PRESSURE LOSSES AND RHEOLOGICAL PROPERTIES OF FLOWING BUTTER Thesis {M the Dog?“ 9‘ M. S. l MICHIGAN STATE UNIVERSITY ' Ronald C. Hanck 1964 IHESIS LIBRARY Michigan State University ABSTRACT PRESSURE LOSSES AND RHEOLOGICAL PROPERTIES OF FLOWING BUTTER by Ronald C . Hanck The pressure losses and rheological properties of butter flow- ing through stainless steel tubing were examined under conditions which were comparable to commercial handling and printing. Pres- sure is required to overcome the internal resistance of butter to flow. Viscosity is a measure of this internal resistance. An extrusion viscometer was constructed to measure the apparent viscosity of butter since its Operation is similar to the actual conditions of flow. The apparent viscosity was calculated from the extrusion viscometer data using the Hagen-Poiseuille equation for flow through tubing. The butter was found to have an average density of 0. 952 g./ml. for 55 to 750 F. under the flow conditions. Since variations are normal in commercial butter this average may be used in power requirement calculations . Flow profiles were obtained by alternately forcing butters of different colors through the various lengths of tubing at different temperatures. The velocity gradient was small within the butter ex- cept near the wall where it was large. As the temperature of the butter decreased from 70 to 550 F. the velocities within the butter be came smalle r . RONALD C. HANCK A linear relationship was found between the logarithm of apparent viscosity and the logarithm of bulk velocity for a range of O. 001 to 1 ft. /sec. The average slope of the regression line was -0. 84649. As the length of the tubing increased the average apparent viscosities decreased but at a decreasing rate. Very small differ- ences were found between the apparent viscosities obtained using a 10. 5-in. and 14. O-in. length of tubing. The influence of temperature on the logarithm of the apparent viscosity was found to be linear having a slope of -0. 0587 for the range of 55 to 750 F. A general empirical equation was determined relating the influence of the bulk velocity and temperature to the decrease in apparent viscosity and is: log n = 7.93446 - 0.84649 log v - 0.0587T Pumping action reduced the apparent viscosity of butter by increasing its temperature and by working. The rate at which the pump operated (52 and 120 r.p.m.) had no apparent influence on the apparent viscosity. The power requirements for various conditions of temperature, bulk flow and tube diameter were determined. PRESSURE LOSSES AND RHEOLOGICAL PROPERTIES OF FLOWING BUTTER BY Ronald C. Hanck A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Food Science 1964 AC KNOW LEDGEMENTS The author expresses his sincere gratitude and appreciation to Dr. T. I. Hedrick, Professor, Department of Food Science and Dr. C. W. Hall, Professor and Chairman, Department of Agricultural Engineering for their inspiration, encouragement, timely guidance and constructive criticism during the course of this study. Thanks are also expressed to Mr. A. L. Rippen, Associate Professor, Department of Food Science for his services as an advisory committee member and to the faculty, graduate students and personnel of the Department of Food Science for their advice and assistance. The author is indebted to Dr. B. S. Schweigert, Professor and Chairman, Department of Food Science and Dr. T. I. Hedrick for the opportunity by making funds available. The author also expresses his love and appreciation to his wife, Phyllis, for her patience, encouragement and typing assistance which helped make the completion of the investigation possible. ii TABLE OF CONTENTS INTRODUCTION . . . . . LITERATURE REVIEW I. II. III . IV. VI. VII. VIII . IX. XI. Viscosity Newtonian fluids Non-Newtonian time -independent fluids Non-Newtonian time -dependent fluids Influence of temperature on viscosity Composition and structure of butter Methods of removing butter from churns Methods used in evaluating the rheological pr ope rtie s of butte r A. Penetrometer B. Compression C . Extrusion , , D. Sectility . , E. Sagging beam Pseudo -viscosity measurements Theoretical cons ide rations Pressure losses Page 10 10 l3 l3 l4 l4 15 15 15 16 18 21 EXPERIMENTAL PROCEDURES . . . . . . . . . II. III . IV. VI. VII. VIII . IX. X. Butter . . . . . . . . . . . . . . . . Equipment verification . . . . . . . . . . Bulk velocity . . . . . . . . . . . . . Flow profiles . . . . . . . . . . . . . . Apparent viscosity of flowing butter . . . . . Pressurelosses ............. Reduction in apparent viscosity under mild agitation................ Reduction in apparent viscosity due to pumping The minimum pressure to initiate flow in tubing, elbows and valve assemblies . . . . . . , Powe r requirements RESULTS.................... I. II. III . IV. VI. VII. VIII . Butter Equipment ve rification Bulk velocity Flowprofiles.............. Apparent viscosity of flowing butter , , , , . Pressurelosses . . . . . . . . . . . . Reduction in apparent viscosity under mild agitation................ Reduction in apparent viscosity due to pumping iv Page 23 23 24 31 31 32 33 34 34 34 35 36 36 41 41 45 47 55 66 76 Page IX. Minimum pressure necessary to initiate flow in tubing, elbows and valve assemblies , , , , , , 76 X. Power requirements , , , , , . . . . . . . . 82 DISCUSSION . . . . . . . . . . . . . . . . . . . . 88 SUMMARY . . . . . . . . . . . . . . . . . . . . 93 LITERATURE CITED . . . . . . . . . . . . . . . . 96 Table 10. 11. 12. 13. 14. L15 T OF TAB LES Tubing and disc specifications . . . . . . . . Brookfield Helipath stand spindle specifications . Cream treatment prior to churning . . . . . . Composition and iodine number of the butter . . Densities of butter at various temperatures . . Penetration and viscosity of quiescent butter at various temperatures , , , . . , . . , . . Viscosity of molasses by the extrusion viscometer method I O O O C O O O O O O O O O O O O Viscosity of molasses by the Brookfield method . Average viscosity of molasses by the Brookfield and extrusion viscometer methods . . . . . . Dimensions used to determine the bulk velocity of butter flowing in stainless steel tubing of various diameters . . . . . . . . . . . . . Results of the correlation and regression analysis for the apparent viscosity versus velocity . . . Results of the correlation and regression analysis on the apparent viscosity versus velocity for each sampleofbutter .............. Results of the correlation and regression analysis on pressure loss versus velocity . . . . . . . Results of the correlation and regression analysis on the pressure loss versus velocity for each sampleofbutter vi Page 26 27 37 37 38 39 42 43 43 45 47 57 62 72 Table Page 15. The influence of pumping on the apparent viscosity ofbutter 77 16. The influence of pumping on the apparent viscosity of butter using the extrusion viscometer . . . . . 79 17. Average minimum pressure losses for elbows and valve assemblies of 1.5-in. diameter . . . . . . 82 18. Loss of head and power requirements for various quantities of butter at different temperatures flowing through tubing of various lengths , , , . , , , , 86 19. Loss of head and power requirements for various quantities of butter at different temperatures flowing through tubing of various lengths . . . . . . . . 87 vii Figure 10. ll. 12. l3. 14. LIST OF FIGURES Amodel for Newton's theory . . . . . . . . . Characteristic flow behavior of fluids . . . . . Actual and apparent flow curves for a non- Newtonianfluid.............. A model for the Hagen-Poiseuille equation for laminarflowintubes . . . . . . . . . . . . Extrusion viscometer equipment arrangement . . Extrusion viscometer . . . . . . . . . . . . Extrusion viscometer in operation . . . . . Brookfield synchro-lectric viscometer, Helipath standandspindles . . . . . . . . . . . . Brookfield viscometer positioned for viscosity measurements on butter . . . . . . . . . . . Arrangement of the extrusion viscometer equipment for use with molasses . . . . Average penetration values on butter after flowing through the various lengths of tubing . . . . . Velocity of butter flowing through stainless steel tubing of various diameters . . . . . . . . Flow profiles obtained from the 7. O-in. length of tubing for the various temperatures . . . . . . Flow profiles obtained at 650 F. for the various lengths of tubing . . . . . . . . viii Page 19 25 28 28 29 29 3O 4O 44 46 46 Figure 15. 16. 17. l8. 19. 20. 21. 22. 23. 24. 25. 26. 27. Effect of tubing length on the apparent viscosity of flowing butter at 700 F. . . . . . . . . Effect of tubing length on the apparent viscosity of flowing butter at 650 F. . . . . . . . . . Effect of tubing length on the apparent viscosity of flowing butter at 600 F. . . . . . . . . Effect of temperature on the apparent viscosity of flowing butter (7.0—in. tubing length) . . , Effect of temperature on the apparent viscosity of flowing butter ( 10. 5-in. tubing length) . . . Effect of temperature on the apparent viscosity of flowing butter with the dotted lines showing the standard error of estimate ( 10. 5-in. tubing length)................. The effect of temperature on the apparent viscosity of butter blowing at 0. 01 ft./ sec. for different lengths of tubing Effect of sample on the apparent viscosity of flowing butter at 700 F. . . . . . . . . Effect of sample on the apparent viscosity of flowing butter at 650 F. . . . . . Effect of sample on the apparent viscosity of flowing butter at 600 F. . . . . . . . . . Effect of sample on the apparent viscosity of flowing butter at 550 F. . . . , . . . . , Effect of tubing length on the pressure loss for butter flowing at 700 F. . . . . , , , , , Effect of tubing length on the pressure loss for butter flowingat650F. . . . . . . . . . Page 49 50 51 52 53 54 56 58 59 60 61 63 64 Figure Page 28. Effect of tubing length on the pressure loss for butter flowing at 600 F. . . . . . . . . . . . . 65 29. Effect of temperature on the pressure loss for flowing butter (3. 5-in. tubing length) . . . . . . . 67 30. Effect of temperature on the pressure loss for flowing butter (7. O-in. tubing length) . . . . . . 68 31. Effect of temperature on the pressure loss for flowing butter ( 10. 5—in. tubing length) . . . .g . . 69 32. Effect of temperature on the pressure loss for ~ flowing butter ( l4. O-in. tubing length) . . . . . . 7O 33. Effect of temperature on the pressure loss for flowing butter with the dotted lines showing the standard error of estimate (10.5-in. tubing length). . 71 34. Effect of sample on the pressure loss of flowing butteratéSOF................ 73 35. The reduction in apparent viscosity with time the butter is mildly agitated at various temperatures , , 74 36. The linear representation of the reduction in apparent viscosity with time the butter is mildly agitated at various temperatures , , , , , , , , 75 37. Effect of pumping rate on the apparent viscosity , , 78 38. The effect and regression lines for the minimum pressure needed to initiate the flow of butter in various lengths of tubing at different temperatures . 80 39. The minimum pressure needed to initiate flow through tubing at various temperatures , , . , . 