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Physical, chemical and rheological studies of the hen's egg Tung, Marvin Arthur 1970

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PHYSICAL, CHEMICAL AND RHEOLOGICAL STUDIES OF THE HEN'S EGG by MARVIN ARTHUR TUNG B.S.A., University of B r i t i s h Columbia, 1960 M.S.A., University of B r i t i s h Columbia, 1S67 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of Food Science We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF August, BRITISH COLUMBIA 1970 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t fr e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis f o r scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. MARVIN A. TUNG Department of Food Science The University of B r i t i s h Columbia, Vancouver 8, Canada ABSTRACT A three-part investigation i s described i n which hardness at regular i n t e r v a l s across the thickness of egg sh e l l s i s measured and related to chemical composition at si m i l a r positions i n the same s h e l l s ; e*gg s h e l l membranes are viewed by electron microscopy to compare the structure of inner and outer layers; and rheology of egg albumen i s studied using a r o t a t i o n a l viscometer. Microindentation tests of 27 egg s h e l l s reveal a maximum hardness at the outer surface, intermediate hardness at the inner surface and a minimum hardness midway across the thickness of the s h e l l . Electron probe microanalyses indicate a gradual l i n e a r increase i n calcium toward the inner s h e l l surface. Magnesium and phosphorus are a maximum at the outer surface and follow quadratic and exponential gradients respectively across the egg s h e l l thickness. Hardness gradients, composition gradients and the hardness-composition relationships change from s h e l l to s h e l l . For i n d i v i d u a l egg s h e l l s , an average of 91 percent of the v a r i a t i o n i n hardness i s accounted f o r by variations i n chemical composition. In pooled data of 27 s h e l l s , 48 percent of hardness variance i s associated with composition changes; whereas 81 percent may be attributed to variations i n composition and pos i t i o n i n the s h e l l . Electron microscopical study and measurement of four egg s h e l l membranes show that the structures consist of an open network of f i b e r s b u i l t up i n layers p a r a l l e l to the membrane surfaces. Two regions are evident i n transverse section. The outer membrane i s three times the thickness of the inner membrane and the combined dimension i s about 100 microns. Each f i b e r has a central core encased by a granular mantle. For the outer membrane, f i b e r core diameters are s i g n i f i c a n t l y greater and f i b e r s usually occupy a larger percentage of membrane volume than i s the case for inner membranes. The inside surface of the inner membrane i s l i n e d by a 0.1 micron layer of material s i m i l a r to the f i b e r mantle. Egg s h e l l membrane structure i s discussed i n r e l a t i o n to microbial penetration. Viscous behavior of egg albumen i s described at 10, 20, 30 and U0°C between shear rates of 220 and 3140 s e c - 1 . Egg albumen i s a time-dependent pseudoplastic f l u i d . Apparent-v i s c o s i t y decay at constant shear rate i s p a r t i a l l y recoverable between 32 hour tests and i s affected by the temperature and shear rate used. Flow behavior i s accurately described by the power-law and E l l i s models. Shear history strongly influences flow behavior with higher shear rates r e s u l t i n g i n greater pseudoplasticity and s e n s i t i v i t y to temperature e f f e c t s . T A B L E O F C O N T E N T S P a g e L I S T O F T A B L E S i x L I S T O F F I G U R E S x i A C K N O W L E D G M E N T S x i v I N T R O D U C T I O N 1 C H A P T E R I . H A R D N E S S A N D C O M P O S I T I O N O F T H E S H E L L 2 R E V I E W O F T H E L I T E R A T U R E 3 E X P E R I M E N T A L M E T H O D S 4 M e a s u r e m e n t o f S h e l l H a r d n e s s 4 P r e p a r a t i o n o f s p e c i m e n s 4 T e s t p r o c e d u r e 5 M e a s u r e m e n t o f A v e r a g e C h e m i c a l C o m p o s i t i o n 6 C a l c i u m a n d m a g n e s i u m d e t e r m i n a t i o n 6 P h o s p h o r u s d e t e r m i n a t i o n 8 E s t i m a t i o n o f o r g a n i c c o n t e n t 8 E l e c t r o n P r o b e M i c r o a n a l y s e s 9 P r e p a r a t i o n o f s p e c i m e n s 9 E l e c t r o n b e a m s c a n s 9 S t e p - s c a n s a c r o s s t h e s h e l l 1 0 R e d u c t i o n o f m i c r o p r o b e d a t a 1 1 C o n v e r s i o n o f m i c r o p r o b e d a t a t o c o m p o s i t i o n 1 2 R e l a t i o n o f H a r d n e s s t o C h e m i c a l C o m p o s i t i o n 1 7 - v -Page RESULTS AND DISCUSSION 17 Results of Hardness Tests 17 Results of Chemical Composition by Solution 2 3 Methods Results of Electron Probe Microanalyses 2 3 Electron beam scans 23 Step-scans across the s h e l l 27 Comparison of Chemical Analyses by Solution 34 Methods and the Electron Microprobe Relation of Hardness to Chemical Composition 35 SUMMARY AND CONCLUSIONS , 40 CHAPTER I I . STRUCTURE OF EGG SHELL MEMBRANES 4 2 REVIEW OF THE LITERATURE 42 EXPERIMENTAL METHODS 44 Preparation of Specimens 44 Examination by Electron Microscopy 45 Measurement of Fiber Dimensions 46 Analysis of Data 46 RESULTS AND DISCUSSION 49 Qualitative Observations on' Membrane Structure 52 Results of Measurements of Membrane Structure 52 Membrane thickness and f i b e r area density 5 2 Mean values of f i b e r measurements 54 Variation i n f i b e r measurements across the 56 membrane - v i -Page SUMMARY AND CONCLUSIONS 6 0 CHAPTER I I I . RHEOLOGY OF EGG ALBUMEN 62 REVIEW OF THE LITERATURE 6 2 EXPERIMENTAL METHODS 6 3 Preparation of Samples 6 3 Test Procedures 6M-Rheological Models 65 Models of time-dependent behavior 6 5 • Models of flow-behavior 67 Temperature Effects on Flow Behavior 6 8 Temperature dependence of flow parameters 6 8 Temperature dependence of v i s c o s i t y 69 S t a t i s t i c a l Methods Used i n Data Analysis 69 RESULTS AND DISCUSSION 70 Sample Quality 70 Results of Time Dependence Tests 70 Recovery of apparent v i s c o s i t y a f t e r storage 70 E f f e c t of shear rate on apparent-viscosity 72 decay Ef f e c t of temperature on apparent-viscosity 72 decay Results of Flow-Behavior Tests 76 E f f e c t of storage on flow behavior 76 E f f e c t of maximum shear rate on flow behavior 76 - v i i -Page The power-law model of flow behavior 78 The E l l i s model of flow behavior 81 Results f o r Temperature E f f e c t on Flow 81 Behavior E f f e c t of temperature on flow-behavior 81 parameters E f f e c t of temperature on apparent v i s c o s i t y 84 SUMMARY AND CONCLUSIONS 90 LITERATURE CITED 91 » • • - v m -LIST OF TABLES Table Page I Atomic Absorption Spectrophotometer 7 Operating Conditions ' . 2 II Diamond Pyramid Hardness (Kg/mm ) across the 20 Thickness of Egg Shells III Analysis of Variance i n Hardness Data 22 IV Percentage Composition of Egg Shells by 24 Solution Methods V Average Percentage Composition of Egg Shells 2 8 by Electron Probe Microanalysis VI Average Percentage Composition at Ten Shell 29 Levels i n 27 Egg Shells by Electron Probe Microanalysis VII F-Ratios from Analyses of the Variance i n 33 Composition of Egg Shells by Electron Probe Microanalysis VIII Multiple Curvilinear Regressions of Hardness 36 on Composition - Pooled Basis (n = 270) IX Co e f f i c i e n t s of Multiple Determination for 37 Regressions of Hardness on Composition -Individual Shell Basis (n = 10) X Multiple Curvilinear Regressions of Hardness 39 on Composition and Shell Level - Pooled Basis (n = 270) XI Thickness and Fiber Area Density of Egg Shell 53 'Membranes XII Mean Values of Egg Shell Membrane Measurements 5 5 XIII Apparent-Viscosity Decay Curves for NV 74 Spindle XIV Apparent-Viscosity Decay Curves f o r MV1 75 Spindle. - i x -XV Power-Law Flow-Behavior Curves for Egg 80 Albumen XVI E l l i s Model Flow-Behavior Curves for Egg 82 Albumen XVII Temperature Dependence of Power-Law Flow- 85 Behavior Parameters XVIII Temperature Dependence of E l l i s Model Flow- 85 Behavior Parameters XIX Temperature Dependence of Apparent V i s c o s i t y 89 Using Shear Rate as.a Parameter - x -LIST OF FIGURES Figure Page 1 Hardness i n 27 egg s h e l l s . The mean + - 18 one standard deviation i s shown at each s h e l l l e v e l . 2 Calcium K a electron beam scan at the outer 25 edge of an egg s h e l l . (790X) 3 Magnesium K a electron beam scan at the 25 outer edge of an egg s h e l l . (790X) 4 Phosphorus K a electron beam scan at the 26 outer edge of an egg s h e l l . (79OX) 5 Magnesium K a electron beam scan at the 26 inner edge of an egg s h e l l . (790X) 6 CaO content of 27 egg s h e l l s . The mean +_ 30 one standard deviation i s shown at each s h e l l l e v e l . 7 MgO content of 27 egg s h e l l s . The mean _+ 30 one standard deviation i s shown at each s h e l l l e v e l . 8 P2°5 content of 27 s h e l l s . The mean +_ one 32 standard deviation i s shown at each s h e l l l e v e l . 9 Schematic diagram of an oblique section 47 through an egg s h e l l membrane f i b e r to i l l u s t r a t e the dimensions measured. 10 WL1 outer egg s h e l l membrane (6660X). 50 11 WL2 inner egg s h e l l membrane (6660X). 50 12 NH1 outer egg s h e l l membrane (7050X). 51 13 NH1 inner egg s h e l l membrane (11200X). 51 14 Fiber core diameters f o r membrane V1L1. The 57 mean and standard deviation at each l e v e l are shown. - x i -Fiber core diameters for membrane WL2. The mean and standard deviation at each l e v e l are shown. Fiber core diameters f o r membrane NH1. The mean and standard deviation at each l e v e l are shown. Fiber core diameters for membrane NH2. The mean and standard deviation at each l e v e l are shown. Average f i b e r mantle thickness for membranes WL1 and WL2. Average f i b e r mantle thickness for membranes NH1 and NH2. Apparent-viscosity decay i n egg albumen tested before and a f t e r 32 hours storage. Tests at 10°C and 3140 s e c - 1 shear rate. Apparent-viscosity decay i n egg albumen at 10°C with shear rates of 1570 and 3140 s e c " 1 . Apparent-viscosity decay curves at 10, 20, 30 and 40°C - NV spindle. Apparent-viscosity decay curves at 10, 20, 30 and 40°C - MV1 spindle. Flow behavior of egg albumen samples tested before and a f t e r 32 hours storage. Tests at 10°C with NV spindle. Flow behavior of egg albumen at 10°;C f o r _ ^ maximum shear rates of 1570 and 3140 sec" . Flow-behavior curves for egg albumen at 10, 20, 30 and 40°C - NV and MV1 spindles. Temperature dependence of the power law parameter m. Temperature dependence of the power law parameter n. Figure Page 29 Temperature dependence of the E l l i s 86 parameter a. 30 Temperature dependence of the E l l i s ' 86 parameter ^-^/2' 31 Temperature dependence of the E l l i s 87 parameter n o• • • • - x m -ACKNOWLEDGEMENTS The author extends his appreciation f o r assistance by Dr. J.F. Richards, Food Science Department; Professor L.M. Staley and Professor E.L. Watson, A g r i c u l t u r a l Engineering Department; Dr. J.B. Farmer, Chemistry Department; Dr. J . Biely, Poultry Science Department and Dr. L.C. Brown, Metallurgy Department, the University of B r i t i s h Columbia. The writer i s grate f u l for the use of an electron probe and hardness tester i n the Metallurgy Department, an electron microscope i n the Biology Department and a viscometer i n the A g r i c u l t u r a l Engineering Department. This research was financed by the National Research Council of Canada. - xiv -INTRODUCTION The hen's egg i s an important food i n most parts of the world f o r which the annual production i s i n excess of 300 b i l l i o n eggs. Preservation of the edible portion of the egg i s aided by a leathery membrane and calcareous s h e l l encasement that minimizes chemical degradation and microbial invasion. The s h e l l also provides a r e l a t i v e l y durable, convenient unit f o r handling the product. Physical and chemical studies of egg shel l s and t h e i r membranes are fundamental to explaining t h e i r roles i n maintaining egg qu a l i t y . Large quantities of l i q u i d