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Freeze-drying rates of apple and potato tissue Davies, Peter Hugh 1966

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FREEZE-DRYING RATES OF APPLE AND POTATO TISSUE by PETER HUGH DAVIES B.S.A., U n i v e r s i t y of B r i t i s h Columbia, 1 9 6 4 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN AGRICULTURE i n the Department of A g r i c u l t u r a l Mechanics We accept t h i s t h e s i s as conforming to the req u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1 9 6 6 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i 1 a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x - t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s m a y b e g r a n b y t h e H e a d o f m y D e p a r t m e n t o r b y h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n - c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t m y w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f A&t>ILUL.TU/{flL MfC/JAMcS T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, C a n a d a D a t e tTV/vf * f/A & i i ABSTRACT The i n f l u e n c e of f r e e z i n g r a t e , r a t e of heat input and d r y i n g chamber pressure on f r e e z e - d r y i n g r a t e was st u d i e d to determine the thermal and p h y s i c a l p r o p e r t i e s of Macintosh apple and Netted Gem potato t i s s u e . The samples were f r o z e n e i t h e r by immersion i n dry i c e and ethanol ( f a s t frozen) or by placement i n a r e f r i g e r a t e d cabinet maintained at a temperature between -10° and +5° F (slow f r o z e n ) . The samples were suspended i n a chamber maintained at a pressure of 550 or 1400 microns of mercury and surrounded by a constant temperature water bath which provided a r a d i a n t heat source of 8 6 ° or 104°F. The weight, and the surface and centre temperature of the sample were recorded continuously d u r i n g f r e e z e - d r y i n g . Vapor d i f f u s i o n was the r a t e l i m i t i n g f a c t o r f o r f a s t f r o z e n samples while heat t r a n s f e r was rat e l i m i t i n g f o r slow f r o z e n samples. Chamber pressure had l i t t l e i n f l u e n c e on the freeze:-drying r a t e of slow f r o z e n samples. o Potato t i s s u e thermal c o n d u c t i v i t y v a r i e d from 0.66x10 BTU/Hr.°F F t . at a pressure of 5 5 0 microns to 0 . 7 8 x i o ~ 2 at 1400 microns. The thermal c o n d u c t i v i t y of apple t i s s u e was i l l 1.0 x: 10 • BfTJ/Hr.°F Ft,., at both pressures. fhe.eufceptlc temperature of,apple and potato tissue was found to be -10°F and -rl 0F k respectively. i v TABLE OF CONTENTS Page ABSTRACT i i TABLE OP CONTENTS i v LIST OF TABLES v i l i LIST OF FIGURES x ACKNOWLEDGEMENTS x i i INTRODUCTION 1 THEORY 4 Freeze-drying Process 4 General Considerations 4 Phase Diagram of Water 5 Sublimation 7 F r e e z i n g Process 7 C r y s t a l l i z a t i o n 7 R e c r y s t a l l i z a t i o n . . . . . 9 E u t e c t i c s 9 Pure Water 9 Simple S o l u t i o n s 1 0 Complex S o l u t i o n s 1 1 F r e e z i n g Rate . 1 3 Heat T r a n s f e r . . . . . 1 3 Mass Tra n s f e r 1 5 V TABLE OF CONTENTS (Cont'd) Page LITERATURE REVIEW 1 6 P l a n t S t r u c t u r e 1 6 Drying Process 1 8 Bound Water 2 0 Rate L i m i t i n g F actors 2 1 F r e e z i n g Rates . . 2 4 A Laboratory Freeze-Drier 2 7 MATERIALS AND METHODS . 2 7 T e s t i n g Equipment 2 7 Experimental M a t e r i a l ' 3 2 Experimental Procedure . 3 4 Sample F r e e z i n g . . . . 3 4 Freeze-drying 3 4 Summary of Experimental Procedure 3 5 RESULTS 3 6 C h a r a c t e r i s t i c s of Sample M a t e r i a l 3 6 Netted Gem Potatoes 3 6 Macintosh Apples 3 7 Netted Gem Potatoes and Macintosh Apples . . . . 3 7 F r e e z i n g Rates . . . . . . . . . . . 3 7 Drying Rates 3 9 CALCULATED RESULTS 3 9 v i TABLE OF CONTENTS (Cont'd) Page Drying Rates and Heat Flow 3 9 Thermal C o n d u c t i v i t y . . . 40 Radiant Heat Transfer C o e f f i c i e n t 4 2 O v e r - a l l Thermal C o n d u c t i v i t y 4 4 DISCUSSION OF RESULTS 46 C h a r a c t e r i s t i c s of Sample M a t e r i a l . 46 Netted Gem Potatoes 46 Macintosh Apples 46 Netted Gem Potatoes and Macintosh Apples . . . . 46 F r e e z i n g Rates 4 7 Drying Rates . . . . . . 48 Fast Frozen Samples 48 Slow Frozen Samples 49 DISCUSSION OF CALCULATED RESULTS . . . . . 5 1 Drying Rate P l o t t e d Against O v e r - a l l Temperature D i f f e r e n c e s 5 1 Thermal C o n d u c t i v i t y From Equation ( 1 2 ) 5 2 Thermal C o n d u c t i v i t y C a l c u l a t e d at the Termination of the Ice Phase 5 3 Radiant Heat T r a n s f e r C o e f f i c i e n t 5 4 O v e r - a l l Thermal C o n d u c t i v i t y 5 5 SUMMARY 5 6 v i i TABLE OF CONTENTS (Cont'd) Page LIST OF REFERENCES CITED . . . . . . . 5 8 APPENDIX I A. Sample - Apple 6 2 I B. Sample - Potato 6 5 I I Termination of Ice Phase 7 1 I I I Thermocouple Heat Conduction 7 2 IV Load Ring Design 7 ^ v i i i LIST OF TABLES TABLE PAGE I Nomenclature . . x l II E x t r a c e l l u l a r Spaces In Apple Tissue from Reeve ( 1 9 5 3 ) . 1 7 III P r o p e r t i e s of Freeze-dried Apple and Peach from Harper ( 1 9 6 2 ) . . . . . . . 2 2 XV Numbers Assigned to Slow Frozen Samples Freeze- d r i e d Under the Conditions S p e c i f i e d 3 6 V Dry Matter Content of Slow Frozen Potato Samples 3 6 VI A n a l y s i s of C e l l Sap of Peeled and Cored Apples 3 7 V I I Average Density of E i g h t F r e e z e - d r i e d Apple and Potato Tissue Samples 3 7 V I I I F r e e z i n g Rates of Fast Frozen Potato . . . . 3 7 XX F r e e z i n g Rates of Slow Frozen Potato . . . . 3 8 X F r e e z i n g Rates of Fast Frozen Apple 3 8 X I F r e e z i n g Rates of Slow Frozen Apple 3 8 X I I Thermal C o n d u c t i v i t y of Slow Frozen Freeze- d r i e d Apple and Potato Tissue as C a l c u l a t e d u s i n g Equation ( 1 2 ) 4 l X I I I Thermal C o n d u c t i v i t y C o e f f i c i e n t (k) of Slow Frozen Freez e - d r i e d Potato C a l c u l a t e d u s i n g Equation ( 2 ) and ( 3 ) . 4 2 XIV Thermal C o n d u c t i v i t y C o e f f i c i e n t (k) of Slow Frozen Freez e - d r i e d Apple C a l c u l a t e d u s i n g Equation ( 2 ) and ( 3 ) 4 3 XV Radiant Heat Tr a n s f e r C o e f f i c i e n t (h ) of Slow Frozen Freez e - d r i e d Potato C a l c u l a t e d Using Equation ( l ) and ( 2 . ) 4 3 i x LIST OF TABLES (Cont'd) TABLE PAGE XVI Radiant Heat T r a n s f e r C o e f f i c i e n t ( h r ) of Slow Frozen F r e e z e - d r i e d Apple C a l c u l a t e d Using Equation ( l ) and ( 2 ) 4 4 XVII O v e r - a l l Thermal C o n d u c t i v i t y (U) of Slow Frozen F r e e z e - d r i e d Potato C a l c u l a t e d Using Equation ( 5 ) 4 5 X V I I I O v e r - a l l Thermal C o n d u c t i v i t y (u) of Slow Frozen F r e e z e - d r i e d Apple C a l c u l a t e d Using Equation ( 5 ) 4 5 X LIST OF FIGURES FIGURE PAGE 1. Phase Diagram of Water . . . . . . 6 2. F r e e z i n g Curve Pure Water and a Simple S o l u t i o n 11 3. F r e e z i n g Curve of a Complex S o l u t i o n . . . . . . 12 4A. Photographs of Apparatus 30 4 B . Photographs of Apparatus 3 1 5 . Slow Frozen Potato Drying Curves 3 9 A 6. Slow Frozen Apple Drying Curves 3 9 B 7 . Drying Rate versus Temperature D i f f e r e n c e Slow Frozen Potato . . . . . 40A 8. Drying Rate versus Temperature D i f f e r e n c e Slow Frozen Apple . 4 0 B 9 . P l o t f o r C a l c u l a t i o n of Slow Frozen Potato Thermal C o n d u c t i v i t y 4 l A 10. P l o t f o r C a l c u l a t i o n of Slow Frozen Potato Thermal C o n d u c t i v i t y . . . 4 l B 11. P l o t f o r C a l c u l a t i o n of Slow Frozen Apple Thermal C o n d u c t i v i t y 4lC 12. Load C e l l W i r i n g Diagram 7 5 x i NOMENCLATURE A Surface Area F t . 2 P'.M1. Dry Matter Grams h r Coefficient of Radiant Heat Transfer BTU/Hr.QF.Ft,2 k Thermal Conductivity Coefficient BTU/Hr,°F.Ft,2/Ft. Kg • Over-all Mass Transfer Coefficient m Slope of line defined y = mx + b MR Moisture Ratio Lbs. Water/Lb. Dry Matter (or Grams) MRX I n i t i a l Moisture Ratio MR2 Final Moisture Ratio P^ Chamber Pressure Microns (j/) Mercury (Hg) PQ Centre Pressure q Heat Flow BTU/Hr. TA Heat Source Temperature °F T<3 Centre Temperature °F Tg Surface Temperature °F U Over-all Conductivity Coefficient BTU/Hr.°F.Ft.2 W-fj Cumulative Weight Loss Lbs. x Sample Thickness Ft. SjH. Drying Rate Lbs. or Grams/Hour p Dried Sample Density L1°sl Ft .J BTU ?\ Latent Heat of Sublimation Lb. © Time Hours x i i ACKNOWLEDGEMENTS The w r i t e r i s g r a t e f u l f o r the as s i s t a n c e and guidance of Pr o f e s s o r E.L. Watson, d u r i n g t h i s study. Thanks are extended to Dr. J.F. Richards, Dr. D.P. Ormrod and Mr. R.B. Hyde, f o r s e r v i n g as members of the committee d i r e c t i n g t h i s research p r o j e c t . Gratitude i s a l s o expressed f o r the ass i s t a n c e of Pr o f e s s o r L.M. S t a l e y , Mr. E. Rudischer, and Mr. W. Gleave, dur i n g the c o n s t r u c t i o n of the t e s t equipment. The w r i t e r i s a l s o indebted to B.C. Tree F r u i t s L t d . , f o r supplying the apples used i n t h i s study. 1 INTRODUCTION Freeze-drying i s the removal of moisture by the s u b l i m a t i o n of i c e from w i t h i n a f r o z e n m a t e r i a l . Sublimation can only be c a r r i e d out at c o n d i t i o n s below the t r i p l e p o i n t of water, where s o l i d l i q u i d and vapor may c o e x i s t . Under normal f r e e z e - d r y i n g c o n d i t i o n s a vacuum i s used, so that the system pressure i s below the vapor pressure of i c e at the product i c e surface temperature. Foods are dehydrated to deprive the m i c r o b i a l p o p u l a t i o n of water r e q u i r e d f o r growth and r e p r o d u c t i o n . Chemical r e a c t i o n s causing the breakdown of food m a t e r i a l s are a l s o i n h i b i t e d by a l a c k of water. F r e e z e - d r i e d foods have l e s s denaturation, l e s s c e l l damage, l e s s co n c e n t r a t i o n of c e l l s o l u t i o n , greater r e t e n t i o n of v o l a t i l e components and f a s t e r r e h y d r a t i o n , than atmospheric or vacuum dehydrated foods. B e n e f i t s of f r e e z e - d r y i n g may be due l a r g e l y to the low d r y i n g temperature although i t i s a l s o thought that f r e e z e - d r y i n g combines the advantages of f r e e z i n g and d r y i n g . Factors which might be expected to a f f e c t the d r y i n g r a t e of a product are those which could a f f e c t any of the u n i t operations involved i n f r e e z e - d r y i n g . These processes are; f r e e z i n g of the product, energy t r a n s f e r to supply the l a t e n t 2 heat of sub l i m a t i o n , vapor t r a n s f e r through the d r i e d m a t e r i a l , and removal of water vapor from the system. The major amount of work reported on f r e e z e - d r y i n g has been done by workers i n t e r e s t e d i n only c e r t a i n aspects of the op e r a t i o n . B i o l o g i c a l s c i e n t i s t s are i n t e r e s t e d i n mai n t a i n i n g experimental m a t e r i a l i n a v i a b l e s t a t e or i n prepa r i n g a sample f o r h i s t o l o g i c a l s e c t i o n i n g i n a c o n d i t i o n approaching i t s normal s t a t e . Food s c i e n t i s t s , on the other hand, are I n t e r e s t e d i n ma i n t a i n i n g the sensory and n u t r i t i o n a l a t t r i b u t e s of the food at lowest p o s s i b l e c o s t . For example, a slow d r y i n g process i s re q u i r e d f o r valuable items such as pharmaceuticals but would not be f e a s i b l e f o r food products since cost i s a l i m i t i n g f a c t o r . Papers r e p o r t i n g the r e s u l t s of f r e e z e - d r y i n g research are being published In both b i o l o g i c a l and food science j o u r n a l s . Comparatively l i t t l e Information i s a v a i l a b l e on the p h y s i c a l p r o p e r t i e s of f r e e z e - d r i e d m a t e r i a l s and on the f a c t o r s a f f e c t i n g f r e e z e - d r y i n g r a t e s . Harper and Tappel (1957) and Burke and Decareau (1964) i n comprehensive a r t i c l e s on f r e e z e - d r y i n g s t r e s s e d the need f o r a d d i t i o n a l i n f o r m a t i o n on the ba s i c p h y s i c a l and thermal p r o p e r t i e s of f o o d s t u f f s that govern the f r e e z e - d r y i n g o p e r a t i o n . This study was designed to determine the e f f e c t of 3 f r e e z i n g - r a t e , system pressure, and r a d i a n t heat source temperature on the f r e e z e - d r y i n g r a t e s of samples of Macintosh apples and Netted Gem potatoes. 