81 40. Friction factor versus Reynolds number for butter flowing through stainless steel tubing , , , 83 41. Arrangement of stainless steel tubing for the calculations of the power required to pump butter at501b./min.......,,..., 84 Symbol XandY LIST OF SYMBOLS Explanation Area A constant Constant of integration Diameter Degrees of freedom Force A constant Length Pressure Pressure loss Volumetric flow rate Radius Reynolds number Rate of shear Standard error of estimate Temperature Weight Re gre s sion equation variable 5 xi Symbol fl Explanation Intercept in regression equation Slope in regression equation Differential sign Natural logarithm base Friction factor Yield value Dimensional constant relating force and mass (32.2 lb. ft/lb. sec.2) Loss of head Exponent in power-law equation Time Bulk velocity Cartesian-coordinate distances A difference Viscosity or apparent viscosity Symbol for microns 3.141593 . . Density Shear stress xii INTRODUCTION The dairy industry will become more mechanized or automated because of economic necessity. As the trend progresses more dairy products will be handled by equipment during processing and packaging. Butter has been transferred from the churn to the printer or bulk container mainly by manual methods in the United States . Attempts have been made to develop methods of emptying the churn mechanically in an effort to eliminate the labor involved and to re- duce the possibility of contamination. The two main methods are the butter truck and the gear type pump. Both of these methods are utilized with churns incorporating specific designs. In order to develop better methods of mechanically handling butter a knowledge of the physical characteristics of flowing butter is very important. Butter is usually subjected to empirical tests which evaluate characteristics of immediate interest to the consumer and except in isolated cases little effort has been made to consider the fundamental flow properties. The science of deformation and flow of materials is often called rheology. Physical properties of materials associated with flow are referred to as rheological properties. An investigation of the rheological properties of butter has not been attempted under flow conditions. Therefore, the objective of this study is to determine the pressure loss and rheological proper- ties of butter flowing through tubing under normal processing condi- tions. This knowledge could then be utilized to improve the methods of removing butter from the churn, improve butter printing equipment, design an inexpensive butter patty dispenser and conceivably lead to a sterile system of batch churning and packaging of butter. Other beneficial results may be realized from the improved handling pro- cedures, such as, longer keeping quality. LITERATURE REVIEW The importance of rheological properties in butter has long been recognized. Many of these properties were first judged by organoleptic methods. Various attempts to find objective mechani- cal tests were endeavors to evaluate characteristics of immediate interest to consumers. The initial tests were purely empirical. However, later investigators have applied modern methods of rheo- logical research with some success. Many of the analytical tests used have evaluated the rheological properties separately and under different specific conditions. I. Viscosity A material when subjected to a force will deform. Deforma- tion is the process of changing the relative position of the parts of a unit. When deformation is irreversible the materials are called fluids. Fluids include gases and liquids as well as those solids which exhibit continuous flow without separation under certain readily realizable conditions. A certain measurable resistance is encoun- tered in a flowing material. This resistance is due to the internal friction of the molecules moving past each other. Viscosity is the measure of the internal friction of a fluid. Newton deduced the fundamental law of viscosity more than 250 years ago (6) . This concept can. be illustrated by a simple model (Fig. l) . Suppose that an inelastic fluid is contained between two parallel planes of area (A) separated by the distance (dy) . The lower plane is stationary while the upper plane is moved with a con- stant velocity (v) by applying of a force (F) so that the flow in the .— ClV F —-- rm“; A _:" v / —. Fig. l. A model for Newton's theory. fluid is laminar. The force per unit area (F/A) is called the shear stress (-r) and the change in velocity (dv) over the distance (dy) is called the rate of shear (S). The relationship between the shear stress and the rate of shear defines a proportionality constant (77) called the "coefficient of viscosity" or simply “viscosity. ” Thus, the equation is: which postulates: l) shear stress is uniform, 2) shear stress is directly proportional to viscosity and 3) viscosity is constant re- gardless of rate of shear. II. Newtonian fluids A plot of shearing stress versus rate of shear is termed a flow curve or rheogram. A linear flow curve passing through the origin is defined by equation 1. A material having such a flow curve is termed Newtonian. Therefore, viscosity is constant and only one other point in addition to the origin is necessary to describe the complete flow pattern of a material as shown in Fig. 2(a) . By rearrangement of equation 1 the absolute viscosity is: I11 _ A: _ shear stress 77 — S rate of shear A material requiring a shear stress of one dyne/sq. cm. to produce a rate of shear of one reciprocal sec. has an absolute viscosity of one poise. Normally the poise is a rather large unit so that the centipoise (0.01 poise) is used. Pure water at 68.40 F. has an absolute viscosity of one centipoise. The English system of units (ft. , 1b., sec.) are also used in which the unit of absolute viscosity is the 1b. sec. /sq. in. or reyn. A more convenient unit is the Newton which equals one millionth of a reyn. Conversion between the metric and English systems of units can be made on the basis that one reyn is equal to 6,895,000 centi- poises. :3 :3 ""3. m m :3 \ (a) (b) (C) "/l S t (d) (e) (f) Fig. 2. Characteristic flow behavior of fluids:-.- (a) Newtonian, (b) Plastic (f' = yield value), (c) Pseudoplastic, (d) Dilatant, (e) Thixotropic and (f) Rheopectic. III. Non -Newtonian time -independent fluids The viscosities of many materials are influenced by the rate of shear. These materials are termed "non-Newtonian. " The viscosity of a non-Newtonian fluid will depend on the rate of shear at which it is measured and will have a number of viscosity values correspond- ing to various rates of shear. The term "apparent viscosity" is used to describe the viscous property of non-Newtonian fluids. Apparent viscosity is expressed in absolute units and is a measure of the resistance to flow at a given rate of shear. It represents the viscosity of a Newtonian liquid exhibiting the same resistance to flow at the chosen shearing stress or rate of shear (Fig. 3). To have meaning the rate of shear used in the measurement must'be provided. The / T / Apparent flow curve L/ // T / Actual flow curve 1 / Single point measurement // // / / / / T / f' / l / S1 S Fig. 3. Actual and apparent flow curves for a non-Newtonian fluid. apparent viscosity of a fluid is obtained experimentally by measuring the shear stress and dividing it by the rate of shear. A rheogram relating shear stress to rate of shear is frequently used to describe the viscous properties of a non-Newtonian material. Non-Newtonian materials can be characterized as having three main types of flow -- pseudoplastic, dilatant and plastic (Fig. 2) . Fig. 2(c) illustrates a pseud0plastic material. The apparent viscosity decreases with increasing values of rate of shear. A dilatant material shows the opposite effect as illustrated in Fig. 2(d) . The apparent viscosity increases with increased rate of shear and will often reach a point where the fluid becomes a solid (25) . The shear diagram of pseud0plastic or dilatant fluids when plotted logarithmically is often found to be linear and may be represented by the power-law equation: T = Ksn 3 Plastics show a decreasing apparent viscosity with increasing rate of shear as illustrated in Fig. 2(b) . This type of flow behavior is characterized by a "yield value" since a certain force must be applied to the material before any shear (or flow) takes place. The material will show a viscosity tending to approach infinite values as the rate of shear is decreased. IV. Non-Newtonian time —dependent fluids Flow properties of some non-Newtonian fluids are also de- pendent on the amount of shearing which has occurred and the history of the fluid. These fluids are considered time -dependent. Time- dependency is indicated by hysteresis loops in the shear diagram. If the viscosity value at a constant shear rate decreases with time of measurement the behavior is termed thixotropic as illustrated in Fig. 2(e) and occurs in addition to the plastic, pseud0plastic or dilatant characteristic of the fluid. Thixotropy was first defined by Peterfi (32) as an isothermal, reversible sol-gel-sol transformation. Translated, the word thixotropy means change by touch, indicating that the material decreases in viscosity on shear, but builds up again when at rest. Some fluids revert to their original viscosity almost immediately while others will recover after several hours . Minard (25) mentioned that there is evidence to suggest that a thixotropic material is basically similar to other non-Newtonians differing only in that the time interval of hysteresis in thixotropic materials is of a large enough magnitude to be detected in practice. If a fluid is subjected to a constant rate of shear for a given period of time and its apparent viscosity increases to some maximum value the phenomenon is called rheopectic. Upon cessation of shear- ing and resting for a time, its apparent viscosity decreases again. Because time -dependency effects are very unpredictable there are 10 no mathematical models to describe their shear diagram. V. Influence of temperature on viscosity The viscosity of most materials decreases with an increase in temperature. Andrade (3) and Sheppard and Houck (35) showed that when no chemical reaction occurs the change in viscosity with temperature in a Newtonian material may be approximated by: eB/T 4 n = K Weltmann (41) mentioned that for some non-Newtonian materials the change in viscosity with temperature can be approximated by: n = Ke 'BT 5 for small temperature ranges. VI. Composition and structure of butter The physical properties of butter are influenced by the com- position of the cream, the details of the manufacturing process and the storage conditions. The properties mainly affected are the appearance, keeping quality and rheological properties such as body and texture, and spreadability. In controlling the rheological proper- ties, the ratio between the lower and higher melting triglycerides in the milk fat normally predominates over the manufacturing condi- tions (19) . The rheological properties of butter will be influenced by the volume of both the dispersed phase (fat globules and crystals) and the continuous phase (liquid fat), by the flow properties of the ll continuous phase, by the deformability of the dispersed phase and by the proportion, form and arrangement of the dispersed particles. King (18) made the first estimation of the relationship between the volume of the dispersed phase and continuous phase by counting the fat globules and measuring their size. Mulder (27) stated that this technique is difficult and not very accurate . Butter made in the conventional method of buttermaking is the result of a two-step concentration; that is, separation of milk (3-4 percent fat) into cream (32-40 percent fat) and the churning of the cream into butter, plus working. The butter consists of 80-83 per- cent fat with the remainder being water and non—fat-solids. A small volume of air is also occluded during manufacture. King (19) described the structural elements of the butter as a complicated type of emulsion. The fat globules and crystals, moisture droplets and curd particles are about 0. 