egg are processed commercially a f t e r removing the s h e l l and membranes. Operations include separating, pumping, heat exchanging, mixing and spray drying -- a l l of which are governed by the viscous nature of the f l u i d s . Rheological studies on egg constituents would provide data useful i n the design and evaluation of l i q u i d egg handling equipment. This thesis describes a three-part investigation of the hen's egg i n which hardness at regular i n t e r v a l s across the thickness of egg shel l s was measured and rela t e d to chemical composition at s i m i l a r positions i n the same s h e l l s ; egg s h e l l membranes were viewed by electron microscopy i n order to compare the structure of inner and outer layers; and rheology of egg albumen was studied using a r o t a t i o n a l viscometer. - 1 -CHAPTER I. HARDNESS AND COMPOSITION OF THE SHELL Most eggs are marketed i n t h e i r s h e l l s ; thus, damaged sh e l l s are undesirable and present a po t e n t i a l public health hazard. Losses due to broken and cracked s h e l l s are estimated at over f i v e percent of the r e t a i l product value. Egg s h e l l strength has received considerable study i n the past decade (W3, H3, T9)* as a r e s u l t of i t s economic importance. Shell hardness i s of inter e s t because hardness of c r y s t a l l i n e materials i s c l o s e l y related to strength (Tl) and may be used as a measure of mechanical properties (M3). Since microindentation hardness tests permit measurements on small amounts of material and on b r i t t l e specimens, egg s h e l l hardness may be tested by t h i s method. Egg s h e l l s are mainly calcium carbonate i n the c a l c i t e form (T2) with small amounts of impurities such as magnesium and phosphorus. These elements are of i n t e r e s t i n r e l a t i o n to hardness because magnesium substitution f o r calcium i n the c a l c i t e l a t t i c e r e s u l t s i n a harder c r y s t a l and furthermore, calcium phosphate i s harder than calcium carbonate. The purpose of t h i s study was to measure hardness and chemical composition point-by-point across the thickness of several egg s h e l l s and to i d e n t i f y the r e l a t i o n between these two c h a r a c t e r i s t i c s . * Alphanumeric characters i n parentheses are i n reference to the l i t e r a t u r e c i t e d . REVIEW OF'THE LITERATURE Brooks and Hale (B6) measured the hardness of twenty egg s h e l l s using r a d i a l sections and reported a l i n e a r gradient of hardness decreasing toward the inner surface. They tested hardness at s h e l l levels 0.25, 0.50, and 0.75 ( s h e l l l e v e l s 0.0 and 1,0 correspond to outer and inner surfaces respectively) because b r i t t l e n e s s of the material prevented measurements near the unsupported edge of the s h e l l s . In a preliminary study by Tung (T3), hardness was tested i n r a d i a l and tangential sections of egg s h e l l . The use of tangential sections permitted hardness determinations between s h e l l l e v e l s 0.02 and 0.90. Egg s h e l l s were found to be hardest near the outer surface, of intermediate hardness near the inner surface and softest midway between. Gradients of hardness between s h e l l levels 0.20 and 0.70 were found to be s i m i l a r for r a d i a l and tangential tests on the same s h e l l s . Variation i n magnesium content i n the s h e l l was reported by Brooks (B7) and l a t e r by Itoh and Hatano (II) who also noted an unequal d i s t r i b u t i o n of phosphorus. The method used i n each case was to progressively dissolve the s h e l l i n five.approximately equal layers and analyze the r e s u l t i n g solutions. Magnesium to calcium r a t i o s were greatest near the outer surface and decreased to a minimum near s h e l l l e v e l 0.70. Gradients were semi-logarithmic for the data of Brooks and l i n e a r for Itoh and Hatano. The phosphorus to calcium r a t i o was a maximum i n the outer layer of the s h e l l and e s s e n t i a l l y constant throughout the remaining portions. - 3 -- 4 -A recent advance i n a n a l y t i c a l chemistry i s the electron microprobe ( B 3 > B 8 , K2, 01) which can be used to measure the chemical composition of a few cubic microns of s o l i d material and i s thus well suited to detecting composition differences i n c r y s t a l l i n e substances. The use of hardness gradient measurement techniques as described by Tung (T3) i n combination with electron probe analysis should provide the point-by-point comparison of hardness and chemical composition required f o r t h i s study. EXPERIMENTAL METHODS Measurement of Shell Hardness  Preparation of specimens Three eggs from each of nine Single-Gomb White Leghorn p u l l e t s provided a t o t a l of 2 7 shell s f o r hardness t e s t s . A l i n e was drawn on the equator of each egg and i t s diameter measured p r i o r to breaking the egg and removing s h e l l membranes by b o i l i n g i n 0.6 M sodium hydroxide. The s h e l l was then thoroughly rinsed i n water and dried i n an oven at 80°C. Thickness at the s h e l l equator was measured. A sample of the s h e l l was mounted i n epoxy (Epon 828 + 10% diethylenetriamine by weight) and the convex surface ground away to expose a tangential section at the s h e l l equator. The surface was polished with a series of emery papers and aluminum oxide lapidary wheels before measuring the length - 5 -of the exposed section i n the d i r e c t i o n of the egg equator. Since the egg i s e s s e n t i a l l y c i r c u l a r i n the plane of i t s equator, the s h e l l diameter and thickness may be used to locate any desired s h e l l l e v e l on the exposed tangential surface (T4) with an estimated error of less than 2 percent. Test procedure Hardness was measured using a Tukon microindentation hardness tester (M3) equipped with a square-based diamond pyramid indenter under 100 g load. The indenter was forced into the polished surface of the s h e l l and the diagonal lengths"of the r e s u l t i n g indentation were measured with an ocular micrometer on the test i n g machine. Diamond pyramid hardness was calculated from the average diagonal length using the equation „ 1.8544 L r - n DP " 72 L 1 ] d 2 where H^p = diamond pyramid hardness, kg/mm L = load on indenter, kg d = average diagonal length, mm. Hardness measurements were standardized during each series of tests by means of a cal i b r a t e d reference block. Three tests were made at s h e l l l e v e l s 0.02, 0.10, 0.20, 0.30, 0.40 and 0.50 st a r t i n g from one edge of the exposed section along a narrow s t r i p containing the equator. A duplicate set of tests was made st a r t i n g at the opposite edge of the section so that the average of six indentations - 6 -was used to calculate hax^dness at each s h e l l l e v e l . A f t e r tests were made from levels 0.02 t o 0.50, the o r i g i n a l t e s t block was cast i n epoxy and ground away t o expose a tangential section f r o m the concave surface on which hardness was measured at l e v e l s 0.50, 0.60, 0.70, 0.80 and 0.90 i n a s i m i l a r manner. Overlapping tests at s h e l l l e v e l 0.50 provided 12 indentations from which hardness a t that l e v e l was calculated. Measurement of Average Chemical Composition  Calcium and magnesium determination For each of the 27 egg s h e l l s , a sample was powdered using a mortar and pestle and 0.3000 g weighed into a 100 ml beaker. Three ml of concentrated HNO^, 3 ml of concentrated HC1 and 9 ml of water were added. The beaker was covered with a watch glass and boiled for ten minutes to dissolve the sample. The solution was f i l t e r e d into a 500 ml volumetric flask and the f i l t e r paper was washed with 20 ml of 0.5 N HC1. Twenty ml of 5 percent lanthanum chloride solution was added and the f l a s k f i l l e d to the mark with water. The r e s u l t i n g solution was anlyzed for magnesium and a portion of i t di l u t e d to s i x times i t s volume and analyzed f o r calcium. The purpose of the lanthanum was to overcome possible interferences by other ions i n the analyzed solutions ( E l ) . Chemicals were of a n a l y t i c a l grade and d i s t i l l e d deionized water was used i n a l l preparations. - 7 A Unicam SP SO atomic absorption spectrophotometer equipped with a s t r i p chart recorder was used i n the analyses for magnesium and calcium. The instrument was f i t t e d with a 10 cm acetylene burner operated to give a f u e l - r i c h luminous flame under the conditions s p e c i f i e d i n Table I. TABLE I. ATOMIC ABSORPTION SPECTROPHOTOMETER OPERATING CONDITIONS Calcium Magnesium Wavelength, nm 422. 7 285. 2 Sl i t w i d t h , nm 0. 08 0. 1 Lamp current, mA ' 12 4 2 Acetylene pressure, kg/cm 0. 7 0. 7 Acetylene flow rate, ml/min 1500 1500 2 A i r pressure, kg/cm 2. 1 2. 1 A i r flow rate, 1/min 5 5 A series of solutions up to 4.0 mg/1 f o r magnesium and 40.0 mg/1 f o r calcium was prepared f o r the spectrophoto-meter c a l i b r a t i o n . The standard curves were concave to the absorbance axes; hence, the lea s t squares quadratic f i t of absorbance to concentration formed the c a l i b r a t i o n curve i n each series of te s t s . Percentage compositions of calcium and magnesium i n the o r i g i n a l samples were based on the - 8 -c a l i b r a t i o n curves, d i l u t i o n factors and o r i g i n a l sample weights. Phosphorus determination Powdered samples of each s h e l l were placed in weighed c r u c i b l e s , dried overnight at 105°C and reweighed. Specimens were then heated in an oven at 1000°C to remove organic matter, and weighed again. Duplicate 0.1200 g portions of the residue from each egg s h e l l were placed i n 250 ml Erlenmeyer f l a s k s , 20 ml of 60% perc h l o r i c acid added v and the mixture boiled for 10 minutes to digest the sample. The solutions were made up to 250 ml with water i n volumetric f l a s k s . F i f t y ml portions of the acid solutions were trans-ferred to 100 ml volumetric flasks to be analyzed for phosphorus (B4). Five ml of 0.1 M sodium molybdate i n 5.0 M s u l f u r i c acid were added along with 2.0 ml of 0.012 M hydrazine sul f a t e and the flasks f i l l e d to volume with water. The flasks were immersed i n b o i l i n g water f o r 10 minutes, then cooled rapi d l y . Absorbance at 8 30 nm was read i n a Spectronic 20 spectrophotometer f o r the unknown and standard phosphate solutions. Values of percentage phosphorus i n the egg s h e l l samples were calculated from the c a l i b r a t i o n curves, d i l u t i o n factors and i n i t i a l sample weights. Estimation of organic content Egg s h e l l s are known to possess an organic matrix - 9 -(S2, T2) that extends through the c a l c i t e c r y s t a l s . An estimate of the organic content of the s h e l l may be derived from the weight loss when heated to 1000°C. Calcium and magnesium, present as carbonates, decompose to t h e i r oxides while phosphorus i s stable as phosphate; thus, weight loss due to carbon dioxide production may be calculated from calcium and magnesium composition. The remaining decrement was attr i b u t e d to oxidation of organic matter since other constituents do not exceed trace amounts (R3). It should be pointed out that t h i s method provided an estimate of organic content subject to inaccuracy due to the combined uncertainties i n measurement of magnesium, calcium and phosphorus and the disregard of possible trace elements. Electron Probe Microanalyses  Preparation of specimens Samples from the equators of a l l 27 experimental s h e l l s were cast i n epoxy along with standard specimens for calcium, magnesium and phosphorus. The epoxy blocks were polished to expose r a d i a l sections of s h e l l with a 0.05 micron f i n i s h , then a t h i n coating of carbon was vacuum evaporated onto the surface of the block to render i t conductive. The standards were c a l c i t e for calcium, magnesium carbonate for magnesium and fl u o r a p a t i t e [Ca,. (PO^) ^F] f o r phosphorus. Electron beam scans Composition of c r y s t a l l i n e materials may d i f f e r - 10 -from c r y s t a l to c r y s t a l boundaries, hence preliminary tests were conducted to determine whether