4 THEORY Freeze-drying Process General c o n s i d e r a t i o n s To freeze-dry a food m a t e r i a l , the sample must be fr o z e n and placed i n an environment s u i t a b l e f o r sub l i m a t i o n of the i c e to occur. At the i c e surface of the fro z e n food, there i s a water vapor pressure which i s d i r e c t l y p r o p o r t i o n a l to the temperature of the i c e . To remove the vapor from the product surfa c e , or from the i c e i n t e r f a c e i n a p a r t i a l l y d r i e d sample, the chamber pressure must be l e s s than the i c e vapor pressure. The t r a n s i t i o n of water molecules from the i c e phase to the vapor phase r e q u i r e s that the water molecule absorb energy (heat of sublimation) from the surrounding m a t e r i a l . To avoid a r e d u c t i o n i n temperature of the system, heat energy must be s u p p l i e d . The amount of water sublimed i s p r o p o r t i o n a l . to the energy suppled by the heat source. A d d i t i o n of heat i n excess of that r e q u i r e d to maintain the subl i m a t i o n rate f o r a p a r t i c u l a r set of c o n d i t i o n s w i l l cause the temperature of the. sample to i n c r e a s e . T h i s increase i n the i c e temperature w i l l tend to a c c e l e r a t e the sublimation r a t e . To achieve the maximum subl i m a t i o n r a t e and ther e f o r e maximum d r y i n g r a t e , heat should be sup p l i e d as r a p i d l y as p o s s i b l e without thawing the m a t e r i a l . 5 As the sample d r i e s , a l a y e r of p a r t i a l l y d r i e d m a t e r i a l i s formed on the outside of a f r o z e n core of undried m a t e r i a l . The d r i e d l a y e r i n h i b i t s the flow of vapor from the r e t r e a t i n g i c e i n t e r f a c e to the vacuum chamber and a l s o r e t a r d s the fl o w of heat from the sample•surface to the i c e i n t e r f a c e . Major f a c t o r s which l i m i t the ra t e of heat input are the r e s i s t a n c e to vapor d i f f u s i o n and the very low thermal c o n d u c t i v i t y of the d r i e d m a t e r i a l . The heat l a b i l i t y of the m a t e r i a l and the p o s s i b i l i t y of thawing the sample r e s t r i c t the magnitude of the temperature gradient which may be created. From the previous d i s c u s s i o n i t may be concluded that the r a t e of heat input and the ra t e of vapor t r a n s f e r determine the temperature of the subliming i c e . Phase Diagram of Water The r e l a t i o n s h i p between the p h y s i c a l s t a t e s of water i s of concern i n food p r o c e s s i n g operations i n v o l v i n g c o n c e n t r a t i o n , dehydration, f r e e z i n g , and vacuum c o o l i n g . Freeze-drying i n v o l v e s a l l of these operations to some exte n t . Pure water e x i s t s i n three s t a t e s , s o l i d , l i q u i d and vapor, each a homogeneous, p h y s i c a l l y d i s t i n c t p a r t of a system. The e q u i l i b r i u m c o n d i t i o n s which e x i s t between the v a r i o u s phases are represented i n Figure 1 . 6 temperature FIGURE 1. PHASE DIAGRAM OF WATER The b o i l i n g p o i n t curve, AO, shows the e q u i l i b r i u m temperature and pressure between the l i q u i d and vapor phases. The m e l t i n g curve, CO, i n d i c a t e s the e q u i l i b r i u m c o n d i t i o n s between s o l i d and l i q u i d . The curve BO, the subl i m a t i o n curve, showing the c o n d i t i o n s f o r e q u i l i b r i u m between i c e and water vapor i s of primary concern i n f r e e z e - d r y i n g . Along the s u b l i m a t i o n curve, molecules can be vaporized by reducing the pressure or r a i s i n g the temperature. The c o n d i t i o n s r e q u i r e d f o r f r e e z e - d r y i n g may be approximated from t h i s type of diagram. For sublimation of pure water to occur the temperature must be l e s s than 0.0099°C and the pressure l e s s than 4.579mm Hg. At the t r i p l e p o i n t , 0 , s o l i d , l i q u i d and vapor are i n e q u i l i b r i u m . The l i n e DO represents the vapor pressure of supercooled water, which i s greater than i c e at 7 the same temperature. Sublimation The process of s u b l i m a t i o n i s a s s o c i a t e d w i t h a thermal change i n a manner analogous to the v a p o r i z a t i o n of a l i q u i d . The l a t e n t heat of s u b l i m a t i o n i s the d i f f e r e n c e i n enthalpy between the s o l i d and the vapor phase and i s equal to the sum of the l a t e n t heats of f u s i o n and v a p o r i z a t i o n . Vacuum i s not e s s e n t i a l f o r f r e e z e - d r y i n g , but i n many cases the most convenient method of m a i n t a i n i n g a vapor pressure s u i t a b l e f o r s u b l i m a t i o n i s by evacuating a chamber u n t i l the t o t a l pressure i s lower than the vapor pressure. By keeping the m a t e r i a l f r o z e n and d r y i n g i t by s u b l i m a t i o n only, shrinkage and m i g r a t i o n of d i s s o l v e d components i s e l i m i n a t e d and the l o s s of v o l a t i l e f l a v o r constituents minimized. F r e e z i n g Process C r y s t a l l i z a t i o n The phase change, c r y s t a l l i z a t i o n , can be d i v i d e d i n t o two sequences, n u c l e a t i o n and c r y s t a l growth. C r y s t a l - l i z a t i o n begins w i t h the aggregation of a group of molecules i n t o a minute ordered p a r t i c l e , a c r y s t a l nucleus, under supercooled c o n d i t i o n s . Ordered aggregates of water molecules are thought to c o n t i n u a l l y form and disappear, u n t i l under s u i t a b l e temperature c o n d i t i o n s , some grow lar g e enough to 8 serve as c r y s t a l l i z a t i o n n u c l e i . The molecular aggregation has an equal chance of growing or d i m i n i s h i n g at the c r i t i c a l s i z e , which i s l a r g e r at the me l t i n g p o i n t than at lower temperatures. Homogeneous n u c l e a t i o n occurs w i t h chance o r i e n t a t i o n of molecules i n t o an i c e l i k e mass; whereas heterogeneous n u c l e a t i o n occurs when water molecules aggregate i n a c r y s t a l l i n e arrangement on a non-aqueous p a r t i c l e having an i c e l i k e c r y s t a l s t r u c t u r e . The presence of i c e n u c l e a t i n g p a r t i c l e s i n food m a t e r i a l s g e n e r a l l y reduces homogeneous n u c l e a t i o n . The second stat e i n c r y s t a l l i z a t i o n , c r y s t a l growth, occurs r e a d i l y at temperatures very cl o s e to the f r e e z i n g p o i n t . The r a t e of c r y s t a l growth depends on the rat e of heat removal and the temperature. The rat e of c r y s t a l growth i n - creases w i t h an i n c r e a s i n g temperature d i f f e r e n c e between the unfrozen s o l u t i o n and the c r y s t a l s u r f a c e . Due to an exponential increase i n v i s c o s i t y , the r a t e of i c e c r y s t a l growth decreases w i t h decreasing temperature. D i l u t e s o l u t i o n s of s o l u t e s w i l l g r e a t l y slow i c e c r y s t a l growth, organic substances being more e f f e c t i v e than i n o r g a n i c . P h y s i c a l . l i m i t a t i o n s of water molecule t r a n s f e r to the f r e e z i n g boundary may cause t h i s h i n d e r i n g a c t i o n . 9 R e c r y s t a l l i z a t i o n During f r o z e n storage and the e a r l y stages of thawing, i c e c r y s t a l s tend to enlarge by r e c r y s t a l l i z a t i o n . In f r o z e n foods the most common form of r e c r y s t a l l i z a t i o n i s that r e f e r r e d to as migratory. F l u c t u a t i n g temperature gradients r e s u l t i n vapor pressure d i f f e r e n c e s and a growth of c r y s t a l s i n an area of low temperature at the expense of c r y s t a l s i n an area of higher temperature. Small c r y s t a l s w i t h t h e i r small mass w i l l disappear i n high vapor pressure areas f a s t e r than c r y s t a l s of greater mass. Vapor pressure d i f f e r e n c e s when reversed would cause the shrunken l a r g e r c r y s t a l s to grow while the sma l l e r c r y s t a l s which disappear would not be macleated. M i g r a t o r y r e c r y s t a l l i z a t i o n can a l s o occur at constant temperature. R e c r y s t a l l i z a t i o n i s of major Importance i f f r e e z e - d r y i n g i s to f o l l o w a prolonged p e r i o d of f r o z e n storage. E u t e c t i c s Pure Water Removal of one BTU of heat from one pound of pure water reduces the temperature one Fahrenheit degree u n t i l the f r e e z i n g p o i n t , or some l e v e l of supercooling i s reached. When n u c l e a t i o n begins and i c e c r y s t a l s grow, the heat of 10 c r y s t a l l i z a t i o n r e l e a s e d causes the temperature to r i s e to the f r e e z i n g p o i n t and remain at t h i s temperature u n t i l a l l the water has "been s o l i d i f i e d . A f t e r pure water i s f r o z e n , the temperature decreases at a rat e of approximately one Fahrenheit degree f o r each 0.49 BTU removed from each pound of i c e . Simple S o l u t i o n s Removal of heat from a simple s o l u t i o n , c o n t a i n i n g a s i n g l e s o l u t e , r e s u l t s i n a s t e a d i l y decreasing temperature u n t i l a c e r t a i n degree of supercooling e x i s t s . The sequence of n u c l e a t i o n , c r y s t a l growth and re l e a s e of heat of c r y s t a l - l i z a t i o n causes the temperature to r i s e to the true f r e e z i n g temperature. A d d i t i o n a l c o o l i n g causes a gradual decrease i n temperature, w i t h water forming pure i c e c r y s t a l s . The remaining s o l u t i o n becomes i n c r e a s i n g l y concentrated and the f r e e z i n g p o i n t decreases. When the l i q u i d phase becomes saturated w i t h s o l u t e and f i n a l l y s l i g h t l y supersaturated, the s o l u t e c r y s t a l l i z e s . The release of heat of c r y s t a l - l i z a t i o n causes the temperature to r i s e to the e u t e c t i c p o i n t , the lowest temperature at which the l i q u i d phase may e x i s t i n the system. Further removal of heat r e s u l t s i n a change of st a t e with no change of temperature. During t h i s p e r i o d , water and sol u t e c r y s t a l l i z e simultaneously i n a constant 11 r a t i o . When c r y s t a l l i z a t i o n of water and sol u t e i s complete, f u r t h e r removal of heat reduces the temperature. Figure 2 shows the d i f f e r e n c e s i n the f r e e z i n g curves of pure water and a simple s o l u t i o n . heat removal FIGURE 2. FREEZING CURVE PURE WATER AND A SIMPLE SOLUTION Complex S o l u t i o n s When the s a t u r a t i o n p o i n t of one component has been-reached i n a s o l u t i o n c o n t a i n i n g s e v e r a l d i s s o l v e d substances, f u r t h e r f r e e z i n g w i l l not increase the concent- r a t i o n of that substance i n the unfrozen m a t e r i a l but w i l l increase•the c o n c e n t r a t i o n of the other components. There- f o r e , the temperature w i l l not be constant on f u r t h e r f r e e z i n g as i n a s i n g l e component s o l u t i o n , but w i l l only show a decrease i n the ra t e of temperature change a f t e r each component has reached i t s s a t u r a t i o n p o i n t . Figure 3 shows the f r e e z i n g curve of a complex s o l u t i o n . 