I . 9 o—Osnooo..-.¢.w..-o.¢-c". - "O“~-'Q .0. I. ‘foo-..'...'.~.,- og-oq'o‘. G- -‘IO'.-‘Q‘ o‘O‘QQODro-nuo-¢.-. ”c'o RHEOLOGICAL PROPERTIES or SLUSH FROZEN ORANGE iUlCE momma W “0‘ ‘C N "O" Q 'U‘V I'T‘ 'va v—yv 'v v—F. -vv - —v _ Thesis for the Degree of M. s. _ MICHIGAN smuumvansm ' . PANAGIOTIS ATHANASOPOULOS ;" ' 1975 . II" -. 'o- \ I 0 § I v ' " .r.‘ . ~‘.‘l~.a.. ',.I.' ‘31". $113.”: :1? \‘J | . .' x ‘- . l -.,. 'u ‘. I . . '\.'~.. -. H" . . . . . I . 'Q I ‘ . . . ‘ C, Q .. . l . D . _ i" o ‘. o. ' , .o. '\ n n u o I o o . . . n I n c ‘A ‘ ‘ c-l‘. IIIIIIIII IIIIIIIIIII IIIIIIIIII I 3 129300105 4620 ABSTRACT RHEOLOGICAL PROPERTIES OF SLUSH FROZEN ORANGE JUICE CONCENTRATE by Panagiotis Athanasopoulos Design problems for cooling and heating, for pumping, and transportation of liquid foods are associated with knowledge of their flow characteristics. The objectives of this study were 1) to deter- mine the rheological parameters of slush frozen orange juice concentrate, and 2) to determine the influence of percent frozen water on flow characteristics of the frozen orange juice concentrate. Commercial frozen orange juice concentrate (45o Brix) was used in this experiment. Measurements were accomplished with a capillary tube viscometer. The experiments were conducted under con- stant temperature conditions. Data obtained from the experimental studies were computer analysed. According to results obtained, the flow behavior index increased with decreasing temperature; the con- sistency coefficient decreased with decreasing temperature, while the apparent viscosity increased with decreasing temperature. Two empirical functions were developed to correlate the rheological parameters to percent of frozen water. In addition a chart was prepared to correlate the friction factor and the generalized Reynold's number. This chart should be useful for pumping and tranSportation design problems. RHEOLOGICAL PROPERTIES OF SLUSH FROZEN ORANGE JUICE CONCENTRATE by Panagiotis Athanasopoulos A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Food Science 1975 ACKNOWLEDGEMENTS The author expresses his sincere gratitude and appreciation to Dr. D. R. Heldman, Professor, Department of Agricultural Engi- neering and Department of Food Science and Human Nutrition and Mr. A. L. Rippen, Professor, Department of Food Science and Human Nutrition, for their encouragement, guidance and help during the course of this study. Thanks are also expressed to Dr. Bedford, Professor, Department of Food Science and Human Nutrition for his service as an advisory committee member and to Dr. Paul Singfifor his advice and encouragement. The author also expresses his love and appreciation to *his wife, Gina, for her encouragement and typing assistance which helped make the completion of the investigation possible. Panagiotis Athanasopoulos TABLE OF CONTENTS Page LIST OF TABLES ... . . . . . . . . . . . . . . . . . . . . . . v LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . vi NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . viii INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . 1 LITERATURE REVIEW . . . . . . . . . . . . . . . . . . . . . . 3 A. PROPERTIES OF FLUID FOODS. . . . . . . . . . . . . . . 3 l. Viscosity . . . . . . . . . . . . . . . . . . . . 4 2. Apparent Viscosity . . . . . . . . . . . . . . . . 7 3. Non-Newtonian time depended fluids . . . . . . . . 7 4. Factors affecting rheological properties . . . . . 7 a. Total solids . . . . . . . . . . . . . . . . . 8 b. Temperature . . . . . . . . . . . . . . . . . 8 5. Some applications of rheological parameters . . . 11 a. Design of transport systems . . . . . . . . . 11 b. Cooling and heating processes . . . . . . . . 12 B. VISCOMETERS . . . . . ... . . . . . . . . . . . . . . 13 C. FLOW PROPERTIES OF ORANGE JUICE . . . . . . . . . . . 15 METHODS AND PROCEDURES . . . . . . . . . . . . . . . . . . . 17 a. Sample . . . . . . . . . . . . . . . . . . . 17 b. Pressure . . . . . . . . . . . . . . . . . . . 17 c. The apparatus . . . . . . . . . . . . . . . . 18 d. Measurements . . . . . . . . . . . . . . . . . 19 iii e. Soluble Solids f. Total Solids RESULTS AND DISCUSSION . SUMMARY AND RECOMMENDATION FOR FUTURE STUDY . BIBLIOGRAPHY . APPENDIX I: COMPUTATION OF UNFROZEN WATER PERCENT iv Page 23 23 24 50 52 Table 10. 11. 12. LIST OF TABLES Effect of total solids on (m) and (n) for Pear Pureé (from figure 4) . . Effect of temperature on (m) and (n) for Pear Puree Flow rate at different temperatures andAIP . Log Q at different temperatures Slope of curves obtained Correlation coefficients Effect of Effect of Influence different Influence Influence different Influence factor (f) temperature on temperature on of temperature shear stress. of temperature of temperature .JP/ZL . of temperature by Wang computer obtained by Wang computer . (n) and (m) percent frozen water on shear rate at on apparent viscosity . on velocity at on GRe and friction Page 10 10 25 27 29 29 33 33 37 38 44 46 Figure 10. 11. 12. 13. 14. 