calcium, magnesium and phosphorus occur uniformly within the s h e l l . The U.B.C. Department of Metallurgy electron microprobe (JEOLCo Model JXA-3A with 20° takeoff angle) was used to obtain q u a l i t a t i v e information on the d i s t r i b u t i o n of calcium, magnesium and phosphorus i n the s h e l l . Calcium X-radiation was analyzed with a quartz c r y s t a l spectrometer whereas magnesium K a and phosphorus K a l i n e s used mica c r y s t a l s . Analysis of phosphorus i n the presence of calcium was complicated by interference of second order Ca (3.090 A) rad i a t i o n with P K a (6.154 A) because both l i n e s are d i f f r a c t e d at the same spectrometer setting. Since the two l i n e s have d i f f e r e n t energies, pulse height analysis was used to exclude the i n t e r f e r i n g calcium s i g n a l . The probe was operated at 15 kV accelerating p o t e n t i a l with 0.05 uA sample current normalized on brass and a minimal spot s i z e . Electron beam scans were made near both edges of one egg s h e l l i n areas that included several c r y s t a l boundaries. Absorbed electron images were recorded to aid i n i d e n t i f y i n g the regions scanned. Step-scans across the s h e l l Five-micron step-scans at 10 second counts were run on r a d i a l sections of 27 egg sh e l l s to measure calcium, magnesium and phosphorus content point-by-point across the - 11 -thickness of each s h e l l . Probe conditions were 15 kV accelerating p o t e n t i a l , 0.05 yA sample current normalized on brass and a spot diameter of about 5 microns. Spots were tested on each standard at one-hour in t e r v a l s for signal c a l i b r a t i o n and d r i f t evaluation. Reduction of microprobe data The s h e l l l e v e l corresponding to each analyzed spot was computed and the raw X-ray i n t e n s i t y data divided into ten portions such that each l e v e l previously tested for hardness was spanned by a set of microprobe data. For example: X = 0.02, 0.0 < X < 0.05; X = 0.10, 0.05 < X < 0.15,..., X = 0.90, 0.85 < X < 0.95 where X i s the s h e l l l e v e l . To evaluate calcium, magnesium and phosphorus X-ray i n t e n s i t i e s at the ten s h e l l l e v e l s of i n t e r e s t , the least squares simple l i n e a r regressions of i n t e n s i t y on s h e l l l e v e l were computed f o r the three elements i n each range and the equations solved f o r the desired s h e l l l e v e l . Thus, calcium, magnesium and phosphorus X-ray i n t e n s i t i e s at s h e l l l e v e l s 0.02, 0.10, 0.20, 0.90 were obtained. This procedure serves to smooth the microprobe data and preserve the e f f e c t of composition gradients where the data are not symmetrical about the s h e l l l e v e l of i n t e r e s t . The amount of data i s also reduced to correspond with the hardness information a v a i l a b l e . - 12 -Conversion of microprobe data to composition D r i f t due to fluctuations i n the instrument e l e c t r o n i c components was evaluated from the periodic tests on standards and a l i n e a r d r i f t correction was applied to the counting rates of the standards associated with the data of each egg s h e l l . Thus, d r i f t was assumed to be l i n e a r between tests of successive s h e l l s and was neglected during the analysis of each s h e l l . This procedure was judged to be s a t i s f a c t o r y since the average d r i f t correction from s h e l l to s h e l l was less than 0.5 percent. The calcium weight f r a c t i o n for each s h e l l l e v e l was calculated by assuming dire c t p r o p o r t i o n a l i t y between X-ray i n t e n s i t i e s and concentrations i n both the c a l c i t e and the egg s h e l l . This method i s simple, yet suitable for the present analysis because of the close s i m i l a r i t y between the standard and unknown. Magnesium and phosphorus X-ray i n t e n s i t y data for the standards and unknowns were modified by a number of correction procedures (G2, S6). The influence of detector dead-time on a l l signals was corrected using N l N2 = ( 1 - y ) C where = observed count rate = true count rate and t = detector dead-time'. The background i n t e n s i t y was then considered. That i s , N 3 = N 2 - B where = corrected count rate and B = background count rate. Apparent weight concentrations of the specimens were calculated by direct p roportionality between X-ray i n t e n s i t i e s and concentrations f o r standards and unknowns. ( N 3 ) u c l = CSTN7J7 O S where C = weight concentration of standard s = apparent weight concentration u and s r e f e r to unknown (egg s h e l l ) and standard. The assumption of p r o p o r t i o n a l i t y i s inaccurate when samples and standard are d i s s i m i l a r because of the d i f f e r i n g e f f e c t s of atomic number, mass absorption and fluorescence on the respective X-ray i n t e n s i t i e s . Microprobe correction procedures f o r atomic numbe absorption and fluorescence require an estimate of specimen composition. However, when the corrections have been applie a better estimate of composition i s available which may be used to recalculate the correction factors. Thus the cycle i s repeated u n t i l no further improvement r e s u l t s . Magnesium and phosphorus apparent concentrations were taken from equation [ 4 ] and calcium concentration from the c a l c u l a t i o n described e a r l i e r . Carbon and oxygen of the c r y s t a l l i n e - 14 -phase were computed on the assumption that calcium carbonate, magnesium carbonate and calcium phosphate were the only inorganic substances present. The remaining weight of the s h e l l was attributed to the organic matrix which i s known to be a protein-acid mucopolysaccharide complex (S2). Composition of the organic material was approximated by 4 7 percent carbon, 4 3 percent oxygen and 10 percent nitrogen. With t h i s information the f r a c t i o n a l weight composition was calculated f o r each element present i n the s h e l l . The average atomic number of a test material has an e f f e c t on electron backscattering and electron retarda-t i o n , hence the correction for these two phenomena i s termed the atomic number correction (DI). Apparent weight concen-t r a t i o n was modified using S R" C. = C, ^ [5] S R s u where R = Z i R i C i [ 6 J R. = the backscatter c o e f f i c i e n t and x C^ = weight concentration for each element i . !•> i s obtained from S = Z.C.S. [7] i l l . c Z i , 1.166 X 10 3E r e 1 where S. = - r— l n = L8J i A. J± - 15 -Z. = atomic number 1 = atomic weight = mean io n i z a t i o n p o t e n t i a l E -E E = - 2 ^ ° [9] E q = accelerating p o t e n t i a l used and E C = exci t a t i o n p o t e n t i a l for the X-ray l i n e studied A mass absorption correction i s required to compensate f o r p a r t i a l absorption of X-rays as they t r a v e l from point of o r i g i n i n the sample to the surface. The modified P h i l i b e r t method (PI, D2) 'was used i n the correction. f < x s ) A u where = apparent weight concentration af t e r atomic number and absorption corrections f T x T = + r ^ T T [ I ] ' E.N.A. 1.2 _ 1 1 1 2 [12] [Z.N.Z.] N^ = atomic concentration ^ cosec 0 [13] = mass absorption c o e f f i c i e n t (H5) 0 = takeoff angle 2.39 X 10 5 E1.5 _ E1.5 o c [14] - 16 -In equation [12] weight concentration, C\ , was used to approximate atomic concentration. Corrections f o r secondary fluorescence may be needed when an element i s analyzed i n the presence of c h a r a c t e r i s t i c and continuous X-radiation of higher energy than the l i n e of i n t e r e s t . In general, enhancement due to continuous r a d i a t i o n i s small and very d i f f i c u l t to evalu-ate i n comparison with that of c h a r a c t e r i s t i c r a d i a t i o n (K2). Thus, only fluorescence by c h a r a c t e r i s t i c emission l i n e s was considered. Corrections bf magnesium and phosphorus i n t e n s i t y r a t i o s f o r fluorescence by calcium c h a r a c t e r i s t i c r a d i a t i o n were calculated with Reed's (RI) s i m p l i f i e d procedure and found to be less than 0.1 percent; hence, fluorescence corrections were omitted. Thus C 4 = C 3 [15] where C^ = apparent weight concentration a f t e r atomic number, absorption and fluorescence corrections. At t h i s point the apparent weight concentrations of magnesium and phosphorus were used to reassess specimen composition f o r the r e c a l c u l a t i o n of atomic number and absorption correction f a c t o r s . In several separate tests of t h i s procedure with a computer program, there appeared to be no advantage i n performing the calculations more than three times. - 17 -For the purpose of presenting the t o t a l chemical composition, weight fractions were converted to percentage composition as oxides; thus egg s h e l l composition was expressed as percent CaO, MgO, P2^5' a n c^ o r g a n i c material. It should be emphasized that the possible presence of trace amounts of other elements and the accumulated errors i n chemical analyses would be r e f l e c t e d i n the organic category because of i t s method of computation. Relation of Hardness to Chemical Composition The electron probe microanalyses provided composition information corresponding to hardness measurements at the same ten s h e l l l e v e l s i n 27 egg s h e l l s ; therefore a t o t a l of 270 sets of data were av a i l a b l e . Relations among the variables were studied by means of analysis of variance, c o r r e l a t i o n and regression methods. Regressions of hardness on chemical constituents, singly and i n combination were computed to assess t h e i r r e l a t i v e importance i n explaining v a r i a t i o n i n the dependent variable. RESULTS AND DISCUSSION Results of Hardness Tests Diamond pyramid hardness numbers at ten leve l s i n each of the 27 egg s h e l l s appear i n Table I I . In polynominal f i t s to the pooled data (n =270), va r i a t i o n of hardness across the s h e l l thickness (figure 1) i s described by the curve 19 -H D p = 184.6 - 350.2X + 591.5X2 - 259.OX3 [16] 2 where H^p = diamond pyramid hardness, Kg/mm X = s h e l l l e v e l . . TABLE I I . DIAMOND PYRAMID HARDNESS (Kg/mm2) ACROSS THE THICKNESS OF EGG SHELLS She l l Number Bird 0.02 0.10 0.20 0. 30 Shell l e v e l 0.40 0.50 0.60 0.70 0.80 0. 90 1 1 178.3 155.2 145.0 133.7 124. 1 116.5 130. 3 14 3. 7 144. 0 162. 7 2 1 180.9 169.1 146.2 124.1 115. 3 120.1 137. 5 148. 6 159. 7 161. 5 3 1 190.0 154.6 135.8 118.8 115. 2 124.9 140. 2 132. 4 150. 7 168. 8 4 2 171.5 149.9 133.6 124. 3 123. 2 129.2 149. 2 141. 0 141. 7 162. 3 5 2 170.5 154.8 137.6 124.6 122. 3 121.8 144. 9 143. 9 160. 2 150. 5 6 2 172.6 146.7 136.9 128.2 129. 6 140.9 150. 4 145. 5 161. 6 169. 5 7 3 184.9 165.7 141.0 138.6 126. 5 140. 7 146. 3 148. 9 16 3. 2 160. 0 8 3 183.7 158. 3 136.0 130.8 126. 6 132.1 157. 3 144. 3 152. 4 165. 8 9 3 188.9 168.2 155.4 145.6 134. 1 128.8 135. 7 177. Q 13 7. 2 160. 8 10 4 176.5 155.8 137.0 121.9 114. 1 108.1 113. 6 ,132. 6 129. 4 .15 3. 4 11 4 176.5 153.1 141.7 136.0 126. 2 117.0 125. 1 131. 9 141. 4 162. 2 12 4 179.6 163.8 151.6 135.2 127. 0 117.7 139. 0 135. 7 155. 5 153. 4 13 5 177.6 146.9 131.6 119.8 122. 0 119.9 130. 5 149. 0 14 3. 3 164. 8 14 5 183.6 133. 6 126.0 125.8 122. 4 128.2 129. 1 148. 7 14 8. 9 150. 3 15 5 187.8 164.9 133. 0 127.5 .124. 3 111.9 117. 2 140. 9 132. 6 157. 2 16 6 173.8 156.6 130.4 119.9 118. 7 111.7 111. 2 135. 6 142. 7 164. 6 17 6 179.1 154.2 126.0 118.1 116. 1 117.8 121. 7 141. 5 145. 1 163. 1 18 6 178.4 153.0 129. 7 125.0 116. 9 119.4 120. 4 138. 1 153. 2 165. 0 Continued TABLE II (Continued) Shell l e v e l S h e l l Number -Bird .0.02 -0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 19 7 165.6 139. 3 124. 4 126.5 129. 0 129. 7 137. 8 152. 3 153.5 143. 6 20 7 177.2 154.4 14 3. 0 121.0 126.0 118. 8 128. 3 135. 7 129. 3 161. 0 21 7 166.9 155.6 132. 4 130.1 124.6 123. 6 128. 5 139. 0 142.6 155. 3 22 8 172.4 153. 3 139. 6 124.7 124.1 123. 9 135. 4 150. 2 148.5 161. 2 23 8 185. 7 148.5 136. 1 124.0 120.6 121. 2 127. 8 141. 7 153.5 180. 4 24 8 174.6 161.2 134. 2 122.5 118.7 121. 4 133. 2 132. 4 160.9 170. 4 25 9 174.1 144.6 132. 4 118.7 114.4 115. 7 121. 0 126. 8 .130.4 142. 7 26 9 159.6 162.2 144. 0 120.6 121.9 115. 