5 to 20p. in size. He stated that under the microscope in polarized light the crystalline fraction of free fat in conventional butter can be perceived as minute crystals resulting from an eventual partial crystallization taking place in the free fat. According to Knoop and Samhammer (20) the main part of the fat in butter is in a liquid or amorphous state with less than 20 per- cent being in the form of minute crystals. They also maintained that the crystalline fat seemed to be relatively insensitive to 12 temperature and mechanical treatment in a certain range. Several authors (10, 12, 27, 37) have stressed the formation of a three-dimensional network from the needle —like fat crystals. The high structural viscosity of butter was explained by Dolby (12) as a crystalline network. Mulder (27) stated that, because milk fat can easily be supercooled and liquid fat often occurs in freshly churned butter in the supercooled state, the increase in hardness is due to the formation of a "skeleton-like structure" as a result of the growing together of the fat crystal. As was pointed out by deMan and Wood (10) the minute fat crystals are responsible for the thixotropic changes in butter because of their anesometric shape (needles) and size (below In) . Upon moving, working or stirring of butter, the links between the interlaced crystals, presumably Van der Waal forces, are broken and the system becomes softer. On standing the crystals in the butter rearrange into a continuous pattern and the system becomes harder. This process is known as "setting." Sone e_1_: 11; (37) connected the recovery of viscosity with the recrys- tallization of the fat and the formation of a crystalline network. Polymorphism, the occurrence of unstable crystal modification, has also been suggested as affecting the hardness of butter. Accord- ing to deMan (9) there is at present no direct evidence to indicate any effect of polymorphism on the rheological properties. 13 VII. Methods of removing butter from churns Various mechanical methods of removing butter from churns have been tried. One method utilizes a butter truck onto which the butter is dumped by partially revolving the churn. Hansen (14) reported the successful use of a stainless steel rotary gear pump connected to one of the points of a conical stainless steel churn to fill bulk containers. The successful pumping of butter for temper- atures of 56.1 to 65. 50 F. have been reported (1) . Pedersen and Fisker (29) emphasized the importance of keeping the length of tubing as short as possible. Swortling and Olsson (38) reported the difficulty they encountered in completely emptying the churn due to air pockets. They also emphasized that the butter should not be completely worked when pumping is contemplated. A double -action piston pump utilizing compressed air was reported to have been successfully used for removing butter at temperatures of 57. 2 to 59. 00 F. from a Kubus butter churn (2) . VIII. Methods used in evaluating the rheological properties of butter The hardness of butter has been used as a factor in evaluating the rheological properties of butter. Methods, with one or two ex- ceptions, have measured the hardness in arbitrary units under a set of conditions particular to each. The methods of measurement which have been used may be classified as follows: penetrometer, compression, extrusion, sectility and sagging beam. 14 A. Penetrometer Mulder (27) reported that the first apparatus to be used in the rheological study of butter was the penetrometer. Brulle (5) rested a vertical rod on a butter sample and loaded it with weights until it penetrated the butter rapidly. A similar device was described by Sohn (36) . A rod, ball or cone is pressed by means of weights or is dropped into the butter. One of three variables (depth of penetration, load or time) is measured; the other two are kept constant. Perkins (30) used a cylinder of metal dropped from a definite height into the butter. The volume of butter displaced by the cylinder was taken as a measure of hardness. Kruisheer 9.29.1: (21) have devised two types of penetrometers. A rod was forced by weights into the sample of butter and after a given time the depth of penetration was measured. The other method utilized a plunger which was forced into the butter at a given rate either by hand or by an electric motor and the resistance measured by a spring balance. B. Compression A cube or cylinder of butter is compressed between parallel plates by the action of weights. Two of three variables (load, time or decreased thickness) are kept constant. The third variable is taken as a measure of hardness. Devices utilizing this principle were devised by Coulter and Combs (7), Dolby ( ll) , Hunziker 15 _e_t_a;l_. (15), Perkins (30) and Scott Blair (34). C . Extrusion Griffiths (13) used a device in which a cylinder with a sharp- edge orifice was filled with butter. The minimum pressure to pro- duce extrusion indicated hardness. Sargent (33) modified the method by placing the sample under water at constant temperature in a cylinder with a piston at one end and a small orifice at the other. The pressure on the piston was increased until the butter was ex- truded through the orifice and was then gradually reduced until extrusion almost ceased before the reading was taken. D. Sectility Dolby (11) reported a device consisting of a wire which was forced through the sample of butter by weights . Coulter and Combs (7) used a number of wires stretched across a frame to which weights were added. Measurement of force can be taken at constant speed or speed of cutting measured under constant load. Kapsalis §_t_a_l. (l6) incorporated the use of a wire in their "Consistometer" which was used to evaluate spreadability and hardness . E. Sagging beam The sagging beam method was developed by Leighton e_t__ai. (22) for use with ice cream. Their method was applied to butter by Coulter and Combs (7) . A cylindrical sample of butter (13 mm. in diameter) is supported by its ends in a horizontal position at a l6 temperature of 800 F. The rate of sag is determined by measuring the time necessary for the cylinder to sag 5 mm. The results were used as a measure of the "standing up properties" of butter. The method is applicable only at the temperatures at which butter is soft. IX. Pseudo -viscosity measurements The possibility of expressing the data in absolute units has been studied. Davis (8) was one of the first to apply modern rheological tests to butter. Davis (8) loaded a cylindrical piece of butter with different weights. He determined the amount of deformation under the applied stress and after the stress was removed. The permanent deformation was used to calculate a viscosity which was defined as the shearing stress divided by the rate of deformation. This he ex- pressed in absolute units. Davis (8) calculated the modulus of elasticity (relaxation time) from the recovered deformation. The modulus was used as a measure of elasticity and the ratio of the viscosity to the modulus was used to describe "springiness. " The viscosity and modulus taken together were considered a measure of firmness. Mulder (27) questioned the correctness of the above. Kruisheer e533. (21) loaded a "stamp" (4 sq. cm.) with dif- ferent weights to determine the penetration into butter after 30 sec. From the results they calculated a "yield-value. " An arbitrary viscosity was also estimated by Scott Blair (34) from his compression data. He calculated the pseudo -viscosity 17 value using: 77 = 0. 01896 Wt where n is the viscosity (cp.); W is the load (1b.) and t is the time (sec.). He showed that he was aware of the difficulties involved when he mentioned that even for Newtonian liquids certain standard conditions must be stipulated such as temperature. For a material like butter, a viscosity may be quoted in absolute units provided the conditions of temperature, stress and rate of deformation are specified. When the conditions varied appreciably during the deter- mination, a mean viscosity was reported. Elastic properties and any possible yield value were neglected. Dolby (12) using Scott Blair's apparatus could not obtain reproducible results with suffi- cient accuracy to detect small differences in firmness. Viscosity values calculated according to Scott Blair's method were also obtained by Mohr and Wellm (26) using a parallel plate plastometer. This instrument was used by Hunziker e_til. (15) and van Dam (39) and later by Sone eta}; (37) . The viscosities determined by the different methods are essentially different and cannot be compared easily. Even though values of so-called viscosity were reported in absolute terms they may not be the same since the conditions were chosen arbitrarily. 18 X. Theoretical considerations Since the apparent viscosity, time dependency and yield stress can be determined from a rheogram, measurements of shear stress and rate of shear over the desired range can be used to reveal the flow properties of a material. However, the selection of equipment to determine these measurements is dictated by the type and magni- tude of these properties. Viscometers of the falling ball, rotational, orifice and capillary tube types have been available, but have been either not suited for use with highly viscous, non-homogeneous, non-Newtonian fluids or have been too expensive for the limited applications. Thus, the choice has been restricted to one which uses higher pressures and larger tubes. This type is usually re- ferred to as extrusion rheometers. Fortunately they are easily constructed since they have not been readily available commercially. Poiseuille (31) derived the equation for laminar Newtonian flow in tubes using a simple force balance (Fig. 4). The force tending to move the cylindrical column is: (P + AP) (1W2) 7 The force tending to keep the cylindrical column from moving is: T(21TyL) + P(1Ty2) 8 For steady state flow these forces must be equal: P(Try2) + AP(1TyZ) = T(21TyL) + P(‘n'y2) 01‘ 19 Fig. 4. A model for the Hagen-Poiseuille equation for laminar flow in tubes. 2L Substituting -r from equation 1 into equation 9: dv _ APy n 217 2L Rearranging the terms: dv = -A—-P- ydy ZLn and integrating: _ AP L2. v — 2Ln ( 2 + C) The velocity is zero at y equal to R: 2 C- R_ ‘ 2 01‘ 2 2 AP R v=—— (Y—-—) 2n 2 2 or 10 ll 12 13 14 15 20 Velocity is maximum when y equals zero. Therefore: _ APR2 max. _ 4nL 16 V The volume flowing through a parabaloid per unit time of revolution is equal to the base area times half the maximum velocity: Q = l/2 Av 17 max. The cross sectional area is: 2 A 2 HR Substituting A in equation 17: 2 Q = l/2TrR v 18 max. Equating equations 16 and 18: ZQ _ APR2 19 ——2 _ TI'R 4nL Rearranging the terms: _ 11’APR4 20 n BQL Van Wazer (it a_l. (40) stated that this is the relationship which was first proposed by Hagen and later verified by Poiseuille. It is called the Hagen-Poiseuille law for laminar flow in tubes . In the derivation the following conditions were postulated: l) the flow was steady; 2) the fluid was incompressible; 3) there were no external forces; 21 4) there was no slippage at the wall; 5) isothermal conditions prevailed throughout; 6) there were no radial and tangential components of the velocity; 7) the axial velocity was a function of the distance from the axis alone; 8) viscosity did not change appreciably with the change in pressure along the tube; 9) the tube was sufficiently long that end effects were negligible. Poisson's ratio is the relative lateral contraction divided by the relative longitudinal strain under unidirectional stress. For incompressible materials Poisson's ratio is equal to 0. 5. Scott Blair (34) reported Poisson's ratio for butter to be approximately 0. 5. XI. Pressure losses A continuous loss of pressure results when a fluid flows in a tube. This pressure loss must be determined in order to design a system which involves fluid flow. Many investigators have experi- mentally established that for adiabatic flow the pressure loss due to friction is a function of the length and diameter of the tube and of the density and velocity of the fluid (17) . Thus, the equation is: h=f —- 21 2g Ulr‘ 2 v c 22 This relationship is known as the Darcy-Weisbach formula. In flow calculations, L, D and v are usually known, therefore, if the fric- tion factor (f) can be determined the pressure loss or loss of head can be calculated. The friction factor has been shown to be a function of the Reynolds number (Re). For laminar flow the friction factor is: 64 ___ _ 22 Re The Reynolds number is defined as: Re=9%CE 23 EXPERIMENTAL PROCEDURES 1. Butter Conventionally churned butter was obtained from three differ- ent manufacturers. Each manufacturer supplied a 60-pound sample from churnings of two different days . The bulk boxes of butter were stored at 340 F. until all were received. Each sample was cut into 2- to 3-pound blocks to facilitate tempering. The blocks were wrapped in regular parchment paper and divided into five groups. The groups were stored at 50, 55, 60, 65 and 700 F. for at least 48 hr. prior to conducting the test. The composition was determined by the Kohman method (24) . The iodine value was determined by the Hanus method (4) . The butter used for the study was considered representative of all conventionally churned winter butter having normal composition and processed under standard commercial conditions. The density (mass per unit volume) of the butter was deter- mined by collecting a sample extruded from the tubing in a weighed container. The sample and container were weighed on an analytical balance to 0. 