1 2 heat removal FIGURE 3. FREEZING CURVE OF A COMPLEX SOLUTION The slope of the f r e e z i n g curve w i l l be i n f l u e n c e d by the amount of var i o u s s o l u t e s present, t h e i r s o l u b i l i t y i n t e r - a c t i o n and t h e i r e f f e c t on the f r e e z i n g p o i n t . The f i n a l e u t e c t i c p o i n t i s reached when the l a s t of the d i s s o l v e d substances reaches i t s s a t u r a t i o n p o i n t . With common food m a t e r i a l s , the s i t u a t i o n Is more complex than w i t h compound s o l u t i o n s because of the c e l l s t r u c t u r e and water b i n d i n g p r o p e r t i e s of the s o l i d c o n s t i t u e n t s . True s u b l i m a t i o n can only occur i f the m a t e r i a l i s cooled below the f i n a l e u t e c t i c but i t i s understood that i n the food i n d u s t r y complete s o l i d i f i c a t i o n i s not always e s s e n t i a l f o r f r e e z e - d r y i n g a q u a l i t y product. 13 F r e e z i n g Rate Slow f r e e z i n g produces la r g e c r y s t a l s e x c l u s i v e l y l o c a t e d i n e x t r a c e l l u l a r areas while r a p i d f r e e z i n g at low temperature w i l l r e s u l t i n t i n y i c e c r y s t a l s l o c a t e d i n t r a and e x t r a c e l l u l a r l y . E x t r a c e l l u l a r i c e c r y s t a l s have a lower vapor pressure than the water present at the c e l l s u r f a c e . T h i s vapor pressure d i f f e r e n t i a l causes water to migrate out of the c e l l and deposit on i c e c r y s t a l s . The slower the f r e e z i n g the gr e a t e r the water m i g r a t i o n . A depressed f r e e z i n g p o i n t of the c e l l s o l u t i o n and c e l l shrinkage are c h a r a c t e r i s t i c of slow f r e e z i n g r a t e s . A l s o at slow f r e e z i n g r a t e s , i c e forms as hexagonal c r y s t a l s which grow i n leng t h and increase i n thickness pushing aside the s o l i d m a t e r i a l of the c e l l . Rapid f r e e z i n g q u i c k l y reduces chemical and enzymatic a c t i v i t y while p reventing so l u t e c o n c e n t r a t i o n and the r e s u l t i n g t i s s u e shrinkage. Heat T r a n s f e r The importance of an estimate of thermal c o n d u c t i v i t y of f r e e z e - d r i e d food products i s shown by the l a c k of agree- ment among researchers on the r a t e l i m i t i n g f a c t o r of the f r e e z e - d r y i n g process, heat t r a n s f e r or mass t r a n s f e r . In a system u t i l i z i n g r a d i a n t heat as the sole energy source, the major b a r r i e r to heat t r a n s f e r i s the conduction across 14 t h e . d r i e d l a y e r , r a t h e r than t r a n s f e r from the heat source to the product. For a sample suspended i n a vacuum system, the only source of heat i s that which i s r a d i a t e d from the w a l l s of .the c o n t a i n e r . M a i n t a i n i n g the chamber w a l l s at a constant temperature w i t h a sample of constant area, the r a d i a n t heat t r a n s f e r can only vary w i t h the surface p r o p e r t i e s and tem- perature according t o : q « h r A ( T A - T s ) ( 1 )* where q = £[g. 7\ (2) The r a d i a n t heat energy must be conducted through the d r i e d sample to the i c e i n t e r f a c e . I f the thic k n e s s of the d r i e d l a y e r i s known i t i s v a l i d to w r i t e : q = k A(T S-T C) (3) x A more u s e f u l method of determing the thermal c o n d u c t i v i t y of the d r i e d l a y e r i s that explained by Lusk e t . a l . ( 1964) . D e t a i l s of t h i s method are o u t l i n e d i n the r e s u l t s and d i s - c u s sion s e c t i o n under thermal c o n d u c t i v i t y . * See Table I f o r l i s t of nomenclature. 15 A knowledge of the c o e f f i c i e n t s of thermal con- d u c t i v i t y f o r f r e e z e - d r i e d food m a t e r i a l s would answer the controversy over which i s the r a t e l i m i t i n g f a c t o r i n freeze - d r y i n g , heat or mass t r a n s f e r . Mass Tra n s f e r Three areas of water vapor t r a n s p o r t are of im- portance i n f r e e z e - d r y i n g ; ( l ) t r a n s f e r from the product surface to the condenser surfa c e , (2) t r a n s p o r t of sublimed water vapor through a r e s i s t a n t d r i e d l a y e r from the i c e i n t e r f a c e to the sample surface and (3) t r a n s f e r of hound water to the sample s u r f a c e . Of concern i n t h i s study i s the movement of water vapor from the i c e surface through a d r i e d zone to the sample s u r f a c e . The t r a n s p o r t of vapor from bound water i s of l e s s e r importance. In l a b o r a t o r y s i z e d f r e e z e - d r i e r s the t r a n s p o r t of water vapor to the condenser i s of r e l a t i v e l y minor importance. Temperature and pressure measurements can be used to determine an o v e r a l l mass t r a n s f e r c o e f f i c i e n t from: * - K g A(P 0-P A) (4) 16 LITERATURE REVIEW Research on f r e e z e - d r y i n g has considered product composition, d r y i n g temperatures, r a t e l i m i t i n g f a c t o r s such as heat and mass t r a n s f e r and f r e e z i n g r a t e s . However, i n many of the s t u d i e s , the r e s u l t s are not r e l a t e d to any of the b a s i c p h y s i c a l or thermal p r o p e r t i e s of the m a t e r i a l . Without a knowledge of these p r o p e r t i e s , the design of commercial f r e e z e - d r i e r s becomes l a r g e l y e m p i r i c a l and optimum c o n d i t i o n s d i f f i c u l t to achieve dur i n g o p e r a t i o n . P l a n t S t r u c t u r e According to Gane and Wager (1958), parenchyma c e l l s are enclosed by a permeable c e l l u l o s e w a l l which I s separated from the i n t e r n a l protoplasmic l i n i n g of the vacuole by a d i f f e r e n t i a l l y permeable c e l l membrane. C e l l sap w i t h i n the vacuole i s l a r g e l y water but a l s o contains s o l u t e s such as sugars, mineral s a l t s , organic a c i d s , and pigments. Water can r e a d i l y pass through the c e l l w a l l while d i s s o l v e d sub- stances are impeded. Each c e l l , when immature, i s j o i n e d to adjacent c e l l s on a l l s i d e s , but during growth, small sepa- r a t i o n s occur i n the middle l a m e l l a and le a d t o the production of minute gas f i l l e d spaces between the c e l l s . These spaces 17 g e n e r a l l y occur at the corners of the c e l l s and form a c o n t i n - uous system of channels which a i d i n gas t r a n s p o r t w i t h i n the t i s s u e . C e l l w a l l s of parenchyma t i s s u e i n f l e s h y f r u i t s and vegetables are u s u a l l y t h i n and ther e f o r e s u s c e p t i b l e to the mechanical damage of e n l a r g i n g i c e c r y s t a l s which may nucleate i n the e x t r a c e l l u l a r space. C a v i t i e s are of t e n observed i n parenchyma t i s s u e c e l l w a l l s which inter c o n n e c t adjacent c e l l s . The membrane present between c a v i t i e s may be r e a d i l y ruptured by i c e c r y s t a l growth, to permit d i f f u s i o n of s o l u t e s between contiguous c e l l s . F leshy f r u i t t i s s u e , such as apple, contains many larg e e x t r a c e l l u l a r spaces while potato t i s s u e has been found to co n t a i n f a r l e s s e x t r a c e l l u l a r space. P l a n t parenchyma t i s s u e , c o n s i s t i n g of r i g i d , unaligned c e l l s i s more subject to c e l l s e p a r a t i o n , c e l l breakage and damage to c e l l u l a r contents du r i n g processing than i s animal t i s s u e . volume of r i p e apple f l e s h c o n s i s t e d of e x t r a c e l l u l a r spaces. The dimensions of the spaces were: TABLE I I EXTRACELLULAR SPACES IN APPLE TISSUE FROM REEVE (1953) Reeve (1953) found that 20 to 25 percent of the Var i e ty Width (microns) Length (microns) Macintosh 300 + 75 590 + 250 Rome Beauty 257 + 75 562 + 231 D e l i c i o u s 269 + 93 487 + 154 18 Hanson (1961) mentioned that the c e l l u l a r arrangement of p l a n t t i s s u e i s not conducive to easy vapor escape. He found that 5 / l 6 i n c h was the maximum thickness of apple d i c e , that could he used i f thawing was to he prevented d u r i n g a normal d r y i n g c y c l e . Meat t i s s u e , i f c o r r e c t l y c u t , forms channels during d r y i n g which promote the removal of water vapor. Saravacos and Charm (1962) , worked w i t h atmospheric dehydration of f r u i t s and vegetables and found that apples d r i e d more q u i c k l y than potatoes. Gane and Wagner (1958), i n t h e i r d i s c u s s i o n of the p r o p e r t i e s of potato i n r e l a t i o n to atmospheric d r y i n g s t a t e d that i t i s d e s i r a b l e to have as few broken c e l l s as p o s s i b l e In the d r i e d m a t e r i a l , to avoid the escape of the s t a r c h g e l which gives the r e c o n s t i t u t e d product an unde s i r a b l e s t i c k y t e x t u r e . Drying Process Hanson (1961) o u t l i n e d the aims of f r e e z e - d r y i n g as, the establishment of the whole mass as a f r o z e n e n t i t y and the sub l i m a t i o n of the fro z e n water under c o n d i t i o n s of n e g l i g i b l e Chemical a c t i v i t y . The mass should be fro z e n without the growth of larg e i c e c r y s t a l s which d i s r u p t mem- branes and change i o n i c c o n c e n t r a t i o n s . I f these requirements are met, the d r i e d m a t e r i a l can be so l i t t l e a l t e r e d that the 19 a d d i t i o n of water r e s t o r e s b i o l o g i c a l a c t i v i t y . Meryman (1962) presented an e l e c t r i c a l analogue of fr e e z e - d r y i n g to demonstrate the interdependence of the u n i t o p e r a t i o n s . Harper and Tappel (1957) s t a t e d that the complete s o l i d i f i c a t i o n of the m a t e r i a l i s not e s s e n t i a l i n the food i n d u s t r y . I t i s , t h e r e f o r e , evident that the p a r t i c u l a r a p p l i c a t i o n of f r e e z e - d r y i n g should be considered i n order to a s c e r t a i n the extent to which the m a t e r i a l should be f r o z e n p r i o r to the d r y i n g stage of the process. Gane (I95l)> from data gathered on apple j u i c e e u t e c t i c temperatures, considered that apple s l i c e s c o n t a i n a l i q u i d phase which i s absorbed by the f r u i t t i s s u e while i t i s - being f r e e z e - d r i e d under normal commercial c o n d i t i o n s . B a r r e t t and Beckett (1951) recommended f r e e z e - d r y i n g at a temperature below, but as clo s e to the e u t e c t i c p o i n t as p o s s i b l e . They i n d i c a t e d that i t i s necessary to dry s l i g h t l y below the e u t e c t i c temperature i n order to o b t a i n the m i n i - mum product damage. The use of temperatures much below the e u t e c t i c serve no u s e f u l purpose and cause vacuum equipment requirements to become i n c r e a s i n g l y complex. Luyet (1962), r e f e r s to a process known as pseudo f r e e z e - d r y i n g . Nonfrozen water, which may e x i s t i n a f r o z e n aqueous medium I f the e u t e c t i c temperature has not been reached 20 or i f the water is bound, slowly diffuses through the tissue and causes a collapse or shrinkage of the remaining frame- work. Kuprlanoff (1958)* postulates that part of the protoplasm may form a gel with ultramlcroscopic capillary cavities. Water and aqueous solutions adsorbed on the internal surfaces become enclosed and w i l l not freeze at normal freezing temperatures due to lowered vapor pressure and sub-cooling effect of the capillaries and also because of the concentration of dissolved substances in them. Bound Water Kuprianoff (1958) alleges that free water does not exist in food materials but i s always combined in some way with the other components present. In foodstuffs water may be present as a continuous phase in which other substances are molecularly dispersed, or i t may be chemically bound. Chemically bound water is held as a hydrate, or by covalent bonding and is not removed by common methods of food processing. Adsorbed water occurs as a mono or polymolecular layer on internal or external^surfaces of the product, held by molecular forces, or in fine pores by capillary condensation. Colloidal substances may bind water of hydration in a gel by dipolar forces. 