6 135. 3 141. 6 150.8 152. 7 27 9 186.4 160.7 140. 7 127.8 121.1 124. 9 134. 9 134. 6 155.0 146. 3 - 22 -TABLE I I I . ANALYSIS OF VARIANCE IN HARDNESS DATA Source of Variation Degrees of Freedom Mean Square F-Ratio Shells (26) 275.9 5.07** - Birds 8 627 .1 11.52** - Shells i n birds 18 119.8 2.20** Shell l e v e l s 9 8792. 161.55** Error 234 54.4 Total 269 ** S i g n i f i c a n t at P < 0.01 Hardness d i f f e r s s i g n i f i c a n t l y (P < 0.01) i n di f f e r e n t egg she l l s as shown by analysis of variance (Table I I I ) . S i g n i f i c a n t differences (P < 0.01) were found among successive s h e l l s from the same bi r d and among sh e l l s produced by d i f f e r e n t b i r d s . The gradient of hardness across the thickness of the s h e l l i s p a r t i c u l a r l y noteworthy. For the cubic function f i t t e d to the pooled data, the minimum occurs at s h e l l l e v e l 2 0.40 with a value of 122.5 kg/mm while surface hardness, by 2 extrapolation, i s 184.6 and 166.9 kg/mm for outer and inner surfaces which represent increases of 51 and 36 percent respectively. The di r e c t r e l a t i o n between hardness and strength of c r y s t a l l i n e materials i s well known (Tl) and the - 23 -importance of s h e l l hardness to crushing strength of eggs has been reported (T3). Gradients of hardness s i m i l a r to those i n egg s h e l l s are common in case-hardened metals (see, for example, p. 175 i n reference M3) which possess durable surfaces, while the core is. sof t so that the material maintains a high shock resistance. The gradient of hardness i n egg s h e l l s may be of fundamental importance to the strength of the egg; however, d i r e c t evidence of t h i s i s not available at present. Results of Chemical Composition by Solution Methods Percentage composition as oxides of calcium, magnesium and phosphorus along with estimated organic content f o r each s h e l l appear i n Table IV. These re s u l t s show r e l a t i v e l y close agreement with egg s h e l l composition reported elsewhere (R2, S8). It should be noted that small amounts of other elements may occur i n the s h e l l , although t h e i r presence was not determined. Results of Electron Probe Microanalyses  Electron beam scans Large amounts of calcium, uniformly d i s t r i b u t e d through the s h e l l , are evident i n the electron beam scan of figure 2. Figures 3 and 5 show that magnesium occurs i n s o l i d s olution with the calcium carbonate and that s l i g h t l y higher concentrations may be present i n a zone near the outer edge of the s h e l l . The phosphorus content (figure H) i s - 24 -TABLE IV PERCENTAGE COMPOSITION OF EGG SHELLS BY SOLUTION METHODS Shell CaO MgO P2°5 Organic Matter ' 1 52.87 0.713 0.588 2.97 2 52.58 0.705 0.515 3.04 3 52.49 0.656 0.611 3.23 4 52.86 0.476 0.485 3.14 5 51.67 0.584 0.487 4.00 6 52.19 0.618 0.517 3.25 7 52.26 0.607 0.462 3.37 8 51.61 0.561 0.694 3.75 9 51. 88 0.59 7 0.586 3.11 10 51.74 0. 552 0.532 3. 86 11 51.99 0.630 0.587 3.43 12 51.92 0.677 0.610 3.65 13 51.26 0.642 0.473 4.14 14 51.70 0.561 0.422 3. 39 15 51.50 0.605 0.617 2.96 16 51.72 0.754 0.629 5.38 17 51.57 0.648 0.468 3.57 18 51.57 0.638 0.428 3.62 19 52.18 0.547 0.499 3.12 20 51.49 0.633 - 0.541 3.81 21 51.94 0.579 0.479 3.22 22 51.9.9 0.767 0.426 3. 30 23 52.07 0.686 0.541 3.15 24 51.28 0.614 0.559 4.25 25 52. 30 0.586 0.494 3.49 26 52.00 0.665 0.595 3.08 27 52. 80 0.586 0.507 2.47 Average •51.98 0.625 0.532 3.47 * Organic matter estimated by difference. Figure 2. Calcium K electron beam scan at the a outer edge of an egg s h e l l . (790x) Figure 3. Magnesium electron beam scan at the outer edge of an egg s h e l l . (790X) 26 -Figure 5. Magnesium K A electron beam scan at the inner edge of an egg s h e l l . (790X) - 27 -r e l a t i v e l y high near the outer surface of the s h e l l and decreases rapidly'toward the s h e l l i n t e r i o r . Several c r y s t a l boundaries are included i n the electron beam scans but no differences are evident in calcium, magnesium or phosphorus content between c r y s t a l s and t h e i r boundaries. Thus, step-scans on r a d i a l sections of the s h e l l should be represen-ta t i v e of composition across the egg s h e l l thickness. Step-scans across the s h e l l To test whether a single step-scan across the thickness of a s h e l l adequately represents i t s composition, three separate step-scans were made i n d i f f e r e n t positions along the equator of one s h e l l . Analysis of the variance i n composition at ten s h e l l levels showed no s i g n i f i c a n t difference (P > 0.05) among the mean MgO and P2^5 c o n ' t e n t of the three separate step-scans of one s h e l l . Mean values of percentage CaO, MgO and ?2®5 a t t ^ i e ten analyzed s h e l l l e v e l s were taken to represent the average composition of each s h e l l (Table V). Egg s h e l l composition varies considerably across the thickness of the s h e l l as shown by average r e s u l t s at ten s h e l l l e v e l s (Table VI), Tests of the composition-shell l e v e l r e l a t i o n show that calcium oxide content increases toward the inner surface of the s h e l l (figure 6) as described by the equation CaO = 51.21+ + 3.13X [17] where CaO = percent calcium oxide by weight . For equation [17] the standard error of estimate i s 1.27. - 28 -TABLE V. AVERAGE PERCENTAGE COMPOSITION OF EGG SHELLS BY ELECTRON PROBE.MICROANALYSIS .Organic Shell CaO MgO P2°5 Matter 1 51.38 0.645 1.138 6.82 2 52.51 0.608 0.779 4.90 3 52.30 0.474 0.816 5.56 4 53.52 0.266 0.43 2 3.84 5 53.73 0.399 0.402 3.19 6 52.90 0.428 1.108 4.56 7 53.34 0.432 0.455 3.81 8 53.35 0.523 0.716 3.59 9 53.06 0.447 0.49 0 4.28 10 53.01 0 .744 0.617 3.74 11 52.73 0 .510 0 .481 4.73 12 52.54 0 .498 0 .566 5.11 13 52.65 0.471 0.363 4.98 14 52 . 82 0 . 354 0.410 4.91 15 52 .15 0 .541 0 .496 5.72 16 52.42 0.569 0.507 5.17 17 53 .20 0.465 0.400 4.00 18 53.02 0.472 0.345 4.31 19 52.07 0.318 0.507 6 . 32 20 52.97 0.302 0.428 4.75 21 52.43 0.389 0.499 5.53 22 52.35 0.579 ' 0 .410 5.28 23 52.56 . 0.449 0 .496 5.16 24 51.77 0.355 0.869 6.75 25 50.42 0.425 ,0 .634 9.04 26 52 .89 0.590 0.611 4.28 27 53.61 0.322 0.305 3.57 Average 52.65 0.466 0.566 4.96 * Organic matter estimated by difference. - 29 -TABLE VI. AVERAGE PERCENTAGE COMPOSITION AT TEN SHELL LEVELS IN 27 EGG SHELLS BY ELECTRON PROBE MICROANALYSIS Shell l e v e l CaO MgO P2°5 Organic Matter* 0.02 50.57 1.166 2.657 7.06 0.10 52.68 0.938 0.888 3.90 0.20 52.11 0.70 2 0.462 5.45 0.30 52.02 0.537 0.363 5.96 0.40 51.89 0 .401 0.308 6.48 0.50 52.33 0.315 0.271 5.87 0.60 53.37 0.205 0.249 4.25 0.70 53.67 0.077 0.180 3.99 0.80 54.06 0.062 0.134 3.33 0.90 53. 85 0.255 0.147 3.30 Average 52.66 0.466 0.566 4.96 Organic matter estimated by difference - 30 -50 48 0 Figure 6. 0.2 0.4 S h e l 0.6 I e v e 0.8 1.0 CaO content of 2 7 egg s h e l l s . The mean +_ one standard deviation i s shown at each s h e l l l e v e l 2 0 0.2 0.4 0.6 0 .8 1.0 S h e l l l e v e l Figure 7. MgO content of 27 egg s h e l l s . The mean + one standard deviation i s shown at each s h e l l l e v e l . - 31 -Magnesium oxide content i s a maximum at the outer surface, f a l l s to a minimum at s h e l l l e v e l 0.75, then increases toward the inner s h e l l surface. The gradient (figure 7, equation 18) i s quadratic with a standard error of estimate of 0.23. MgO = 1.22 - 2.86X + 1.89X2 [18] where MgO = percent magnesium oxide by weight. Phosphorus concentrations are high near the outer surface of the egg s h e l l and follow an exponential decrease (figure 8) given by P 20 5 = 0 .1U3X u ' , £ ± [19] where P2^5 = P e r c e n - t phosphorus pentoxide by weight X = s h e l l l e v e l Analysis of the variance (Table VII) i n the composition data shows that calcium and magnesium contents are s i g n i f i c a n t l y d i f f e r e n t (P < 0.01) for the s h e l l s of d i f f e r e n t birds and f o r successive s h e l l s from a single hen; however, the phosphorus data do not show s i g n i f i c a n t differences. Highly s i g n i f i c a n t differences i n chemical data among ten positions across the thickness of egg s h e l l s r e f l e c t the presence of calcium, magnesium and phosphorus composition gradients discussed e a r l i e r . - 32 -Figure 8. p 2 ° 5 content of 2 7 s h e l l s . The mean + one standard deviation i s shown at each s h e l l l e v e l . - 33 -TABLE VII. F-RATIOS FROM ANALYSES OF THE VARIANCE IN COMPOSITION OF EGG SHELLS BY ELECTRON PROBE MICROANALYSIS Source of Variation Degrees of Freedom CaO MgO P2°5 Shells (26). 5 .17** 2.9 8** 1.05ns - Birds 8 6 .32** 4.84** 1.53ns - Shells i n birds 18 4 .67** 2.16** 0.8 3ns Shell l e v e l s 9 32 .73** 86.69** 36.13** Error 2 34 Total 269 ** S i g n i f i c a n t at P < 0.01 ns Not s i g n i f i c a n t at P < 0.0 5 - 34 -Comparison of Chemical Analyses by Solution Methods and the Electron Microprobe The 27 sets of composition data, obtained by analyzing egg s h e l l solutions (Table IV), were compared with corresponding electron probe r e s u l t s (Table V) using t - t e s t s of t h e i r meaas. CaO and MgO determinations show s i g n i f i c a n t differences (P < 0.01) f o r the two methods, whereas F^^s c o m P o s i t i o n s are e s s e n t i a l l y the same. Lower MgO values by the electron probe method are expected because the average i s based on composition between s h e l l l e v e l s 0.0 and 0.95 and magnesium content i s known to increase at the inner s h e l l surface (H7, T6). Furthermore, the solu t i o n methods included egg s h e l l samples from the poles of the s h e l l whereas electron probe analyses were r e s t r i c t e d to the equator. Since the physical structure of the s h e l l varies.along i t s length [for example, thickness (T8) and^porosity (Wl)], the chemical nature may also change. The s i g n i f i c a n t c o r r e l a t i o n c o e f f i c i e n t of 0.525 (P < 0.01) between the pairs of MgO compositions indicates a l i n e a r r e l a t i o n between the two methods. - 35 -Relation of Hardness to Chemical Composition Hardness proved to be a c u r v i l i n e a r function of calcium, magnesium and phosphorus content, thus multiple c u r v i l i n e a r regressions were used to determine the r e l a t i o n of hardness to composition i n the pooled data f o r ten s h e l l l e v e l s i n 27 egg s h e l l s . Of the three chemical constituents i n the regressions (Table VIII), magnesium contributes least to the explanation of variance i n hardness, while v a r i a t i o n i n calcium i s the most important contributor. When the data are considered on a pooled basis, the c o e f f i c i e n t of multiple determination i s 0.482; thus, there i s an appreciable r e s i d u a l variance i n hardness a f t e r chemical composition i s considered. ' Examination of the hardness-composition r e l a t i o n i n the data of i n d i v i d u a l s h e l l s reveal d i f f e r e n t regressions from s h e l l to s h e l l . C o e f f i c i e n t s of multiple determination (Table IX) indicate that, on the average, 9 0.9 percent of the v a r i a t i o n i n hardness can be explained by variations i n calcium, magnesium and phosphorus i n the same s h e l l . When two of the chemical constituents are considered the average increase i n explanation of re s i d u a l variance by including the t h i r d component i n the regression i s 51.3, 49.5 and 63.0 percent for calcium, magnesium and phosphorus respectively; therefore, each of the three i s important to the regression. TABLE VIII. MULTIPLE CURVILINEAR REGRESSIONS OF HARDNESS ON COMPOSITION - POOLED BASIS (n = 270) Independent Variable Regression 1 2 c o e f f i c i e n t 3 4 CaOt -133.14** -19 0.6** -134.5** -(CaO) 2 1.312** 1.848** 1.326** -MgO - 3.448ns 8.704ns - - 19. 9 8** (MgO)2 4.115ns 8.868** - 10. 7 5** P2°5 25.91** - 28.21** 25. 30** ( P 2 ° 5 ) 2 - 2.614** - - 2.816** - 2. 597** Constant 3500. 5046. 3532. 136. 6 Sytt 13.96 15.33 13.96 15. 94 R 2 t t t 0.482 0. 371 0.478 0. 