0001 g. The volume of the containers was determined by allowing water to flow into each container from a burette. The average volume was 7. 3 ml. The procedure was checked for 23 24 accuracy by repeating the above for larger containers (180 ml.) . An average density was used in the calculations. The depth of penetration by a conical weight was determined on the samples of butter for different testing conditions as an indication of the relative hardness. The measurements were made with a "Precision" Universal Penetrometer equipped with a cone which weighed 102. 5 g. A 5-sec. release time was used. The cone's penetration was observed to 0.1 mm. Penetration and viscosity values were determined on samples of butter held undisturbed for 48 hr. at the different temperatures. The purpose was to provide maximum pressure limits necessary to overcome the resistance of butter to flow after having been stored for periods of time. II. Equipment verification An extrusion viscometer was constructed to determine the apparent viscosity of butter under flow conditions (Fig. 5) . The equipment consisted of four interchangeable stainless steel tubings of equal diameter (0. 313 in.) and lengths of 3. 5, 7. 0, 10. 5 and 14. 0 in. (Table 1) ._ A disc containing a hole in its center was made to fit the tubing. The disc was attached to a sample container by an 1.5-in. stainless steel female fitting. The container (Fig. 5) was made from a l. 5-in. diameter stainless steel tubing. Compressed nitrogen was used as a source of pressure. The pressure on the 25 10 U'II-pUONt—a Fig. 5. Extrusion viscometer equipment arrangement. Pressure source connector Pressure gauge Air cylinder Shutoff valve Pressure gauge OOCDQO‘ Pressure regulator Two -way valve Stainless steel tee Sample container Stainless steel tubing TAB LE 1--Tubing and disc specifications If!!! \‘il fl -e—-:£; 26 +>__ .. . Dimensions in inche s Dimensions in inches Tubing Disc No. a b c No a b c A 3.5 0.375 0.313 A 1.875 0.313 0.313 B 7.0 0.375 0.313 B 1.875 0.313 0.375 C 10.5 0.375 0.313 D 14.0 0.375 0.313 container was controlled by a Thomas Air Pressure Regulator (Model 911) . The pressure applied was measured by one of four Marshalltown gauges having maximum ranges of 15, 60, 100 and 150 1b. /sq. in. A two -way valve was inserted in the line between the pressure regulator and the sample container to allow for accu- rately adjusting the pressure prior to applying it to the sample. The sample container and tubing were positioned horizontally using a 27 level to eliminate gravitational effects (Figs. 6 and 7). The extrusion viscometer and the Hagen-Poiseuille equation results were checked for agreement with the Brookfield synchro- lectric viscometer (Model HBT) using molasses as the test fluid (Fig. 8). The molasses, a commercial product, was stored at 340 F. for 24 hr. prior to testing. The molasses was stirred with a spoon to simulate conditions similar to extrusion viscometer method. The Brookfield spindle attachments were tempered in the 340 F. The spindle was lowered into room for about 15 min. before use. the molasses from the cross-bar (see Table 2) for 30 sec. using TABLE 2--Brookfield Helipath stand spindle specifications l r d —-n-—e I J C - l -b L. _ a Dimensions in inches Spindle a b c d e T-A 4.5 0.5 1.894 0.0625 0.0290 T—B 4.5 0.5 1.435 0.0625 0.0290 T-C 4.5 0.5 1.065 0.0625 0.0290 T-D 4.5 0.5 0.804 0.0625 0.0290 T-E 4.5 0.5 0.604 0.0625 0.0290 T-F 4.5 0.5 0.430 0.0625 0.0290 28 Fig. 6. Extrusion viscometer. Fig. 7. Extrusion viscometer in operation. Fig. 8. Brookfield synchro-lectric viscometer, Helipath stand and spindles. Fig. 9. Brookfield viscometer positioned for viscosity measurements on butter. 30 the Helipath stand. The stand's lowering action was stopped and the dial reading recorded for the different spindles and spindle speeds. The dial reading was multiplied by a conversion factor correspond- ing to a particular rotational speed and spindle to obtain the viscos- ity in centipoises. The conversion factors were supplied on a calibration chart by the manufacturer. The pressure tube equipment was also tempered in the 340 F. controlled temperature room. The arrangement of the equipment was changed slightly for use with the molasses as shown in Fig. 10 by placing the sample container in the vertical position. The 1 applied pre 5 sure ll E 2 ,- _ 3 4 Fig. 10. Arrangement of the extrusion viscometer equipment for use with molasses. 1. Sample container 3. Stainless steel tubing 2. Stainless steel tee 4. Rubber stopper 31 equipment was leveled and the shortest tubing attached. A rubber stopper was inserted in the open end of the tubing to keep the molas- ses from flowing out. The effect of gravity was found to just over- come the internal resistance of the molasses in the sample container. The two were considered to compensate for each other. The samples were collected for 30-sec. time periods and weighed. III. Bulk velocity The bulk velocity is the rate a given quantity of butter will flow from the end of the tubing in 1 sec. In order to determine the apparent viscosity of butter for the desired rate of shear, the bulk velocity was calculated for butter flowing at 10 lb. /min. through tubing of various diameters . IV. Flow profiles The actual shape of the velocity profile was obtained for moving butter by filling a sample container with butter colored dark blue and a second sample container with butter of normal color. Each sample was alternately used to force the other through the different lengths of tubing at different temperatures. Extreme care was taken to pro- vide a flat surface perpendicular to the center line of the tubing at the entrance for each trial. The resulting cylindrical samples were tempered at a low temperature and cut in half to show the flow profiles . 32 V. Apparent viscosity of flowing butter The apparent viscosity of flowing butter was determined from the extrusion viscometer data using the Hagen-Poiseuille equation. The data were obtained from tests conducted in rooms with controlled temperatures. The extrusion viscometer and nitrogen supply were stored in the room at least 24 hr. prior to testing. The test was conducted by placing the butter in the sample container and attaching it to the pressure equipment. The tubing was connected to the other end. Pressure was applied directly to the surface of the butter. The pressure was changed by increments of l or 21b./sq. in. at 70° F. and increments of 51b./sq. in. at 65, 60 and 550 F. Data were gathered for each length of tubing at 55 to 730 F. All samples of butter were tested before changing to the next temperature . Prior to each set of tests using a particular tubing, the pres- sure loss for the sample container was determined by forcing the butter through a disc similar to the disc holding the tubing except that the diameter of the hole in its center was equal to the diameter of the inside of the tubing (Table 1). The pressure loss was deter- mined by slowly applying pressure to the system until the butter started to flow out of the hole in the disc. After several replicates, the gauge pressure noted just before the observed movement was recorded to the nearest lb. /sq. in. The sample container loss was 33 subtracted from the measured pressure loss obtained for each tubing length to obtain the pressure loss along the tubing. The extruded butter was collected in weighed containers for 15 sec. The rate of flow was allowed to become steady after the pres— sure was applied before the sample was taken except for the fastest flow rates. For these the sample had to be taken immediately upon applying the pressure. The extruded butter was cut at the exit of the tubing with a spatula and the stop watch started. At the end of 15 sec. the edge of the weighed container was used to cut the butter at the exit of the tubing. Three samples were taken for each pressure. The temperature of the butter was determined by inserting the ther- mometer into butter in the tubing after each test. Preliminary graphs of the results of apparent viscosity versus velocity revealed that the data approximated a linear relationship on log-log paper. A regression and correlation analysis were made on the data using the CDC 3600 computer. The data were grouped according to temperature, length of tube and sample of butter. The regression coefficients and the standard error of estimate were used in the equation: Y = a + bX i SE VI. Pressure losses The pressure loss versus the logarithm of velocity was found to be a linear relationship. A regression and correlation analysis 34 were performed on the data obtained from the extrusion viscometer. VII. Reduction in apparent viscosity under mild agitation The Brookfield viscometer was used to determine the decrease in apparent viscosity of butter under mild agitation. The measure- ments were conducted in the rooms with controlled temperature. A Brookfield spindle was revolved at a constant speed while positioned at a constant depth in the sample of butter (Fig. 9). The same spindle depth was obtained by lowering the spindle from its cross-bar into the butter using the Helipath stand. The lowering time was 30 sec. Brookfield readings were taken while the spindle revolved continuously. VIII. Reduction in apparent viscosity due to pumping A variable speed Waukasha rotor-type pump was used to evaluate the influence of the rate of pumping on the apparent viscosity of butter. The butter was forced manually into the pump on the first pass. The pump speeds used were 52 and 120 r.p.m. Measurements of penetration value, temperature and apparent viscosity (Brookfield and extrusion viscometer methods) were taken after each pass through the pump. IX. The minimum pressure to initiate flow in tubing, elbows and valve assemblies The same procedure was used to determine the minimum pres- sure to initiate flow in the different lengths of tubing at various 35 temperatures as was used to determine the pressure loss for the sample container (part IV). The minimum pressure was also ob- tained for elbows (l. 5 in. diameter) and for a direction change in three -way valve assemblies (1. 5 in. diameter). The length along the center line through the elbows and valve assemblies was 4. 5 in. and 5.3 in. respectively. The average minimum pressure obtained for the elbows and valve assemblies was compared to the minimum pressure obtained for different lengths of tubing. X. Power requirements The apparent viscosity and bulk velocity data from the extru- sion viscometer were used to calculate the Reynolds number and friction factor. Also from the results, an equation for calculating the apparent viscosity at various temperatures and bulk velocities was determined. The above relationships were used to calculate the loss of head and power requirements for various quantities of butter at 55, 60 and 650 F. flowing through tubing having diameters of l. 5 in. and 3.0 in. RESULTS 1. Butter The date of churning along with the cream treatment prior to churning is provided in Table 3 for each sample of butter. The average result of two replicates on each sample from the Kohman analysis and the Hanus test is presented in Table 4. The results of the density for each sample of butter collected as the butter flowed from the end of the tubing at the different temperatures are presented in Table 5. Each value represents an average of three determinations. The average density was 0. 