 8 kJmol 1 for a shear rate range of approximately 1 13 s 1 (Khandari, Gill & Sodhi, 2002) A study performed on wh ole ara pulp found that at a constant shear rate of 50 s 1 the activation energy of the consistency coefficient was 11.03 kJmol 1 while the consistency coefficient of butia pulp had an activation energy range of 8.3 to 10.01 kJmol 1 for a shear rate ra nge of 15.59 to 300 (s 1 ) (Haminiuk, Sierakowski, Maciel, Vidal, Branco & Masson, 2006; Haminiuk, Sierakowski, Vidal & Masson, 2006) The consistency coefficient for orange juice concentrate ha d an activation energy of 6.6 kJmol 1 at approximate shear rates of
68 0 500 (s 1 ).Comparing the activation energy for a food that displays slippage, tahin, had a n E a of 30.3 (kJmol 1 ) which was higher than orange pulp (Alpaslan & Hayta, 2002) Industrial samples used to determine the rheological properties were probably pasteurized using a pulp pasteurizer while the non industrial sample was pasteurized as pulpy juice before finishing. One sample was not pasteurized before finishing to assess the effect of pectin methylesterase. The unpasteurized sample was placed in refrigerated storage for 2 day s before rheological analysis. Rheograms of shear stress versus shear stress showed a much higher shear stress for the unpa steurized sample while slippage was still present (Figure 2 7). Both the consistency coefficient and the apparent activation energy were higher for the unpasteurized sample. Pectin methylesterase (PME) desertifies pectin and results in gel formation with in the presence of divalent cations. Gel formation modifies the rheological properties of citrus juices and pulp. To minimize the removal of pectin methoxy groups, PME needs to be inactivated. Most PME is inactivated by heating at 88 C for 10 15 seconds (Kimball, 1999) Gel fo rmation in the pulp affects the quick fiber test by giving higher concentration values because less juice is mechanically removed as water molecules are entrapped in the gel and a more viscous liquid phase entangles the solid particles. The consistency coe fficient ranged from 829.49 to 55.16 Pa s n while the E a ranged from approximately 19 to 25 kJmol 1 Both of these increases are due to the gel formation in the pulp. The flow behavior index was not greatly affected and all values remained below 1.0 and ra nged from 0.18 to 0.75 In order to have the true rheological characterization without the interference of gel formation the pulpy juice should be pasteurized to inactivate pectin methylesterase.
69 Conclusion 1 (standard deviati on range of 6 to 21 1 ) behaved as a pseudoplatic fluid that was modeled with the power law at 4 to 80 C at shear rates below 2 4 s 1 .Orange pulp displayed slippage at shear rates above 2 and 4 s 1 Slippage was more pronounced at low temperatures as well as at high concentrations. Both temperature and concentration had a small effect on the flow behavior index as it ranged from 0.18 to 0.42 and displayed no particular trend with temperature or concentration Conversely, t he consistency coefficient wa s greatly affected by temperature and concentration. As the temperature increased K decreased, while as the concentration increased the consistency coefficient increased. The average apparent activation energy for the consistency coefficient ranged from 7 .1 to 10.2 kJmol 1 and was affected by concentration Although similar in trend, the rheological behavior of orange pulp varied widely depending on the source and handling conditions In this study the relationship between shear rate and shear stress was determined for orange pulp at different concentrations and temperatures Because of the presence of slippage, with the determined parameters (K and n), only the friction factor without slippage, that is at very small shear rates can be calculated. Therefor e, w ith th e s e data alone calculations can not be performed to optimize and design processing equipment and determine proper pump selection because the relationship between shear rate and shear stress cannot be correlated directly to a friction coefficient. Hence, pressure drop in pipes and fittings cannot be calculated. Determination of slippage coefficients using capillary viscometry is needed to complete the characterization of orange pulp.
70 Table 2 1. Average (n = 3) power law parameters, activation ener gies, and relative standard deviation for different temperatures and concentrations of orange pulp. 1 1 1 1 Temperature (K) n K (Pas n ) n K (Pas n ) n K (Pas n ) n K (Pas n ) RSD (%) RSD (%) RSD (%) RSD (%) 277 0.42 70.0 0 .41 123.5 0.36 137.2 0.39 233.6 24.2 77.9 14.2 51.1 13.2 51.8 28.6 40.1 293 0.32 50.5 0.29 91.3 0.40 109.7 0.33 180.1 3.74 60.0 5.3 49.4 22.8 43.5 14 .5 51.7 311 0.37 50.9 0.34 83.6 0.30 88.9 0.30 146.7 34.5 61.9 35.6 50.9 23.9 47.2 9.0 47.4 331 0. 37 43.0 0.25 61.5 0.29 78.3 0.23 115.1 34.2 47.9 16.5 48.5 17.9 45.1 4.5 47.6 353 0.18 33.0 0.22 59.9 0.22 74.9 0.21 112.6 60.2 55.9 57.01 0.8 40.6 4.3 47.9 11.7 E a (kJmol 1 ) -7.1 -9.7 -8.2 -10.2 RSD (%) -53.0 -8.1 -27.4 -18.5
71 T able 2 2. Power law parameters for various fruit and vegetables (Krokida, Maroulis & Saravacos, 2001) Material Temperature C Concentration (% solids) Shear Rate (s 1 ) n s n ) Apple 25.0 18.2 100 2000 0.4 20.2 29.2 63.2 5 50 1.0 0.2 29.6 52.8 100 2000 0.9 40.1 82.0 8.1 5 50 0.3 9.0 27.0 8.1 100 2000 0.3 12.7 30.0 8.09 5 50 0.3 11.6 Apricot 27.0 1.9 5 50 0.3 167.5 30.0 5.3 5 50 0.3 6.8 27.0 6.3 5 50 0.4 7.2 Currant b lack 32.5 49.9 ND 1 0.0 Guava 24.0 15.4 100 10000 0.8 5.3 23.4 10.3 100 10000 0.5 3.9 Mango 25.0 16.0 20 250 0.3 12.3 25.0 17.0 20 250 0.3 27.8 50.0 18.7 20 250 0.4 4.3 25.0 16.0 20 250 0.3 10.0 24.2 9.3 20 250 0.3 2.1 36.4 28.8 100 600 0.8 0.4 0.9 65.1 100 500 0.7 16.5 Peach 27.0 2.8 5 50 0.4 85.6 26.9 54.9 50 700 1.0 0.1 30.0 7.6 5 50 0.3 7.2 Pear 26.4 36.1 1 2000 0.4 81.4 26.3 60.3 100 1000 1.0 0.2 55.4 28.8 0.1 2600 0.5 10.4 27.0 14.6 100 2000 0. 4 5.3 Pineapple 7.5 41.1 0 500 0.8 0.8 37.5 21.7 100 600 0.9 0.1 Raspberry 30.0 27.7 3 2000 0.9 0.5 Tamarind 24.0 21.8 3 1300 0.8 0.0 46.9 35.7 10 400 0.7 1.2 Tomato 25.0 21.1 4 576 0.3 91.6 40.7 18.7 ND 0.3 19.7 55.6 15.5 500 800 0.4 3.9 57. 3 30.0 500 800 0.4 13.4 20.0 8.1 0 10 0.4 5.7 33.6 24.7 4 576 0.4 98.6
72 Table 2 3. Power law parameters and apparent viscosities at selected shear rates (s 1 ) for 1 orange pulp (Levati, 2010) Temperature C n K (Pa s n ) 11 0.082 97.31 25 0.114 67.286 38 0.137 53.226 50 0.152 50.836