320 ** S i g n i f i c a n t at P < 0.01 ns Not s i g n i f i c a n t at P < 0.05 t Percentage compositions by weight are used i n the regression f o r the indicated compounds t t Standard error of estimate t t t C o e f f i c i e n t of multiple determination - 37 -TABLE I X . COEFFICIENTS OF MULTIPLE DETERMINATION FOR REGRESSIONS OF HARDNESS ON COMPOSITION-INDIVIDUAL SHELL BASIS (n = 10) Independent Variables Range Mean Ca, Mg, P t 0.771 - 0.993 0.909 Ca, Mg 0.419 - 0.968 0.754 Ca, P 0.490 - 0.940 0.820 Mg, P 0.564 - 0.974 0 . 813 t Ca represents CaO and 2 2 (CaO) , Mg represents MgO and (MgO) and P represents ?2®5 2 and (P2O,-) where percentage compositions by weight are used i n the regressions for the indicated compounds. - 38 -Hardness i s known to be a cubic function of s h e l l l e v e l as given i n equation [16] for which the c o e f f i c i e n t of multiple determination i s 0.79 5 on the pooled-data basis. Since chemical composition also varies across the thickness of the s h e l l , regressions of hardness on composition and s h e l l l e v e l were considered (Table X). The c o e f f i c i e n t of multiple determination of 0.814 represents a 9.3 percent increase i n explanation of res i d u a l variance due to inc l u s i o n of composition data. Another equally v a l i d i n t e r p r e t a t i o n i s that i n c l u s i o n of s h e l l l e v e l i n the regression of hardness on composition explains an additional 64.1 percent of the re s i d u a l variance i n hardness. It i s evident, therefore, that variations i n hardness of egg sh e l l s are not e n t i r e l y explained by variations i n calcium, magnesium and phosphorus compositions across the thickness of egg s h e l l s . Large improvements i n regressions by including s h e l l l e v e l suggest the presence of factors important to s h e l l hardness that are associated with s h e l l l e v e l . Two additi o n a l factors worthy of consideration are c r y s t a l l i t e s i z e and the organic matrix that extends through the egg s h e l l . C r y s t a l l i t e size i s reported to be much smaller toward the inner surface of the s h e l l than near the outer surface (S2) and, for metals, hardness increases as the grain size decreases (H2). Organic matter i s known to be - 39 -TABLE X. MULTIPLE CURVILINEAR REGRESSIONS OF HARDNESS' ON COMPOSITION AND SHELL LEVEL - POOLED BASIS (n = 270). Independent variable Regression c o e f f i c i e n t 2 3 CaOt - 27 .21ns - 28 . 41ns - 26 . 65ns (CaO) 2 0 .279ns 0 .290ns 0 .273ns MgO - 1 .410ns - 1 .429ns - 1 .507ns (MgO)2 1 . 500ns 1 .785ns 1 .559ns P2°5 1 .617ns 2 •620ns - 0 .181ns ( P 2 ° 5 > 2 - o .167ns - 0 .261ns - 0 .029ns Xtt -324 -333 .4** -324 -347 2 X 529 O A A . 3 " " 546 531 . 3** 584 .3** X 3 -224 .4** -234 •3 A A . 3 " " -225 .9** -254 rt A A . / " " Constant 842 .7 877 .1 827 .1 184 .6 Syttt 8 .42 8 .39 8 .40 8 .78 R 2 t t t t 0 .814 0 .814 0 .814 0 .796 Percentage compositions by weight are used i n the regression f o r the indicated compounds t t S h e l l l e v e l t t t Standard error of estimate t t t t C o e f f i c i e n t of multiple c o r r e l a t i o n ns Not s i g n i f i c a n t at P < 0.05 ** S i g n i f i c a n t at P < 0.01 - UO -present throughout the egg s h e l l (SU) i n the form of f i b r i l s and v e s i c l e s , and there i s evidence of histochemical differences across the thickness of the s h e l l (S2). Mean values of estimated organic content obtained i n t h i s research (Table VI) show variations with s h e l l l e v e l . These observations are suggestive; however, there i s no d i r e c t evidence l i n k i n g c r y s t a l l i t e size and the nature of the organic matrix with hardness i n the hen's egg s h e l l . SUMMARY AND CONCLUSIONS Hardness and chemical composition were measured at ten positions across the thickness of 27 egg s h e l l s . Hardness varies i n a c u r v i l i n e a r manner with maximum values at the outer surface, intermediate values at the inner surface and minimum values midway between. Calcium content increases toward the inside of the egg s h e l l whereas magnesium and phosphorus are a maximum at the outer surface and follow quadratic and exponential gradients res p e c t i v e l y . For the data of i n d i v i d u a l s h e l l s , v a r i a t i o n i n chemical composition explains an average of 9 0.9 percent of the v a r i a t i o n i n hardness; however the r e l a t i o n s h i p between hardness and composition d i f f e r s from s h e l l to s h e l l . From the analysis of pooled data f o r a l l s h e l l s , variations i n composition account for U8.2 percent of the v a r i a t i o n i n hardness. Inclusion of s h e l l l e v e l i n the regression increases the c o e f f i c i e n t of multiple determination to 81.U percent; - Ul -thus, a d d i t i o n a l unknown factors associated with s h e l l l e v e l , may have an appreciable influence on egg s h e l l hardness. / CHAPTER I I . STRUCTURE OF EGG SHELL MEMBRANES Egg s h e l l membranes form a f l e x i b l e leathery p a r t i t i o n between the egg albumen and the s h e l l . This structure consists of matted f i b e r s with a combined thickness of about 65 microns (R3). Two layers are evident at the a i r c e l l region of the egg where the f i b e r s separate to form the inner and outer membranes. At other locations i n the egg, the membranes appear as a single layer; however, they may e a s i l y be pulled apart. Although the inner membrane i s thinner than the outer membrane (R3), the inner layer i s more e f f e c t i v e i n preventing b a c t e r i a l invasion of the egg (Gl, L I ) . The object of t h i s i n v e s t i g a t i o n was to elucidate the structure of the egg s h e l l membranes with p a r t i c u l a r emphasis on differences between the inner and outer layers. REVIEW OF THE LITERATURE The fibrous nature of egg s h e l l membranes has been known for over a century according to descriptions of early studies by l i g h t microscopy (Nl, S8). Fiber diameters of 0.5 to 1.5 microns were reported; however, descriptions of f i n e structure were not possible at that time due to l i m i t a t i o n s imposed by the available microscopes. - 42 -- 43 -Recent studies (Ml, S4) of egg s h e l l membranes by electron microscopy revealed two d i s t i n c t regions i n the cross section of i n d i v i d u a l f i b e r s - an inner electron dense core and a l i g h t e r granular mantle surrounding the core. The core o consists of a-keratin f i b r i l s 30 to 40 A i n diameter and the mantle i s thought to be a mucopolysaccharide material. The two regions are separated by an o p t i c a l l y empty gap; however, i t i s not known whether the gap i s present i n the normal tissue or i s an a r t i f a c t r e s u l t i n g from the preparations f o r electron microscopy. Observations on a transverse section through the membranes (S4) indicate that f i b e r diameters are somewhat larger i n the outer membrane than i n the inner. In a single plane section through the membrane, fi b e r s are cut i n cross section and l o n g i t u d i n a l l y ; thus, the f i b e r s must run i n varying d i r e c t i o n s throughout the membrane. At the inner surface of the inside membrane there i s a thi n layer of material that appears to be continuous over the surface. Experiments with fresh eggs have shown that t h i s layer i s impermeable to egg albumen (B9, NI); therefore, i t may serve to exclude egg albumen from the spaces between f i b e r s i n the membrane. In general, studies on egg s h e l l membranes have been q u a l i t a t i v e i n nature with l i t t l e information on f i b e r sizes and orientations along with the variations i n these - 44 -c h a r a c t e r i s t i c s at d i f f e r e n t positions i n the membrane. The present experiment was i n i t i a t e d to provide quantitative measurements of f i b e r size and o r i e n t a t i o n i n egg s h e l l membranes. EXPERIMENTAL METHODS Preparation of Specimens Two fresh eggs were randomly selected from the production of Single-Comb White Leghorn p u l l e t s (WL1 and WL2) and another two from New Hampshire p u l l e t s (NH1 and NH2). The eggs were opened, contents were discarded and albumen was washed from the egg i n t e r i o r using phosphate buffer solution (pH =7.4). Membrane samples were taken from the a i r c e l l region of each egg i n such a manner that observations could be made on transverse sections that would be approximately l a t i t u d i n a l with respect to the egg geometry, that i s , almost p a r a l l e l to the egg equator. A piece of the inner membrane was excised and placed i n 3% gluteraldehyde-phosphate buffer solution for a 30 minute primary f i x a t i o n . A small part of the s h e l l with the adhering outer membrane was treated with the f i x a t i v e for 90 minutes. Following f i x a t i o n , membrane samples were washed i n phosphate buffer. The egg s h e l l was d e c a l c i f i e d using a 6% solution of the disodium s a l t of ethylene diamine t e t r a - a c e t i c (EDTA) containing 6% paraformaldehyde with the pH adjusted to 7.4 - 45 -by sodium hydroxide. Membrane samples were then cut into small pieces and further fixed and stained for 2 hours with 1% osmium tetroxide i n phosphate buffer. The tissue was dehydrated with a series of increasingly concentrated ethanol solutions , followed by replacement with propylene oxide, then i n f i l t r a t e d and embedded i n Epon 812 (L3). Transverse sections of the membranes were cut at o 900-1500 A with a Porter Blum ultramicrotome. The sections were picked up on carbon coated grids and stained f o r 15 minutes with uranyl acetate saturated i n 70 percent methanol, then washed and stained for 10 minutes i n lead c i t r a t e solution (R2). Examination by Electron Microscopy The sections were examined i n a P h i l i p s 75C electron microscope at 60kV and images were recorded using an electron o p t i c a l magnification of 830 diameters. Micrographs were printed at t o t a l magnifications of 6000 to 7000 times. Some higher magnifications up to 40,000 times were used to examine fi n e structure of the membranes. Transverse sections of the outer membranes were recorded by choosing several adjacent f i e l d s and preparing composites of the r e s u l t i n g micrographs. These methods provided views of complete transverse sections through both the inner and outer s h e l l membranes of the four eggs. - 46 -Measurement of Membrane Dimensions A coordinate system was applied to each transverse section by marking a rectangular area on the micrographs such that one pair of opposite sides coincided with the outer and inner boundaries of the membrane. Fiber dimensions (figure 9) were measured from micrographs of transverse sections for each of the four outer and inner membranes. Many f i b e r s were cut obliquely and appeared to be e l l i p t i c a l i n the section. The mantle surrounding the f i b e r core was not of uniform thickness even i n f i b e r s cut at r i g h t angles to t h e i r major axes; thus, the least diameter of the e l l i p t i c a l section was assumed to be the true f i b e r diameter and f i b e r core dimensions were measured i n preference to the combined core and mantle dimensions. Average mantle thickness was evaluated i n the d i r e c t i o n of the least diameter of the f i b e r section. Each f i b e r i n the membrane section provided f i v e measurements: f i b e r core diameter ( d c ) , maximum core diameter (d ), average mantle thickness (t ), m m ' the distance from the f i b e r center to the outside edge of the membrane section (x) and the angle between the outside edge of the membrane section and the major axis of the f i b e r cross section (<}>). Analysis of Data Linear measurements from the micrographs were converted to actual dimensions in the tissue using the appropriate magnification factors. The position of the f i b e r - 47 -Figure 9 . Schematic diagram of an oblique section through an egg s h e l l membrane f i b e r to i l l u s t r a t e the dimensions measured. - H8 -i n r e l a t i o n to the membrane surfaces was derived from the distance between the f i b e r center and the outside edge of the membrane. This dimension was divided by the t o t a l membrane thickness to give a number between 0 and 1.0 which was c a l l e d membrane l e v e l . The proportion of the transverse section occupied by f i b e r s was computed f o r each membrane. Fibers were