15. LIST OF FIGURES MOdel of theoritical determination of shear- rate shear relationship (from Charm 1971) Characteristic flow behavior of fluids (from Heldman 1975) Flow behavior curves for Pear Pureés at different temperatures. Flow behavior curves for Pear Pureés at 150° F . Tube viscometer equipment arrangement . Details for connecting sample reservoir and copper tubing . Orange juice concentrate rheograms at different temperatures. Orange concentrate rheograms at (a) 20° F and (b) 32°F Relationship between (m) and Z of frozen water. Correlation between(n) and Z of frozen water Influence of temperature on (n) and (m) Change of (m) and percent of frozen water with temperature Effect of temperature on shear stress-rate of shear relationship. . . . . . Influence of temperature on apparent viscosity at different shear stress Influence of shear stress and temperature on apparent viscosity . vi Page 20 21 26 28 32 32 34 34 39 41 42 Figure 16. l7. l8. Correlation between apparent viscosity and percent of frozen water . . . . . . . . . Effect of shear rate on velocity of orange jtte concentrate . Friction factor (f) against generalized Reynolds number (GRe) for laminar flow of slush frozen orange juice concentrate computed from 16 - f/GRs . . . . C \0 vii Page 43 45 47 b" Cp GRe fic LI Na NOMENCLATURE Area . . Constant in equation (12). . . . . . . Intergration constant in equation (7). Distance between two parallel heated surfaces. Shear rate . Specific heat of the product . . . . . Pressure gradient . . . . . . . Tube diameter. . . . . . . . . . . . Activation energy Friction force . Friction factor Generalized Reynold's number . Convective heat transfer coefficient . Kinetic energy . . Reaction rate constant . Thermal condutivity Tube length . . . . Latent heat . . . . . . . . . . Coefficient of viscosity . . . . Apparent viscosity . Consistency soefficient . . . . Consistency coefficient at the bulk properties . . . . . . . . . . . . . viii CID cm sec"I . cal/gr0C dynes cm"2 CID cal/mole dyne . cal/cmzmin.°C cm gr/g l/min . cal/cm.min.°C cm cal/gr points points dynes cfixzsec"n dynes crfizsec"2 R8 fl dy Consistency coefficient at wall temperature . Flow behavior index. . . Product density Volumetric flow rate . Tube radious Gas constant . Shear stress . Yield stress equation (2) Absolute temperature . Velocity . Mean velocity Velocity gradient Flow rate . Percent frozen portion of water. Distance gradient mean ix . dynes cm 2 2 SEC 3 cm mc3 sec'I cm dynes cm- dynes cm' 0K cm sec"I cm sec-I cm sec"I gr/sec wt/wt CIT] INTRODUCTION The methods used in freezing fruit juices may be divided into two categories depending upon the rate of freezing. They are the slow and quick freezing categories. Juices containing small quantities of colloidal and suspended matter, such as apple juice, may be frozen slowly without causing any particular physical change in them. When the frozen juices are thawed and agitated, they are completely recon- stituted. These juices can be solidly frozen in large containers by using an air blast freezer. In slowly frozen juices containing a considerable amountof colloidal and suspended matter, such as orange juice, much of the col- loidal and suspended matter is coagulated. When thawing a slowly frozen juice, the coagulated material usually settles. On the other hand, in quick frozen juices, less colloidal and suspended matter is coagulated. In this case, the coagulated particles are much finer and do not settle so rapidly when the juice is thawed (Tressler et. al 1968). As a rule, the more rapidly the juice is frozen, the less the clearing or settling after thawing. Rapid freezing also permits much less chemical, enzymatic and microbiological changes than slow freezing does. Continuous slush- freezing methods are usually used for these juices. Juice is slush- frozen, and is automatically filled into cans which are closed and frozen solid by passing through a freezing tunnel. The votator is widely used for slush-freezing; both for single strength and concentrated juices. Frozen slushes are the basis of a new technique developed during the last years which can be used as a concentration process. According l to this method, called "slush evaporation", the evaporator is fed by slush-frozen juice, and water is removed by both vaporization and sublimation. Since slush-frozen juices have to be mechanically handled, it is important to know the rheological properties of these slushes. The flow behavior index (n) and consistency coefficient (m) must be con- sidered when machinery or equipment are designed. No investigations have been attempted, on the rheological properties of frozen slushes. Therefore, the objectives of this study were to establish the flow behavior of slush-frozen orange juice con- centrate by determining if it is a Newtonian or a non-Newtonian liquid; to determine the rheological parameters of slush-frozen orange juice con- centrate at temperatures as low as those used by industry; and to determine the influence of percent frozen water on flow characteristics of the slush-frozen orange juice concentrate. This knowledge could then be utilized to improve freezing procedures, and pumping, and also for designing fast transportation systems. L ITERATURE REV IEW The term rheology has been defined as a "Science devoted to the study of deformation and flow" (Reiner, 1960). Rheology encom- passes the area of fluid flow which is so important in many segments of the food industry. It should not be assumed that the theories developed for other materials will apply directly and ideally to food products (Anon., 1973). Many added parameters tend to make the situation much more complex. The rheological properties of food products may be in- fluenced by factors such as temperature, humidity, and chemical or microbiological reactions. So, parameters are frequently experimentally measured and concepts are developed which are not utilized in any other field. A. PROPERTIES OF FLUID FOODS The consistency of a fluid is the prOperty