952 g. /ml. The penetration and viscosity results presented in Table 6 were determined on samples of butter held for at least a week at the indicated temperatures prior to conducting the determinations . The apparent viscosities of the samples below 550 F- were beyond the maxi- mum range of the Brookfield viscometer. Fig. 11 shows the average penetration values for butter after flowing through the different lengths of tubing for the four temperatures. 36 37 TABLE 3--Cream treatment prior to churning . . Holding Pasteurization Date temperature Sample temperature , churned (de F ) overnight g. ° (deg. F.) A 1-14-64 165 (30 min.) 40 B 1-13-64 160 (30 min.) 45 C 1-14-64 160 (30 min.) 58 D 1- 9-64 160 (30 min.) 58 E 1-13-64 190 (30 sec.) 46 F 1-12-64 190 (30 sec.) 46 TABLE 4--Composition and iodine number of the butter Composuion Iodine Sample ber Fat Moisture Salt Curd num (percent) (percent) (percent) (percent) A 80.2 16.0 2.6 1.2 28.1 B 80.7 15.5 2.6 1.2 28.2 C 80.6 16.5 2.0 0.9 28.0 D 80.0 17.0 2.0 1.0 28.7 E 80.0 16.9 2.2 0.9 28.3 F 80.0 17.0 2.2 0.8 27.8 TABLE 5--Densities of butter at various temperatures 38 Temperature Average Density Average Sample (de F ) temperature ( /ml ) den31ty g. ' (deg. F.) g. ° (g../m1.) A 73.2 0.945 B 73.2 0.948 C 72.4 0.947 D 72.8 72'9 0.959 0‘948 E 73.4 0.946 F 72.6 0.944 A 65.3 0.953 B 66.0 0.953 C 65.6 0.962 D 64.7 65'3 0.953 0'953 E 65.0 0.953 F 66.2 0.953 A 62.8 0.967 B 63.6 0.922 C 61.0 0.928 D 60.7 “'9 0.955 0’945 E 60.8 0.941 F 62.5 ,0.955 A 57.2 0.976 B 56.8 0.955 C 56.0 0.956 D 57.0 56'7 0.950 0'9“ E 56.6 0.960 F 56.7 0.956 Average 0.952 39 TABLE 6--Penetration and viscosity of quiescent butter at various temperatures Temperature Penetration value Viscosity (a) Sample (deg. F.) (mm.) (cp.) A 72.4 20.7 268, 000 B 72.2 18.4 408, 000 C 72.2 19. 5 406, 000 D 72.5 19.9 367, 000 E 72.3 19.5 341,000 F 72.4 19.4 296, 000 Average 72.4 19. 6 349, 000 A 59.8 6.1 6,670,000 B 59.5 5.6 7, 180, 000 C 59.9 5.5 7, 060,000 D 60. 0 6.1 7, 050, 000 E 60.0 6.0 7, 180, 000 F 60.1 5. 9 5, 700, 000 Average 59. 9 5. 9 6, 820, 000 A 54.6 4. 9 B 54.2 4. 3 C 54. 0 4.4 Beyond range D 54. 0 4. 5 of viscometer E 53.8 4.7 F 53. 8 4. 7 Average 54.1 4.6 A 48.8 4. 0 B 47.4 3.2 C 47.6 3.4 Beyond range D 47.2 3.6 of viscometer E 47.2 3.6 F 47.1 3.6 Average 47.6 3. 6 (a) Brookfield viscometer with Helipath stand using spindle T-C at 10 r.p.m. for 72° F. and spindle T—F at 10 r.p.m. for 600 F. 40 26.0 24.0 22.0 E’ 20.0 E :53) 18.0 (0 > g 16.0 13 84 3 14.0 C. a) 0.. 12.0 10.0 8.0 1 1 55 Temperature (deg. F.) Fig. 11. Average penetration values on butter after flowing through the various lengths of tubing. 41 11. Equipment verification The results using the molasses to verify the proper application of the Hagen-Poiseuille equation with the constructed extrusion viscometer are presented in Tables 7, 8 and 9. In Tables 7 and 8 are shown the individual viscosity results from three trials using the extrusion viscometer and the Brookfield viscometer. Pressures and time used with the extrusion viscometer were selected to provide a reasonable size sample for weighing. Spindles and their speeds also were selected to provide adequate torque; however, at the tempera- ture selected the readings were made on the low range of the dial. Approximately 350 F. was selected because preliminary trials re- vealed that slight changes in temperature had a smaller influence on the viscosity of the molasses than at lower temperatures. Average viscosities obtained using the Brookfield and extrusion viscometer were 11, 900 cp. at 36. 50 F. and 12,000 cp. at 36.4OF. respectively. III. Bulk velocity Fig. 12 illustrates the normal bulk velocities when moving different amounts of butter per min. through the various diameters of stainless steel tubing. The tubing dimensions are presented in Table 10 along with the calculated velocity for moving butter at 10 lb. /min. The normal range of bulk velocities expected is between 0.01 ft. /sec. to lft./sec. 42 TABLE 7--Viscosity of molasses by the extrusion viscometer method #— —_ Tub- Pressure Temper- Viscos- Temper- Viscos- Temper- Viscos- in g ( lb ./ ature ity ature ity ature ity (No.) sq. in.) (deg. F.) (cp.) (deg. F.) (cp.) (deg. F.) (cp.) 2 2 36.0 14,800 36.0 14,200 36.4 12,800 3 36.0 13,200 36.0 11,900 36.4 10,200 4 36.1 12,600 36.0 11,900 36.4 11,500 5 36.1 13,100 36.0 12,800 36.4 12,500 3 3 36.0 12,000 .. .. .. .. 4 36.1 12,100 36.1 11,900 36.5 11,700 5 36.1 12,600 36.1 12,300 36.5 11,800 6 36.1 11,000 36.1 11,500 36.5 12,000 7 36.2 12,000 36.1 11,500 36.5 11,400 4 4 35.9 11,800 5 35.9 12,200 .. .. .. .. 6 36.0 11,300 36.0 12,300 36.3 12,500 7 36.0 11,000 36.0 11,800 36.3 12,200 8 36.1 10,800 36.0 11,600 36.3 12,300 9 36.0 11,700 36.3 12,000 5 6 36. 0 12, 250 7 36.0 11,650 .. .. .. .. 8 36.1 12,600 36.2 12,500 36.4 12,800 9 36.1 12,000 36.2 12,000 36.4 12,200 10 36.2 11,800 36.4 11,900 11 36.2 11,200 36.4 11,500 43 TABLE 8--Viscosity of molasses by the Brookfield method Spin- S d Temper— Viscos- Temper- Viscos- Temper- Viscos- dle pee ature ity ature ' ity ature ity (No.) (“Pm“) (deg. F.) (cp.) (deg. F.) (cp.) (deg. F.) (cp.) T-A 2.5 36.5 13,400 35.9 14, 100 34.4 16, 600 5.0 36.5 12,800 35.9 12, 500 34.4 16,000 10. 0 36. 5 12, 500 35. 9 12, 700 34.4 15, 500 20.0 36.5 12,300 35.9 11, 900 34.4 15,400 50.0 36.5 11, 900 35.9 12,400 34.4 14, 600 100.0 36.5 11, 700 35.9 12,400 34.4 14, 200 T-B 2.5 36.5 .. 35.9 .. 34.4 .. 5. 0 36. 5 10, 900 35. 9 12, 800 34. 4 14, 100 10.0 36.5 11,200 35.9 12, 800 34.4 14, 100 20.0 36.5 11, 000 35.9 12, 600 34.4 13, 900 50.0 36.5 10, 800 35.9 12, 300 34.4 13, 500 100. 0 36. 5 10, 500 35. 9 12, 500 34.4 13, 600 T-C 2.5 36.5 35.9 34.4 5.0 36.5 .. 35.9 .. 34.4 .. 10.0 36.5 12,800 35.9 13,600 34.4 15,200 20.0 36.5 12, 800 35.9 12,400 34.4 15,600 50.0 36.5 11,850 35.9 12, 300 34.4 15, 000 100.0 36.5 11, 800 35.9 12,200 34.4 15, 600 TABLE 9--Average viscosity of molasses by the Brookfield and extrusion vis comete r methods $W Temper- Viscosity Range Difference ature (deg. F.) (GP-1 (Cp.) (cp.) Brookfield 36. 5 11, 900 10, 500 to 13, 400 2, 900 35. 9 12, 600 11, 900_t0 14, 100 2, 200 34.4 15, 500 13, 500 to 16, 600 3, 100 Extrusion 36. 0 12, 100 10, 800 to 14, 800 4, 000 viscometer 36. 1 12, 100 11, 200 to 14, 200 3, 000 36.4 12, 000 10, 200 to 12, 800 2, 600 44 0.7 0.6 0.5 0' Q) \m 0.4 :5 > f: U .9 o 0.3 :> i :3 m 0.2 0.1 0.0 Mass flow rate (lb./min.) Fig. 12. Velocity of butter flowing through stainless steel tubing of various diameters. 45 TABLE 10--Dimensions used to determine the bulk velocity of butter flowing in stainless steel tubing of various diameters Inside Bulk Inside Bulk diameter velocity (a) diameter velocity (a) (in.) (ft./sec.) (in.) (ft./sec.) 0.402 3.1900 2.370 0. 0917 0.902 0.6330 2.870 0.0625 1.402 0.2610 3.870 0.0344 1.870 0.1470 4.870 0.0217 (a) Butter flowing at 10 lb. /min. with a density of 59.3 lb./ cu. ft. IV. Flow profiles Figs. 13 and 14 illustrate the flow profiles obtained using the colored butters under different combinations of temperature and length of tubing. The profiles shown were selected from 3 to 8 samples and are representative of all the samples within the group. The samples at 700 F. were soft, making them difficult to obtain without some damage as they flowed from the end of the tubing. Samples from the 14.0-in. tube were also difficult to obtain because the end of the tubing was beyond easy reach while controlling the extrusion viscometer. The depth of field used in taking the pictures and the angle at which the light was placed to illuminate the sample caused minor surface irregularities to be intensified. 46 550 F. Flow direction —-— Fig. 13. Flow profiles obtained from the 7. 0 in. length of tubing for the various temperatures. 3.5 in. 7.0 in. 10.5 in. 14. 0 in. Flow direction ——— Fig. 14. Flow profiles obtained at 650 F. for the various lengths of tubing. V. presented in Table 11. 0. 9738 to 0. 9975. Apparent viscosity of flowing butter 47 The results of the correlation and regression analysis are The correlation coefficients ranged from Figs. 15 through 21 are the graphs of the result- ing equations. The lines representing the regression equations have negative slopes ranging from -0.76375 to -0.92422. The decrease TABLE 11--Results of the correlation and regression analysis for the apparent viscosity versus velocity 1 T Tem- Regression Standard Corre- Degrees ube . . . length per- coeff1c1ents error of lation of (in.) ature estimate coeff1c1ent freedom (deg.F.) a b SE (a) DP 3.5 72.9 3.80550 -0.86124 0.03430 0.9975 88 3.5 66.4 4.29250 -0.81920 0.05509 0.9950 70 3.5 62.3 4.41815 -0.90617 0.08075 0.9902 82 3. 5 56.6 4.36642 -0.92422 0. 13072 0.9758 67 7.0 72.9 3.65436 -0.86170 0.04359 0.9915 88 7.0 66.4 4.21283 -0.76375 0.06441 0.9839 85 7.0 62.4 4.26132 -0.86374 0.07955 0. 9758 88 7.0 57.2 4.26912 -0.88070 0.09431 0.9738 82 10.5 72.6 3.65645 -0.83444 0.02735 0.9973 88 10.5 66.4 4.06036 -0.81467 0.06442 0.9840 85 10.5 62.2 4.18515 ~0.876l8 0.03112 0.9958 85 14.0 72.9 3.61148 -0.82927 0.03502 0.9934 88 14.0 66.4 4.02311 -0.82536 0.03578 0.9942 88 14.0 62.1 4.12343 -0.89901 0.03695 0.9941 85 (a) DF corrected 48 in apparent viscosity with an increase in bulk velocity may be illus - trated by comparing the results from the 14. 0-in. length of tubing at 600 F. for various velocities. The apparent viscosity was 6, 510, 000 cp. at 0,001 ft. /sec. while at 0.01 ft. /sec. it had de- creased to 866, 000 cp. For 0.1 ft. /sec. the apparent viscosity is only 115, 000 cp. The effect of the length of tubing on the apparent viscosity for butter flowing at different temperatures is shown in Figs. 15 through 17. As the distance the butter flows increases, the decrease in ap- parent viscosity becomes less. At a constant velocity of 0.1ft./sec. and at 600 F. the apparent viscosity is 211, 000 cp. for a distance of 3. 5 in. For a distance of 7. 0 in. the apparent viscosity is 133, 000 cp. which is a decrease of 78, 000 cp. as the distance increased 3. 5 in. Less decrease (18, 000 cp.) is found between the 7.0-and10.5- in. lengths of tubing and only 10, 000 cp. between the 10. 5- and 14. 0- in. lengths of tubing. The graphs in Figs. 18 through 20 are of the same regression equations but grouped according to the length of tubing to show the influence of temperature on the apparent viscosity of flowing butter. The apparent viscosities at 550 F. for lengths of tubes 10. 5 in. and 14. 0 in. could not be obtained because the pressure required exceeded the capacity of the extrusion viscometer. Fig. 20 illustrates the location of the standard error of estimate for the regression lines obtained from the data using the 10. 5-in. tube. 49 7 10 " a 3.5 in. Y = 3.80550 - 0.86124X i 0.03430 b 7.0 in. Y = 3.65436 - 0.86170X :1: 0.04359 c 10.5 in. Y = 3.65645 - 0.83444X :1; 0.02735 - d 14.0 in. Y = 3.61148 - 0.82927Xi 0.03502 01 _ U 3‘ .g 6 E3 10 _ a; : E .. H L...» m a _. {L <1 ._ d c b a 105 I I I LIIIJI \T\ [\1 Lilli 10"3 10’2 10'1 Velocity (ft. /sec.) Fig. 15. Effect of tubing length on the apparent viscosity of flowing butter at 70° F. 50 10'3 10‘2 107 r. r a 3.5 in. Y = 4.29250 - 0.81920X 3: 0.05509 ; b 7.0 in. Y = 4.21283 - 0.76375X :1: 0.06441 l‘ c 10.5 in. Y = 4.06036 - 0.81467X :1: 0.06442 d 14.0 in. Y = 4.02311- 0.82536X 3: 0.03578 d. ._ U 3‘ '5’ 0 10°... .3 - > .— E’ ~— Q) L— H (‘0 .— CL 0.. < 1" dc b a‘ 105 I J J inl llllli ! I I VT§1\?)'I 10 Velocity (ft. /sec.) Fig. 16. Effect of tubing length on the apparent viscosity of flowing butter at 65° F. i 51 107 ._ a 3.5 in. Y=4.41815-0.90617X.