assumed to be c i r c u l a r i n cross section with the mantle uniformly d i s t r i b u t e d around the f i b e r core. Thus, for f i b e r s that passed through the plane of the section i n a d i r e c t i o n other than normal to the section, the exposed oblique sections were e l l i p t i c a l and the areas calculated accordingly. The r a t i o of t o t a l exposed f i b e r area and membrane section area was termed f i b e r area density. Mean values of f i b e r core diameter and mantle thickness were computed f o r the outer and inner membranes of each egg. T-tests were used to determine whether the mean f i b e r core diameter and mantle thickness d i f f e r between outer and inner membranes of the same egg. Similar comparisons were also made among outer membrane dimensions and among inner membrane dimensions of the four eggs by means of t - t e s t s . The data f o r each membrane were then separated into portions according to membrane l e v e l i n order to examine f i b e r dimensions at d i f f e r e n t locations across the thickness of the structures. On the basis of equal membrane - 49 -l e v e l i n t e r v a l s , data were divided into ten and four groups for outer and inner membranes respectively. Means and standard deviations were then computed for each group of data. RESULTS AND DISCUSSION Qualitative Observations on Membrane Structure E a r l i e r descriptions of egg s h e l l membrane structure (Ml, S4) are confirmed by t h i s study. Individual f i b e r s possess a central core surrounded by a mantle with a d i s t i n c t separation between the two regions (figures 10 to 13). Higher magnifications reveal the orderly fibrous nature of the core i n contrast, to the granular appearance of the mantle. Mantle thickness i s variable even f o r f i b e r s cut i n cross section. The mantle layer i s often continuous around adjacent f i b e r s and appears to cement f i b e r s together where they cross. In a single section, f i b e r s are cut i n cross section and l o n g i t u d i n a l l y as well as at angles intermediate to the two extremes; thus, the f i b e r s t r a v e l i n many directions to form a matted network. At s i m i l a r magnifications, f i b e r s i n the outer membrane appear larger than those of the inner membrane. For some pairs of membranes, p a r t i c u l a r l y from the White Leghorn b i r d s , there appears to be larger i n t e r f i b e r spaces i n the inner membrane. Inside boundaries of inner membranes have a 0.1 micron thick layer of material s i m i l a r i n electron - 50 -Figure 10. WL1 outer egg s h e l l membrane (66 60X). Figure 11. WL2 inner egg s h e l l membrane (6660X). - 51 -Figure 12. NH1 outer egg s h e l l membrane (70 50X). Figure 13. NH1 inner egg s h e l l membrane (11200X). - 52 -density to the mantle substance (figures 11 and 13). The WL2 inner membrane has two layers separated by a narrow gap. Since the other membrane surfaces are of open structure and i n t e r f i b e r spacings are larger than b a c t e r i a l dimensions, t h i s continuous layer i s the only v i s i b l e physical b a r r i e r to microbial penetration of egg s h e l l membranes. Results of Measurements of Membrane Structure  Membrane thickness and f i b e r area density Outer egg s h e l l membranes are approximately three times as thick as inner membranes (Table XI). The combined structures range from 7 3 to 114 y i n thickness. Fiber area density provides a measure of combined f i b e r size and spacing c h a r a c t e r i s t i c s i n the plane of the membrane section. For the membranes of the White Leghorn eggs, outer membranes have a f i b e r area density twice that of inner membranes. This r e s u l t confirms the more open appearance of the inner membrane (figure 11) r e l a t i v e to the outer (figure 10). The closeness of the f i b e r area densities f o r the two NH1 membranes i s r e f l e c t e d by t h e i r q u a l i t a t i v e s i m i l a r i t i e s evident i n figures 12 and 13. - 53 -TABLE XI. THICKNESS AND FIBER AREA DENSITY OF EGG SHELL MEMBRANES Membrane Thickness, JJ Fiber area densityt WL1 - outer 53.2 0.554 - inner 19.5 0.272 WL2 - outer 6 5.5 0.490 - inner 24.3 0.238 NH1 - outer 91. 8 0. 369 - inner 22.4 0.388 NH2 - outer 80.9 0.456 - inner 27.7 0 .331 t Fiber area density i s defined as the r a t i o of t o t a l exposed f i b e r area and membrane section area. - 54 -Mean values of f i b e r measurements The mean f i b e r core diameter (Table XII) of the outer membrane i s s i g n i f i c a n t l y greater (P < 0.01) than the mean f i b e r core diameter of the inner membrane for each of the four eggs. Comparisons among corresponding WL1 and WL2 membranes indicate that mean f i b e r core diameters d i f f e r (P < 0.01) between the outer membranes whereas the inner • membrane f i b e r core diameters are e s s e n t i a l l y the same (P > 0.05). T-tests of the NH1 and NH2 membranes reveal no s i g n i f i c a n t differences (P > 0.05) of the mean f i b e r core diameters i n the pair of outer membranes and i n the pa i r of inner membranes. In a l l comparisons between corresponding 'membranes of the White Leghorn and New Hampshire eggs, mean f i b e r core diameters were s i g n i f i c a n t l y greater (P < 0.01) for the New Hampshire eggs. The mean f i b e r mantle thickness i n the White Leghorn eggs does not d i f f e r (P > 0.05) between outer and inner membranes nor between membranes of d i f f e r e n t eggs. Mantle thickness i s greater i n the inner NH1 membrane than i n the outer membrane whereas the reverse i s true f o r the NH2 membranes. In general, f i b e r s i n the New Hampshire membranes possess thicker mantles (P < 0.01) than those i n White Leghorn membranes. The average c o e f f i c i e n t of v a r i a t i o n of 57.8 percent indicates that mantle thickness i s highly variable i n egg s h e l l membranes. TABLE XII. MEAN VALUES OF EGG SHELL MEMBRANE MEASUREMENTS Membrane Number of f i b e r s measured microns microns • t t t , degrees WL1 - outer 459 0.681 0.105 -0.34 - inner 145 0.481 0.102 2.04 WL2 - outer 571 0.789 0.102 -0.76 - inner 222 0.475 0.096 -2.07 NH1 - outer 443 0.871 0.149 -3.22 - inner 152 0.574 0.172 0.53 NH2 - outer 433 0.842 0.151 1.57 - inner 128 0.592 0.120 1.37 t Diameter of f i b e r core t t Thickness of f i b e r mantle t t t Angle between outer edge of membrane section and major axis of f i b e r cross section - 56 -It should be noted that f i b e r size i s reported as f i b e r core diameter and average mantle thickness f o r reasons discussed e a r l i e r . Overall f i b e r diameter may r e a d i l y be computed as the sum of f i b e r core diameter and twice the mantle thickness. The angle <f> (Table XII), between the outer edge of the membrane section and the major axis of an exposed section through a f i b e r , r e f l e c t s the f i b e r d i r e c t i o n i n r e l a t i o n to the surfaces of the membrane. If f i b e r s are assumed to be c y l i n d r i c a l , <f> = 0° represents a f i b e r i n a surface p a r a l l e l to the membrane surfaces, whereas <f> = + 90° describes a f i b e r passing diagonally across the thickness of the membrane. Since the mean value of c}> for the f i b e r s i n each membrane approaches zero, f i b e r s are located i n surfaces approximately p a r a l l e l to the membrane surfaces. Variation i n f i b e r measurements across the membrane Average f i b e r core diameters at ten outer membrane lev e l s and four inner membrane le v e l s are shown i n figures 14 to 17. No consistent trend i s evident i n mean f i b e r core diameter across the thickness of the four outer and the four inner membranes; however, f i b e r diameters are d i s t i n c t l y smaller f o r the inner membranes of each p a i r . For each of the in t e r v a l s across the membrane, f i b e r core diameters show considerable v a r i a t i o n as i s i l l u s t r a t e d i n the figures by the v e r t i c a l bars which represent the standard deviation. - 57 -0 . 2 0 0.5 1.0 0 . 4 0 . 6 0 . 8 M e m b r a n e l e v e l Figure 14. Fiber core diameters f o r membrane WL1. The mean and standard deviation at each l e v e l are shown. 0 . 4 0 . 6 0 . 8 M e m b r a n e l e v e l Figure 15. Fiber core diameters for membrane WL2. The mean and standard deviation at each l e v e l are shown. - 58 -0 0 . 2 Figure 16 0 . 4 0 . 6 0 . 8 0 0 .5 1.0 • M e m b r a n e level Fiber core diameters for membrane NH1. The mean and standard deviation at each l e v e l are shown. 0 . 4 0 . 6 0 -8 M e m b r a n e l e v e l Figure 17. Fiber core diameters for membrane NH2. The mean and standard deviation at each l e v e l are shown. - 59 -0.5 1 0 0.4 0.6 0.8 Membrane level Figure 18. Average f i b e r mantle thickness f o r membranes WL1 and WL2. .0.3 tsi C 0) c o 0.1 Outer 0.2 • = NH1 A r NH 2 ± Inner 0.4 0.6 0 8 Membrane level 0 0.5 1.0 Figure 19. Average f i b e r mantle thickness f o r membranes NH1 and NH2. - 60 -The average mantle thickness fluctuates across the membrane (figures 18 and 19); however, the variations appear to be random. SUMMARY AND CONCLUSIONS The s h e l l membranes of four eggs were subjected to electron microscopical examination at r e l a t i v e l y low magnifications. Micrographs were assembled to permit measure-ments of pos i t i o n and dimensions for each f i b e r i n transverse sections through the membranes. Egg s h e l l membranes consist of a fibrous network that i s separated into two d i s t i n c t layers. The outer membrane i s three times as thick as the inner membrane and the combined structure i s approximately 100 microns i n thickness. Fibers are oriented i n many directions i n surfaces that p a r a l l e l the membrane surfaces. The fib e r s of outer membranes are larger than those of inner membranes and spacings among the f i b e r s may d i f f e r from membrane to membrane. A 0.1 micron continuous layer of tissue i s present at the inside surface of the inner s h e l l membrane. Since the remaining structures are an open network, t h i s layer may be of fundamental importance i n retarding b a c t e r i a l penetration of egg s h e l l membranes. Individual f i b e r s within the membranes possess a central core surrounded by a granular mantle of varying thickness. Fiber core diameters are s i g n i f i c a n t l y larger (P < 0.01) i n the outer membrane than i n the inner membrane of an egg. - 61 -Variations i n f i b e r core diameter and mantle thickness occur across the thickness of egg s h e l l membranes; however, these variati o n s appear to be random. CHAPTER I I I . RHEOLOGY OF EGG ALBUMEN Rheological properties of f l u i d foods influence the design of materials handling and processing equipment. Since most foods have a complex viscous nature ( C l , H4, L2, SI, W2) that changes with composition, temperature, shear rate and duration of shearing; studies of food rheology are la r g e l y empirical. Three hundred m i l l i o n pounds of egg albumen are processed annually on t h i s continent (Fl) by means of operations that include separating, pumping, mixing, heating, cooling and spray drying; however, very l i t t l e information i s a vailable on the physical properties of t h i s f l u i d . Lack of adequate rh e o l o g i c a l characterization of egg albumen has undoubtedly been an obstacle i n the design of processing equipment. The purpose of t h i s research was to supplement available data on the viscous behavior of egg albumen. REVIEW OF THE LITERATURE Flow of egg albumen through c a p i l l a r y tubes under constant pressure has been used to compare consistencies of samples subjected to d i f f e r e n t experimental conditions ( B l , S5). Such information i s useful i n detecting changes i n v i s c o s i t y ; however, single point v i s c o s i t y measurements do not characterize flow behavior over a range of shear rates as required f o r design purposes. Damping properties of int a c t eggs have been studied using a torsion pendulum - 62 -- 63 -( A l , RH); however, the data show small correlations with the viscous nature of the egg components. The modulus of r i g i d i t y of thick albumen has been evaluated by means of the displacement of a small n i c k e l sphere i n a magnetic