73 A B Figure 2 1. Effect of shear rate on shear stress at ( ) 4 C, ( ) 21 C, ( ) 37.5 C, ( X ) 57.5 C and ( ) 80 C for 1 Valencia orange pulp. A) Shear rate 0 80 s 1 B ) R egion prior and immediately after slippage occurs.
74 A B Figure 2 2. Effect of shear rate on shear stress at ( ) 4 C, ( ) 21 C, ( ) 37.5 C, ( X ) 57.5 C and ( ) 80 C for 1 Valencia orange pulp. A) Shear rate 0 80 s 1 B) R egion prior and im mediately after slippage occurs.
75 A B Figure 2 3. Effect of shear rate on shear stress at ( ) 511 gL 1 ( ) 585gL 1 ( ) 649 gL 1 and ( X ) 775 gL 1 for 4 C for Valencia orange pulp. A) Shear rate 0 80 s 1 B) R egion prior and immediately after slipp age occurs.
76 A B Figure 2 4. Effect of shear rate on shear stress at ( ) 511 gL 1 ( ) 585gL 1 ( ) 649 gL 1 and ( X ) 775 gL 1 for 80 C for Valencia orange pulp. A) Shear rate 0 80 s 1 B) R egion prior and immediately after slippage occurs.
77 Figur e 2 5. Plot of ln( ) vs ln( ). The linear portion ( ) indicates the region where power law applies.
78 Figure 2 6. A pparent activation energy of consistency coefficient for each batch at low shear r ates in the absence of slippage ( ) batch 1 ( ) batch 2, ( ) batch 3.
79 Figure 2 7 Effect of pasteurization on shear stress at selected shear rates at 4 C for 795.1 gL 1 orange pulp.( ) Unpasteurized and ( ) Pasteurized. Figure 2 8. Variation among batches of industrial and non industrial orange pul p at 4 C and 503 gL 1 ( ) Industrial Early mid orange pulp source 1 ( ) Industrial Early mid orange pulp source 2 and( ) Non industrial Valencia orange pulp
80 Figure 2 9. Vane geometry used with AR 2000 rheometer.
81 CHAPTER 3 DETERMINATION OF PRESSU RE DROP FOR ORANGE PULP Introduction The complete fundamental rheol ogical characteristics of orange pulp are not fully understood. Orange pulp can be described as a power law fluid that displays slippage at very low shear rates. Rheological characterizatio n using rotational rheometers does not allow predicting friction factors, hence pressure drop in pipes and fittings because slippage occurs at shear rates lower than what is found in industrial conditions Capillary viscometers are used to measure apparent viscosity of concentrated suspensions at shear rates produced in industrial processes such as extrusion, mixing, pumping, and conveying (Shukla & Rizvi, 1995; Wang, Lam, Joshi & Chen, 2010) The use of capil lary viscometry to determine the slippage coefficient is recommend ed but complicated because it requires several independent determinations at several flow rates and with several pipe diameters. O ther e ffects such as partial migration, and entrance effects need to be corrected for (Shukla & Rizvi, 1995) Wall slippage can be detected throu gh the methods of Mooney and Jastrzebski but are limited to Newtonian fluids and not suitable for non Newtonian suspensions that have significant migration (Wang, Lam, Joshi & Chen, 2010) In capillary flow, the section that is perpendicular to the direction of flow has shear rates and shear forces that are different from the total flow wh ich causes the particles in the suspension to migrate away from the wall and towards the center (Wang, Lam, Joshi & Chen, 2010) For pseudoplastic fluids with slippage, shear rates are higher at the wall (Shukla & Rizvi, 1995) Also when the particle density is different from the suspending liquid, particle migration is increased which increases flow instability. In less concentrated
82 fluids or fluids without sus pended parti cles less friction is created and, therefore have a decreased pressure (Wang, Lam, Jo shi & Chen, 2010) The objective of this study was to determine slippage coefficients and pressure drop of orange pulp by capillary viscometry. A modified correction approach was taken to correct for the e ffects of slippage and particle migration. P ressu re drop and flow rate w ere measured and slip coefficients for orange pulp were calculated from capillary and rotational viscometry measurements. Materials and Methods Materials Early 1 ) samples were donated by Citrosuco 1 ) produced at the Citrus Research and Education Center (CREC) pilot plant (Lake Alfred, FL) were used for this study. Sodium benzoate was purchased from Fisher Scientific (Waltham, MA). Eq uipment and Instrumentation An industrial juice extractor, FMC 10 79 (Lakeland, FL) with prefinisher #2 was used to produce pulpy juice that was pasteurized in a nominal 0.0254 m ( 1 in ) diameter Feldmeier Double Tube Heat Exchanger (Syracuse, NY). The pulp y juice was heat treated to inactivate pectin methyl esterase at 91 C for approximately 20 s and immediately cooled to 4 C. Pasteurized pulpy juice was then finished with a FMC screw finisher (Model 35, FMC Corporation, Hoopeston, Illinois) at 50 psi wit h a J.U. 5 2 No. 20 mesh screen to produce high concentration pulp at the CREC pilot plant. Pulp densities were determined with the FMC, FoodTech Procedure for Citrus Products Analysis Approximately 500 g of pulp w ere weighed poured in a 20 mesh
83 screen b asket, place d on a Quick Fiber apparatus from FMC (currently John Bean Technology Corp.) Serial No. 67 94, ( Philadelphia, PA) and mechanically sh aken for 2 min. Pulp concentration was calculated as: (3 1) Once high concentration w as confirmed, sodium benzoate was added at 0.05% as a preservative to increase storage time Average concentrations of 854 1 9 74 9 2 1 649 2 6 and 545 20 1 were used. The large standard deviations in concentration are due to the variability in pulp source and to the difficulty in adjusting the concentration of the large quantit ies of juice by adding single strength pulp free orange juice and confirming concentrations with the Quick fiber method explained above. Figure 1 3 is a schematic of the experimental set up. Prior to pressure readings, approximately 19 L of pulp w ere loaded in the feed tank and the a section of a 22.91 mm diameter (1 in nominal) pasteurizer was prime d with a semihydraulic diaphragm pump model 9910 D1064 4 from Hypro Hi gh Pressure (New Brighton, MN) Pulp was re circulated to the feed tank until a constant flow was achieved indicating the removal of any entrapped air and data pressure and flow rate data were collected The total system length (pipe and connection hoses) was 11.27 m. In addition pulp temperature was adjusted (4, 10, 21.5, 33, or 50 C 2.5 ) using the pasteurizer heating (steam) or cooling ( chilled water ) sections. Ve rification of steady state temperatures was done by ensuring that the temperature in the feed tank and the temperature at the discharge were within 2.5 C Temperature was measured with type T thermocouples from Omega