+.0.08075 - b 7.0 in. Y=4.26132-0.86374X;t0.07955 c 10.5111. Y=4.18515-0.87618X;t0.03112 - d Y = 4.12343 — 0.89901xa: 0.03695 )— L d. _ U >~ .1: U) 8 106.. .2 — > _ .5 L g h g )— 4 )- dcb a \ 105 I llllllLl I IJlllLl 10'3 10'2 10 Velocity (ft. /sec.) Fig. 17. Effect of tubing length on the apparent viscosity of flowing butter at 600 F. -l 52 107 E a 72.90 F. Y = 3.65436 — 0.86170X 3: 0.04359 -- b 66.40151 Y = 4.21283 - 0.76375X i 0.06441 *- c 62.40 F. Y = 4.26132 — 0.86374X :1; 0.07955 d 57.20 F. Y - 4.26912 0.88070X :1: 0.09431 Apparent viscosity (cp.) cd\ 105 1 I I I 1111) I I I; I I I 10'3 10'2 10 Velocity (ft. /sec.) Fig. 18. Effect of temperature on the apparent viscosity of flowing butter (7. O-in. tubing length) . -l 53 107 C a 62.6°F. Y = 3.65645 -0.83444X 4. 0.02735 b 66.4°F. Y = 4.06036 -0.81467X_+_ 0.06442 _ c 62.2°F. Y=4.18515-0.87618X:l;0.03112 Q: )— 0 >4 3: 8 6 o 10 .— 52 P > _. H — c: Q) — 3.. r0 _. 04 9.. <1 7‘ )- a b c\ 5 l 111L111] \l I [hill 10 3 2 T - 10' - 10 . 10 Velocity (ft. /sec .) Fig. 19. Effect of temperature on the apparent viscosity of flowing butter (10. 5-in. tubing length) . 54 107 ._ a 72.60 F Y = 3.65645 - 0.83444X :1: 0.02735 —\ b 66 40 F Y = 4.06036 - 0.81467X i 0.06442 \\ c 62.2°F Y=4.18515 -O.87618Xi0.03112 Apparent viscosity (cp.) Velocity (ft. /sec.) Fig. 20. Effect of temperature. on the apparent viscosity of flowing butter with the dotted lines estimate ( 10. 5-in. tubing length) . showing the standard error of 55 The apparent viscosity versus temperature is shown in Fig. 21 for a constant rate of shear of 0.01 ft. /sec. The slope of the lines is -0. 0587. Thus, apparent viscosity decreases rapidly as the temper- ature increases. The apparent viscosity using the 10. 5-in. length of tubing at 55° F. is 2, 250, 000 cp. It decreases to 1, 150,000 cp. at 60° F. and 590, 000 cp. at 65° F. The results from the regression and correlation analysis are presented in Table 12 on viscosity versus velocity for different samples of butter. The correlation coefficients varied from 0. 9935 to 0. 9996. The lines representing the regression equations are illustrated in Figs. 22 through 25. VI. Pressure losses The results of the correlation and regression analysis on the pressure loss versus velocity for different lengths of tubing and temperatures are presented in Table 13. The number of replicates ranged between 69 and 90 for a given length of tubing and tempera- ture. The correlation coefficients ranged between 0. 3506 to 0.9377. The low correlation coefficients were from data obtained using the shorter tubing (3. 5 and 7. 0 in.) and lower temperatures (55 and 600 F. ) . Figs. 26 through 28 show the lines representing the re- gression equations and illustrate the effect of length of tubing on the pressure loss at various flow velocities. The pressure losses in- creased as the velocity increased. For the 10. 5—in. length of tubing 56 Apparent viscosity (cp.) 5 l J l l 50 55 60 65 70 75 10 Temperature (deg. F .) Fig. 21. The effect of temperature on the apparent viscosity of butter flowing at 0. 01 ft. /sec. for different lengths of tubing. 57 TABLE 12--Results of the correlation and regression analysis on the apparent viscosity versus velocity for each sample of butter i—l— But- Tem- Regression Standard Corre- Degrees sta5r1n- per- coefficients error of lation of ple ature estimate coefficient freedom (deg. F.) a b SE (a) DF A 72.8 3.64644 -0.87916 0.02246 0.9984 13 B 72.3 3.64242 -0.90014 0.01565 0.9994 13 C 73.3 3.66592 -0.86824 0.01424 0.9991 13 D 72.6 3.70306 -0.80760 0.02720 0.9941 13 E 73.3 3.68582 -0.81527 0.02240 0.9965 13 F 72.8 3.87016 -0.72975 0.01844 0.9940 13 A 65.4 4.24026 -0.81619 0.02797 0.9971 13 B 66.6 4.31262 -0.69145 0.02439 0.9960 13 C 67.5 4.16397 -0.73334 0.01275 0.9991 10 D 65.2 4.15825 -0.77612 0.02629 0.9980 13 E 66.4 4.19921 -0.77474 0.01519 0.9994 13 F 66.0 4.22243 -0.76918 0.01937 0.9983 13 A 62.6 4.41034 -0.75315 0.01978 0. 9978 13 B 63.7 4.19529 -0.83903 0.02116 0.9989 ' 13 C 61.7 4.32366 -0.82802 0.02648 0.9965 13 D 61.0 4.38332 -0.85989 0.02146 0.9980 13 E 60.8 4.38396 -0.82075 0.02823 0.9935 13 F 62.4 4.28860 -0.79697 0.01632 0. 9985 13 A 56.9 4.43540 -0.85385 0.01507 0.9990 13 B 57.2 4.39406 -0.83464 0.00866 0.9996 13 C 56.6 4.41049 -0.85211 0.01604 0.9985 13 D 57.3 4.20067 -0.86472 0.01967 0. 9988 10 E 56.9 4.27915 -0.83498 0.01826 0.9990 13 F 57.1 4.17151 -0.86760 0.02148 0.9991 10 (a) DF corrected 58 107 )— L.— )— d. U ._ >~ ti '0') 8 6 .3 10 r > _ p _ C.‘ I— <0 :3 I— 9 - \\ A < T \._ C _ B F — D E 5 I IIJIIIII 1 IIIIII 10 3 . 2 . 10 10 | 10 Velocity (ft. /sec.) Fig. 22. Effect of sample on the apparent viscosity of flowing butter at 70° F. 59 107 _ )— d. U — >~ .t.’ 8 § 10°— > _ *2 I A g _ F 0.. _ E Q. . <1 _ _ D B C 5 10 111111111 I llllL 10'3 10'2 10' Velocity (ft. /sec.) Fig. 23. Effect of sample on the apparent viscosity of flowing butter at 650 F. 60 107 d. :1 ~ D >~ E .123 5 C :> r' “ P'- C‘. _ 33 _ A g __ F B < _ p P 5 lllJllJll I lllllld 10 3 2 l 10' 10 10’ Velocity (ft. /sec.) Fig. 24. Effect of sample on the apparent viscosity of flowing butter at 600 F. 61 107 I- 8“ e A : c 4.1 a 10°— '5‘ L:- E \ *5 — D 23 .. F (0 0" — Q: 4: _ 1053 I llllllllz l I Illlll 10 10 10 Velocity (ft. /sec.) Fig. 25. Effect of sample on the apparent viscosity of flowing butter at 55° F. 62 TABLE 13--Results of the correlation and regression analysis on pressure loss versus velocity -: Tub- Tem- Standard Corre- De- mg per- Regression error of lation grees length ature . . estimate coef- of coeff1c1ents , , f1c1ent free- dom (in.) (deg. F.) a b SE (a) DF 3.5 72.9 11.64056 2.39662 0.58321 0.9180 88 3.5 66.4 33.94985 8.10970 2.38179 0.9156 70 3.5 62.3 50.36779 7.80264 6.81659 0.5821 82 3.5 56.6 47.39012 6.54752 10.49731 0.3506 67 7.0 72.9 16.43128 3.42433 1.04984 0.7820 88 7.0 66.4 52.36254 14.95041 4.51138 0.8381 85 7.0 62.4 67.56852 13.87937 8.35944 0.5589 88 7. 0 57.2 67.61422 11.63275 9.80365 0.4703 82 10.5 72.6 24.59113 5.95443 0.98820 0.9377 88 10.5 66.4 58.66845 14.32616 5.15964 0.7707 85 10.5 62.2 86.09827 16.95727 4.00025 0.8517 85 14.0 72.9 29.07278 7.05309 1.20345 0.9061 88 14.0 66.4 72.76564 17.11135 2.99934 0.9156 88 14. 0 62.1 102. 00550 17.48606 6.17015 0. 7276 85 (a) DF corrected 63 Rm Gov um. maggofi Meagan. MOM mmoH madmmonm 05. do Aumaofi mawndu mo 33mm .om .mfm A.oom\ .3 .3833, 11.0 d s S n 1 J 3. e m... S S I m ./ I on...» m. L o @334 n. xeommog + @835... u w .8 0.3 e omwwed 0 x339... + 223:3 u w .8 mg: 0 In on $35.2 «xmmemwn +£23.62 u w .8 es s Smmmdnxmeeemn+339: In. Ema e I oofi 64 .h 0mm um wag/03 umfldn. notH mmoH oudmmoum 6:“ no fipwcofi mafia—Du mo “0.0me .NN .wfim A.oom\ J: >fioo~o> 02 73 ~72 _.+- 4. q _ — q _ _ _ _ _ _ 1111M \Q. 1.. U \ 1 \MV 1 wmm®®.NHXmmHH~.>~ +vomon.mh u? #3on p ..I wommfi .m H NofionJl + mvwoonm u Mr .Gw m .od 0 wmzm JV H NawomaJl + wmmom.mm n .w .Gfl 0.5 0. whawm.m H Noumea: .w + mwmwoém u M. .5 m .m .m In ON ow op ow OOH ('ut °bs/°q1) ssoI sxnssexd 65 .h ooo Hm mate/03 umpudn. .HoH mmoH ondmmonm 9.3 do newsofi mafia» mo 36am .wN .mfm A.oom\ J: >fioo~o> oS 72 ~73 ________ :__e_4n 1 e m8: .D D” 695030.: + ommooJoH n V .5. o .E n mmoooé H Xnmnmmnfi + wmwmoéw u w .5 mg: 0 II on wvommd H X30564 + mmmomfio n .w .5. 0;. D. $wa H XvomowK + mpwomdm n .w .3 mlm m 3. \d L I 3 TD I ow \U \D OOH ('ut 'bs/ 'qI) ssoI exnssexd 66 at 650 F. the increase was from 22. 5 to 37.4 lb. /sq. in. as the velocity increased from 0. 01 to 0.1 ft. /sec. The pressure increased as the length of tubing increased. The increase was from 42.6 to 84. 5 lb. /sq. in. for lengths of tubing of 3. 5 to 14. 0 in. at a bulk velocity of 0.1 ft. /sec. and 600 F. Figs. 29 through 32 reveal the effect of the temperature on the pressure loss for butter flowing through different lengths of tubing. The pressure increased from 28. 5 to 79.2 lb. /sq. in. as the tem- perature decreased from 72. 6 to 62.20 F. at a bulk velocity of 0.1 ft. /sec. The standard error of estimate is shown in Fig. 33 for tubing length of 10. 5 in. and 72. 6, 66.4 and 62.20 F. The results of the correlation and regression analysis on the pressure loss versus velocity for each sample of butter are pre- sented in Table 14. ’The correlation coefficients ranged from 0. 8659 to 0. 9940 which indicated good correlation between data from the same sample. However, greater variations occurred among the samples as shown in Fig. 34. VII. Reduction in apparent viscosity under mild agitation The reduction in the apparent viscosity of butter under constant agitation is illustrated in Fig. 35 for four different temperatures. Each point represents the average of 18 trials. The same data are illustrated in Fig. 36 as a log-log relationship. 67 . 73mg: mafia; .cflnm .mv H6356. mafia/0G new mmoH mpsmmonm 9.3 Go ondumnomEou mo 80me .mm .mfim A.omm\ J: >fioo~o> 002 2-02 ~-o2 .4. _ a z n _ I 1 n _ _ o i ,llldll I em r113 1111 l as 116 1110 1 I oo SETS n xmmeem .e + 288:. u w .m 66.6... e I on $65.6 n 6333;. + sandman n w .m swims e eSwm.~ 0 833 .w + 328.2 n .4. .m seen a 5.235 nxmeedmd+emo$i u» Hm odds e 1 oS ('ut 'bS/ 'qI) ssoI 3.111398ch 68 . Axumcofi mafia:— .S.Io .nv noun—Do. wag/0G pom mmoH opdmmoua 9.3 do oudumuomgou mo “.03me .om .mfm A.omm\ J: Vfloofio> OS 72 ML: _ _ _ _ e 4 _ _ _ _ _ _ _ T d o ,IIIIINIIII 1 ON d 1 IL 9 S S n I 1 O¢ 9 0.1 S S \D I U .a. U 0 \© Hm. 38980823.:+-Ee§eu> .m 68$. 6 I on Tvomm.w H thmthQ + wacm§b n V .nH o¢.mo o wmfifimJu H NawomoJL + me©M.Nm n V .M Ovéwo Q wwwvoé H NMM$N¢.M + mNHmwg: n V .rm O©.N~. m. 1 OOH 69 . AgquoH mafia?» .GwIm .0: umfidfl mag/OS H3 mmoH mndmmonm 93 do DHSHMHDQEDD mo Doommm .Hm .wfim A.oom\ J: Vfioo~o> oS - 72 ~72 _ _ :2 q H _ _ e _ o I o~ 1116 d I 1 9 S S n I I 3. e o... S S m... I oo b m. L on U \ 308.4 s x8393 + Redeem u w o~.~e 6 $82 .m n. 6338.: + mended... u H 64.66 D In o~wmednxm$men +m2emé~uw 66.3 d 02 70 . . Afiumcofi mad?» G670 .EV .1638. mEBOG .HoH mmoH oudmmoum may do ouSDMHDQEoD mo «comm .Nm .mfim Ado: .6: Vfiooao> 63 H.3 , ~72 6412.4. _ se______ _ 6 6:6: .6 336666.21. 6686.2: n w .m on .66 e smeeednxmflzfi1.66666» "w .m 06.66 6 I 633.2 «Neommos +3.29%. I» .m oe.~.e e [8 d I... n I S S n m I3. I O S S m W I66 ..o m. on 00H 71 . «£923 means» . 57m .0: 6665366 mo 60.26 0.“ mmofi 6usmm6um 6:6 no 6a «.663 .6: .3833, HIGH 6666:6066 65 m5 .5 6666QE66 mo ”.66: \5 0:6 662: 66.306 W .mm .mE ON OOH ('Ut 'bS/ 'qI) ssoI exnsssxd 72 TABLE 14--Results of the correlation and regression analysis on the pressure loss versus velocity for each sample of butter But- Tem- Standard Corre- De- ter per- Regression error of lation grees sam- ature coefficients estimate coef- of ple ficient free - (a) dom (deg. F.) a b SE DF A 72.8 16.18960 2.98352 0.60246 0.9114 13 B 72.3 16.66171 2.77435 0.36820 0.9678 13 C 73.3 17.20780 3. 59710 0.41260 0. 9595 13 D 72.6 16.80197 4.24693 0.68045 0.8854 13 E 73.3 16.49905 4.11626 0.57410 0.9199 13 F 72.8 20.66515 6.05787 0.47424 0.9461 13 A 65.4 60.40789 15.31006 2.70486 0.9292 13 B 66.6 56.76020 18.42651 1.14395 0. 9877 13 C 67.5 44.63889 13.96980 0.63935 0.9940 10 D 65.2 47.43741 13.32182 1.80313 0.9692 13 E 66.4 49.62400 13.23481 1. 33405 0. 9832 13 F 66.0 55.19688 16.25084 1.78659 0.9698 13 A 62.6 86.29430 27.51587 3.13139 0.9604 13 B 63.7 56.80435 13.35821 1.69587 0. 9728 13 C 61.7 74.93718 17.99875 2.57551 0.9360 13 D 61.0 86.51364 17.84711 2.30650 0.9490 13 E 60.8 84.52483 21.31428 3.66153 0.8659 13 F 62.4 67.55212 19.33516 0.96292 0.9913 13 A 56.9 92.72694 18.39757 1.73396 0.9715 13 B 57.2 83. 99577 18.67517 1.20483 0. 9864 13 C 56.6 93.49690 20.50733 2.02376 0.9610 13 D 57.3 58.42069 12.23036 1.56728 0.9633 10 E 56.9 65.66187 14.83491 1.87766 0.9665 13 F 57.1 52.23334 9.77518 1.28330 0. 9755 10 (a) DF corrected OOH Rm Omo 6.6 H6356. mama/0G Ho 6699 6ufimm6nm 636 Go 39:66 00 666mm .0m .mfim A.666\ .6: VfiooH6> HIGH ~-62 H _ 73 “HI 0 'UI‘UID _\\ \\\ _ __.d n H..— Nmmood H N3mmm5~ + NH Nmm .wo mm~00.m H Nwmwflm4m + mwwmszw omoomd H 032.00.: + womaméw Hmmhm .N H th000 J: + wfinmméé. wmmooé H 03 Nwmmémfi + mmwowém 02 2 .m H Nwwmfim .NN + 030N460 VVVVVV NFQU'UUKH 0 0N. .06. 00 00 00H ('11; ’bS/ 'qI) ssoI exnssexd A.nmU 0 I. . OHV VumeUmTV “£006.ansz cp.) 6 Apparent viscosity (10 74 7 O 50.00 F. (T-F spindle at 10 r.p.m.) A 54.10 F. (T-F spindle at 10 r.p.m.) 6 “ D 59.10 F. (T-E spindle at 10 r.p.m.) 0 71.7° F. (T-C spindle at 10 r.p.m.) 5 I- 4 — 3 I— ). 