f i e l d and by torsion between concentric cylinders (B7). Kaufman ejt a l . (Kl) c i t e d unpublished data i n which v i s c o s i t y of commercial unfrozen egg products at pasteurization temperatures did not change greatly over a range of shear rates. Preliminary tests on thick and th i n egg albumen, separately and combined, at temperatures up to U0°C, showed decreasing apparent v i s c o s i t i e s with increasing shear rates. Shearing also causes a breakdown of structure during tests i n a pressurized c a p i l l a r y viscometer (S5) and i n a r o t a t i o n a l viscometer at a constant rate of shear (T5). Thus egg albumen exhibits pseudoplastic, time-dependent flow behavior at moderate temperatures. The following experiments were designed to evaluate the rh e o l o g i c a l behavior of egg albumen over a moderate range of shear rates and temperatures. EXPERIMENTAL METHODS Preparation of Samples Two l o t s of s i x t y fresh eggs were used i n t h i s experiment. Twenty randomly selected eggs from each l o t were weighed, albumen height measured and Haugh score calculated (B5) to serve as a general i n d i c a t i o n of egg q u a l i t y . The albumen from each l o t of. sixt y eggs was combined and forced - 64 -six times through a number 3 Buchner funnel. This procedure homogenized the thick and thin portions of the albumen and was intended to simulate the commercial practice i n which albumen i s passed through a fine mesh screen to remove suspended materials. Samples were taken f o r measurements of pH and percentage solids (H6). Test Procedures Viscous properties were measured with a Haake r o t a t i o n a l viscometer (VI) equipped with MVI and NV narrow-gapped concentric cylinder spindles and cups. The MVI spindle with a gap width of 0.96 mm provided a maximum shear rate of 1320 sec 1 whereas the NV spindle had a maximum shear rate of 3140 s e c - 1 and was double-gapped with widths of 0.70 and 0.80 mm. C a l i b r a t i o n constants f o r the spindles were established by means of o i l v i s c o s i t y standards. Output from the dual-range to r s i o n dynamometer was fed to a 10-inch, two channel, s t r i p chart recorder through a switch that permitted sel e c t i o n of either recorder channel. One channel was ca l i b r a t e d at twice the s e n s i t i v i t y of the other to increase precision of measurement for smaller signals. Sample temperatures were maintained within +_ 0.5°C by a thermostatically controlled water jacket surrounding the measuring head. Each sample was f i r s t tested for time dependence by recording the- shear-stress decay curve at a constant rate of shear. The shear-stress curve reached a maximum a f t e r one or two seconds due to recorder response and i n e r t i a l e f f e c t s , then appeared to follow a logarithmic decay to an - 65 -equilibrium value i n f i v e to ten minutes. When the shear stress reached a constant value, flow-behavior curves were obtained by decreasing the shear rate over a series of steps and then increasing the shear rate stepwise to the o r i g i n a l value while recording the corresponding shear stresses. The maximum shear rate used i n obtaining flow curves did not exceed the shear rate of the time-dependence t e s t s . The following tests were performed using one l o t of egg albumen. Recovery of shear strength was investigated at 10°C i n three samples sheared at a rate of 3140 sec-"1", a f t e r which the samples were stored i n a i r t i g h t p l a s t i c containers at 4°C for 32 hours and then retested under i d e n t i c a l conditions. Shear rates of 1570 and 3140 sec"''" were used on t r i p l i c a t e samples to determine the influence of shear rate on the time-dependent c h a r a c t e r i s t i c . The second l o t of albumen was tested at temperatures of 10, 20, 30 and 40°C using each of the two spindles. Shear-stress decay curves and equilibrium flow-behavior curves were obtained f o r a l l tests and a t o t a l of three runs were made at each experimental condition. Rheological Models  Models of time-dependent behavior Data were sampled from the chart paper by a method (C2) designed to preserve data equally throughout i t s range. Since shear stress appeared to decrease lo g a r i t h m i c a l l y with time, the range between the i n i t i a l usable maximum and the - 66 -e q u i l i b r i u m s h e a r - s t r e s s w a s d i v i d e d i n t o t e n e q u a l l o g a r i t h m i c i n t e r v a l s a n d t h e c o r r e s p o n d i n g s t r e s s e s a n d t i m e s w e r e r e c o r d e d . F o r t h e p u r p o s e o f a n a l y s i s , n a n d n - n w e r e c a l c u l a t e d f o r e a c h d a t u m . , w h e r e n i s a p p a r e n t v i s c o s i t y i n p o i s e a n d n i s t h e a p p a r e n t v i s c o s i t y a t e q u i l i b r i u m f o r a r u n . D a t a f o r t h e t h r e e r u n s a t e a c h e x p e r i m e n t a l c o n d i t i o n w e r e p o o l e d a n d t r e a t e d a s a s i n g l e c u r v e . U s i n g n a n d n ~ n e a s d e p e n d e n t v a r i a b l e s a n d t i m e a s t h e i n d e p e n d e n t v a r i a b l e ; l i n e a r , l o g a r i t h m i c a n d h y p e r b o l i c f u n c t i o n s w e r e t e s t e d f o r a c c u r a c y o f f i t t o t h e d a t a . F u n c t i o n s t h a t s u i t a b l y f i t t e d t h e d a t a w e r e : n = a l " b i l o g 1 t 2 0 - * l o g (n-n e> = a 2 - b 2 t [21] a n d l o g (n-n e) = a 3 - b 3 l o g t [22] w h e r e t i s t i m e i n s e c o n d s a n d a ^ , a 2 , a 3 , b ^ , b 2 , b 3 a r e c o n s t a n t s . E q u a t i o n s [20] a n d [21] a r e s i m i l a r t o m o d e l s s u g g e s t e d b y W e l t m a n n (W4) a n d H a h n e t a l . ( H I ) f o r s t r e s s r e l a x a t i o n i n t h i x o t r o p i c s y s t e m s . E q u a t i o n [22] w a s u s e d i n s u b s e q u e n t a n a l y s e s b e c a u s e i t d e s c r i b e d t h e d a t a m o s t a c c u r a t e l y w i t h a n a v e r a g e c o e f f i c i e n t o f d e t e r m i n a t i o n o f 0.8 3 c o m p a r e d w i t h 0.7 2 a n d 0.7 7 f o r E q u a t i o n s [20] a n d [21] r e s p e c t i v e l y . - 67 -Models of flow-behavior Equilibrium flow-behavior data were f i t t e d by the well known power-law equation n = my11'1 [23] » h • \k]1/n *<l/B)-1 where n = apparent v i s c o s i t y , poise -1 Y = rate of shear, sec T = shear s t r e s s , dynes cm~^ m = the consistency index, and n = the flow-behavior index Values f o r m and n were derived from the intercept and slope of the least-squares l i n e a r f i t of log n to log y f o r each experimental condition. The power-law i s the simplest and most widely used empirical model for non-Newtonian behavior (B2). Newtonian flow i s characterized by a flow-behavior index of unity, whereas values less than one apply to pseudoplastic materials. This model f i t s the flow curves of many pseudoplastics over one or two decades of shear rate but does not apply to the extremes i n shear rate because the equation predicts an i n f i n i t e v i s c o s i t y as the shear rate approaches zero and a zero v i s c o s i t y f or i n f i n i t e shear rates. The E l l i s model was also used to describe the flow-behavior data i n the form where n o = apparent v i s c o s i t y at zero shear rate T,/0 = shear stress corresponding with 1/2 n a = a parameter This three-parameter model i s more generally applicable to r e a l f l u i d s p a r t i c u l a r l y at low shear rates because i t describes a zero-shear v i s c o s i t y , n o . Since equation [25] i s not suited to a d i r e c t s o l u t i o n , the parameters computer method. Temperature Ef f e c t s on Flow Behavior  Temperature dependence of flow parameters Flow-behavior parameters of polymer solutions have been shown to be dependent on temperature (T7) , thus the power law and E l l i s model parameters were examined as functions of temperature. The data were tested with several d i f f e r e n t functions and were found to be suitably described by equations s i m i l a r to those of Turian (T7). V T l / 2 and a were evaluated using a t r i a l - a n d - e r r o r log m = log m° + A 0 [26] n = n° + B 0 [27] log n Q = log n° + C 0 log T 1 / 2 = log TJ / 2 + D 0 (1/a) = (l/a)° + E 0 [28] [29] [30] - 69 -rn rpo where 0 = — [31] T° = a reference temperature, 10°C T = temperature, °C A, B, C, D, and E are constants and the superscripted terms are values of the parameters at the reference temperature T°. Temperature dependence of v i s c o s i t y Over a moderate range of temperatures the v i s c o s i t y of most f l u i d s changes according to the Arrhenius equation n = A e A E / R T [32] where A = a constant AE = a c t i v a t i o n energy for viscous flow R = gas constant T = temperature, °K Flow-behavior data were grouped according to shear rate and each set of data was f i t t e d by equation [32] to evaluate A and AE. S t a t i s t i c a l Methods Used i n Data Analysis A l l r h e ological models were f i t t e d to data by least-squares regression methods. Time-dependence tests each provided 30 observations whereas flow-behavior tests usually consisted of 24 separate measurements. In order to evaluate the e f f e c t s of cer t a i n experimental conditions on viscous behavior, pairs of regressions were tested for differences of slope and l e v e l with a covariance analysis outlined by Snedecor (S7). RESULTS AND DISCUSSION Sample Quality Average Haugh scores of 89.8 and 85.0 were obtained for twenty eggs from l o t s 1 and 2 respectively. The corresponding percentage solids were 12.92 and 11.36 and pH values during the tests were e s s e n t i a l l y constant at 8.4 +_ 0.2. These data indicate that the albumen was of high q u a l i t y ; hence, some caution i s recommended when estimating rh e o l o g i c a l properties of low quality albumen on the basis of the data reported herein. From the r e s u l t s of previous experiments at 2°C on egg albumen of high and low quality (T5), the e f f e c t of lower qu a l i t y albumen would be more pronounced i n the time-dependent c h a r a c t e r i s t i c than i n the equilibrium flow-behavior. Results of Time-Dependence Tests  Recovery of apparent v i s c o s i t y a f t e r storage In figure 20, the apparent-viscosity decay curve fo r three samples at 10°C and a shear rate of 3140 sec i s compared with the curve for tests repeated on the same samples 32 hours l a t e r . Since the two curves d i f f e r i n slope and l e v e l (P < 0.01), albumen does not recover i t s o r i g i n a l time-dependent c h a r a c t e r i s t i c . A c r i t e r i o n of thixotropy i s that the material returns to i t s o r i g i n a l structure when l e f t undisturbed f o r a period of time following mechanical a g i t a t i o n . If s t r u c t u r a l breakdown i s non-reversible, the f l u i d i s said to - 70 -- 71 -0.5 1.0 , 1.5 2 . 0 2 . 5 Log t Figure 20. Apparent-viscosity decay i n egg albumen tested before and a f t e r 32 hours storage. Tests at 10°C and 3140 sec" 1 shear rate. - 0 . 8 P ^ 1 . 4 h cn o - 2 . 0 h - 2 . 6 Figure 21 L o g t Apparent-viscosity decay i n egg albumen at 10°C with shear rates of 1570 and 3140 s e c " 1 . - 72 -be rheodestructive (M2). There i s , however, an appreciable recovery of structure because the apparent v i s c o s i t y near, the beginning of the second curve i s much higher than the apparent v i s c o s i t y of the i n i t i a l curve at equilibrium. On the basis of these r e s u l t s , the s t r u c t u r a l breakdown mechanism i n egg albumen at constant shear rate appears to be a combined thixotropic-rheodestructive process. E f f e c t of shear rate on apparent-viscosity decay The e f f e c t of d i f f e r e n t shear rates on apparent-v i s c o s i t y decay at 10°C i s shown in figure 21 for shear rates of 1570 and 3140 sec \ Both the slope and l e v e l of the curves d i f f e r s i g n i f i c a n t l y (P < 0.01) with the more rapid decay and extensive breakdown at the higher shear rate. As a r e s u l t of t h i s observation, low shear rates are recommended for operations i n which the viscous structure of albumen i s to be preserved. E f f e c t of temperature on apparent-viscosity decay Apparent-viscosity decay curves at 10, 20, 30 and 40°C are presented f o r the NV spindle (figure 22, Table XIII) and f o r the MV1 spindle (figure 23, Table XIV). It should be noted that data for the two spindles are considered separately because of t h e i r d i f f e r i n g shear rates (for the NV spindle, -1 -1 Y = 3140 sec while for the MV1 spindle, y = 1320 sec ). In covariance analyses of a l l possible pairs of l i n e s from the two sets of data, the slopes are e s s e n t i a l l y the same - 73 -- 1 . 