84 (Stamford, CT ). Pressure was determined with a PX44E0 500GI high pressure flush diaphragm transmitter from Omega (Stamford, CT ). The flow rate was controlled by adjusting the flow rate of a by pass at the discharge of the pump that re circulated a portion of the flow back to the feed bucket. Flow rate was measured with a n electromagnetic flow meter model 8711 wafer sensor and tra nsmitter model 8732 from Rosemount (Chanhassen, MN) The upper flow rate value limit was set to 8.37 m 3 hr 1 Conf i rmation of flow meter calibration was done by weighting the total mass of pulp collected over selected periods of time at five flow rates wi th a concentration of approximately 543 1 at 21 C. Pressure, temperature, and flow rate data was collected using a National Instruments data acquisition board model NI 9219 (Austin, TX) and a computer program written in LabVIEW10 (Austin, TX) (Figures 3 1 and 3 2) Each pulp batch was anal yzed separately. Capillary viscometry determinations were carried out in a block design with pulp batch and temperature blocks, and random ized pulp concentration. Temperature was blocked to reduce experimental time associated with sample thermal equilibrat ion. Each pressure drop determination was run for 1 min. The mean and standard deviation of triplicates were reported. Calculations In this experiment, the inlet was the pressure from the pump while the outlet was atmospheric pressure therefore only one pressure sensor was needed In this study, the pressure transducer was placed at approximately 2.6 m (114 diameter > 90 diameter required) from the discharge of the pump which results in fully developed flow. Therefore, entrance corrections were not necess ary (Figure 1 3). The sensitivity of the pressure transducer was rather small in view of the low pressures (8.71 64.85 psi) that
85 were measured as a result of slippage It would have been best to use a smaller range pressure transducer to achieve the most a ccurate pressure measurements Experimental p ressure and flow rate data w ere collected knowing that slippage decreases pressure drop due to friction compared to flow without slippage (Appendix A) c ) was determined from th e difference between the flow rates of the measured (Q m ) and calculated without slippage (Q ws ) at the same pressure. Data from chapter 2 of shear stress vs. shear rate at shear rates where slippage does not occur were used to calculate Q ws The procedure u sed for determining the flow rate without slippage for a given pressure drop for orange pulp is : 1. Estimate friction factor using the generalized Reynolds number for power law fluids (Equation 3 2 ). (3 2 ) Where D is the diameter ( 3 ), v is the velocity (ms 1 ) and the power law parameters K and n at shear rates l ow enough to avoid slippage ( Chapter 2). Approximations of both were determined from an Arrhenius like approach because the temperatures used in the capi llary viscosity experiments were different from the rotational rheology Because in all cases Re was below the critical value for laminar flow, the friction factor was calculated as: (3 3 ) 2. Determine flow rate without slippage (Q ws ) at the same pressure drop recorded 4 ) (3 4 )
86 Where p is pressure (Pa), g is gravity (m/s 2 ), z is elevation (m), g c proportionality factor for gravit ational force, L is length of pipe (m), K fe is the coefficient for expansion, is the velocity after expansion, K fc is the coefficient for contraction, is the velocity after contraction and K ff is the coefficie nt for valves and fittings. The K ff for a 180 U Shaped bend was 0.2. Also the velocity is equal to the volumetric flow rate divided by cross sectional area. Due to the horizontal step up of the capillary system, the elevation was null. The velocity term was also null because the pipe diameter was constant T here were no sudden contractions or expansions therefore, those terms were neglected Equation 3 4 can then be rewritten in terms of flow rate (without slippage) as: (3 5 ) m is measured pressure drop (Pa). 3. Calculate the corrected slip coefficient c ) (Equation 3 6 ), (3 6 ) where shear stress at the wall w ) is calculated from the measured pressure drop (Equation 3 7 ) (3 7 ) Relative standard deviations of the measured flow rates were calculated. Results and Discussion Pressure Determination Figures 3 3 to 3 7 show the relationship between measured flow rate and pressure drop at each concen tration for selected temperature s As the measured flow
87 rate increased the measured pressure drop increased. From these figures it can also be determined that as the concentration decreased the measured flow rate increased indicating that the performance o f diaphragm pump used for this research was affected by pulp concentrations pulp At 4 C 1 the measured pressure drop increased from 250.9 to 376 .9 kPa as the measured flow rate increased from 5.59 x 10 5 to 2.1 x 10 4 m 3 s 1 At 4 C and for 1 the maximum flow rate was 2.1 x 10 4 m 3 s 1 while at the same temperature the maximum flow rate for 570 1 was 7.66 x 10 4 m 3 s 1 Figures 3 3 through 3 7 show the remaining relationships for the other con centr ations at selected temperatures The increase in flow rate caused more friction in the capillary tube therefore a higher pressure drop. As the concentration decreased there was less resistance to flow because fewer particles were present. At all tempe ratures, the higher the concentration, the higher the pressure drop s The highest pressure drop was at the fastest flow rate for the highest concentration and the lowest temperature Figures 3 8 to 3 11 show the relationship between measured flow rate and pressure drop at each temperature for selected concentrations. As the measured flow rate increased the measured pressure drop increased. At an average concentration of 854 1 and 4 C the measured flow rate increased from 5.59 x 10 5 to 2.1 x 10 4 m 3 s 1 as pressure drop increased from 250.9 to 376 kPa. At the same concentration but at 50 C, the flow rate increase from 9.23 x 10 6 to 5.74 x 10 4 m 3 s 1 as the pressure drop increased from 85.2 to 371.6 kPa. Figures 3 8 to 3 11 show the remaining relatio nships for the other temperatures at selected concentrations. Another relationship determined from these figures is that as the temperature increased the measured flow rate