21 Bound water i s generally considered as that fraction of the moisture content which does not crystallize at some prescribed temperature such as -20°C (-4°F), but i s unavail- able as a solvent in the system. Proteins with their many charged groups are the principal water binding substances of tissue. Any material capable of binding water strongly w i l l decrease the amount of water susceptible to crystallization. Rate Limiting Factors In slow frozen products moisture transfer to the surface would encounter less resistance to diffusion and flow than i t would through a series of intact c e l l s . Carl and Stephenson (1965) stated that conduction of heat from the surface to the ice interface would be greater in fast frozen samples due to the structural continuity and moisture transfer would be restricted due to non continuous channels. Conversely In slowly frozen samples, with ruptured c e l l walls, heat transfer would be decreased and vapor flow would be increased. Kramers (1958), found that in the freeze-drying of solutions and suspensions the sublimation rate decreased as the soluble solids content increased. This change was believed to be caused by a decrease in vapor permeability rather than a decrease in thermal conductivity. Permeability decreases with increasing concentration of the solution to an 2 2 extent that i t i s i m p r a c t i c a l to freeze-dry a m a t e r i a l i n i t i a l l y c o n t a i n i n g more d i s s o l v e d substance than i n the e u t e c t i c composition. thermal c o n d u c t i v i t y of f r e e z e - d r i e d D e l i c i o u s apples and c l i n g s t o n e peaches t i s s u e s . Thermal c o n d u c t i v i t y was measured under va r i o u s degrees of vacuum w i t h heat flow transducers. Vapor d i f f u s i v i t y was found by measuring the flow r a t e and pressure drop of toluene through f r e e z e - d r i e d t i s s u e . Perm- e a b i l i t y was a l s o measured by passing dry n i t r o g e n gas through the f r e e z e - d r i e d t i s s u e and measuring the mass flow r a t e and pressure. The r e s u l t s were as f o l l o w s : Harper ( 1 9 6 2 ) , determined the d i f f u s i v i t y and TABLE I I I PROPERTIES OF FREEZE-DRIED APPLE AND PEACH FROM HARPER ( 1 9 6 2 ) . Apple (30°C) Peach (27°C) D i f f u s i v i t y of toluene cm 2/Sec. - i n sample - i n a i r 0 . 0 1 4 9 O . 8 6 5 * 0 . 0 1 9 1 0 . 0 8 5 5 P o r o s i t y 0.88 0.91 Thermal C o n d u c t i v i t y BTU/Hr. Ft- °F - 1 0 0 mm Hg - 0 . 0 1 mm Hg 0 . 0 2 4 4 0 . 0 0 8 6 0.0249 O . O O 8 9 * Apparent decimal e r r o r i n o r i g i n a l p u b l i c a t i o n 23 Lusk et a l . (1964) , working w i t h f r e e z e - d r i e d f i s h determined the thermal c o n d u c t i v i t y by measuring the temper- ature gradient caused by energy input to one side of a s l a b of the m a t e r i a l . They concluded that the thermal c o n d u c t i v i t y of the dry m a t e r i a l i s the most important v a r i a b l e governing the d r y i n g time of f i s h products because i t l i m i t s the r a t e of heat t r a n s f e r . Saravacos (1965).* s t u d i e d the r o l e of moisture t r a n s f e r i n the f r e e z e - d r y i n g r a t e s of model food g e l s . Shrinkage of r a p i d l y f r o z e n g e l s was a t t r i b u t e d to m e l t i n g of the i c e core due to the low vapor p e r m e a b i l i t y of the d r i e d l a y e r . Mink and Sachsel (1962) , mentioned that the i c e phase i n a f r e e z e - d r i e d sample recedes u n i f o r m l y around the sample due to the r e l a t i v e l y high thermal c o n d u c t i v i t y of the f r o z e n s e c t i o n compared to that of the d r i e d s e c t i o n . In t h i s way the i c e mass i s n e a r l y i s o t h e r m a l . The authors a l s o mentioned that In most p r a c t i c a l f r e e z e - d r y i n g s i t u a t i o n s mass t r a n s f e r does not l i m i t the r a t e of d r y i n g . Under these c o n d i t i o n s heat t r a n s f e r by conduction or conduction and r a d i a t i o n l i m i t s the d r y i n g r a t e to about o n e - f i f t h of that permitted by mass t r a n s f e r c o n s i d e r a t i o n s . This i n f o r m a t i o n was obtained from a study of the f r e e z e - d r y i n g of beef muscle. 24 Radiant heat t r a n s f e r to both sides of a meat s l a b , i n d i c a t e d that mass t r a n s f e r i s not r a t e l i m i t i n g up to a thickness of 2 to 3 inches. Harper (1957)* concluded that heat t r a n s f e r i s the rate l i m i t i n g f a c t o r i n f r e e z e - d r y i n g of meat t i s s u e . However C a r l and Stephenson (1965)* working w i t h f r e e z e - d r i e d potato t i s s u e , and Hanson (1961) , working w i t h apple t i s s u e concluded that water vapor t r a n s f e r and not heat t r a n s f e r i s the r a t e l i m i t i n g f a c t o r . / ' F r e e z i n g Rates F r e e z i n g r a t e s a f f e c t f r e e z e - d r y i n g r a t e s by changing the p h y s i c a l c o n d i t i o n of the m a t e r i a l . G o l d b l i t h et a l . (1965) , i n s t u d i e s on shrimp, showed that commercially q u i c k - f r o z e n samples thawed and r e f r o z e n i n l i q u i d n i t r o g e n (-320°F) re q u i r e d c o n s i d e r a b l y longer d r y i n g time than samples r e f r o z e n i n a i r at 0°F. They a t t r i b u t e d the e f f e c t of the f r e e z i n g r a t e to the s i z e of i c e c r y s t a l formed by the two f r e e z i n g modes a f f e c t i n g the water vapor t r a n s f e r path. In the same s e r i e s of t e s t s , the chamber pressure was v a r i e d to determine the e f f e c t on d r y i n g r a t e . No s i g n i f i c a n t d i f f e r e n c e i n d r y i n g r a t e was found between pressures of 1500 microns and 80 microns of mercury. 25 Saravacos (1965) found that gels f r o z e n at -10°C - f r e e z e - d r i e d at a f a s t e r r a t e than gel s f r o z e n at dry i c e or l i q u i d n i t r o g e n temperatures. This d i f f e r e n c e was a t t r i b u t e d to the more porous s t r u c t u r e l e f t by the subl i m a t i o n of l a r g e r i c e c r y s t a l s formed i n the samples f r o z e n at -10°C. The author s t a t e d that the r e l a t i v e l y h i g h d r y i n g r a t e found i n the f a l l i n g - r a t e p e r i o d was an i n d i c a t i o n that s u b l i m a t i o n from the i c e i n t e r f a c e and water d e s o r p t i o n from the p a r t i a l l y d r i e d l a y e r of the g e l occurred simultaneously. Fennema and Powrie (1964) mention that i n f r u i t the slow removal of heat w i l l r e s u l t i n a continuous i c e phase moving inward w i t h l i t t l e or no n u c l e a t i o n o c c u r r i n g i n advance of the f r e e z i n g boundary. Rapid heat removal r e s u l t s i n a discontinuous i c e phase composed of many minute c r y s t a l s a r i s i n g from numerous n u c l e i . C a r l and Stephenson (1965)* i n t h e i r study on f r e e z - i n g r a t e s , m i c r o s c o p i c a l l y examined samples of potato and mush- room which had been subjected to various f r e e z i n g regimes and subsequently f r e e z e - d r i e d . P r a c t i c a l l y a l l the c e l l w a l l s of samples fr o z e n over a two hour p e r i o d were found to be ruptured. C e l l w a l l rupture was apparently caused by la r g e i c e c r y s t a l s formed duri n g the r e l a t i v e l y long p e r i o d of c r y s t a l growth i n the maximum c r y s t a l l i z a t i o n zone. Fast f r o z e n samples passed through the zone of c r y s t a l l i z a t i o n 26 i n one minute thus forming smaller i c e c r y s t a l s that d i d not d i s r u p t the c e l l s t r u c t u r e . Kramers (1958), found that the vapor p e r m e a b i l i t y of f r e e z e - d r i e d m i l k , water p l u s l a c t o s e , and orange j u i c e decreased as the r a t e of f r e e z i n g i n c r e a s e d . Burke and Decareau (1964) , reported, that the f i n e pore s t r u c t u r e obtained by quick f r e e z i n g reduced the rate of d r y i n g of products produced by the a c c e l e r a t e d freeze - d r y i n g method. A l s o , the product r e s i s t e d r e h y d r a t i o n because of gas trapped i n the f i n e pores. Examination of i c e c r y s t a l formation i n blanched and unblanched vegetables by Weier and Stock i n g (1949) pro- vided no evidence of a d i f f e r e n c e i n the s i z e and l o c a t i o n of c r y s t a l growth. Slow f r e e z i n g r a t e s of both blanched and untreated samples promoted e x t r a c e l l u l a r i c e formation where the c r y s t a l s become r e l a t i v e l y l a r g e . During formation they o f t e n punctured c e l l u l o s e w a l l s and pushed between the c e l l s . Lee et a l . (1946, 1949), worked on the e f f e c t of f r e e z i n g r a t e on the texture of vegetables and of s t r a w b e r r i e s , r a s p b e r r i e s and s l i c e d peaches packed i n syrup. They found l i t t l e d i f f e r e n c e i n appearance or texture among very slow, intermediate and very f a s t f r e e z i n g r a t e s . Fennema and Powrie (1964) , s t a t e d that texture de- 27 crease d u r i n g f r e e z i n g i s caused by mechanical damage, volumetric changes and co n c e n t r a t i o n of nonaqueous c o n s t i t u e n t s . The extent and type of mechanical damage depends on the nature of the product and the rat e at which the change of state occurs. Slow f r e e z i n g allows a greater opportunity f o r con- c e n t r a t i o n damage than r a p i d f r e e z i n g . A Laboratory F r e e z e - D r i e r MacKenzie and Luyet ( 1 9 6 4 ) described equipment designed to study the r a t e s of f r e e z e - d r y i n g f r o z e n m a t e r i a l s . The apparatus allows a continuous r e c o r d i n g to be made of weight changes and