which governs its flow characteristics, which in turn, are essential in estimation various engineering quantities, such as heat transfer coefficients, evaporation rates, and pumping and mixing requirements. Since these flow character- istics are dependent upon the properties of the fluid, it is necessary to discuss methods utilized in measurement of these properties. Because fluid foods exist in variable conditions the methods to be discussed will not be adequate for all situations. These methods and the parameters used to describe fluid properties are the best available and can lead to ac- ceptable results in many design situations. I. Viscosity 3 Viscosity has been defined as the internal resistance of a liquid to flow, and it is indicated by the coefficient of viscosity given by the equation thug; _ (I) In this equation (1) is the shear stress,r'is the coefficient of vis- cosity and du/dy is the velosity gradient which exists between two sur- faces. The model in Fig. I) can be used for theoretical determination of shear-rate of shear (which is equivalent to du/dy) relationship. As shear stress has been defined the ratio F/A =’1, and as rate of shear the ratio, -du/dy =J'(Charm, 1971). Equation (I) describes Newtonian fluids. The plot of’tvs -du/dy is a straight line passing through the origin. The slope of the line is the viscosity coefficient or viscosity. Since H is a constant, a single determination of it can completely characterize the flow behavior of the liquid. (Heldman, 1975) There are many liquids employed in the food industry which do not hold on to this simple relationship. Such liquids are often suspensions of solids or emulsions of liquids in a liquid medium. Both can be called dispersions. The discrete particles (the discontinuous phase) may in- teract with each other and also with the medium (the continuous phase) by which they are surrounded. If the interaction depends on the flow rate then the coefficient of viscosity is no longer a constant, and for such systems a one point measurement is no longer adequate, because it does not characterize the flow rate. Such liquids are called non-Newtoniane As the amount of pectin as well as other suspend and colloidal material increases the products and become increasingly non-Newtonian (Holdsworth, 1973; Muller, H.G. 1973). They also show continuous flow even for the smallest applied force. The Bingham-plastic behavior is one in which a finite yield (ry) is required before a Viscous reaponse is obtained. The relationship between the shear stress and rate of shear for a variety of fluids, considered to be non-Newtonian, is illustrated in Fig. (2). The Newtonian behavior is described by the equation (I). The plot shear stress vs rate of shear, for Bingham-plastic behavior, is a straight line described by equation (2) -t=m( -‘-“3)+“ (3) Where (m) is consistency coefficient and (n) is flow behavior index. For pseudolplastic fluids parameter (n), in equation (3), is 0(n<1 and for dilatant ones is I2100, a certain chart developed by Dodge and Metzner @959) can be used for evaluation of (f). The (GRe) is defined as follows (Heldman 1975): - 2 n h GR. = ..22 ..... 9 ....... (11) 2n-3 m[3nil] n n The following expression is generally used for kinetic energy computation, ibr a power-low fluid KE = ---- (12) where (a) is constant equal to two (a=2) during turbulent flow but varies according to following equation when laminar flow occurs (Heldman, 1975) 4n+2) (5n+3) ( (13) From this last expression it is apparent that parameter (a) is not affected by consistency coefficient (m) but is determined by flow behavior index (n). b Cooling and heating processes The most flmportant factor in design problems dealing with heat transfer is the computation of convective heat transfer coefficients for pseudoplastic fluids. There are several expressions proposed by investigators which can be used for convective heat transfer coefficient, when tubular heat ex- changer is used for heating or cooling. One of them is the following, presented by Charm and Merrill (1959)- I 3 0.14 €2-13 . 2 .39.. / a: 32:3" (14) K KL ms 2(3n-I) Where he is convective heat transfer coefficient, D tube diameter, K 13 is product thermal conductivity, W is flow rate, Cp is product spec- ific heat, L' is tube length, n is flow behavior index, mb and ms is consistency coefficient at the bulk properties and at the mean wall temperature. Other expressions and examples are given by Heldman (1975). B, VISCOMETERS Viscosity measurements are accomplished indirectly by using in- struments measuring time, force, or flow rate. A large number of in- struments have been utilized to measure the rheological prOperties of fluid food products. All these instruments can be classified in two categories: (a) rotational rheometers including the coaxial-cylinder type and the cone and plate type, and (b) capillary tube rheometers. The solid components, present in the orange concentrate, have an effect on its flow behavior. The dimensions of these components are not always negligible with reapect to the gap between inner and outer cylin- der of a rotational viscometer; therefore measurements in the rotational viscometer might be erroneous, (Rozeme et al. 1974). So in this experi- ment a capillary tube rheometer was used. The theory about this instru- ment is somewhat complicated and an analysis of it in detail would be beyond the purpose of this study. However, it is intentional that some basic information pertaining to general concepts of this