88 increased because at higher temperatures more molecular movement (less particle ent anglement) caused increased flow. Also the highest pressure drop was at the lowest temperature with the fast flow rate at all concentrations. All these observations are consistent with the results from rotational rheology determinations from Chapter 2 Some of the figures show pseudo linear trends for the relationship between flow rate and pressure drop because only four flow rates were tested. Using a greater range of flow rates would show the power relationship between flow rate and pressure drop. Figures 3 12 and 3 13 illustrate the difference between experimental pressure drop and the calculated pressure drop assuming no slippage at the same flow rate The calculated pressure drop was determined with Equation 3 4 The measured pressure drop was always sma ller for every concentration at all temperatures because with slippage the pulp particles have migrated away from the wall leaving the slip layer of liquid which reduced the friction and therefore the pressure drop. The highest calculated pressure drops we re at 4 C and decreased as temperature increased. Tables 3 1 through 3 5 give the calculated pressures assuming no slippage for each temperature. In summary, for all experimental conditions, as the measured flow rate increased the pressure drop increase d. As the concentration decreased at a particular temperature the pressure drop decreased. As the concentration decreased the measured flow rate increased. Increasing the temperature at a particular concentration decreases the pressure drop. As the tempera ture increased at any concentration the measured flow rate increased. Orange pulp was pumped through the capillary system using a diaphragm pump. Using this type of positive displacement pump had the issues of pulsing flow and not
89 being able to handle the same flow rates at all concentrations and temperatures Due to orange pulp characteristics, a progressive cavity pump would have been most effective at providing non pulsating flow rate, allowing more accurate determination of pressure drop and flow rate with higher signal to noise ratios (Appendix A) Relative standard deviations of the of the measured flow rate were calculated. The highest concentrations had the highest relative standard deviations (up to 69%) while the lowest concentration had the lowes t relative standard deviations (up to 38%). Other sources of variability in the data most likely came from the pulp its self. Two different sources of orange pulp were used along with two different types of oranges. Because orange pulp is a biological ma terial it is subject to natural variability. One sample was extracted, pasteurized and finished on site while the other was from a commercial source. The commercial source had a more gel like texture which could possibly affect its rheology and even the re sults of the quick fiber tests Variations in the way the pulp was extracted finished, and stored could have resulted in the different pulp quality which were used in the study. Fruit puree flow rates versus pressure curves have been determined for differ ent diameter capillary viscometer system s and can be found in Table 3 6 All flow rates ranged from 2.77 x 10 5 to 1.6 x 10 3 m 3 s 1 which fell in the flow rate range of the orange pulp tested. All fruits had significantly lower pressure readings at approx imately the same diameter (0.025 m) capillary tubes. Apple puree had an approximate pressure range of 58 120 kPa while apricot puree ranged from 37 to 180 kPa. Nectarine puree had a smaller pressure range (10 50 kPa) in comparison to apple and apricot. Wit h a pressure range of 10 to 42.5 kPa, strawberry puree had the smallest range. All four fruits tested in the Yeow et al (2001) study had smaller
90 pressure drops when compared to orange pulp. A reason for this difference could be that a puree has smaller pa rticles in suspension in comparison to the orange pulp tested which could lead to the lower pressures because of less friction The Yeow et al. (2001) study did not state whether the purees displayed slippage which would have affected the flow rate and pre ssure drop. A study performed by Levati (2010), calculated the pressure drop at diffe rent flow rates of high concentration orange pulp using calculated power law parameters (Table 3 7). One similar trend found in this study was that as the temperature inc reased from 11 to 50 C the pressure drop decreased at all flow rates. At similar temperatures to this study, 10 and 50 C, Levati (2010) had higher measured flow rates which had higher pressure drops. First, the flow behavior index and consistency coeffi cient used in determining pressure were different. Levati used a shear rate range of approximately 0 to 1300 s 1 to determine n and K while only a shear rate range of up to 4 s 1 was used in this study because after 4 s 1 slippage began. Significantly smal ler K and n values were used by Levati. A second major difference is that all values were not corrected for slippage. It is know n that slippage has a big impact on flow rate, pressure drop and power law parameters. The effect of slippage on calculated flow rate was determined by other studies and other materials The first study was performed on a model suspension material composed of polymer Ethylene Vinyl Acetate 460 and soda lime glass beads. For all particle concentrations of 35, 41, 45% and flow rates of 0 to 0.075 cm 3 s 1 the experimental pressure data was lower when compared to the predicted without slippage (Lam, Wang, Chen & Joshi, 2007) The second study was performed on cultured
91 buttermilk at 5 C. At both capillary diameters (1.86 and 3.34 mm) and flow rate ranges of 0 .25 to 2 m 3 s 1 the experimental was lower than the initial and equilibrium pressure drop (Butler & O'Donnell, 1999) Flow Rate and Corrected Slip Coefficient Determination Figure 3 14 shows the relationship between measured flow rate and the slippage coefficient. As the measured flow rate increased the slippage coefficient increased. At 50 6 to 1.7 x 10 3 m 2 s) 1 At all temperatures this was seen except at 4 C where at a concentration of 870 gL 1 negative values were sliding friction may be a significant factor (Steffe, 1996) be found in Tables 3 1 through 3 The slippage coefficient is used to determine the flow rate without slippage at the measured pressure d rop. The movement of particles from the wall is a direct action of the heterogeneous shear ing that is perpendicular to flow (Wang, Lam, Joshi & Chen, 2010) At higher flow rates more shearing takes place at the wall which causes more particle migration and a greater difference between the measured flow rates and the flow rates without slip page. Figure 3 15 shows the corrected slippage coefficient at a constant flow rate of 2.10x10 4 m 3 s 1 Only a clear relationship exists between concentration and corrected slippage coefficient at 4 and 30 C. As the concentration decreased The lack of consistent trends on this graph could be due to the fact that these values are based on extrapolated data ( Table 3 8 )