sample temperature d u r i n g f r e e z e - d r y i n g . Heat input can be maintained at a constant l e v e l or, by means of a feedback c o n t r o l from the centre temperature sensor, adjusted to c o n t r o l a constant centre temperature. With t h i s apparatus the b a s i c p h y s i c a l processes of f r e e z e - d r y i n g can be a c c u r a t e l y determined. The authors mentioned that the e f f i c i e n c y and convenience of t h e i r method i s f a r s u p e r i o r to s t r a i n gauge load c e l l s and s p r i n g balances used as weighing d e v i c e s . MATERIALS AND METHODS Te s t i n g Equipment A l a b o r a t o r y s i z e d f r e e z e - d r y i n g apparatus u t i l i z i n g r a d i a n t heat energy was const r u c t e d . The d e t a i l s of t h i s 28 apparatus are shown i n Figure 4. The d r y i n g chamber was a f i v e hundred m i l l i l i t e r g l a s s f r e e z e - d r y i n g f l a s k immersed i n a constant temperature water bath which served as a r a d i a n t heat source f o r the suspended sample. A constant water l e v e l was maintained so that the shape f a c t o r could not change d u r i n g the measuring p e r i o d . A p a r a l l e l arm connecting tube served to connect the flask to the vacuum system and a l s o to permit lead wires to be run to the r e c o r d i n g apparatus. E i g h t copper wires and one constantan wire were passed through a Kovar to glass s e a l . A brass compression r i n g gland was j o i n e d to the Kovar tube to serve as a vacuum s e a l . I t was found necessary to coat the wires and s e a l p e r i o d i c a l l y w i t h c e l l u l o s e acetate lacquer to prevent l e a k s . Vapor was removed through the second arm of the connecting tube and was condensed i n a side arm f l a s k immersed i n a dry i c e ethanol mixture. A McLeod gauge was i n s t a l l e d between the d r y i n g chamber and the side arm f l a s k to measure the system pressure. A needle valve was placed between the condenser and vacuum pump to maintain a constant pressure by p r o v i d i n g a c o n t r o l l e d leak of a i r i n t o the system. The Ba l z e r s Duo 5 vacuum pump was capable of ma i n t a i n i n g a t o t a l pressure of one micron on an empty dry system. 29 The sample weighing device was a t h i n r i n g s t r a i n gauge load c e l l , the design of which i s given i n appendix IV. F o i l gauges were used since wire gauges were found to be u n s a t i s f a c t o r y , p o s s i b l y due to entrapped gas. To prevent overheating the load c e l l was operated i n t e r m i t t e n t l y . Power from a twelve v o l t storage b a t t e r y was a p p l i e d f o r approximately one minute i n f i v e minutes. Samples were f r o z e n i n a c i r c u l a r p l a s t i c h o l d e r , one and three quarters of an i n c h i n s i d e diameter and'three- eighths of an i n c h i n depth. Two thermocouples were f r o z e n i n the sample so that the surface and centre temperatures could be measured. The sample i n the h o l d e r was suspended from the load c e l l . The load c e l l r i n g was suspended on a t h i n rod from the top of the connecting tube. Lead wires from the vacuum t i g h t Kovar s e a l were connected to a two channel Moseley r e c o r d e r . One m i l l i v o l t f u l l s c a l e s e n s i t i v i t y was used to record weight change. ' F i v e m i l l i v o l t f u l l s c ale s e n s i t i v i t y was used to record centre and surface temperatures, since a dry i c e , ethanol mixture was used as a reference thermocouple temperature. Thermocouple leads were taken through a m u l t i - p o i n t switch to the recorder so that both temperatures could be measured on a s i n g l e channel. Amphenol connectors were i n s t a l l e d to s i m p l i f y the connection of the measuring d e v i c e s . The recorder A. McLeod Gauge D. Switching Unit B. Cold Trap E. Recorder C. Constant Temperature Bath F. Vacuum Pump FIGURE 4A. PHOTOGRAPHS OF APPARATUS A. P a r a l l e l Arm Connector D. Load C e l l B. Vacuum Tight Seal E. Sample Holder , C. Freeze-drying F l a s k F. Sample FIGURE 4B. PHOTOGRAPHS OF APPARATUS 32 was grounded and operated through a V a r i a c power supply to reduce noise s i g n a l s . C a l i b r a t i o n of the load c e l l was c a r r i e d out i n a i r to give a reading of f i v e grams per i n c h and checked under atmospheric c o n d i t i o n s w i t h balance weights. Because the reading changed w i t h temperature and vacuum, the c a l i b r a t i o n was re-checked under opera t i n g c o n d i t i o n s u s i n g f i x e d weights f r o z e n i n t o a small block of i c e . S e n s i t i v i t y remained con- stant but the zero reading was suppressed when operat i n g i n . a vacuum. Experimental M a t e r i a l . Netted Gem potatoes, grown i n a dry b e l t area, and purchased a t 4 a l o c a l store were used. Macintosh apples from a c o n t r o l l e d atmosphere storage were suppled by B.C. Tree F r u i t s L i m i t e d f o r use as experimental m a t e r i a l . Both apples and potatoes were s e l e c t e d f o r u n i f o r m i t y of s i z e and shape i n an e f f o r t to provide u n i f o r m i t y of m a t u r i t y i n the m a t e r i a l s used. Two samples were taken from a s i n g l e potato by c u t t i n g cross s e c t i o n a l segments approximately one h a l f of an i n c h t h i c k from the centre of the tuber at r i g h t angles to the l o n g i t u d i n a l a x i s . The s l i c e s were f i t t e d to the p l a s t i c frame. Apple samples Mere taken from the side of an i n d i v i d u a l f r u i t . Both apple and potato samples were f i t t e d to the p l a s t i c frame by u s i n g a c i r c u l a r c u t t e r . Copper-constantan 33 thermocouples were i n s t a l l e d i n the centre of each sample by- feeding the thermocouple through a hypodermic needle which was p o s i t i o n e d on a diameter of the sample by means of guide holes i n the p l a s t i c sample h o l d e r . Thus the hypodermic needle could be withdrawn, l e a v i n g the thermocouple j u n c t i o n at the geometric centre of the sample. Surface thermocouples were f o r c e d through the t i s s u e , p e r p e n d i c u l a r to the f i r s t thermocouple, u n t i l the j u n c t i o n was b a r e l y d i s c e r n i b l e at the opposite s u r f a c e . D u p l i c a t e moisture determinations were made by the A'.O.A.C1. o f f i c i a l vacuum oven method number 27 .3 on a l l apples and potatoes used. For potato samples the dry matter content was used as an i n d i c a t i o n of mat u r i t y whereas f o r apples, m a t u r i t y was evaluated by the determination of pH, percentage t o t a l a c i d and so l u b l e s o l i d s content of the expressed c e l l sap from three apples. Four l o t s w i t h three apples per l o t were t e s t e d . Apples f o r t h i s e v a l u a t i o n were s e l e c t e d on the b a s i s of u n i f o r m i t y of col o u r and s i z e so as to be as s i m i l a r as p o s s i b l e to those used i n the d r y i n g t e s t s . A refractometer was used to ob t a i n the s o l u b l e s o l i d s content. Percentage t o t a l a c i d was c a l c u l a t e d as malic a c i d from a pot e n t i o m e t r i c t i t r a t i o n of d i l u t e d c e l l sap. The t i t r a t i o n was made w i t h sodium hydroxide to a pH of 8 . 8 . 34 Experimental Procedure Sample F r e e z i n g A l l prepared samples were placed i n p l a s t i c f r e e z e r bags p r i o r to f r e e z i n g . To o b t a i n r a p i d r a t e s of f r e e z i n g the samples were Immersed i n a dry i c e , ethanol mixture at -108°F. For the slow f r e e z i n g r a t e s the samples were placed i n a household r e f r i g e r a t o r f r e e z i n g compartment maintained between -10°F. and +5°F. Centre temperatures.were measured u s i n g copper-constantan thermocouples. To determine the zone of maximum c r y s t a l l i z a t i o n and an e s t i m a t i o n of the f i n a l e u t e c t i c p o i n t , the centre temperatures were recorded d u r i n g the f r e e z i n g process. Four samples of apple and f o u r samples of potato t i s s u e were f r o z e n at both of these r a t e s . An e s t i m a t i o n of the e u t e c t i c temperatures of the experimental m a t e r i a l s was obtained from v i s u a l examination of the time temperature r e c o r d s . The zone of maximum c r y s t a l l i z a t i o n was taken as the re g i o n of the curve w i t h the minimum r a t e of temperature change. The p o i n t at which the slope underwent a f u r t h e r change f o l l o w i n g the maximum c r y s t a l l i z a t i o n zone was taken as the e u t e c t i c p o i n t . Freeze-drying A sample was suspended from the load c e l l r i n g and the thermocouples i n the sample were connected to the appro- 35 p r i a t e l e a d s . The f r e e z e - d r y i n g f l a s k was seated to the ground g l a s s cover, immersed i n the constant temperature bath and connected to the vacuum system. The chamber pressure was r e g u l a t e d to the d e s i r e d pressure and the sample allowed to f r e e z e - d r y to a constant weight. The sample weight and surface and centre temperatures were recorded throughout the d r y i n g p e r i o d . The pressure i n the system was noted at r e g u l a r i n t e r v a l s . The sample was then removed and the f i n a l moisture content determined, (A^O.A.C. method 2 7 - 3 ) . The r e c o r d of sample weights was used to c a l c u l a t e the moisture l o s s at h o u r l y i n t e r v a l s d u r i n g the d r y i n g c y c l e . The i n i t i a l segment of the d r y i n g curve was not c l e a r l y d e f i n e d , because s e v e r a l minutes were r e q u i r e d to e s t a b l i s h thermal and pressure e q u i l i b r a t i o n i n the system. Therefore, the f i n a l moisture content was used as the b a s i s f o r the c a l c u l a t i o n of moisture removal. Drying curves were then r e p l o t t e d on a r i t h m e t i c graph paper as moisture content (grams) against time. The slope of these curves was used to determine the d r y i n g r a t e s (grams of water l o s t per hour). Summary of Experimental Procedure 36 TABLE IV NUMBERS ASSIGNED TO SLOW FROZEN SAMPLES FREEZE-DRIED UNDER THE CONDITIONS SPECIFIED Drying temperature (°F) 86 104 Drying pressure/(( Hg.) 550 1400 . 550 1400 Apple — 3 4 5 6 1 2 Potato 14 16 12 10 15 17 13 11 RESULTS C h a r a c t e r i s t i c s of Sample M a t e r i a l Netted Gem Potatoes TABLE V DRY MATTER CONTENT OF SLOW FROZEN POTATO SAMPLES Test Number Percent Dry Matter 10 29.4 11 29.4 12 3 0 . 4 13 30.4 14 29 .2 15 3 0 . 2 16 34.4 17 26.4 Mean = 3 0 . 0 + 2.06 37 Macintosh Apples TABLE VI ANALYSIS OF CELL SAP OF PEELED AND CORED APPLES TEST A B C D MEAN Soluble S o l i d s fo 12.6 12 .3 12 . 8 12.2 12 .5 + 0.25 pH 3 .85 3 . 7 4 . 0 3.65 3 . 8 + 0.135 % T o t a l Acid"(malic) 3 .35 3.15 3.50 3.15 3.29+ 0.146 Netted Gem Potatoes and Macintosh Apples TABLE V I I AVERAGE DENSITY OF EIGHT FREEZE-DRIED APPLE AND POTATO TISSUE SAMPLES • Apple Potato Moisture R a t i o 0 .06 Density Lbs/Ft3 15.0 0.03 6.2 F r e e z i n g Rates TABLE V I I I FREEZING RATES OF FAST FROZEN POTATO Moisture R a t i o Maximum C r y s t a l - l i z a t i o n (°F) - E u t e c t i c o Time from 40 to ( F) _40°F (min) 3 . 8 0 3.34 3.20 3.05 2 9 - 2 7 - 1 3 1 - 2 9 + 1 2 8 - 2 6 - 1 2 6 - 2 3 - 1 3.05 2 .85 4 . 