methodology is included herewith in favor of a sufficient communication. For capillary tube rheometers the pressure gradient and the volumetric flow rate of the fluid are measured. From these measurements shear rate and shear stress are obtained. The following assumptions are 14 inherent to all capillary viscometers; (a) flow is steady, (b) proper- ties are time independent, (c) flow is laminar, (d) fluid velocity has no radial or tangential components, (e) the fluid exhibits no slippage at the wall, (f) the fluid is incompressible, (g) the fluid viscosity is not influenced by pressure, and (h) the measurement is conducted under iso- thermal conditions (Heldman, 1975). To obtain a laminar flow at a steady state and to have a negligible entrance and exit flow-effects we have to use a small dia- ueter tube (normally less than 1/4 inc.), and the length to diameter ratio must be high (usually higher than 100) (Saravacos, 1968). In most cases a tube viscometer can be used to determine the viscometric constants of various fluid foods. Gravity-flow capillary viscometers have been used widely in the laboratory for Newtonian fluids. A pressure tube viscometer is always used for the determination of the rheological parameters for non-Newtonian liquid foods. For a non-Newtonian fluid, obeying the power-law equation (3), the flow through a capillary tube is given by the equation (Brown, 1961) RAP I+3n “ 4Q “ I+3n “ Q n --- = m < ---- > ( --- ) = m < ---- ) < --5 > (15) 2L 4n m3 n flR observing equations (3) and (15) we obtain the following expressions for shear stress 2L and for shear rate 1+3 x= < ---‘-‘ > ( 53- > (17) n 41R3 By rearranging equation (15) as 15 .AP - n log ( 2L ) — logm nlogn( 3n+I ) (3n+I)logR +logQ (18) and by plotting log (AP/2L) versus log Q the value of (n) can be deter- mined from the slope of the resulting curve, while the parameter (m) can be evaluated from the intercept. The tube viscometer used in these experiments for determining rheological properties of slush-frozen orange juice is described in the next chapter. C. FLOW PROPERTIES OF ORANGE JUICE Orange juice concentrate is a suspension of particles in a liquid called orange juice serum. The latter contains a significant amount of pectin, besides sugar acids and other soluble materials. Both whole orange juice and orangteuice serum show non- Newtonian behavior and have been characterized as non-Newtonian, pseu- doplastic, thixotiopic liquids. This behavior was defined by Ezell(l959) and confirmed by Charm (1963). The rheological properties of concentrated orange juice may be explained on the basis of the contribution on the flow behavior of each one of the component systems (Mizrahi and Berk, 1970). Depectinized orange juice serum is a Newtonian liquid, and can be considered as the basic liquid medium. The soluble pectic substances impart to the serum non-Newtonian behavior and thixotropic properties. The suspended material seems to be responsible for most of the non-Newtonian behavior and time dependence of flow properties. The disintegration of coarse pulp par- ticles results the irreversible decrease in apparent viscosity. Flow characteristics of slush-frozen orange juice are not presented in the literature. To our knowledge no studies have been attempted in this temperature range. 16 METHODS AND PROCEDURES All experiments were conducted in a refrigerated room in which temperature could be controlled. The apparatus, and all instruments used, were placed in this room. a Sample. Commercial frozen orange juice concentrate, in 12 fluid oz. (354 cm3) paper cans was used. This juice was shipped from Indian River, Florida. It was prepared by TREESWEET PRODUCTS CO. It was held in a refrigerator at 15° F. about five days after the day it was bought. TREESWEET PRODUCTS CO. provided the following information on the lot of orange juice concentrate. The source was Valencia oranges extracted by Brown machine-reamers, and concentrated in triple effect vacuum pans (temperature not exceeding 800 F.). Its pulp was 9 to 11% in reconstituted juice, acidity in concentrate 2.32 to 2.56%, pH in reconstituted juice, approximately 3.80 - 3.90. This orange juice con- centrate was packed on July 18, 1974. The content of six cans was emptied into a glass beaker and placed in the experimental room at 20° F. (-6.67°C) to equalize with the room temperature. A portion of this sample of about 1.7kg (3.4 lb.) was used for making the experimental measurements. The sample was thor- oughly mixed by stirring before measurements were made. To avoid any loss of moisture, the sample was covered with aluminum foil b nggggrg‘ Air under pressure was used in order to obtain flow of the orange juice.concentrate through the capillary tube. Compressed air for the experiment was obtained from.the air line system in the 17 18 laboratory and was transferred to the air pressure vessel at about 18 psig. A steel vessel, normally used for gas transportation, suitable for pressure up to 120 psia was used. The dimensions of this vessel are: height 107 cm, inside diameter 26 cm, and the volume 56781 cubic cm. This vessel was equipped with an air valve near the bosom for connecting to the air pressure line, and with components near the top, as illus- trated in Fig. 5. 1 Pressure regulator, to regulate air pressure to desirable level. 