2 — L 1 II— 0 000 O 0 O G ‘ 0 I I I I 1 I 1 I I I 1 2 3 4 5 6 7 8 9 10 Time (min.) Fig. 35. The reduction in apparent viscosity with time the butter is mildly agitated at various temperatures . 75 66236260222622 62.523265. 6.6 n6uwfim6 3028 m2 263.902 62%. 682.6 232.3 Vimoomfir 622626236 222 2203622062 62? mo Godumuc6m6um6u 2662.2: 6&8 .0m .mfm TESS 6829 0H m o w N H wd 0.0 v.0 N.0 To 22____+_ 2 2.12.22._.4. 2 01) 4119033111 iuereddv 9 00 ('do 0 .—q 0N V11] rat 3N E m 76 VIII. Reduction in apparent viscosity due to pumping The effect of moving the butter through a pump at two different rates is presented in Table 15 for five passes through the pump. The average of three determinations on the apparent viscosity versus the number of passes through the pump at each rate is illustrated in Fig. 37. The apparent viscosity results from the extrusion viscometer are presented in Table 16 showing the decrease in apparent viscosity with each pass through the pump. Only three passes through the pump could be used because the temperature of the butter became too high to effectively utilize the extrusion viscometer equipment. IX. Minimum pressure necessary to initiate flow in tubing, elbows and valve assemblies The minimum pressure necessary just to overcome the inertia of butter in tubing is illustrated in Fig. 38 for different temperatures and lengths of tubing. The lines represent the regression equations determined from the data. Fig. 39 shows the increase in pressure necessary to initiate flow at different temperatures for various lengths of tubing. The figure was constructed by using the regression equation for the 10. 5- in. length of tubing (see Fig. 38). The results of 30 trials at each temperature on the minimum pressure determinations for elbows and valve assemblies are presented in Table 17. 77 TABLE 15--The influence of pumping on the apparent viscosity of butter Pump Passes Temper- Pene- Trial through Viscosity tration speed (No .) pump ature (cp .) value (r.p.m.) (No.) (deg. F.) (mm.) 52 1 1 66.4 661,000 21.1 2 66.6 392,000 22.7 3 67.0 329,000 25.0 4 67.6 275,000 25.4 5 68.2 242,000 26.7 52 2 1 67.0 470,000 21.8 2 67.8 344,000 25.2 3 68.1 267,000 25.9 4 68.8 226,000 27.4 5 69.1 182,000 28.2 52 3 1 64.7 698,000 19.9 2 68.0 347,000 23.5 3 68.4 262,000 25.7 4 68.8 214,000 26.8 5 68.9 192,000 27.9 120 1 1 65.7 708,000 19.8 2 67.3 411,000 23.9 3 67.9 304,000 25.0 4 68.3 256,000 26.7 5 68.6 202,000 27.8 120 2 1 65.2 458,000 20.1 2 67.2 341,000 21.9 3 68.1 277,000 26.4 4 68.8 194,000 27.4 5 69.4 181,000 28.1 120 3 1 65.5 870,000 20.8 2 67.5 379,000 24.2 3 68.4 264,000 25.3 4 68.9 227,000 26.6 5 69.4 189,000 27.8 cp.) 5 Apparent viscosity (10 10 78 .L. l l l l 0 1 2 3 4 Passes through pump . 37. Effect of pumping rate on the apparent viscosity. 79 TABLE 16--The influence of pumping on the apparent viscosity of butter using the extrusion viscometer =—..— Passes ‘ . . Pene- Pump Trial through Temper- Viscosuy tration speed (No ) pump ature (a) value (r.p.m.) (No.) (deg. F.) (cp.) (mm.) 52 1 l 68. 5 152, 000 22.2 2 70.0 45, 300 25.8 3 72.6 17, 800 33.2 52 2 1 68.1 134, 000 21.8 2 70.3 31,000 25.5 3 72.4 11, 700 35.1 52 3 1 69.7 76, 300 23.5 2 71.0 27,000 27.2 3 72.9 11, 600 36.8 120 l 1 70. 0 95, 000 23.4 2 71.8 33,200 27.2 3 72.3 12, 500 33.5 120 2 l 69. 5 116, 000 22.1 2 71.0 38,000 27.1 3 72. 5 13, 500 34.4 120 3 1 70.0 74, 100 26.0 2 72.4 20, 400 29.1 3 73.0 11, 600 34.8 (a) Viscosities determined at constant pressure and variable rate of shear. 80 50%- a o 3.5m. Y= 58.30-0.75X:t3.06 b a 7.01:... Y: 75.12-0.94X:t3.49 _ c A10.5'm. Y= 86.54-1.07X:t3.99 d®<> 14.0in. Y=109.82 -1.34Xi6.27 Minimum pressure (1b. /sq. ft.) O J l - 1 l 50 55 60 , 65 70 75 - Temperature (deg. F.) Fig. 38. The effect and regression lines for the minimum pressure needed to initiate the flow of butter in various lengths of tubing at different temperatures . 50 4o .5 ci‘ L” 53° 30 (D H :3 U) U) G) H 8* 20 8 :3 .5 .E 2 10 0 Fig. 39. 81 I l 5 10 50° F. 55 I 15 Length (in. ) 60 20 The minimum pressure needed to initiate flow through tubing at various temperatures . 65° 70 75 25 82 TABLE l7--Average minimum pressure losses for elbows and valve assemblies of 1. 5-in. diameter Tempe r - Minimum Diffe r - ature pressure Range ence (deg. F.) (lb./sq. in.) (1b'/Sq° m') (lbfl sq. 1n.) Elbows 72.0 1.95 1.50 to 2.25 0.75 65.1 2.99 2.50 to 4.00 1.50 57.0 5.11 4.50 to 5.75 1.25 Valve 71.3 1.94 1.50 to 2.25 0.75 assemblies 65.5 5.55 4.25 to 6.00 1.75 56.8 9.43 8.75 to 10.25 1.50 X. Power requirements A plot of the calculated friction factor versus the calculated Reynolds number is illustrated in Fig. 40. Since the data were determined for laminar flow, a logarithm scale was used for the friction factor to show a wider range of values. The general relationship for the apparent viscosity versus the bulk velocity and temperature for flowing butter is: log n = 7.93446 - 0.84649 log v - 0.0587T 24 which is considered valid for temperatures between 55 and 750 F. The following is an example of the calculations for determin- ing the power requirements. A printer operating at 50 lb. /min. is supplied with butter at 550 F. through a 2. O-in. stainless steel tubing (Fig. 41) . 83 L 105_ y... ._ 8 U #— JR 5: +—— .2 S 104: 103 l llllllll 11111111: lJL 10'4 10‘3 10'2 Reynolds numbe r Fig. 40. Friction factor versus Reynolds number for butter flowing through stainless steel tubing. 84 FTP—:4 ft . —AD Printer 6 ft. Butter 5 pump 4 ft . Fig. 41. Arrangement of stainless steel tubing for the calcu- lations of the power required to pump butter at 50 1b. /min. hopper Given: W = 50 lb. /min. T = 550 F. p = 59.31b./cu. ft. D = 1.87 in. L = 15. 5 ft. (includes 1. 5 ft. for the four elbows) Bulk velocity: -2 (50) (1.87)2 V:5.16x10 =0.738 ft./sec. Apparent viscosity: log n = 7.93446 - 0.84649 log v - 0.0587T log n = 7.93446 + 0.11169 - 3.17900 77 = 73, 700 cp. Reynolds number: ( 1. 87) ( 0. 738) ( 59. 3) Re: 4 (12)(6.72)c10- )(7.37){10 ) = 0.138 Friction factor: 64 f‘ 0.138 ‘ 465 85 Loss of head: .—. (465)(15. 5)(12)(0.738)2 h = . (l.87)(64.4) 39195 Horsepower: Hp = (50)(391+ 6) = 9.4 hp. (includes 80% motor (0.8)(0.8)(3.3 x 10 ) efficiency and 80% pump efficiency) The loss of head and power requirements is presented in Tables 18 and 19 for butter flowing under various conditions. The calculated power requirements revealed that a 50 F. decrease in temperature about doubles the horsepower required (0.18, 0. 35 and 0.69 hp. at 65, 60 and 550 F.) to move the butter. Increasing the diameter from 1. 5 to 3. 0 in. reduced the power required from 1. 81 to 0. 35 hp. for moving butter at 60° F. through 20 ft. of tubing at 10 1b. /min. This reduction is even greater as the quantity of butter increases. 86 .22 .222 .022 mg; ".2835. m0 >fimfi®Q Adv oo .2 mm ooo .: moo oooH .o oow .mm omo .N on ooH oo.~m~ oow .o omH .N womoo oom .3. gm; om om mo .m who .2 omo .m mofio .o ooo fin: memo om o2 mm .m 3 N. omo .m Noao .o ooo .53 mom .o om o2 3.2 mmm oma .m $20.0 ooo .$2 mend o2 2: mm ~32 oo .oNN omo .m mom owom .o ooo .2 oNo .N om oog ooo: oNo .m ooo J owmoo oom.m~ onJ om om No .m «on omo .N mfimo .o ooo .mw memo om o2 Hm; Nwm omo .N mdmoo oowfiw memo om o2 Zoo Hm; omo.~ mdmoo oow.mw Nomo o2 oH oo Nov; oo .wmfi ooo .N oma omovo oow .o omo .m om ooH cm .82. 2.3 .2 Sm om: .o ooo .2 SM .2 om o... E .o om mayo .2 mHoo .o ooH :3. memo om o~ ooo S mwo J 2006 ooo :3. moNo oN o2 mo.o o~ mwo .2 good ooH :3. mono 3 2 mo mow; 2.5: 2...: .82. 3 2.2.2 40%.: . 2...? 2.2 .322 E22 wok/om vmog mo m @8322 awfimoomtr i A a: \ n: mused “mum Gofioflnh mpfiogom -039? 3&qu Adv numm namwp nomuom mmod “220.2254 225m 2223...? -892. @2222 mgumdma mdowumcw mo wad?» Awsouau mag/0G monsoonmoncnmu “220.83% pm. .5350. 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DISCUSSION Small variations in the density of the butter flowing from the end of the tubing were expected since variations in composition occur normally. The average density at the different temperatures in- creased from 0.948 g. /ml. at 72.90 F. to 0.961 g. /ml, at 56.70 F. which is normal for materials decreasing in temperature. However, at about 620 F. the average density was slightly out of order with densities at other temperatures. Densities at about 620 F. showed the greatest variation among samples (0. 922 to 0. 967 g. /ml. ) . The possibility of more air being trapped in the containers may be a cause. The range of densities given by McDowall (23) for butterfat was 0, 91 to 0.95 g. /ml. at 94° F. When the non-fat: portion of the butter is considered, the average density of 0. 952 g. /ml. is reason- able. Since variations are unavoidable in commercial butter the average density was used in the calculations. The average minimum penetration values were found to be 3. 6, 4.6, 5. 9 and 19. 6 mm. at corresponding temperatures of 47.6, 54.1, 59. 9 and 72.40 F. respectively. After the butter had flowed through the various lengths of tubing considerable softening had occurred as indicated by the increased penetrations values (Fig. 11) . However, no significant differences in the penetrations values were found for 88 89 butter after it had flowed through the various lengths of tubing. The lack of differences may be a result of the method of collecting the samples of butter from the end of the tubing which masked any other effects. But it could also suggest that the softening occurred before the butter entered the tubing or during the first 3. 5 in. This soften- ing may occur very rapidly followed by little or no softening. An- other possibility could be that mo st of the softening occurs within a small distance from the wall and the bulk. of the sample remains at about the same hardness for the different distances moved. The results from measuring the viscosity of molasses revealed that similar values can be obtained from the Brookfield and extrusion Viscometers on a time -independent fluid. The temperature of the molasses increased about two degrees when poured into the sample container in the extrusion viscometer method but was the same for all trials (about 36.00 F. ) . The temperature of the molasses was constant during each trial by the Brookfield method but varied from 34.4 to 36. 5° F. among trials. When the influence of temperature is considered, the average viscosities obtained from each method seemed to be about the same. The flow profiles (Figs. 13 and 14) revealed a variation in velocity does occur in the butter across the diameter of the tubing. The velocity gradient is small in the butter except near the wall. Here the velocity gradient is large. The parabolic flow profile 90 becomes flatter as the temperature is lowered from 70 to 550 F. due to the increase in the viscous properties of the continuous phase. As the distance the butter flowed increased the parabolic profile became more pronounced (Fig. 14) indicating that the velocity gradient even though small is still present. Mulder ital. (28) using colored butter in their moisture dispersion studies concluded that the gradient of velocity was large in the butter near the walls of a perforated disc through which it was forced and small for the remainder. The relationship between the logarithm of apparent viscosity and the logarithm of velocity was found to be linear. The average slope of the regression lines was -0. 84649. An increase in the velocity from 0. 01 to 0.1 ft. /sec. resulted in a decrease in apparent viscosity of 751,000 cp. at 600 F. This linear relationship is in agreement with the results obtained by Sone 91:3}. (37) using a parallel plate plastometer at lower rates of shear and for 68 and 77° F. Temperature increases resulted in very rapid decreases in the apparent viscosity of butter (Figs. 18 and 19) . The similar apparent Viscosity results obtained for 55 and 600 F. are probably due to the extrusion viscometer method in that the butter is softened considerably as it is forced into the tubing. Attempts to plot the apparent viscosity versus the temperature as an Arrhenius function 91 did not result in a straight line. A plot of the logarithm of the apparent viscosity versus the temperature did suggest a linear relationship having a slope of -0. 