5 0 4 .35 38 TABLE IX FREEZING RATES OF SLOW FROZEN POTATO Moisture R a t i o .Maximum C r y s t a l l i z a t i o n (°F) Time from 40 to 20°F (min) 3.15 3.58 4.12 3.20 30 - 23 31 - 26 3 1 - 2 9 31 - 27 108 70 81 57 TABLE X FREEZING RATES OF FAST FROZEN APPLE Moisture R a t i o Maximum C r y s t a l - , 0 , Time from 40 to l i z a t i o n ( GF) E u t e c t i c ( F) _4o0p ( m ± n ) 6.60 6.40 6.26 6.13 31- - 22 - 10 3 0 - 2 2 + 8 3 0 - 2 2 - 10 2 9 - 1 6 - 10 2.23 3.50 2.20 2.05 TABLE X I FREEZING RATES OF SLOW FROZEN APPLE Moisture R a t i o Maximum C r y s t a l l i z a t i o n (°F) Time from 40 to 20°F (min) 6.30 6.30 6 .80 6.50 30 - 28 31 - 24 31 - 27 31 - 26 48 . 0 4 2 . 5 37.5 37.5 39 RESULTS Drying Rates The weight of moisture i n the sample was plotted. versus time f o r each sample d r i e d . The r e s u l t a n t d r y i n g curves are presented i n Figure 5 f o r potato samples and Figure 6 . f o r apple samples. CALCULATED RESULTS Drying Rates and Heat Flow . combination showing the d r y i n g r a t e , and sample surface and centre temperature at h o u r l y i n t e r v a l s i s presented i n Appendix I A f o r apple samples and Appendix I B f o r potato samples. The r a t e of heat flow and d r y i n g r a t e at the time the Ice phase i s completely sublimed are given i n Appendix I I . Drying Rate P l o t t e d Against O v e r - a l l Temperature D i f f e r e n c e Tabulated data f o r each temperature and pressure The o v e r a l l c o n d u c t i v i t y c o e f f i c i e n t U i s defined i n the us u a l way; 1 1 x U " h r k and q = UA(T A-T C) (5) (6) combining equation 6 w i t h equation 2 y i e l d s : dw d© UA 7\ (7) 1 I 1 i • I I 4 r r M 1 M l I 1 1 I i i. 1 1 l . 1 1 '1 1 I 1 1 i 1 1 1 - j - 1 1 i 1 i I i ! H i i 1 M 1 i 1 1 1 1 1 i •  i 1 1 i I I i 1 I III! I i | j 1 1 1 i !• ! I i 1 i i i 1 1 i 1 1 1 1 1 1 I 1 1 i I 1 1 ! i i 1 i i M M 1 1 1 i 1 I 1 1 ' 1 i i ! 1 I i i M i l | 1 I 1 •1 1 ! j 1 1 1 1 i . j j 1 i ! ! in! M M I 1 1 1 i 1 j : i 1 I 1 1 1 ! 1 ! ! I 1 1 i 1 1 ! . i 1 i 1 I 1 1 j ! , i i i i — M l I I I i _ 1 1 i 1 M M I 1 1 1 1 1 4 V > 1 i i 1 ! 1 1 1 I i M M •-K )4op. -1400 1 i 1 1 1 1 < M i I | j 1 1 i i i j _ f*r"gt I 1 1 1 ! •1 i \ 1 I L 1 | j 1 i 1 I ' _ ' 1 1 -T - t L L 1 I i i 1 1 1 \ I 1 i \ 1 1 1 1 n I i i I 1 1 1 | 1 ! i 1 l i \ i 1 i 1 i i i ? | 1 - - 1 1 I I ! * H i \ j i 1 i 1 i : ' M i i r r | | I 1 1 ! 1 I - l 1. i 1 | . i 1 1 . 1..! 1. i M n k Lf > i 1) j 1 j i • 1 1 1 ! 1 1 i Q i i i i 1' 1 I ! M I I | M M M M M M 1 1 ! 1 1 1 i 1 V \ i 1 \ i 1 1 1 11 i i i i ! i • -550, /1U~ 1 1 1 1 i I- I ! ! 1 ! 1 \ i 1 SI V 1 1 r • | i 1 1 1 i 1 1 . N 1 Iv 1 ! I • I 1 I 1 1 ! 1 1 V 1 \ 1 I 1 t i j 1 1 1 1 i j \ \ 1 i i i I 1 1 i ! I i 1 VI 1 X V > I 1 < ' s . 1 i i 1 1 1 i 1 I 1 k,l r , . I • 1 I 1 ' 1 1 i- j t 1 i u> 1.1 1 S i i i I C O 1 I • j ! i - l i 1' s. 1J I k c » 1 1 1 I I i M i l 11 N i s 1 i 1 ! 1 i i i i I 1 I . i V I i i 1 i . s i I V l \ 1 ! c S i r 1 i 1 i -1 1 I I 1 ! 1 i i 1 1 I 1 1 S 1 i 1 i I i ! i ' 1 i I p 1 I 1 < i | I 1 1 1 I 1 I 1 I V 1 1 1 | 1i 1 ! 1 I i 1 1 ! *\ \ i > k i 1 i 1 ! 1 | 1 1 1 I 1 r 1 1 I V S I | . I N 1 ( 1 i 1 1 1 ! I 1 1 i \ s. 1 1 I I N s 1 1 i 1 f r \ j 1 i 1 V I 1 M V 1 I i _ i I 1 i k 1 1 1 V 1 1 i i ! i ! 111 i I 1 i > r > 1 1 * .̂  1 1 1 1 >. « > 1 1 i • i i 1 : i 1 L r-v ' ! i 1 i i l i t l Y M M * > i 1 1 1 l 1 1 i i 1 i 1 | -v 1 JIM 1 1 1 1 1 1 1 1 N l 1 r < j ' > 1 i I 1 1 1 I 1 •j > I J c [> i v , 1 1 •1. 1 1 1 I 1 - I > l 1 1 1 ( 1 1 1 1 I 1 I 1.. 1 ! \ V i " N i 1 1 1 i 1 i ! 1 ^ i c 1 s * i 1 1 i 1 1 I 1 i 1 i 1 ! i kX 1 1 t b 1 1 1 1 »| 1 i i . ! ! i i 1 1 «L. c- 1 1 1 i v» 1 t 1 i i i 1 1 i 1 11 I I 1 I s * J " j t i ! i 1 1 * 1 1 i 1 i i ! 1 1 i ; »&i 1 1 i 1 1 1 i i V V 1 1 i i i ! c ^ 1 1 M M I I 1 1 1 | 1 1 i 1 1 1 K 1 V I I 1 i 1 1 ! i i S I 1 1 1 1 1 | 1 1 i 1. ~i H i T ~ 1 1 ! i > 1 1 1 i i 1 | 1 1 1 i i 1 1 1 1 i f v I 1 n 1 1 I 1 1 1 1 1 1 i i I 1 v - t M J l } K 1 1 i i , M l i i i 1 i i 1 1 1 I I 1 i J . i i | i « » 1 1 1 i ! .1 1 ' i s t. 1 i ) i I 1 ' i i r = r . J 1 ! * 1 i 1 i | j 1 1 i 1 •> r. i i i i i i i ; c * i P - i- i t 1 i 1 i 1 .1 i T 3 L 1 I i 1 1 1 t i 1 i i ! 1 i 1 1 i i 1 ' i I 1 1 1 : i i i i ) i i ! 1 1 i ! i i ! 1 1 1 ! I 1 1 i L i i 1 | l i- i i i h i i . >- 1 i i -1 ] 1 1 1 J 1 I \> i H 1' A ) 1 1 lUl 1 ! IL: _ l I i li > i ! 1 I i 1 1 1 1 i i 1 1 1 1 1 I 1 I i ! 4 | | 1 I i 1 ! i | 1 1 .Tl 1 I 1 i 1 1 1 1 . 1 1 I 1 f 1 1 1 ! ' vm i R 1 1 1 I 1 1 1 I 1 1 1 1 ! I I 1 I I 1 i i I 1 i i 1 1 i j i 1 1 I 1 j I i i 1 1 1 1 1 i 1 I I l 1 i J ] 1 • I. i i i J ] r J] s 1 I | 1 1 1 j I 1 I i 1 IG 9 | 5 L 0 t ? ROZ I ? J.IJ NO u s 1 I I i i 1 1 1 i i i 1 1 i 1 1 1 i i I i i 1 i 1 1 i i | 1 ! 1 I i 1 1 1 t • i i I •1 1 1 1 i i r | 1 1 1 1 1 1 i l I 1 ! i 1 1 1 1 1 7*" 1 1 1 i 1 1 1 I t i i 1 i i i 1 i | i i i I . 1 1 i | i 1 1 I 1 i i 1 1 4- i i 1 1 t— 1 i — i — 4-H 1 -1 i ! 1 i t 1 ! 1 1 1 1 1 I 1 ! i 1 1 1 1 I i r r I - 1 4 i ' 1 i I 4 _ n x 1 1 I 1 i i I 1 1 i~ I I j 1 1 M l ; 1 1 i i 1 1 1 i ! i i i i _ l 1 i i 11 r T H i i 1 1 t i 1 i 1 | ! 1 1 1 i i i 1 1 1 i i i i i ; i i i i .1 1 1 I I I ! 1 1 1 1 . 1 1 —1 II 1 i 1 1. 1 1 1 H T T L I m 1 .1 1 1 1 i 1 1 I 1 1 1 i 1 J 1 r 1 1 i • 1 I I _ L 1 1 1 1 > 1 1 1 1 i i 1 1 1 1 | 1 1 1 J L i ~ _ _ ~ i 1 1 1 l l l 1 1 " <v f i 1 1 i i ! 1 1 1 j 1 l ' i i . i i i i i i i 1 l i n i • i I i - i I 1 | ! I i i i 1 < < i i i i i i i ! > 1 | 1 1 1 I ; i i i 1 ' i • ^ ° F ; -1400, / ^ u L l 1 1 i 1 1 1 I | 1 1 I _ l L J I I I ! i • M i i ( i u 1 i i i i l | 1 i 1 I 1 i J _ .1. _! i 1 1 ..!_ i T T i r j 1 • i i I i ! 1 -1 I I 1 ! i i i 1 1 1 1 1 ! I I I i 1 • n c L O l >5Q- I i 1 i \ 1 i 1 y i j 1 j 1 1 ! i 1 I ! - J u '—!—1 1 I 1 * T ! S M i l i 1 1 i 1 1 1 1 I I I 1 i " T 1 ! 1 i 1 i ..1 ' U l I L i i \\\ 1 1 1 1 1 I I 1 ! i 36OF4- 1 +00 11 Uir' i 1 _\._\ 1 i ! I I • i n • L' 1 1 1 1 I 1 i i I .« I \ 1 1 1 I I i i i 1 1 i i 1 1 1 I 1 1 i i i i : i i i j ' V | 1 I i 1 I 1 I I i 1 1 i i ! 1 1 t 1 1 i i 1 I I 1 1 1 I I i j 1 1 1 1 1 1 1 i | I | I \ 1 J . l I j ! I ! 1 1 1 i I 1 I 1 ^ 1 1 i l l i i i 1 1 i \ I i i 1 1 1 I i j 1 i i 1 1 1 N ' T " i i i ; i i I 1 I i v I 1 i i i 1 1 1 I ! i I" 1 1 i I i 1 1 I 1 i n i 1 '. 1 i t 1 i \ M " 1 ! 1 1 j I i i i 1 1 1 1 i i . 1 1 1 1 1 1 i i i I i 1 1 1 I 1 1 \ 1 1 I l I I 1 I 1 1 | 1 1 i 1 t I m | | 1 I \ 1 i I I 1 | 1 1 1 I i 1 l i - L U M | 1 > < ^ \ 1 1 I i 1 1 | i I i I 1 h iB 1 a. i \ ! J k i > ! 1 i 1 I I i 1 1 1 1 1 1 1 i 1 1 I. ' ! ft 1 \ K 1 1 1 1 1 ! I i I i i I I 1 1 -1-1 ! 1 | 1 j - i p H i IM i 1 ! 1 1 I I 1 1 1 I 1 I I I ! 1 i 1 \ 1 1 1 j I 1 _ j J _ L . L 1 1 1 1 1 I 1 1 ! 1 -M 1 1 1 I 1 1 1 1 1 M I i 1 C ) 1 ! i r i ! i 1 • 1 I i i 1 1 i • 1 1 1 1 1 1 1 i 1 1 1 i « i I N i \ i \ i ! i t 1 1 l 1 » I 1 I 1 1 1 i i 1 4 i i J 1 | i ( 1 l 1 1 1 1 1 ! L L I i i \ ' i 1 i 1 I ! 1 1 1 1 1 i MM 1 \ •1 1 1 1 1 1 ! 1 1 1 1 i | i m s 1 1 1 1 1 1 — I - i 1 ' \ n i i | 1 1 1 1 1 t i 1 1 1 1 1 1 t l i i 3 L_ > 1 1 1 V I | 1 1 1 i i i > IS 1 i 1 1 I 1 i 1 ! > _ \ ' ( I I I s i i -i 1 ! I 1 i 1 1 1 1 1 1 1 1 ! 1 i i i i i i 1 t i i i ! ! 1 \ l l l l i I I i ! i i 1 1 1 ! 1 • I ! _> 1 I S i I I 1 J 1 • i 1 1 I I i r\ i i r •> 1 1 I i j 1 I ! 1 * I I * * ! 1 i ! 1 * I I 1 1 1 1 o 1 1 i I I - i i i 1 I 1 1 t 1 1 1 I i 1 I 1 I I v l 1 J N J 1 1 > 1 ( I 1 1 1 I 1 i i i 1 i 1 I \ \ I I 1 1 i i i 1 N , s i f 1 ' ' 1 1 1 1 i 1 . _[ 1 _ _. U _ J > v L ( 1 I 1 1 1 t I 1 t i i 1 1 1 ! ! -( i i | I I I i N ' 1 ! t 1 1 1 1 i i 1 i I 1 i 1 i i i I i l i | 1 i 1 ! | 1 1 1 L-1 U I i > 1 1 1 1 1 1 i 1 i 1 I 1 i 1 i 1 1 1 L n ! i _ I _ i > 1 1 1 i 1 I 1 1 i 1 1 . 1 i 1 M l ! i _ u _ L 1 1 i i 1 1 1 1 1 1 1 i 1 1 1 1 ! ! 1 1 1 _ i J ; 1 1 1 .1 1 I l a I I i 1 1 1 1 1 ! 1 ' i i i i I i 1 i ! 1 1 1 1 i ) i i i i , - 1 1 i • 1 ! i | 1 1 1 - " I ! I J- 1 i 1 3 l- > 1 1 1 , , i 1 1 { 1 ! i ' V X | 1 J> ! 1 1 I i 1 i __ _ 1 j +! 1 i j | 1 1 I 1 | i i i r 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 i 1 i i 1 1 1 1 i I 1 1 l 1 1 1 l i i TIRE. i 1 1 i i i 11 ! i 1 1 1 1 1 1 1 i i i i i t I i 1 1 ! 4 t-4 U - 4 4 - 1 - _ 1 _ i \ i i i 1 4 4 - i 1 1 4 1 4 - 1 1 1 J _ 1 t i I i I L 1 F 1 i i L _ - 3L0 — ri ROZ t-A PP DR 4_ j j NGr 3 u D 1 1 t -J _ I 1 o 1 - i IX V —1 1 1 1 r 1 ! i i i i i r 1 1 1 1 1 1 1 i i I i i i 1 1 i 1 i 1 1 i 1 i 1 ( ̂  1 i ! | 1 t i l _ i 1 \ n 1 | | 1 | 1 1 1 I i 1 ! 1 1 1 ! 1 i 1 i r ! I r _ r 1 1 1 1 • i 1 ! 1 1 1 I ! 1 1 1 1 i i 1 1 1 i | ! j 1 I I I I i i 1 1 i i i i 1 1 1 i _ i i 1 I M 1 i 1 1 -i i 1 1 1 _ i I ' M 1 I i 1 1 1 1 l i 11 r l 1 1- i i 1 1 ! i I I J ! I ! I I 1 1 i i 1 1 1 l i ' • 1 . . 1 1 1 I 1 I i t - I l - l i i - \ i - M i - i i 1 1 ' 1 I i 40 Thus assuming a constant l a t e n t heat of su b l i m a t i o n , a p l o t of d r y i n g r a t e (^-i) versus the o v e r - a l l temperature d i f f e r e n c e (T -T ) y i e l d s a l i n e whose slope i s p r o p o r t i o n a l to the over- a l l thermal c o n d u c t i v i t y c o e f f i c i e n t U. The r e s u l t s obtained du r i n g potato and apple f r e e z e - d r y i n g are p l o t t e d i n the above manner i n Figures J and 8 r e s p e c t i v e l y . Thermal C o n d u c t i v i t y F o l l o w i n g the procedure of Lusk et a l . (1964) to evaluate the thermal c o n d u c t i v i t y of the d r i e d l a y e r at any time i n the d r y i n g c y c l e , the thic k n e s s of the d r i e d product i s r e l a t e d to the cumulative weight l o s s . WL = Axp(MR 1-MR 2) (8) (9) Ap(MR x-MR 2) Combining equations 3 and 9 , y i e l d s : kA(T s-T c) = WL (10) - q Ap(MR!-MR2) However s u b s t i t u t i n g a value f o r q from equation (2) %L = k A 2 P(MRi-MR 9) (Tq-Tp) ( l l ) d© > Wj_, P l o t t i n g dw against ( T s - T c ) w i l l r e s u l t i n a s t r a i g h t l i n e d© ~WL which should pass through the o r i g i n . Therefore the slope of the l i n e i s : m = k A 2p(MRi-MR 2) (12)  1 1 , 1 i i I . M L ! J i i 1 1 i I 1 i i i 1 | 1 i i 1 i 1 1 i I 1_ I I 1 i 1 1 1 MM i I 1 1 ! 1 1 i i j i 1 i l i | 1 i i i ! i I i M M i i 1 1 i 1 i i 1 i i 1 I i 1 i i i • 1 I i i i 1 i 1 1 1 i - 1 i i 1 i i 1 _j 1 I i i 1 1 - i 1 I i I 1 | 1 i j I i 1 i 1 i i" i 1 i i 1 1 1 1 I 1 1 i 1 1 1 | I i 1 | I l 1 i | 1 1 1 ; 1 1 i 1 1 1 I i i i i i i • 'n\ M M M M M ! i i i ' 1 1 1 1 i i M ~ M 1 M ~1 . . . . . . l i i ' c v ? i 1 I M I i 1 i i i i _ J J _ l . - M l ! J I M ! 1 1 1 1 M M 1 1 I i i M i ! _ 1 MlOV 71 U'rYrf/y'W'o-! - 1 - I 1 1 l 1 M M • i 1 ! 1 1 i I M • M i i r V T i P • 1 1 i i J I M | i | 1 i 1 i i i i n i 1 i ! j I M M i 1 i i 1 ! 1 1 1 1 i i « / - _ _ / [ J n i M M I i i i i ! 1 1 i i 1 i y 9 > r v H' • i i 1 - M M 1 i 1 i i 1 I 1 i " i n i * i !' 1 i 1 1 1 1 i 1 i i I 1 r s J If LT I I .1 ! f I 1 1 1 1 1 i ; i X 4- J / • - r 1 i 1 : 0 - 1 1 j 1 1 1 1 1 I I i ™ r i i 1 ! i cL • I 1 1 l i | J — i | i i M M I M I I 1 1 I 1 i 1 I i 1 i Mi i i 1 1 —1— ! 1 1 i i ! ! 1 1 1 1 1 1 1 i i i i 1 - A | - I ,1 i . i M i r M M r i i- I i t 1 1 1 L i ! | ~ i p H - — — — v - 1 I 1 1 i ! 1 1 i i i i i i !l I I 1 I M i M M I i i ! , .i i i i 1 (. ! i ii—* ! 1 1 1 1 i 1 i i 1 1 1 ii M M i 1 i i j 1 ! 2 1 1 i 1 1 f i i i 1 I i 1 L | " M M i i i 1 1 I £2 1 1 1 ! i i i 1 A H i - i i i 1 i 1 M M 1 i i 1 1 1 I i> M j L c l i 1 1 l t i i i i 1 1 1 i i 1 M l ! I I I M 1 i 1 i 1 I V4 i I i : 1 1 i i .1 I 1 i 1 M M I 1 i | i 1 i i I 1 i i J . 1 1 1 I -rrrr 1 i 1 i 1 I 1 i 1 i i i 6 : . l 1 i l 1 I 1 1 " ' i I 1 i i 1 1 1 1 i i 1 1 r j*1—1 i i ! i I 1 I | 1 i ! 1 1 ! I « I 1 1 ! i 1 i 1 1 I i <• i I i i M M i i 1 I •M ' f r S 1 | 1 1 1 1 I i I : i 1 1 # i 1 l 1 l i - U i 1 i W 1 1 1 I ' " 4 " I 1 1 i 1 _ i 1 1 1 i ! ! 1 1 1 1 i j ! i i i i 1 i i . 1 -\ t- j 1 1 i —' 1 1 1 ! icd-i 1 n ! r V 1 1 1 1 1 1 i i 1 i I i i j - • 1 ! 1 I 1 1 1 1 j i 1 1 1 ! 1 lrk J V J; 1 1 1 1 1 i i i i ! I I l ! 