92 S ources of error such as pulp source processing technique machinery and pulp quality affected slippage coe fficient determinations A major difference between this study and other studies t hat determine d slippage coefficients was that this study did not use multiple capillary tube radii because data without slippage at very low shear rates was available. Sodium benzoate was added at such a small level (0.05%) that no effect was seen on the results of the capillary viscometry data. T he corrected slip coefficient and wall shear for apple sauce, ketchup, mustard, and tomato paste was determined (Table 1 11) (Kokini & Dervisoglu, 1990) For apple sauce, the corrected slip coefficient ranged from 0.0030 to 0.025 m 2 ( Pa s ) 1 while the wall shear stress ranged from 40 to 150 Pa. Ketchup has a corrected slip coefficient range of 0.0034 to 0.042 m 2 ( Pa s ) 1 and a wall shear stress range of 50 to 200 Pa. Mustard corrected slip coefficient ranged from 0.0046 to 0.037 m 2 ( Pa s ) 1 while the wall shear stress range was the same as for ketchup. Tomato paste which is the most similar to orange pulp had a corrected slip coefficient range of 0.00018 to 0.0065 m 2 ( Pa s ) 1 and a wall shear stress range of 250 750 Pa. The study by Kokini and Dervisoglu (1990) also found that as wall shear When determining the slip parameters for the four semi solid foods three different capillary radii were used with extremely small diameters (0.0043 0.0885 cm). The smaller capillary tubes produce smaller flow rates with l ess shearing In food processing, small diameters like the ones used in this study to predict flow rate and slippage are not used. Another factor that needs to be considered when comparing the semi solid food data to orange pulp data is the size of the sus pended solids. A suspension of orange pulp and single strength orange juice has much larger particles
93 than the particles suspended in ketchup or mustard. Because the conditions are not similar between the Kokini and Dervisoglu (1990) and this study a fair comparison cannot be made. Using a model co a rse food suspension of green peas and aqueous sodium carboxy methylcellulose, an alternative method to wall slip correction was performed in a study by Chakrabandhu and Singh (2005). Instead of measuring at diff erent radii, variable particle concentrations were used. Through the entire range of concentrations (0, 15, 20, 25, 30 %v/v), flow rates (1.26 x 10 4 to 3.15 x 10 4 m 3 s 1 ) and temperatures (85, 110, 135 C) the slip coefficient ranged from 3.09 x 10 3 to 1.01 x 10 2 m ( Pa s ) 1 at wall shear stress range of 19.4 to 125 Pa. The slip coefficient was used instead of the corrected slip coefficient because it was not based on tube radius. T hat study also derived power equations to determine slip coefficient as a function of wall shear stress. Equations can be found in Table 1 12. Chakrabandhu and Singh (2005) also determined that as the wall shear stress increased the slip coefficient increased. Using model suspensions is a good way to confirm methods to determin e the slip coefficient but using real materials allows determining variation in sa mples which need to be accounted for practical applications Conclusions Orange pulp flow was characterized by capillary viscometry accounting for slippage at selected te mperatures of (4, 10, 21, 30, and 50 C) and a range of concentrations (854 g 19, 749 21, 649 26, and 545 1 ). As the measured flow rate increased the measured pressure drop increased monotonously confirming that at all flow rates in this experiment slippage was present. Generally as the measured
94 flow rate increased the slippage coefficient increased. T he slippage coefficient ranged from 5.2 x 10 5 to 1.7 x 10 3 m 2 (Pas) 1 with a standard deviation range of 4.1 x 10 7 to 2.8 x 10 3 Overall Conclusions Orange pulp is a very difficult fluid to characterize because it displays slippage over a range of temp eratures (4 to 80 1 ). Orange pulp is non Newtonian pseudoplastic fluid that can be best modeled with the power law at very low shear rates 0 to 4 s 1 Rheological data showed that slippage takes place at shear rates between 2 and 4 s 1 and is more pronounced at low temperatures and high concentrations. In general, as the concentration increased the average activation energy increased. To account for the increased flow rate at the slip Having a complete characterization of orange pulp is the foundation for the design and optimization of processing equipment Future Work Although we covered the most relevant factors affecting the rheolog ical behavior of orange pulp (i.e. concentration and temperature) we became aware of other potential sources of variability that need to be addressed. First, biological variety would need to be addressed. Depending on the variety of orange fruit, different size and amount of juice vesicles could be present which could possibly affect the rheological behavior. A second factor that could possible affect rheological behavior is the equipment and processing conditions used to produce citrus pulp For example we hypothesize that the pressure used in the extraction and finishing, affects the rheological behavior of citrus pulp The last source of variability that needs to be addressed is the different pulp
95 storage conditions and time. Depending of the storage cond itions/time structural changes such as ice crystal formation in the pulp could affect the rheological characterization. Additional research could also be done with the capillary viscometer study. Determining pressure drop at more flow rates would lead to a better understanding of the power relationship between flow rate and pressure drop. Also the pump used in the study was only temperature rated to 60 C, using a pump that functioned at higher temperatures could provide pressure drop data at higher temper atures. Knowing the true flow rates and pressure drops at highe r temperatures would be important in the designing and optimization pulp processing equipment.