0 0 0.5 1.0 1.5 2.0 2.5 L o g t Figure 22. Apparent-viscosity decay curves at 10, 20, 30 and U0°C - NV spindle. 0 . 5 1.0 1.5 2.0 2.5 L o g t Figure 23. Apparent-viscosity decay curves at 10, 20, 30 and 40°C - MVI spindle. TABLE XIII. APPARENT-VISCOSITY DECAY CURVES FOR NV SPINDLE Temperature, °C V Sytt r 2 t t t 10 1.138 -0.637 0.086 0.943 20 1.075 -0.676 0.089 0.939 30 0.827 -0.658 0.095 0.925 UO 0.695 -0.715 0.082 0.949 t a^, bg are constants defined by equation [22] t t Standard error of estimate t t t C o e f f i c i e n t of determination (n = 30) - 75 -TABLE XIV. APPARENT-VISCOSITY DECAY CURVES FOR MVI SPINDLE Temperature, °C a3 + V Sytt r 2 t t t 10 1.272 -0.4 39 0.166 0.790 20 1.027 -0.529 0.145 0. 821 30 0.678 -0 . 399 0.232 0.531 40 0.457 -0.514 0.148 0.792 t a^, are constants defined by equation [22] t t Standard error of estimate t t t C o e f f i c i e n t of determination (n = 30) - 76 -(P > 0.05) over the temperature range; however, the le v e l s are s i g n i f i c a n t l y d i f f e r e n t (P < 0.01). That i s , the rate of s t r u c t u r a l breakdown appears unaffected by temperature although v i s c o s i t y i s generally lower at higher temperatures. Results of Flow-Behavior Tests  E f f e c t of storage on flow-behavior Power-law equations.for the flow curves (figure 24) of the samples tested at 10°C before and a f t e r 32 hours of re f r i g e r a t e d storage are, respectively n = 0.32 Y ~ ° ' 2 4 [33] n = o.i8 Y " 0 , 1 8 [34] The flow curves d i f f e r s i g n i f i c a n t l y (P < 0.01) i n both slope and l e v e l , thus egg albumen appears to undergo a dete r i o r a t i o n i n viscous structure when tested and stored. Flow behavior indices (n) increase from 0.76 to 0.82 ind i c a t i n g that egg albumen becomes more Newtonian as a r e s u l t of t h i s treatment. E f f e c t of maximum shear rate on flow-behavior Flow curves f o r samples tested with the NV spindle at 10°C, at maximum shear rates of 1570 and 3140 sec \ are shown in f igure 25. The power-law equations for the data are r) = 0.32 Y " 0 , 2 3 [35] and n = 0.32 y " 0 , 2 4 [36] f o r maximum shear rates of 1570 and 3140 sec res p e c t i v e l y . Slopes of the two curves do not d i f f e r (P > 0.05); however, the l e v e l s are s i g n i f i c a n t l y d i f f e r e n t (P < 0.01). It should be noted that the flow curves are based on equilibrium apparent v i s c o s i t i e s over a c e r t a i n range of shear rates and - 77 --1 .12 L o g y Figure 24. Flow behavior of egg albumen samples tested before and a f t e r 3 2 hours storage. Tests at 10°C with NV spindle. 2.5 2.7 2.9 3.1 3.3 3.5 L o g J Figure 25. Flow behavior of egg albumen at 10°C f o r maximum shear rates of 1570 and 3140 s e c - 1 . - 78 -that the extent of s t r u c t u r a l breakdown i n the f l u i d at a given temperature i s determined by the maximum shear rate. Although most of the data for the two curves are within the same range of shear rates, the flow properties are quite d i f f e r e n t (P < 0.01). These r e s u l t s indicate that egg albumen rheology i s strongly dependent upon the shear history of the f l u i d . The power-law model of flow behavior Power-law parameters for the albumen flow curves . (figure 26) at 10, 20, 30 and 4 0°C are shown i n Table XV f o r NV and MVI spindles. For each of the four temperatures, flow curves obtained by the two spindles are s i g n i f i c a n t l y d i f f e r e n t (P < 0.01) thus, dependence of albumen flow behavior on shear his t o r y i s confirmed. The average c o e f f i c i e n t of determination of 0.762 f o r the eight curves indicates that the power-law accurately describes the flow behavior of egg albumen over the range of shear rates tested. Covariance analyses of the six possible pairs of flow curves obtained from the NV-spindle show s i g n i f i c a n t differences (P < 0.05) i n slopes f o r a l l pairs except the 20-30°C and 30-40°C •comparisons. A l l pairs of curves are s i g n i f i c a n t l y d i f f e r e n t (P < 0.01) i n l e v e l . Thus, the flow curves f o r egg albumen between shear rates of 520 and 3140 sec 1 show some differences among flow-behavior indices and s i g n i f i c a n t differences among apparent v i s c o s i t i e s at ten degree i n t e r v a l s from 10 to U0°C. MVl-spindle r e s u l t s do not d i f f e r i n slope (P > 0.05); however, a l l pairs of curves d i f f e r i n l e v e l (P < 0.01) except for the 20-30°C l i n e s . - 79 -Figure 26. Flow-behavior curves for egg albumen at 10, 20, 30 and H0°C - NV and MVI spindles. - 80 -TABLE XV. POWER-LAW FLOW-BEHAVIOR CURVES FOR EGG ALBUMEN Spindle Temperature, °C m n r 2 t NVtt 10 0.351 0.757 0.798** 20 0.457 0.704 0.760** 30 0.433 0.674 0.942** 40 0.424 0.667 0.897** MVIttt 10 0.256 0.846 0.516** 20 0.260 0.826 0.781** 30 0.298 0.799 0.480** 40 0.250 0.799 0.920** t C o e f f i c i e n t of determination t t Shear rates 520 - 3140 s e c - 1 t t t Shear rates 220 - 1320 s e c - 1 ** S i g n i f i c a n t at P < 0.01 with 22 degrees of freedom - 81 -It should be noted that for the NV-spindle t e s t s , flow-behavior indices are smaller and show greater decreases per 10°C temperature r i s e than for the MVI-spindle t e s t s . Experimental conditions for the two sets of tests are i d e n t i c a l except that NV-spindle tests are at higher shear rates. Thus, for higher shear rates, egg albumen flow behavior becomes more pseudoplastic and furthermore shows greater pseudoplasticity per unit increase i n temperature. The E l l i s model of flow behavior E l l i s model parameters for the flow behavior of egg albumen at 10, 20, 30 and 40°C are shown i n Table XVI along 2 with the c o e f f i c i e n t of determination (r ) for each condition. The average c o e f f i c i e n t of determination (0.625) indicates that the E l l i s model accurately (P < 0.01) describes albumen flow properties over the range of shear rates studied; however, 2 the power-law provides a better f i t of the data (average r = 0.762). Because of lower accuracy of f i t and r e l a t i v e d i f f i c u l t y i n evaluating flow parameters, the E l l i s model i s not j u s t i f i e d as a c o n s t i t u t i v e equation for egg albumen over the moderate range of shear rates studied. Results for Temperature Effects on Flow Behavior  E f f e c t of temperature on flow-behavior parameters The power-law parameters f o r the flow curves of figure [26] vary with temperature as shown i n figures [27] and [28]. Consistency c o e f f i c i e n t s (m) do not follow a cl e a r trend; however, flow-behavior indices (n) st e a d i l y decrease - 82 -TABLE XVI. ELLIS MODEL FLOW-BEHAVIOR CURVES FOR EGG ALBUMEN Spindle Temperature a T l / 2 r 2 t NVtt 10°C 1.51 - 0.124 78.4 0.76 5* 20 1.72 0.121 56.2 0.72 5* 30 1.76 0.086 51.1 0.9 2 8* 40 1.82 0.081 47. 8 0. 844* MVIttt • 10 1.29 0.194 53.6 0.506* 20 1. 35 0.176 44.5 0.755* 30 1.40 0.168 46. 3 0.479* 40 1.42 0 .140 37.2 0.881* t C o e f f i c i e n t of determination f t Shear rates 520 - 3140 sec" 1 t t t Shear rates 220 - 1320 sec" 1 ** S i g n i f i c a n t at P < 0.01 with 22 degrees of freedom - 83 -- 84 -with increasing temperature. Greater pseudoplasticity for higher temperatures indicates that egg albumen i s more susceptible to s t r u c t u r a l breakdown at increased shear rates within the 220 to 3140 sec range. As pointed out i n an e a r l i e r discussion, smaller values of n° and B (Table XVII) f o r NV-spindle tests that for MVI-spindle t e s t s , indicate that egg albumen flow behavior i s more pseudoplastic and more sensit i v e to temperature changes at higher shear rates. Variation of E l l i s model parameters with temperature i s shown i n figures [29] to [31] with.values of the constants i n Table XVIII. Interpolation to evaluate flow parameters between 10 and 40°C i s possible by means of these equations; however, these r e s u l t s are based on t r i p l i c a t e tests at only four temperatures and extrapolation beyond t h i s range i s not recommended. Eff e c t of temperature on apparent v i s c o s i t y Figures [32] and [33] show the temperature dependence of apparent v i s c o s i t y using shear rate as a parameter. Ac t i v a t i o n energies for viscous flow of egg albumen (Table XIX) increase with shear rate and are consistently lower f o r the MVI-spindle data than for comparable shear rates with the NV spindle. A possible "reason f o r t h i s difference i s the more extensive s t r u c t u r a l breakdown of albumen proteins when subjected to the higher maximum shear rates i n the NV apparatus. Since the a c t i v a t i o n energy for viscous flow i s a r e f l e c t i o n of the attractions among p a r t i c l e s i n the f l u i d , higher values would be expected with the increased surface area of the disrupted protein molecules. - 85 -TABLE XVII. TEMPERATURE DEPENDENCE OF POWER-LAW FLOW-BEHAVIOR PARAMETERS NV Spindle MVI Spindle m°t 0.38 0.26 n° 0.75 0.84 A 0.023ns 0.0027ns B -0.030* -0.017* t Items i n t h i s column.are defined i n equations [26] and [27]. ns Not s i g n i f i c a n t at P < 0.10. Si g n i f i c a n t at P < 0.10. TABLE XVIII. TEMPERATURE DEPENDENCE OF ELLIS MODEL FLOW-BEHAVIOR PARAMETERS NV Spindle MVI Spindle T1St 0.13 0.19 0 T 1/2 73.0 53.0 (l / c t ) ° 0.64 0.76 C -0.070* -0.043* D -0.069* -0.046* E -0.035* -0.022* t Items i n t h i s column are defined i n equations [28] to [30]. * S i g n i f i c a n t at P < 0.10. - 86 -Figure 30. Temperature dependence of the E l l i s parameter T Figure 31. Temperature dependence of the E l l i s parameter n . - 88 -Figure 32. Temperature dependence of apparent v i s c o s i t y using shear rate as a parameter - MV1 spindle - 0 . 9 Figure 33. Temperature dependence of apparent v i s c o s i t y using shear rate as a parameter - NV spindle - 89 -TABLE XIX. TEMPERATURE DEPENDENCE OF APPARENT VISCOSITY USING SHEAR RATE AS A PARAMETER Spindle * Y A t A E f t NV 520 0.0015 22.5 1050 0.00041 28.4 1570 0.00024 30.8 3140 0.00016 32.4 MVI 220 0 .0091 14. 3 440 0.0049 16 .8 660 0.0032 19 .0 1320 0.0028 19 .4 t Constant defined by t t A c t i v a t i o n energy of equation [32] viscous flow, kcal mole - 1 SUMMARY AND CONCLUSIONS Rheological behavior of egg albumen was measured with a narrow-gapped concentric cylinder viscometer at temperatures of 10, 20, 30 and 40°C between shear rates of 220 to 3140 sec ^ . Apparent v i s c o s i t y decreases with time at a constant rate of shear by a combined th i x o t r o p i c -rheodestructive process. Temperature has l i t t l e e f f e c t on the rate of s t r u c t u r a l breakdown although apparent v i s c o s i t i e s decrease with increasing temperature. Higher shear rates r e s u l t i n a more rapid and extensive breakdown i n egg albumen structure. Egg albumen displays pseudoplastic flow behavior. Storage subsequent to t e s t i n g , as well as the use of d i f f e r e n t maximum shear rates, r e s u l t s i n d i f f e r e n t flow curves. The power-law and E l l i s models accurately describe the flow data; however, the power-law i s preferred because of a s l i g h t l y better f i t to the data over the range of shear rates studied. Flow-behavior parameters are temperature dependent and the apparent v i s c o s i t y follows an Arrhenius r e l a t i o n f o r the temperatures tested. Activation energies of viscous flow vary from 14.3 to 32.4 kcal per mole under the conditions of t h i s experiment. - 90 -LITERATURE CITED A l Atanasoff, J.V. and Wilcke, H.L. Measurement of the v i s c o s i t y of eggs by the use of a torsion pendulum. J. Agr. Res. 54(9): 701-709, 1937. Bl B a l l , H.R. and Gardner, F.A. Physical and functional properties of gamma i r r a d i a t e d l i q u i d egg white. 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