1 1 1 1 1 I ! & 1 1 1 | i 1 i i i ! . i \ 1 1 1 i i 1 T H H - 1 1 1 j 1 | 1 I 1 i | i I i i —,— I A I I t t : i 1 j 1 r r t ; ! I >*-1 1 H - i i I ! i 1 t I ' < 1 t i i X i i t — • - i : 1 1 M i 1 i 1 I i i . ! .1 1 1 I I I ! :: -h- i 1 : i 1 | i I 1 | i • i •• i i i t H j i i 1 1 k _ • 4- 1 ! i . i I 1 1 1 i 1 . M 1 1 1 1 1 t i l ! M M M M 1 ! I 1 1 i 1 1 l i | i i i i I i t i 4 J ! 14! 1 i 1 i 1 1 f j ! i i ! 1 I 1 1 1 1 +f- 1 1 ! 1 M M 1 M • t ! h ; i' Cv-' •tr- I 1 1 1 i 1 ! i 1 1 ! J i I | 1 1 1 1 i I 1 I M i l 1 1 i j 1 1 1 1 i i 'Ml. M > 0\ 11 1 1 1 1 1 i M M 1 ! 1 1 ' 1 M M 1 1 1 t I | 1 U 1 L M i ' 1 j 1 1 1 1 1 1 i j ! M ~t ! 1 - j i i i | 1 1 i M M I 1 .M J , . . 1 t i i ! • 1 1 i 1 | 1 1 M M 1 1 I 1 M M 1 * - —"T A , i i 1 I 1 I 1 1 1 1 1 i ; . i i ! ! i . 1 M M 1 — 1 : 1 1 I I • M M 1 1 1 i : i i ; 1 1 I M i 1 1 1 1 1 1 1 M M M M i i i 1 i i •: ' I I i i — i i I | 1 i M ! i 1 i 1 ! \ 1 1 1 i MM I I 1 _ u . 1 1 M M ! 1 1 1 1 1 M ' ' i i~y~ . . . _ . U. i i MM 1 1 i " 1 ' i r I i 1 1 1 1 1 1 ' rv 1 1 1 1 i Mi i ! 1 ! ! I M M ' 1 1 i 1 i 1 1 1 1 * 1 ! i I 1 -A i 1 1 1 b 3 i 1 M I • 1 - H - H i t,Ai i 1 i 1 i 1 ! 1 M M 1 91 i 1 L I 1 p 1 ! l o | 20 i LL TO, i 1 I i i 1 1 M I ; 1 ! 1 1 1 Tl ( 1 ~j I I | i i " t l i 1 1 i i ! 1 I 1 j j i - j - | 1 i " i i 1 t 1 | r _ - _ r c •-\ f l 1 44 1 1 1 1 - i n 44- 1 I 1 1 ..J i i | ; j I 1. 1 1 i 1 l i 1 1 i i 1 1 i « 1 i 1 I i i 1 i i TTTrl TTR 8.v H B V T M 7 AT i J R _ fSTT? P E PIT iR ! , ) 1 | 1 1 | 1 i l l ! 1 -J JT _ I 1 ' I K ! 1 1 Hi | i j ~ 1 1 i | i 1 1 i SLOW K N L A P P T . T C I 1 1 1 | I 1 I l 1 i J ' ' 1 1 1 t i 1 M ! 1 i i 1 1 1 1 1 i 1 i j ! i i 1 I 1 ! J 1 1 1 I 1 1 1 I i i 1 | 1 . 1 ] | 1 M i l 1 i | 1 | 1 ( 1 1 | 1 1 4= 4 J 1 1 ! M M _ J 1 j 1 1 I 1 I I l | 1 I 1 — J J 1 M M 1 1 1 1 I I 1 1 1 1 1 I 1 1 1 l 1 I M M i 1 1 ! I 1 1 1 1 1 1 1 1 1 M { — i 1 • ! 1 : "1 i' i l I i I > _ 1 1 1 l i I i ! 1 i • 1 ! 1 I 1 i 1 i 1 i 1 - 1 i 1 1 1 1 1 i i I 1 | i !'•- MT — -— L 1 r i i 1 1 M~! 1 l i i ...... 4- 4- l J 1 I - 1 1 I I i 1 4 4 ! —i—j-~f— 4- 4 1 The r i g h t term of equation 12 c o n s i s t s of a constant m u l t i p l i e d by the c o e f f i c i e n t of thermal c o n d u c t i v i t y . This constant can be evaluated f o r from the p r o p e r t i e s of the m a t e r i a l being t e s t e d . Thus the thermal c o n d u c t i v i t y c o e f f i c i e n t may be c a l c u l a t e d . Graphs u s i n g t h i s p l o t t i n g method are shown i n Figures 9 and 10 f o r potatoes at 550 microns and 1400 microns. Figure 11 shows a s i m i l a r graph f o r the f r e e z e - d r i e d apple data. TABLE XII THERMAL CONDUCTRVITY OF SLOW FROZEN FREEZE-DRIED APPLE AND POTATO TISSUE AS CALCULATED.USING EQUATION (12) BTU/HR. °F.FT?/FT. ... Drying Pressure>aHg. 5 5 0 1400 Apple 1.0 x 10~ 2 1.0 x 10- 2 Potato 0 . 6 6 x 10 ~ 2 O . 7 8 x 10" 2 Thermal C o n d u c t i v i t y at the end of the Sublimation P e r i o d At the time the l a s t of i c e phase i s sublimed from the sample, the centre temperature i n d i c a t e d begins to r i s e . At t h i s p o i n t of I n f l e c t i o n i n the temperature curve the thickness of d r i e d m a t e r i a l i s known to be h a l f the sample t h i c k n e s s . A value of the heat flow r a t e i s obtained from equation (2) and used i n conjunction w i t h equation (3) to  i i 1 i I L. L L L I j i l J - L I _ .... , 1 | | U ± 4 - I L i" 1 !~ r ! 1 i~ _ r •-i 1 1 j n 1 1 " 1 i : - — i " "\ _ L i - L L !--- - L L ----- -L I -- - ----- . _ 1 i ----- . I_ i - . - ~( ~ - ± 1 . - . 1 - 1 . - z - - i - 1 i i r-TEV - 1 1 L ..1 _ 4 . 1 _ L L 1 1 1 1 — 1 L .)„ J . J _ ! r L I i - c 1 ' i " i 1 I 1 ' r" ~ r i i - X - h i i • 1- i ...|._ _ _>> i c [& " _ _ r A f I1 ~ r _ _L ~\~ 1 1 I _-j„ i i c 0" ' _ _ — _ _ — _ — _ l e>» i- i -_ _ _ — _ _ _ — _ — — — — — — - - 1 1 - — 1 l - 1 * i li J 1 1 j _ 1/ ( > — i -- -- - - ------ ---------------• - ---- k - • - -------- _ -_ - ---- - -- -1 i .J J _ i 4 - L _ i _ u _ 4 _ . _.L j . . j » 4 _ i i 1 X " i r i i i ! I i I 1 i ) K • £ o ... i. _ 1 ! • : 1 _ L i - r -i _ i _ _ L . L 1 i i i i 1 i _ i 1 1 1 J _ _ _ tc J 1 _ i _ Li'"' | i I n 1 i 7 V ' i i T l t—|— r J C ._L..'/_ i i 1 i 1 X J i Ctl! . . . l\ • 1 X c n i i / _ i r c L i / i 1. _ l . <' A. } X i L _ l 2i i _ r x i l 1 i =•+_ i i O u t X I _c2 X / * 4 I i _ [Of n 1 • 1 O n ! : J 1 i i i r i i 1 I I / 1 ! I _ _ > * _ _ L t t J _ i r > i i 1 1 1 t TJfi 1 J I i 1/ i • 1 1 i i i d i | I \ | I al 1 i i i i n i I i 1 l "1 1 _ H _ V •• i J 1 1 i --- - - — —Sr — • -- J I 1 I 1 1 j 1 '\/ 1 _ i 1 i 0 4 i c \ A / _ 1 j < i i 1 4 £_ 1 i 1 _t i 1 I y I J i 4 1 1 1 i 7x _ L l _ L i 1 i 1 j i i t i i i I 1 1 i 1 ! 1 i 1 1 ! 1 I i .1 .!_ r JL + 1 1 I l l i 1 i i ~ r T T I T — i u , i 1 l .. L i . ._!_ 1.. ' j I _ i A ) _ L 1 r J . ,30.. .4c K 1 T i ~ _ L _ L i _ . L T«S 1 i -r 'GRAy - i - T I 1 w 1 1 n 1 I 1 + _ L 1 Wo:- | i i 1 1 1 1 I T 1 i . i . i . i r 1 i _ ..1 L i 1 1 i I i 1 _ PIGUF IE- -1C ) -PLOT- it r OA iLGl ILATId )N[0F- SLOW- i i 9 i * v. i I i i T ? R f Y 7 . 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OF THERMAL- CONDUCTIVITY SLOW 42 c a l c u l a t e a value of the thermal c o n d u c t i v i t y at t h i s p a r t i c u l a r p e r i o d i n the f r e e z e - d r y i n g c y c l e . The c o e f f i c i e n t s c a l c u l a t e d u s i n g t h i s method f o r potato samples are shown i n Table X I I I and f o r apple samples i n Table XIV. Radiant Heat T r a n s f e r C o e f f i c i e n t The c o e f f i c i e n t of heat t r a n s f e r can be evaluated at any time d u r i n g the d r y i n g c y c l e . For convenience i n comparison, the c o e f f i c i e n t was evaluated at the t e r m i n a t i o n of i c e sub- l i m a t i o n . Equating equations ( l ) and (2) allows the c a l c u l a t i o n of the c o e f f i c i e n t from the d r y i n g r a t e and the temperature d i f f e r e n c e between the heat source and sample s u r f a c e . Co- e f f i c i e n t s f o r slow f r o z e n f r e e z e - d r i e d potatoes and apples are presented i n Tables XV and XVI r e s p e c t i v e l y . © TABLE X I I I THERMAL CONDUCTIVITY COEFFICIENT (k) OF SLOW FROZEN FREEZE-DRIED POTATO CALCULATED USING - EQUATION (.2) AND (3) BTU/HR. °F.FT.2/FT. Temperature 86 °F 104°F Pressure Sample k Sample k M Hg BTU/Hr.°F.Ft. BTU/Hr.°F.Ft. 1400 16 2.72 x 1 0 " 2 10 8.48 x 1 0 " 2 17 3.14 x 10~ 2 11 3.22 x 1 0 - 2 550 14 3.81 x 1 0 " 2 12 3.96 x 1 0 - 2 15 4.26 x 1 0 - 2 13 4.48 x 10-2 4 3 TABLE XIV THERMAL CONDUCTIVITY COEFFICIENT (k) OF SLOW FROZEN FREEZE-DRIED APPLE CALCULATED. USING EQUATION ( 2 ) AND ( 3 ) BTU/HR. °F.FT.2/FT. Temperature 8 6 ° F 104°F Pressure M. Hg Sample k BTU/Hr.°F.Ft. Sample k BTU/Hr.°F.Ft. 1400 3 4 1 . 8 5 x 1 0 - 2 3 . 6 1 x 1 0 - 2 1 2 3 . 6 1 x 1 0 " 2 3 . 8 9 x 1 0 ~ 2 5 5 0 7 8 5 6 2 . 0 5 x 1 0 ~ 2 TABLE XV RADIANT HEAT TRANSFER COEFFICIENT ( h r ) OF SLOW FROZEN FREEZE-DRIED POTATO CALCULATED USING EQUATION ( l ) AND ( 2 ) BTU/HR. OF.FT. 2 Temperature 8 6 ° F 1 0 4 ° F Pressure JX. Hg Sample BTU/Hr.°F.Ft.2 Sample BTU/Hr.°F.Ft.2 i 4 o o 1 6 1 7 1 . 5 8 0 O . 7 6 6 1 0 1 1 1 . 0 8 1 . 4 6 5 5 0 1 4 1 5 0 . 8 0 0 0 . 8 2 4 1 2 1 3 0 . 8 1 5 0 . 5 9 3 44 TABLE XVI RADIANT HEAT TRANSFER COEFFICIENT ( h r ) OF SLOW FROZEN FREEZE-DRIED APPLE CALCULATED USING EQUATION ( l ) AND (2) BTU/HR. OF.FT. 2 Temperature 86°p 104°F Pressure _ h r _ - h r yOCEg Sample BTU/Hr. °F. F t . 2 b a m P l e BTU/Hr. °F . F t . 2 1400 3 1.09 1 0 .88 4 1.29 2 1.49 550 7 5 1.27 8 6 O v e r - a l l Thermal C o n d u c t i v i t y The o v e r - a l l thermal c o n d u c t i v i t y c o e f f i c i e n t can be c a l c u l a t e d from e i t h e r Equation ( 7 ) , at any time dur i n g the d r y i n g c y c l e , or Equation ( 5 ) , from i n f o r m a t i o n gained at the te r m i n a t i o n of the i c e phase. C a l c u l a t e d values of o v e r - a l l thermal c o n d u c t i v i t y are presented i n Table XVII f o r the slow f r o z e n , f r e e z e - d r i e d potato and i n Table X V I I I f o r slow f r o z e n f r e e z e - d r i e d apple. C a l c u l a t i o n s were based on the c o n d i t i o n s at the end of the subl i m a t i o n p e r i o d . 45 TABLE XVII OVER-ALL THERMAL CONDUCTIVITY (U) OF SLOW FROZEN FREEZE-DRIED POTATO CALCULATED USING EQUATION (5) BTU/HR. OF.FT. 2 Temperature 860F 104°F Pressure M Hg Sample U BTU/Hr.OF.Ft. 2 Sample U BTU/Hr.OF.Ft.2 1400 16 17 0.833 . 0.555 10 11 0.915 O.865 550 14 15 0.601 0.634 12 13 0.616 0.492 TABLE X V I I I OVER-ALL THERMAL CONDUCTIVITY (U) OF SLOW FROZEN FREEZE-DRIED APPLE CALCULATED USING EQUATION (5) BTU/HR. °F.FT'.2 . Temperature 86 °F 104°F Pressure M Hg U U Sample BTU/Hr.°F.Ft.2 S a m P l e BTU/Hr,°F.Ft.2 1400 550 3 4 7 8 0.570 0.830 1 2 5 6 0.640 0.932 0.647 46 DISCUSSION OF RESULTS C h a r a c t e r i s t i c s of Sample M a t e r i a l Netted Gem Potatoes Potato c h a r a c t e r i z a t i o n by the percentage dry matter of the samples used f o r f r e e z e - d r y i n g , Table V, showed u n i f o r m i t y except f o r samples 16 and 17 which were of higher and lower dry matter content than the other samples. A l l dry matter contents were higher than that normally expected. The use of potatoes grown i n a dry c l i m a t e , p l u s prolonged storage w i t h subsequent water l o s s , would account f o r a higher than expected dry matter content. Macintosh Apples The a n a l y s i s of apple c e l l sap f o r s o l u b l e s o l i d s , pH, and percent t o t a l a c i d , Table V I , i n d i c a t e d that the ex- perimental m a t e r i a l was of uniform m a t u r i t y . As the samples had been stored under the same c o n d i t i o n s and were s e l e c t e d f o r experimental use on the b a s i s of u n i f o r m i t y of s i z e and c o l o u r , a uniform m a t u r i t y was expected. Netted Gem Potatoes and Macintosh Apples Density e v a l u a t i o n of f r e e z e - d r i e d apple and potato t i s s u e , Table V I I , i s presented w i t h corresponding moisture r a t i o s . The d e n s i t y of potato i s s i m i l a r to f i b r e i n s u l a t i n g board and apple s i m i l a r to b a l s a wood. Density values are 47 necessary f o r use i n the thermal c o n d u c t i v i t y c a l c u l a t i o n , u s i n g equation (12). F r e e z i n g Rates F r e e z i n g curves of both apple and potato samples showed a wide v a r i a t i o n i n the temperature range of maximum c r y s t a l l i z a t i o n . In f a s t f r o z e n samples, the heat of c r y s t a l - l i z a t i o n appeared to be removed at such a r a p i d r a t e that the sample was always supercooled to a minor l e v e l . Slow f r o z e n samples a f t e r i n i t i a l s u percooling increased i n temperature to approximately 1°F below the m e l t i n g p o i n t of pure i c e and then continued to c o o l . The temperature zones of maximum c r y s t a l l i z a t i o n are g e n e r a l l y higher f o r the higher moisture r a t i o samples. This i s expected since higher moisture content would be as s o c i a t e d w i t h lower concentrations of s o l u t e . Apple t i s s u e at both f a s t and slow f r e e z i n g r a t e s cooled more r a p i d l y than potato samples t r e a t e d i n the same manner. The slower c o o l i n g of the potato t i s s u e would I n d i c a t e that potato t i s s u e has a low thermal d i f f u s i v i t y . A low thermal c o n d u c t i v i t y and a high d e n s i t y could c o n t r i b u t e to a low value of thermal d i f f u s i v i t y . For both apples and potatoes the f a s t f r e e z i n g was approximately e i g h t y times the r a t e of slow f r e e z i n g . The e u t e c t i c p o i n t of potato t i s s u e was found to be 48 -1°F while the e u t e c t i c of apple t i s s u e was found to be -10°F as shown i n Tables V I I I and X. No ex p l a n a t i o n was found f o r the h i g h value found f o r one sample i n Table X. Drying Rates Fast Frozen Samples Fast f r o z e n samples of both apple and potato t i s s u e could not be f r e e z e - d r i e d under the c o n d i t i o n s of temperature and pressure used i n these experiments. When f r e e z e - d r y i n g was attempted on f a s t f r o z e n samples, there was i n every case evidence of thawing, a shrunken appearance and a s t e a d i l y I n c r e a s i n g centre temperature. The centre temperature r a t h e r q u i c k l y passed the m e l t i n g p o i n t and caused the sample to thaw. This continuously decreasing temperature d i f f e r e n c e between source and centre i n d i c a t e d that heat was being s u p p l i e d to the i c e i n t e r f a c e at a r a t e i n excess of that r e q u i r e d by the sublimed water vapor. Therefore, heat was being s u p p l i e d f a s t e r than the water vapor was able to d i f f u s e through the d r i e d m a t e r i a l to the vacuum chamber. Thus the d r y i n g r a t e of f a s t f r o z e n potato and apple samples was c o n t r o l l e d by vapor d i f f u s i o n . These conclusions are i n agreement w i t h the f i n d i n g s of Hanson (1961) and C a r l and Stephenson ( 1965) . Since the f a s t f r o z e n samples t e s t e d d i d not t r u l y f r e e z e - d r y , d r y i n g curves were not prepared f o r these samples. 