2 Pressure gauge,A MARSHALLTOWN, IOWA USA MFG CO, Oto 30 psig gauge was used. 3 Air valve, to connect the air pressure vessel and the viscometer (sample vessel). The air pressure vessel was held overnight in the refrigerated room to allow the compressed air to reach the room temperature. Since measurements were obtained at pressures of 14, 12, 10, 8, and 6 psig when the air vessel was refilled, a considerable amount of cooled air ( 6 psig) existed. Time of about 3-4 hours was estimated as sufficient for the new air to obtain the desirable temperature, so three measurements per day were scheduled. c The apparatus. Tube viscometer, illustrated in Fig. 5, was used in this experiment. It consisted basically of a stainless steel reser- voir for the orange juice sample; a tin vessel surrounding this reser- voir, working as a constant temperature bath; a short piece of stainless steel tube between the reservoir and the capillary tube; and a straight copper capillary tube. As reservoir, a stainless steel vessel 16 cm high and 13 cm inside diameter was used. Four bolts supported the reservoir in a 1.9 center position inside the tin vessel which served as a bath. In the Space between these two vessels coolant (ethylene glycol) was recircu- lated from the constant temperature cooler bath. For all measurements, smooth wall copper tubing with an inside mean diameter of 0.48 cm and a 77.4 cm in length was used. The mean diameter was computed from the volume of the distilled water required to fill it completely. A stainless steel tube, with 3.4 cm inside diameter, and 9 cm long, welded horizontally near the bottom of the reservoir, was used to connect the reservoir and the capillary tube. The latter was connected to the apparatus through a rubber stopper as illustrated in Fig. 6 in detail. The end of the capillary tube was stopped using a rubber stopper (Fig. 5) while a piece of string of about 30 cm long (I foot), ending in a 100p was used to prevent entrance of the juice into the capillary tube before starting measurements were begun. For this purpose the loop-end of the piece of string acted as a stopper for the capillary tube (Fig. 6). The apparatus was then connected to the cooling bath so all the components were held at constant temperature; the mean room temperature. An AMINCO SILVER SPRING, Maryland (serial 17845 - 20, Volt 115, wt 1250, 60-cyc1es) bath cooler was used, which had a temperature range from -140° F. to +3600 F. This bath cooler was equipped with a small pump to recirculate liquid coolant (ethylene glycol). d Measurements. Approximately 1.7 kg (3.4 lb) of orange juice concentrate was removed from the sample, after a gentle agitation, and was placed in the reservoir of the apparatus. The slush-frozen orange juice was gently agitated by a mixer. A GTZI laboratory mixer (Gerald 20 Air from ‘1’ valve pressure vessel .4 cooling bath pressure gauge sir valve 0‘ .//' I -—-) pres Air to regulator reservoir 107cm 26cm air-pressure eir valve vessel ...) Air in Fig. 5.' Tube viscometer equipment arrangement. 21 »< peace pea .ensu uneaaaneo menace Rev ease Rev .nerOpu noonsm gov .wnuuamanv .onsu deans neonnaepm Adv moans» pounce on: adopnoees cannon wnupoosnoo you uaaepen _ a an. is! I. .ov ...J u any any .0 £3 22 K. Heller Co. -Las Vegas ) was used with variable speed. Speed was controlled by using a CT 21 motor electronic controller able to con- trol speed in a range of O to 277 RPM (slow shaft) or from O to 5,000 RPM (fast shaft). The temperature was checked from time to time, using a o to 230° F., 2°, Partial 1mm. (SARGEN'IWELTH, SCIENTIFIC co.) ther- mometer. When the temperature of the orange juice was constant, the mixer was removed from the reservoir. After removing the piece of string, the cover was placed on the vessel and secured with wing nuts. The air pressure vessel was connected to the apparatus to provide the desired pressure. The rubber stOpper was attached to the discharge end of the capillary tube. Using the regulator, the air pressure was adjusted to the de- sired level and the air valve was opened. After a delay of 2 to 3 min- utes for pressure equilibration measurements were obtained. At this time the components and orange juice concentrate were at temperature equili- brium, and practically isothermal flow could be expected. The rubber stOpper was then removed, and after 3 to 4 seconds, when a steady flow was obtained, samples were collected in preweighed small glass beakers. The beakers were placed in the refrigerated room for at least 2 hr. before making the measurements in order to avoid increase in the collected juice temperature. This permitted reusing the product for subsequent trials. The procedure prevents changes in the physical prOperties of the juice due to temperature changes. A temperature change of 2 to 4° F. (I.8-3.6o C) was observed. Samples were weighed and re-used by mixing with remaining por- tions of the orange juice. Weight was converted to volume by dividing .23 with density (p). This was determined by weighing a certain volume of orange juice concentrate at these low temperatures. It was found, that one cubic centimeter had an average weight of 1.174 grams. The density increases with decreasing of the temperature, but at the region below to 4° C it decreases as the temperature is decreasing. The average measured density was used to compute the volumetric flow rate. In computing pressure difference, AP, the gravitational affect was added, and the factor 6.7 x 104 was used to convert psig to dynes per square centimeter. Each experiment, including one sample at each pressure and at a given same temperature, conducted in triplicate. Samples were col- lected at seven different temperatures, namely, 