0587. This relationship is in agreement with the equation given by Weltmann (41) for some non- Newtonian materials (see equation 5). The results on the apparent viscosity from the different samples of butter showed a variation but no definite pattern. The variation was small within given sample of butter as indicated by the high correlation coefficients (0. 9935 to 0. 9996) . However, the variations among the samples of butter were greater (correlation coefficients ranged from 0. 9738 to 0. 9915) . The variations among the results from different samples of butter also became greater at 55 and 600 F. (Figs. 24 and 25) . The variations within the same sample are probably due to temperature fluctuations and small dif- ferences in the amount of softening which occurred just prior to flowing through the tubing. The variations between the samples of butter are probably due to the presence of triglycerides having dif- ferent melting points and to the effects of the processing conditions. Large variations in pressure losses were found among the various samples of butter (correlation coefficients ranged from 0. 3506 to 0. 9377) . However, no pattern could be found for compo- sition or processing influences to explain the variations. The variation within the same sample was small as indicated by the 92 correlation coefficients which ranged from 0. 8659 to 0. 9940. The results on the reduction of the apparent viscosity of mildly agitated butter were shown to be a linear relationship between the logarithm of apparent viscosity and the logarithm of time. This suggested a similar relationship between the apparent viscosity and the distance butter moves through tubing for a given velocity. Such a relationship was not found. The relationship may exist and was simply masked by variation in other factors, such as, differences in the samples of butter or temperature. Pumping reduced the apparent viscosity of butter by increasing its temperature and by working. The rate of pumping had no apparent influence on the apparent viscosity (Fig. 37) . The use of the extru- sion viscometer is not recommended for studying effects of pumping since the rate of shear has been shown to be a factor in measuring the apparent viscosity and also because additional softening will occur as the butter is forced into the tubing. The average minimum pressure loss for elbows and valve assemblies per unit length was less than the average minimum pres- sure for straight tubing per unit length. This lower pressure loss was probably due to differences in the softness of the butter during the trials. Since softening of the butter does occur in butter pumping systems, the actual center line distance may be used in determining the total length of tubing in loss of head calculations. SUMMARY The butter had an average density of 0. 948 g. /ml. at 72. 90 F. and 0.961 g. /m1. at 56.70 F. The average minimum penetration values for the butter used were 3.6, 4.6, 5. 9 and 19.6 mm. at corresponding temperatures of 47.6, 54.1, 59. 9 and 72.40 F. respectively. Penetration values increased after the butter had flowed through the various lengths of tubing (3. 5, 7. 0, 10. 5 and 14. 0 in.) but no significant differences in the penetration values were found for butter after flowing the vari- ous distances . The velocities of the butter flowing in the tubing were shown to vary by using two different colors of butter. The velocity gradient was small within the butter except near the wall where it was large. As the temperature of the butter decreased from 70 to 550 F. the velocities within the butter became smaller. A linear relationship was found between the logarithm of ap- parent viscosity and the logarithm of bulk velocity for a range of 0.001 to 1 ft. /sec. The average slope of the regression line was -0. 84649. The average correlation coefficient was 0. 9887. As the length of the tubing increased the average apparent viscosities decreased but at a decreasing rate. Very small differences were 93 94 found between the apparent viscosities obtained using a 10. 5-in. and 14. 0-in. length of tubing. The influence of temperature on the logarithm of the apparent viscosity was found to be linear having a slope of -0. 0587 for the range of 55 to 750 F. A general empirical equation was determined relating the influence of the bulk velocity and temperature to the decrease in apparent viscosity and was: log n = 7.93446 - 0.84649 log v - 0.0587T The pressure loss increased from 18. 5 to 24.2 lb. /sq. in. as the bulk velocity increased from 0.1 to l. 0 ft. /sec. at 700 F. for butter flowing through a 10. 5-in. length of tubing (0. 313 in. diameter). An increase in the length of tubing from 3. 5 to 14. 0 in. resulted in an increase in pressure loss from 26 to 56 lb. /sq. in. at 0.1 ft. /sec. and 650 F. A decrease in the temperature of the butter from 72.6 to 62.20 F. increased the pressure loss from 18. 5 to 69. 5 lb. /sq. in. Pumping reduced the apparent viscosity of butter by increasing its temperature and by working. The rate at which the pump operated had no apparent influence on the apparent viscosity. The center line distance through an elbow or valve assembly may be used in determining the total length of tubing in calculating the loss of head. 95 The calculated power requirements revealed that a 50 F. de- crease in temperature about doubles the horsepower required (0.18, 0.35 and 0.69 hp. at 65, 60 and 550 F.) An increase in the diam- eter of the tubing from 1. 5 to 3. O in. reduced the power required from 1. 81 to 0. 35 hp. for moving butter at 600 F. through 20 ft. of tubing at 10 lb. /min. 10. ll. LITERATURE CITED Anonymous (1955) . Forségsmerjeriet meddeler: forsalg med udpumpning of smdr fra kaernen. (Report from the Research Dairy: Pumping butter from the churn) Maelkeulidende 68(22):510-14. Cited in Dairy Sci. Abstracts 18(6) :474. (Original not seen.) Anonymous ( 1958) . Ny smorpump prouas pa Eslous mejeri. (New butter pump tested at Eslov Dairy) . Svenska Mejerilidn 50(41) :554—55. Cited in Dairy Sci. Abstracts 20:2804. (Original not seen.) Andrade, E. N. da C. (1930) . The viscosity of liquids. Nature 125(3154):580-84. Association of Official Agricultural Chemists ( 1960) . Official Method of Analysis. 9th ed. , Washington. Brulle, R. (1893). C. R. Acad. Sci. Paris 116:1255. Cited by (27) . (Original not seen.) Cajori, F., ed. (1946). Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World. Univ. of Calif. Press, Berkeley. (Revised English translation) . Coulter, S. T. and W. B. Combs (1936). A study of the body and texture of butter. Univ. Minn. Tech. Bul. 115. Davis, J. G. ( 1937) . The rheology of cheese, butter and other milk products. J. Dairy Res. 8(2):245-64. deMan, J. M. ( 1963) . The kinetics of milk fat crystallization. Milchwissenschaft 18(2) :67 -70. deMan, J. M. and F. W. Wood ( 1958). Thixotropy and setting of butter. Dairy Ind. 23(4):265-67. Dolby, R. M. (1941a). The rheology of butter. 1. Methods of measuring the hardness of butter. J. Dairy Res. 12:329- 36. 96 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 97 Dolby, R. M. (1941b). The rheology of butter. II. The rela- tion between the rate of shear and shearing stress. The effect of temperature and of reworking on hardness and/or structural viscosity. J. Dairy Res. 12:337-43. Griffiths, E. ( 1931) . Spreadability of butter. Report U.K. Food Invest. Board 258. Hansen, R. ( 1954) . Pumpning of smdrret fra kaerne til dritler eller pakkenmaskine. (Pumping of butter directly from churn into casks or wrapping machine). Nord. Mejeritidsskr 20( 9):l30-32. Cited in Dairy Sci. Ab— stracts 17(6) :468. (Original not seen.) Hunziker, O. F., H. C. Mills and G. Spitzer (1912). The moisture control of butter. 1. Factors not under control of the buttermaker. Purdue Agr. Expt. Sta. Bul. 159: 285-360. Kapsalis, J. G., T. Kristoffersen, I. A. Gould and J. J. Betscher ( 1960) . Effect of chemical additives on the spreading quality of butter. J. Dairy Sci. 43( 11): 1560-69. King, H. W. (1954) . Handbook of Hydraulics. 4th ed. McGraw-Hill Book Co. , Inc., New York. King, N. ( 1947) . Globular and free fat in butter. 1. A method for counting and measuring the fat globules in butter and application to the working process. Neth. Milk Dairy J. 1:19. King, N. ( 1964) . The physical structure of butter. Dairy Sci. Abstracts 26(4): 151-62. Knoop, E. and E. Samhammer (1962). Rontgenographische Untersuchungen zur Butterstruktur. XVI. Int. Dairy Congr. B:135-44. (English summary) Kruisheer, C. 1., P. C. den Herder, B. M. Krol and E. M. T. Mulders (1938) . The consistency of butter. Chem. Weekbl. 55:719-33. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 98 Leighton, A., A. Leviton and O. E. Williams (1934). The apparent viscosity of ice cream. I. The sagging beam method of measurement. 11. Factors to be controlled. III. The effects of milkfat, gelatin and homogenization temperature. J. Dairy Sci. l7( 9) :639-50. McDowall, F. H. (1953). The Buttermakers Manual, New Zealand Univ. Press, Wellington. Milk Industry Foundation ( 1949) . Laboratory Manual; Methods of Analysis of Milk and Its Products. Washington. Minard, R. A. ( 1954) . An industrial rotational viscometer and its use with materials of varying complexity. A paper delivered at the First International Instrument Congress and Exposition of the Instrument Soc. of Amer- ica, Convention Hall, Philadelphia. Mohr, W. and J. Wellm (1948) . Viscosity measuring of highly concentrated cream. Milchwissenschaft 3:181-85. Mulder, H. ( 1953) . The consistency of butter. A paper, pp. 91-123, in, G. W. Scott Blair, ed. Foodstuffs Their Plasticity, Fluidity and Consistency. Interscience Publishers Inc., New York. Mulder, H., F. C. A. denBraver and T. G. Welle (1956). The working of butter. 1. Theory. 11. Microscopic examination of the dispersion of the moisture of butter. III. Changes in moisture dispersion caused by the work- ing of butter. IV. Application of the theory of the work- ing of butter to workers of different types and to printing machine. Neth. Milk Dairy J. 10:199-239. Pedersen, A. H. and A. N. Fisker (1956) . Removal of butter from the churn by means of a pump. XIV Int. Dairy Congr. B:307-15. Perkins, A. E. ( 1914) . An apparatus and method for determin- ing the hardness of butterfat. Ind. and Eng. Chem. 6:136-41. Poiseuille, J. L. M. (1842). Compt. Rend. 15:1167. Cited by (41) . (Original not seen.) 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 99 Peterfi, T. (1927) . Wilhelm Rowx' Arch. Enlwicklungsmech. Organ 112:660. Cited by (41) . (Original not seen.) Sargent, J. D. (1935) . The spreadability of butter. 11. The measurement of "body" in butter by physical determina- tion. New Zealand J. Sci. Tech. 16:213-16. Scott Blair, G. W. ( 1938) . The spreading capacity of butter. J. Dairy Res. 9(2):208-14. Sheppard, S. E. and R. C. Houck (1930) . The fluidity of liquids. J. Rheology 1(4):349-71. Sohn, C. E. (1893). Analysis 18:221. Cited by (27). (Original not seen.) Sone, T. , M. Fukushima and E. Fukada ( 1962) . The rheo- logical behavior and thixotropy of butter. XVI Int. Dairy Congr. B: 165-74. Swortling, P. and T. Olsson ( 1957) . Tomning av karnan med pump. (Emptying of butter churn by means of pump. ) Svenska Mejeritidn. 49(20):291-92, 295. Cited in Dairy Sci. Abstracts 20:523. (Original not seen.) van Dam, W. (1927). Versl. Landbk. Onderz. 32:233. Cited by (27) . (Original not seen.) Van Wazer, J. R., J. W. Lyons, K. Y. Kim and R. E. Colwell ( 1963) . Viscosity and Flow Measurement. Interscience Publishers, New York. 406 pp. Weltmann, Ruth N. ( 1960) . Rheology of pastes and paints. A paper, pp. 189-248, in F. R. Eirich, ed. Rheology Theory and Application. Academic Press, New York. or. 0‘— A‘Hh‘m_“_.o-__ . _ . ““AM- MICHIGAN STATE UNIVERSITY 12 0 ll IIIIIIII“ 3014 832 3 93