96 Table 3 1. Average values of experimental and calculated pressure, measured and corrected flo w rate for slippage, wall shear stress and corrected slip coefficient for orange pulp at 4 C and capillary diameter of 0.02291 m. Concentration (gL 1 ) Experimental pressure (kPa) Calculated pressure at Q m assuming no slip (kPa) Q m (m 3 s 1 ) Q ws (m 3 s 1 ) W all shear stress (Pa) m 2 (Pa s) 1 870 376.9 5558.4 2.10E 04 8.27E 05 191.5 1.68E 05 321.8 4623.9 1.20E 04 4.92E 05 163.5 1.02E 04 281.9 3964.1 8.37E 05 3.24E 05 143.2 8.30E 05 250.9 3257.7 5.59E 05 1.93E 05 127.4 5.04E 05 761 414.6 4982.7 4.89E 04 9.38E 05 210.7 5.21E 05 384.3 4492.6 3.77E 04 7.13E 05 195.3 4.34E 05 343.7 4113.6 2.59E 04 5.54E 05 174.6 3.23E 05 315.4 3786.4 1.96E 04 4.46E 05 160.3 2.63E 05 675 372.4 5072.1 6.13E 04 1.35E 04 189.28 7.03E 05 346.0 4619.5 4.97E 04 1.0 7E 04 175.86 6.15E 05 333.9 4366.6 4.16E 04 9.33E 05 169.69 5.28E 05 311.9 3974.8 3.28E 04 7.37E 05 158.50 4.45E 05 570 318.4 4278.4 7.66E 04 1.49E 04 161.7 1.06E 04 298.4 3975.0 6.36E 04 1.24E 04 151.6 9.38E 05 292.7 3883.3 5.83E 04 1.17E 04 148. 7 8.70E 05 278.8 3672.5 5.01E 04 1.02E 04 141.6 7.84E 05
97 Table 3 2. Average values of experimental and calculated pressure, measured and corrected flow rate for slippage, wall shear stress and corrected slip coefficient for orange pulp at 10 C and c apillary diameter of 0.02291 m. Concentration (gL 1 ) Experimental pressure (kPa) Calculated pressure at Q m assuming no slip (kPa) Q m (m 3 s 1 ) Q ws (m 3 s 1 ) W all shear stress (Pa) m 2 (Pa s) 1 843 397.9 2661.5 2.83E 04 9.25E 05 202.2 4.2E 04 334.8 22 81.7 1.82E 04 6.09E 05 170.1 3.2E 04 292.9 1986.4 1.37E 04 4.45E 05 148.8 1.6E 04 262.8 1774.2 9.37E 05 3.05E 05 133.6 1.6E 04 767 391.6 2835.2 5.53E 04 1.39E 04 199.0 5.8E 05 367.4 2658.1 4.61E 04 1.14E 04 186.7 5.2E 05 339.1 2456.7 3.61E 04 9.66 E 05 172.3 4.3E 05 310.9 2241.6 2.65E 04 7.28E 05 158.0 3.4E 05 663 361.1 3166.6 7.23E 04 1.58E 04 183.5 8.6E 05 353.5 3040.7 6.37E 04 1.43E 04 179.7 7.7E 05 334.4 2892.2 5.35E 04 1.25E 04 170.0 6.7E 05 310.7 2685.6 4.15E 04 1.03E 04 157.9 5.5E 05 557 306.5 2508.6 8.86E 04 2.32E 04 155.7 1.2E 04 300.8 2432.2 8.26E 04 2.17E 04 152.9 1.1E 04 288.5 2302.6 7.16E 04 1.90E 04 146.6 1.0E 04 272.3 2193.7 6.32E 04 1.72E 04 138.4 9.3E 05
98 Table 3 3. Average values of experimental and calculated pre ssure, measured and corrected flow rate for slippage, wall shear stress and corrected slip coefficient for orange pulp at 21 C and capillary diameter of 0.02291 m. Concentration (gL 1 ) Experimental pressure (kPa) Calculated pressure at Q m assuming no sl ip (kPa) Q m (m 3 s 1 ) Q ws (m 3 s 1 ) W all shear stress (Pa) m 2 (Pa s) 1 827 390.8 2129.7 3.74E 04 1.34E 04 198.61 8.7E 04 350.1 1948.8 2.86E 04 1.02E 04 177.93 7.0E 04 316.0 1723.4 1.95E 04 6.94E 05 160.61 4.1E 04 284.0 1595.5 1.51E 04 5.28E 05 14 4.32 3.8E 04 763 383.2 2530.5 5.75E 04 1.85E 04 194.8 5.6E 05 344.6 2411.3 5.51E 04 1.56E 04 175.1 6.2E 05 332.8 2170.6 4.91E 04 1.22E 04 169.1 6.0E 05 310.2 2046.5 3.84E 04 1.00E 04 157.6 5.0E 05 658 341.8 2552.9 8.24E 04 2.37E 04 173.7 9.4E 05 323.8 2412.4 7.05E 04 2.01E 04 164.6 8.5E 05 310.1 2271.9 6.18E 04 1.70E 04 157.6 7.9E 05 302.4 2192.4 5.57E 04 1.53E 04 153.7 7.3E 05 549 286.5 1882.3 1.04E 03 3.08E 04 145.6 1.4E 04 276.9 1849.1 9.33E 04 2.83E 04 140.7 1.3E 04 273.4 1799.8 8.92E 04 2.64E 04 138.9 1.3E 04 260.9 1269.8 8.01E 04 2.38E 04 132.6 1.2E 04