20,22, 24, 26, 28, 30, and 32° F. (-6.67, -5.56, -4.45, -3.34, -2.23, -1.12, 0° C), and for five different pressures at each temperature, 14, 12, 10, 8, and 6 psig. The time for running each experiment was in a range of 10 to 30 seconds. A GRALAB Universal Timer, model 1971, (Dimco-Gray Company, Dayton, Ohio), capable of timing any interval from one second to sixty minutes, used to measure time intervals during experiment. The weight from the capil- lary tube ranged from about 50 to 270 grams. The weight was determined by analytical balance (Mettler PSN) to the second significant figure. The experiments were conducted by beginning with the highest pressure followed by experiments at lower pressures. e Soluble solids, For soluble solids determination an ABBE re- fractometer was used. The juice was found to be 45 Brix. f Total solids. For total solids determination the vacuum oven (Vacuo) official method was used. The orange juice contained 47.3% total solids. RESULTS AND DISCUSSION For each experimental measurement the pressure difference (AP) and the volumetric flow rate (Q) were calculated. The pressure difference, measured in p s i, was converted to dynes per sq. cm by mul- tiplying by the appr0priate conversion factor (6.7 x 104). The average I volumetric flow rate (Q) for all the temperature values (Table 3) was plotted vs..AP/2L resulting in the curves shown in Fig. 7. These rheograms indicate that slush-frozen orange juice concentrate is a non- Newtonian liquid, as expected. If the liquid was Newtonian, the curves in Fig. 7 would be straight lines. Plotting of log (AP/2L) vs. log (Q), Gable 4) results in a characteristic straight line (Fig. 8). The av- erage of the three trials from Table 3 was used in log (Q) computation. Both rheograms, Fig. 7 and Fig. 8, were obtained by using Wang computer (700 series). Least squares fit-power curve (AP/2L = K0“) and linear regression analysis (log-AP/ZL = log K + n log Q) programs were used for Fig. 7 and 8 reapectively. The slopes of the curves from the first pro- gram are slightly different than that from the latter one (Table 5). Both columns in Table 5 should be identical. The slight difference due to the fact that logarithms fordP/ZL and for Q were taken to the third significant figure. Since the results obtained by using least square fit-power curve program are more accurate, the computer outputs for this program were used in the calculations. Correlation coefficients for each curve and for both plots are presented in Table 6. The slope of each curve, Fig. 7 and 8, represents the flow behavior index (n). To evaluate the consistency coefficient (m), 24 I I III 25 6325830 soon as: usoseusmees 25 a. owo.s «Ne.m hes.m mom.m sum.n mm~.m H-.m .aae oma.s sme.m Hoe.m Hme.m sos.m em~.m mm~.n .pm>a one N mm~.e aese.m nmo.n Has.m ems.m wae.m e-.m .xse em~.e s-.a was.m non.m mam.m mmo.m Hmm.e .aae mwe.s ms~.e ema.m mma.m mm¢.m ~a~.m mam.e .uopa owe m soe.e Nem.s Haa.m one.m eom.m. oa~.m ooa.¢ .xma mno.a oa~.w muo.w ASN.5 mam.“ mum.s «Ho.e .aaa moa.a cos.» mac.» -e.e Nmo.e soe.o Hmo.o .uo>u man a s-.a some.» sac.» mue.e eoe.e wmm.o ome.a .xma -o.~s meH.HH Hs~.on HNH.oH wee.m use.w oau.» .aaa wso.~a ms~.HH Hm~.oa Naa.os .sam.a wem.w aem.m .um>a man m meo.~a sam.as mem.os aes.oa smo.oa mma.a ems.m .xua oa~.mH oam.ma mam.ms awe.- amm.a~ Hmm.oa ouo.HH .aee smm.mn one.ms ma¢.ma mem.~H mma.~a so~.sa moH.HH .uu>a mac e mos.ma ease.ms mea.na ome.- nom.ua amm.sa wea.sa .xma Aoo o v Aoo NH.H-V no om~.~-o no osm.m-v Aoo me.a-v Aoo om.m-v Aoo eo.e-v mag moan m son an owN .m sea .m oi; m ONN m oou ...mmm: III AN 03680 ouem 30am m ewe—us messages—=3 unouommwo us 3.3 soamnum mgmfi. 1x10“ 8x10 0 S? 3 2.0 F o 5 6X10 b a .32 F u o . 5 3 a 11110 __ \\ Q: Q i i 1 i 1 0 h. 8 12 I6 20 Flow rate ch/sec Fig. 7. Orange juice concentrate rheograms at different temperatures. 27 mHo.o Nem.o omm.o mmm.o Nmm.o man.o can.o nae.m Nam.o oen.o mun.o Hmn.o hmm.o ao~.o . mmo.o Nem.m mmm.o num.o oom.o mmw.o sow.o omw.o -w.o mmo.n Hmc.a Hmo.H HHo.H coo.H «mm.o mmmzo mum.o oHe.n omH.H emH.H mNH.H mmo.~ emo.Hp «mo.H c¢o.~ mme.m m own m com m 0mm m cow m cam e cum m com AN nu was Am canoe u essay» cause can we oweuo>e can we 0V 0 w o H m nousuewoeaou usouommap us 0 won .e mqm u a o w e a e < mmouum neon» mufimooea> unoueaee so ousunuoeaou mo ooaosamanuoH mummy Shear stress, dynes/cm? F180 IhOO 1200 800 h00 13. 39 6F 32F lfiib 800 1286 1600 Rate of shear, sec'I Effect of temperature on shear stress-rate of shear relationship. 40 A correlation between apparent viscosity and percent frozen water was attempted, at different shear stresses. The correlation coefficient obtained was 0.896 for the lowest shear stress (626.4 dyn cm'z) and 0.931 for the highest shear stress (1462.8 dyn. cm'z). Apparent viscosity changes with shear stress, so we can not developaan equation correlating the apparent viscosity and the percent frozen water. Fig. 16 shows the plot of the apparent viscosity vs. percent of frozen water at three different shear stresses. The velocity of the orange juice concentrate was computed for different conditions. In Table II the effect of temperature at differ- ent shear stresses on the velocity is illustrated. The relationship between shear rate and velocity is shown in Fig. 17, on log - log co-ordinates. The plot is a characteristic straight line. The friction factor (f) for laminar flow can be evaluated from equation (10), or using the expressing: f = 16 ’ GRe (24) Using the equation (11) the GRe was computed at the highest shear stress, and in turn, friction factors were evaluated using the above relationship (Table 12). Friction factor (f) was plotted vs. GRe on log - log co- ordinates, as shown in Fig. 18. At a given temperature, (m) and (n) can be computed using equations (22) and (23) and used in equation (11). Using the value for GRe obtained and graph (18), the friction factor (f) can be evaluated. After finding the friction factor, the friction loss may be computed from the following common expression: ‘ZL 12?