99 Table 3 4. Average values of experimental and calculated pressure, measured and corrected flow rate for slippage, wall shear stress and corrected slip coefficient for orange pul p at 30 C and capillary diameter of 0.02291 m. Concentration (gL 1 ) Experimental pressure (kPa) Calculated pressure at Q m assuming no slip (kPa) Q m (m 3 s 1 ) Q ws (m 3 s 1 ) W all shear stress (Pa) m 2 (Pa s) 1 868 384.6 2200.3 4.70E 04 1.60E 04 195.4 1 .3E 03 328.7 1955.9 2.91E 04 9.71E 05 167.0 1.1E 03 275.1 1720.1 1.65E 04 5.39E 05 139.8 7.4E 04 168.7 896.0 1.28E 05 3.95E 06 85.7 1.4E 04 724 309.3 2123.2 6.83E 04 2.14E 04 157.2 8.3E 05 291.2 1402.3 5.73E 04 1.78E 04 148.0 7.4E 05 225.3 1649. 1 2.53E 04 7.64E 05 114.5 4.3E 05 78.4 695.3 1.02E 05 2.84E 06 39.9 5.2E 06 608 265.6 1596.3 7.86E 04 2.60E 04 135.0 1.1E 04 227.8 1373.4 5.18E 04 1.69E 04 115.8 8.5E 05 188.1 1041.5 2.79E 04 8.96E 05 95.6 5.6E 05 71.1 365.2 6.20E 06 3.14E 06 36.1 2.3E 06 522 231.5 1143.1 8.79E 04 3.29E 04 117.7 1.3E 04 200.0 1037.7 6.24E 04 2.25E 04 101.6 1.1E 04 168.0 914.7 4.00E 04 1.39E 04 85.4 8.5E 05 107.3 304.5 2.54E 04 4.39E 06 54.5 7.4E 05
100 Table 3 5. Average values of experimental and calculate d pressure, measured and corrected flow rate for slippage, wall shear stress and corrected slip coefficient for orange pulp at 50 C and capillary diameter of 0.02291 m. Concentration (gL 1 ) Experimental pressure (kPa) Calculated pressure at Q m assuming no slip (kPa) Q m (m 3 s 1 ) Q ws (m 3 s 1 ) Wall shear stress (Pa) m 2 (Pa s) 1 864 371.6 1879.3 5.74E 04 2.10E 04 188.8 1.7E 03 306.0 1764.4 4.38E 04 1.49E 04 155.5 1.5E 03 236.0 1421.4 1.99E 04 6.66E 05 119.9 8.6E 04 85.2 638.5 9.23E 06 2.75E 06 43 .2 1.4E 04 729 291.1 1878.2 7.73E 04 2.50E 04 147.9 9.8E 05 258.4 1700.5 5.34E 04 1.70E 04 131.3 7.7E 05 205.4 1352.1 2.38E 04 7.62E 05 104.3 4.3E 05 79.2 550.7 9.25E 06 2.88E 06 40.2 4.4E 06 644 249.2 1376.1 8.58E 04 2.98E 04 126.7 1.2E 04 220.9 1240.8 6.03E 04 2.08E 04 112.2 9.8E 05 178.2 1011.2 3.06E 04 1.05E 04 90.6 6.2E 05 68.4 328.4 9.46E 06 3.52E 06 34.8 4.8E 06 529 211.5 957.2 9.59E 04 3.67E 04 107.5 1.5E 04 188.8 848.8 6.34E 04 2.43E 04 95.9 1.1E 04 147.8 710.5 3.46E 04 1.29E 04 75.1 8.0E 05 63.6 249.3 9.26E 06 3.81E 06 32.3 4.7E 06
101 Table 3 6. Approximate flow rate and pressure drop for various fruit purees (Yeow, Perona & Leong, 2001) Fruit Puree Diameter X Length (cm x m) Temperature C Approximate Q (m 3 s 1 ) Approximate Pressure (kPa) Apple 2.5 x 7 30 2.77 x 10 5 1.6 x 10 3 58 120 Apricot 2.5 x 7 30 2.77 x 10 5 1.6 x 10 3 37 180 3.65 x 6 30 2.77 x 10 5 1.6 x 10 3 18 40 Nectarine 2.5 x 7 30 2.77 x 10 5 1.6 x 10 3 10 50 3.65 x 6 30 2.77 x 10 5 1.6 x 10 3 5 15 Strawberry 2.5 x 7 25 2.77 x 10 5 1.6 x 10 3 10 42.5 Table 3 7. Pressu re drop of orange pulp for a capillary system of 49 mm inner diameter at different temperatures and flow rates (Levati, 2010) Temperature C Approximate Q (m 3 s 1 ) Approximate Pressure (kPa) 11 1.38 x 10 4 1.8 x 10 3 1420 1800 25 1.38 x 10 4 1.8 x 10 3 610 900 38 1.38 x 10 4 1.8 x 10 3 400 590 50 1.38 x 10 4 1.8 x 10 3 375 50 0 Table 3 8. Extrapolated pressure drop, flow rate without slippage, wall shear stress and corrected slipped coefficient at a measured flow rate of 2.1x10 4 m3s 1 Temperature C Concentration 1 ) Extrapolated p ressure drop (kPa) Q without slippage (m 3 s 1 ) Wall shear stress (Pa) m 2 (Pa s) 1 4 870 382.1 7.24E 05 194.2 1.97E 05 761 324.1 3.80E 05 164.7 2.90E 05 675 291.6 3.76E 05 148.2 3.23E 05 570 236.3 3.44E 05 120.1 4.06E 05 10 843 348.1 6.91E 05 176.9 2.21E 05 767 296.1 6.71E 05 150. 5 2.64E 05 663 278.3 7.84E 05 141.4 2.58E 05 557 218.7 1.00E 04 111.1 2.74E 05 21 827 316.2 5.87E 05 160.7 2.62E 05 763 249.6 5.56E 05 126.9 3.38E 05 658 250.0 1.38E 04 127.1 1.58E 05 549 199.3 1.53E 04 101.3 1.55E 05 30 868 321.3 5.57E 05 163. 3 2.63E 05 724 221.8 1.95E 07 112.7 5.17E 05 607.6 167.8 2.71E 07 85.3 6.83E 05 521.6 106.0 9.80E 10 53.9 1.08E 04 50 863.7 245.9 6.63E 05 125.0 3.19E 05 728.6 196.1 7.27E 05 99.7 3.83E 05 644.3 152.4 1.12E 04 77.5 3.53E 05 528.9 123.1 5.30E 0 6 62.5 9.10E 05
102 Figure 3 1. Complete 1 inch capillary system setup to measure the pressure drop and flow rate of orange pulp. Pump Feed Bucket Valve Flow Mete r r Pressure Transducer r