- = f 9-- (25) P gcR 41 I90 5. O . 170 h I 4.) 0H 3 3 I50 «H > I 4.! a E a. 13 0. .¢ 110 90 20 22 211 26 28 30 32 Temperature OF. Fig. Th. Influence of temperature an apparent viscosity at different shear stress. C2 626.h dynes/cm? A 10112.8 dynes/cm2 O Ih62.8 dynes/cm? Apparent Viscosity op. 42 200 150‘ 100 VI ‘0 I 1 I 28 26 2h 20 Temperature OF. Fig. IS. Influence of shear stress and temperature on apparent viscosity. 200 I t I t vb ya"‘ ”I (a) 180 L '0' 6 160 I I, [I 1” (b) (C) 120 100 0 20 40 60 80 Percent frozen water Fig. 16. Correlation between apparent viscosity and percent of frozen water. (a) at 626.4 dyn. cm'2 (b) at 1042.8 dyn. cm"2 (c) at 1462.8 dyn. cm'2 43 mo.MN no.ON oo.ON oo.o~ Hm.m~ cm.wa om.ma oHo N No.on Nm.em ma.Nm Hm.Hm Nm.om ¢.wN mm.mN owe m mm.om an.o¢ nn.¢¢ om.N¢ mo.o¢ mm.mm ow.om mam e em.oo o¢.No mm.om mo.om em.em ww.m¢ mm.o¢ mod n om.mm mH.nn mm.¢n mw.mo N¢.no mm.No an.ao mmo e Aooo o Aoo-.H-v Auom~.~-v Aoosm.m-v Auoms.s-v Acosm.n-v Aooeo.e-v so II. a on a com a owN a com a cam a cum a com mm new NI 0 o e\8 o <\o I D h u a o o a o > WW. AN\m< unencumwo um mufloo~o> so ounueuoaaou mo ooaosuwcHuamH mqm 62.59 193.7 .0826 24(-4.45°C) 67.42 218.9 .073 26(-3.34°0) 69.85 227.9 .0702 28(-2.23°C) 74.53 258.3 .0619 30(-1.12°0) 75.19 252.7 .0616 32( 0°C) 85.30 338.8 .0472 46 47' I. 0. 0.0 .001 IO I00 1000 10000 GRe Fig. 18. Fr1ct16n factor (r) against generalized Reynolds number (GRe) for laminar flow of slush frozen orange Juice concentrate computed from fslb/GReCData from T111319 12) 48 The results may be used in pumping and transportation calcu- lations. In addition, the convection heat transfer coefficient, Hc, is needed in slush-freezing of orange juice concentrate either for packing as frozen product or for freeze concentration. The mean heat transfer coefficient can be evaluated from the following expression, presented by Pigford (1955). 1/3 1/3 - n+ Nu = 1.75 ---- (Gz) (26) An where n is the flow behavior index, flu is the mean Nusself number, Nu - £59 and 02 the Graetz number, G = 23%, where D is the tube dia- meter, L is the length and k is the thermal conductivity. Equation (14) can be used as well for he determination in tubular heat exchangers. For plate heat exchangers the following equation has been pro- posed by Skelland (1967). Hog, -12- = Nu = 6/3 (n+1/2n+I) (27) where b" is the distance between the two parallel heated surfaces and Zn 3n n = 5 4 - ---- + --------- 28 j / 2n+I 4n+I 5n+I ( ) This equation can be used for heat transfer coefficient evaluation. The source of errors in this experiment can be evaluated by considering the following: a. The same sample was used for all measurements; freezing and thawing may have affected the results obtained. b. The same density was used to convert the sample weight to volume for all temperatures. c. Weighing accuracy of the samples which were collected. d. Inherent errors in instruments used in this research. 49 Despite the possible errors mentioned above, reasonable results were obtained. These may be used in design problems for pumping and transportation of frozen orange juice concentrate. Convective heat transfer coefficient can be evaluated as well, as it is explained in the above paragraphs, and may be used for problems dealing with design systems for cooling and thawing processes (Heldman 1975). Tubular heat exchangers are usually used for chilling orange juice concentrate, but recently plate-type heat exchangers were used successfully (Wells 1974). Freeze concentration and slush evaporation (Lowe et.al 1974) are pro- cesses in which rheological parameters can be used, either in slush- freezing step (by using the convective heat transfer coefficient) or in pumping the slush-frozen juice (using GRe and f), and in evaporation (Harper, 1760). SUMMARY A tube viscometer was constructed using a stainless steel reservoir and a capillary copper tubing. The rheological parameters of slush frozen orange juice concentrate of 45° Brix were evaluated by measuring the pressure gradient and the flow rate at certain time inter- vals. Data obtained were computer OWang computer, 700 series) analy- zed in order to evaluate flow behavior index (n) and consistency coef- ficient (m). At temperatures below the initial freezing point, 26° P {-3.3400), (m0 decreased and (n) increased with a decrease in temperature. The percent frozen water at different temperatures was computed and evaluation of its influence on the values of the rheological para- meters was attempted. A linear relationship between percent frozen water and both (m) and (n) was obtained. The correlation coefficients were -0.947 and 0.938 respectively. Two empirical equations were derived relating the percent frozen water and the rheological parameters (n) and am); they were: n = (0.64877) + x (0.698) 10"3 m a (13.425) - x(35.41) x 10‘3 These equations indicate the higher the percent frozen water, the higher the (n) and the lower the (m). Apparent viscosity increased with a decline in temperature. The apparent viscosity was highest at low shear stresses. A correlation between the apparent viscosity and the percent of frozen water was ob- served. The correlation coefficients were 0.896 at the lowest shear 50 5.1. stress and .931 at the highest one. The plot of shear rate and velocity in log- log coordinates resulted in a straight line. Finally a graph was prepared relating the friction factor (f) to generalized ReynoldS- number (GRe). This graph is useful for pump- ing and transportation calculations. Further studies are necessary with products containing different r} amount of pulp and soluble pectic substances in a range covering the commercial orange juice concentrations. Equations may be developed, by addition to equations (22) and (23), to obtain relationships between II rheological parameters and pulp or soluble pectin contents. 10. 11. 12. 13. 14. BIBLIOGRAPHY Anonymus 1973. Physics in the food Industry. Food Manufacture 48, No 7, 23. Bogue, D.C. 1959. Entrance effects and prediction of turbulence inton-Newtonian flow. Ind. Eng. Chem. 51; 874. Brown, R. 1961. Designing laminar flow systems. Chemical Engineering June 12, 243. Charm, S.E. 1960. Viscometry of nonrNewtonian food materials. Food Research 25, 351. Charm, S. E. 1963. The direct determination of shear stress- shear rate behavior of foods in the presence of yield stress. Food Science 28, 107. Charm, 8. E. 1971. The fundumentals of Food Engineering 2nd addition. AVI Publishing Co., Westport, Conn. Charm, 8. E. and Merrill, E. W. 1959. Heat transfer coefficients in straight tubes for pseudoplastic fluids in stream flow. Food Research 24, 319. Dodge, D. W., and Metzner, A. B. 1959. Turbulent flow of non-Newtonian system. Am. Inst. Chem. Engin. J. 5, 189. Ezell, G.H. 1959. Viscosity of concentrated orange and grapefruit juices. Food Tech. 13, 9. Harper, J. C. 1960. Viscometric behavior in relation to evaporation of fruit pureés. Food Tech. No 14, 557. Harper, J. C., and Leberman, K; W. 1964. Rheological behavior of pear pureés. Proc. First Intern. Congr. Food Science and Technology pp. 719-728. Harper, J. C., and El Sahrigi, A. E. 1965. Viscometric behavior of tomato concentrates. J. Food Science 30, 470. Heldman, D.R. 1975. Food Process Engineering. AVI Publishing Co., Westport, Conn. Holdsworth, S. D. 1973. Consistency and Texture of Fruit products. Food'Manufacture 48, No 7, 25. 52 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30' 31. 53 Lowe, C. Mg, and King, C. T. 1974. Slush evaporation: A new method for concentration of liquid foods. J. Food Science 39, No 2, 248. Luyet, B. 1968. In the freezing preservation of foods, eddited by Tnssler et a1., vol. 2, chp. I., AVI Publishing Co., Westport, Conn. Mizrahi, S. & Berk, Z. 1970. Flow behavior of concentrated orange juice. Journal of Texture Studies I, 342. Mizrahi, S. & Berk, Z. 1972. Flow behavior of concentrated orange juice: Mathematical treatment. Journal of Texture Studies 3, 70. E} Muller, H. G. 1973. An Introduction to Food Rheology. Crane, Russak & Companu, Inc., New York. Pigford, R. L. 1955. Non-isothermal flow and heat transfer inside vertical tubes. Chem. Eng. Progr. Symp. '7 Ser. 17 51, 79. E} Ram, A. & Tamir, A. 1964. A capillary viscometer for non-Newtonian liquids. Industrial and Engineering Chemistry 56 No 2, 47-53. Reiner, M. 1960. Deformation, Strain and Flow. Lewis, London. Rozema, H. & Beverloo, W. 1974. Laminar Isothermal flow of non-Newtonian Fluids in a Circular Pipe. Food Science + Technology vol. 7, No 4, 223. Russopoulos, N. V. 1956. Geoponiki Chimia, Part I, p. 146 (Greek). Saravacos, G. 1968. Tube viscometry of fruit pureés and juices. Food Tech. 22, No 12, 89. Skilland, A. H. 1967. Non-Newtonian flow and heat transfer. John'Wiley and Sons, New York. Treesweet Products Co. Personal communication. Tressler, Van Arson Copley 1968. The freezing preservation of foods. Vol. 2. AVI Publishing Co., Westprot, Conn. USDA Ag. Handbodk No. 66, 1948. Van Wazer, J. R., Lyons, J. W., Kim. K. Y. and Colwell, R.E. 1963. Viscosity and Flow measurement. New York-London-Sydney Interscience Publishers - a division of John.Wiley and Sons, Inc. New York. Wells, J. E. 1974. Chills concentrate from 60°F to 15°F more efficiently, uniformily, Food processing 35, No 12, 28. APPENDIX COMPUTATION OF UNFROZEN WATER RECENT The following equation was used (Heldman 19751 to determine unfrozen water percent: 1:- 3- - I- = Ln 11,, (I) Rg TA '1' where L is the product of latent heat of fusion per unit mass and molecular weight of water, Rg the gas constant 1.987, TA is the freezing point of pure water 492° K, TA is the freezing point of the orange juice 486° K, and XA is mole fraction of water in solution. Using the appropriate values in the equation (I) we obtain: 144 x 18 I I Ln XA - --------------- 8 - 0.0327 and XA = 0.8405 I.987 492 486 The next step is the equivalent molecular weight E MZW deter- mination. From the definition of moll fraction: XA 3 ------------- (2) Wu/IS + T.S.%/EMW where the Wu is the unfrozen portion percent. The total solids in orange juice we worked with have been determined: T.S. I=47.3‘7.., and H202 is 100 - 47.3 = 52.7%. So, EMW can be computed from (2). We found EMW = 101.28. Using temperatures from 20°F to 26°F in equation (I), one value of XA for each temperature was computed, and from equation (2), the unfrozen portion of the water was evaluated. Since the original product contains 52.7% water, the percent water frozen will be: (52.7 - Mu) / 52.7 x 100 "7'1? 1711!! "1171171111 17.1 171.17 T