103 Figure 3 2. Screen shot of LabVIEW X front panel.
104 Figure 3 3 Measured pressure drops and standard deviat ions produced at flow rates with slippage at 4 C and selected concentrations: 870 7 1 ( ), 760 24 1 ( ), 67 5 13 1 ( )and 569 11 1 ( ) Figure 3 4 Measured pressure drops and standard deviations produced at flow rates with slip page at 10 C and selected concentrations: 843 16 1 ( ) 767 8 1 ( ) 663 27 1 ( ) and 557 6 1 ( )
105 Figure 3 5 Measured pressure drops and standard deviations produced at flow rates with slippage at 21 C and selected concentra tions: 827 32 1 ( ) 763 21 1 ( ) 658 23 1 ( ) and 549 19 1 ( ) Figure 3 6 Measured pressure drops and standard deviations produced at flow rates with slippage at 30 C and selected concentrations: 868 34 1 ( ) 724 21 1 ( ) 607 49 1 ( ) and 522 46 1 ( )
106 Figure 3 7 Measured pressure drops and standard deviations produced at flow rates with slippage at 50 C and selected concentrations: 864 39 1 ( ) 729 44 1 ( ) 644 35 1 ( ) and 5 29 3 1 ( )
107 Figure 3 8 Measured pressure drops and standard deviations produced at flow rates 1 and selected temperature: 4 C ( ),10 C, ( ) 21 C, ( ), 30 C ( x ) and 50 C ( )
108 Fig ure 3 9 Measured pressure drops and standard deviations produced at flow rates with slippage at an average concentration of 749 1 and selected temperature: 4 C ( ) ,10 C ( ) 21 C ( ) 30 C ( x ) and 50 C ( )
109 Figure 3 10 Measured pressure drops and standard deviations produced at flow rates with slippage at an average concentration of 649 1 and selected temperature: 4 C ( ) ,10 C ( ) 21 C ( ) 30 C ( x ) and 50 C ( )
110 Figure 3 11 Measured pressure drops and standard deviati ons produced at flow rates with slippage at an average concentration of 543 1 and selected temperature: 4 C ( ) ,10 C ( ), 21 C ( ) 30 C ( x ) and 50 C ( ) Figure 3 12 Experimental and calculated pressure drop of orange pulp at different flow rates for 4 C and average concentrations. 87 1 1 ( ) calculated ( ) experimental, 76 1 1 ( ) calculated ( ) experimental, 67 5 1 ( ) calculated ( 1 ( ) calculated ( ) experimental.
111 Figure 3 13 Experimental and c alculated pressure drop of orange pulp at different flow rates for 50 C and average concentrations. 86 4 1 ( ) calculated ( ) experimental, 72 9 1 ( ) calculated ( 1 ( ) calculated ( ) experimental and 52 9 1 ( ) calculate d ( ) experimental.
112 Figure 3 14 Measured flow rate vs. slip coefficient for 50 C at selected concentrations: 864 1 ( ) 729 1 ( ) 644 1 ( ) and 529 1 ( )
113 Figure 3 15. Corrected Slippage coeffecient at a constant flow rate of 2. 1x10 4 m 3 1 at selected temperatueres: 4 C ( ), 10 C ( ), 21 C ( ), 30 C ( x ), and 50 C ( ).
114 APPENDIX C APILLARY VISCOMETRY In the LabVIEW X program, pressure (pounds per square inch ), temperature at the inlet of the pump and exit of the capillary s ystem ( C) and measured flow rate (m 3 hr 1 ) were measured. With the data collected in LabVIEW the pressure in pounds per square inch was converted to Pascal and average for each concentration and temperature combination. The measured flow rate was converte d to m 3 s 1 and then averaged for each concentration and temperature combination. The velocity was calculated from the measured flow rate in m 3 s 1 and the cross sectional area. With these variables determined the procedure for determining flow rate withou t slippage and slip coefficient for a given pressure drop for orange pul p was determined ( Equations 3 5 through 3 10 ) Figure A 1. Pressure drop (psi) over time (s) 1
115 Figure A 2 Inlet ( ) and outlet ( ) temperatur es of 30 C 1 collected in L abVIEW for replicate 3. Figure A 3. Flow rate (m 3 1 ) over time (s) for 30 C 1 for replicate 3.
116 Figure A 4. Measured pressure drops produced at flow rates with slippage at an average concentratio n of 843 1 and selected temperature for replicate 3: 4 C ( ) ,10 C ( ), 21 C ( ) 30 C ( x ) and 50 C ( ) Figure A 5. Measured pressure drops produced at flow rates with slippage at 50 C and selected concentrations for replicate 3: 820 1 ( ) 692 1 ( ) 672 1 ( ) and 526 1 ( )
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123 BIOGRAPHICAL SKETCH Elyse Meredith Payne was born in Spartanburg, South Carolina but raised in Orlando, Florida. She attended the University of Florida from 2004 to 2009 where she completed a Bachelor of Food Science and Human Nutri tion. Continuing her education Upon completion of the requirements for a master in food science at the University of Florida, Elyse intends to seek a po sition within the citrus industry where she can apply her current and developing skill set.