49 Slow Frozen Samples The d r y i n g curves f o r apples and potatoes, F i g u r e s 5 and 6 , i n d i c a t e d that as d r y i n g c o n d i t i o n s became more r i g o r o u s , higher temperature or lower pressure, d r y i n g r a t e increased and d r y i n g time decreased. For potatoes, v a r i a t i o n s i n i n i t i a l moisture content and sample weight caused the p o s i t i o n s of the d r y i n g curves to be d i s p l a c e d from the expected order. The i n i t i a l d r y i n g r a t e could not be p l o t t e d a c c u r a t e l y since the weight measuring device r e q u i r e d s e v e r a l minutes to reach e q u i l i b r i u m c o n d i t i o n s when operating i n a vacuum. The temperature d i f f e r e n c e between a heat source at 104°F and i c e i n e q u i l i b r i u m w i t h a 1400 micron pressure i s almost i d e n t i c a l to the temperature d i f f e r e n c e between a heat source at 86°F and i c e at a pressure of 550 microns of mercury. For t h i s reason there i s l i t t l e d i f f e r e n c e i n d r y i n g r a t e between these two c o n d i t i o n s , p a r t i c u l a r l y since water vapor t r a n s f e r i s not a r a t e - c o n t r o l l i n g f a c t o r w i t h these products. The co n c l u s i o n that the r e s i s t a n c e to vapor t r a n s f e r i s not a r a t e l i m i t i n g f a c t o r i n freeze-dehydration of apple and potato samples i s based on the small d i f f e r e n c e s between the d r y i n g r a t e s observed at the two pressures used i n these experiments. 50 The r e l a t i v e l y high i n i t i a l d r y i n g r a t e s are thought to have been due to evaporative c o o l i n g of samples, which had warmed durin g the chamber l o a d i n g process, and the removal of surface moisture condensed on the sample. This i c e would have a high e m i s s i v i t y and would sublime at a greater r a t e than moisture w i t h i n the sample m a t e r i a l . I t was observed that the i c e temperatures measured by thermocouples i n the sample centre corresponded to vapor pressures i n excess of the measured pressure. Using vapor pressure t a b l e s f o r i c e , the measured pressures of 100 and 1000 microns were found to be a s s o c i a t e d w i t h d r y i n g chamber pressures of 550 and 1400 microns. The d i f f e r e n c e between the measured pressure and the chamber pressure i s caused by the f a c t that to remove vapor from the d r y i n g chamber a pressure drop i s r e q u i r e d between the sample i c e surface and the c o l d t r a p . As i t was necessary to i n s t a l l the vacuum gauge on the vapor l i n e between the d r y i n g chamber and the c o l d t r a p , the pressure i n d i c a t e d by the McLeod gauge was c o n s i s t e n t l y lower than that e x i s t i n g at the i c e s u r f a c e . The discrepancy between the a c t u a l and measured pressure i s greatest at lower pressures, since the s p e c i f i c volume of the vapor Increases very r a p i d l y w i t h decreasing pressure. The Ice temperature measurement can be used to i n d i c a t e the pressure at the i c e su r f a c e . However, i n some m a t e r i a l s the 51 pressure drop through the d r i e d l a y e r would again l e a d to an erroneous pressure. DISCUSSION OF CALCULATED RESULTS Drying Rate P l o t t e d Against O v e r - a l l Temperature D i f f e r e n c e s Graphs of the d r y i n g r a t e p l o t t e d against temperature d i f f e r e n c e between the h e a t i n g source and the sample centre, as shown i n Figures 7 and 8 r e s u l t i n a broken curve. The r e g i o n of constant temperature d i f f e r e n c e , the upper r i g h t hand p o r t i o n of the graph, i n d i c a t e s that the d r y i n g r a t e i s dependent on the r a t e of heat t r a n s f e r to the i c e i n t e r f a c e and that there i s n e g l i g i b l e r e s i s t a n c e to vapor d i f f u s i o n . I f t h i s were not the case, the centre temperature would increase and by doing so, decrease the temperature gradient - i n order to increase the vapor pressure g r a d i e n t . As explained i n the theory s e c t i o n , t h i s would reduce the heat input and increase the vapor t r a n s p o r t . The second r e g i o n of the curve, the lower and l e f t hand p o r t i o n of the graph, begins at the t e r m i n a t i o n of su b l i m a t i o n and slopes toward the o r i g i n . During t h i s p e r i o d moisture i s removed by the de s o r p t i o n of bound water and the d r y i n g r a t e i s d i r e c t l y p r o p o r t i o n a l to the temperature d i f f e r e n c e . The f a c t that t h i s l i n e decreases l i n e a r l y w i t h decreasing temperature d i f f e r e n c e and passes through the 52 o r i g i n r e q u i r e s that the o v e r a l l thermal conductance (u) he of constant value i n t h i s r e g i o n . As the t h i c k n e s s of the d r i e d l a y e r i s constant throughout t h i s p e r i o d , and the r a d i a n t heat t r a n s f e r c o e f f i c i e n t changes but l i t t l e , i t would appear that the thermal conductance of the d r i e d m a t e r i a l i s v i r t u a l l y constant throughout t h i s d e s o r p t i o n p e r i o d . Thermal C o n d u c t i v i t y From Equation (12) The thermal c o n d u c t i v i t i e s c a l c u l a t e d u s i n g equation (12) are shown i n Table X I I . These values appear to agree reasonably w e l l with those shown i n Table I I I as reported by Harper f o r f r e e z e - d r i e d apple and peach t i s s u e . Very small v a r i a t i o n s i n the p o s i t i o n of the surface thermocouple, as w e l l as v a r i a t i o n s i n the dimensions of the thermocouple j u n c t i o n were found to cause e r r o r s i n the measured surface temperature. For t h i s reason, p l u s the unstable d r y i n g c o n d i t i o n s at the beginning of each run, the p o i n t s shown on the graphs i n Figures 8, 10 and 11 e x h i b i t some s c a t t e r , p a r t i c u l a r l y d u r i n g the e a r l y stages of d r y i n g . Equation ( l l ) assumes that the i c e i n t e r f a c i a l area w i t h i n the sample i s constant, but i n f a c t the area decreases as d r y i n g progresses because of edge e f f e c t s . The d r y i n g r a t e , used as a measure of heat i n p u t , would be increased by sample edge e f f e c t s . The net r e s u l t of these e r r o r s would tend to increase the c a l c u l a t e d thermal c o n d u c t i v i t y above 53 i t s true v a l u e . Since the values found agreed f a i r l y w e l l w i t h p u b l i s h e d values (see Table I I I ) , these sources of e r r o r were f e l t to be s m a l l . Equation (12) a l s o assumes that the m a t e r i a l i n the dry l a y e r i s completely dry f o l l o w i n g the passage of the i c e phase. Such an assumption would lead to the c o n c l u s i o n that the d r i e d l a y e r was t h i n n e r than i t a c t u a l l y was, and so the c a l c u l a t e d value of the thermal c o n d u c t i v i t y would be l e s s than the true value, p a r t i c u l a r l y d u r i n g the e a r l y stages of d r y i n g . The c o n d u c t i v i t y measured by Harper was on f r e e z e - d r i e d m a t e r i a l u s i n g a steady-state method and f o r t h i s reason the value could be lower than that obtained dur i n g the f r e e z e - d r y i n g process. No l i t e r a t u r e references were found to compare w i t h the thermal c o n d u c t i v i t y c o e f f i c i e n t c a l c u l a t e d f o r f r e e z e - d r i e d potato t i s s u e at the two pressures. Thermal C o n d u c t i v i t y C a l c u l a t e d at the Termination of the Ice Phase The most seriou s o b j e c t i o n to values of thermal c o n d u c t i v i t y , Tables X I I I and XIV, c a l c u l a t e d at the t e r m i n a t i o n of the i c e phase was caused by the v a r i a b l e surface temperature mentioned i n the previous s e c t i o n . As the c a l c u l a t i o n i s based on only one p o i n t i n the d r y i n g c y c l e , an erroneous temperature reading could lead to an erroneous c o n d u c t i v i t y 54 c o e f f i c i e n t . Any tendency f o r the m a t e r i a l to dry i n the immediate v i c i n i t y of the centre thermocouple would cause an increase i n the recorded centre temperature which would prematurely i n d i c a t e the te r m i n a t i o n of s u b l i m a t i o n . I f t h i s were the case, the c a l c u l a t e d c o n d u c t i v i t y would be co n s i d e r a b l y higher than the true thermal c o n d u c t i v i t y . The p r e v i o u s l y mentioned method u s i n g Equation (12) f o r c a l c u l a t i n g thermal c o n d u c t i v i t i e s i s thought to be more r e l i a b l e than t h i s method because the complete d r y i n g c y c l e i s used f o r c a l c u l a t i o n r a t h e r than an i n d i v i d u a l p o i n t i n the d r y i n g c y c l e . However, i t i s i n t e r e s t i n g to note that since the method u s i n g Equation (12) g e n e r a l l y tended to p r e d i c t low values f o r the thermal c o n d u c t i v i t y f o r the p a r t i a l l y d r i e d sample, the values reported i n Tables X I I I and XIV might reasonably represent the true c o n d u c t i v i t y of the p a r t i a l l y d r i e d m a t e r i a l . Radiant Heat Tra n s f e r C o e f f i c i e n t The r a d i a n t heat t r a n s f e r c o e f f i c i e n t s , Tables XVI and XVII were subject to the surface temperature measurement e r r o r p r e v i o u s l y mentioned. These values however would be those expected f o r a m a t e r i a l w i t h an e m i s s i v i t y of 0 .90 to 0 . 9 5 . As a l l heat conducted through the sample must a r r i v e by r a d i a t i o n , a large value of thermal c o n d u c t i v i t y should 55 be a s s o c i a t e d w i t h a large value of the c o e f f i c i e n t of r a d i a n t heat t r a n s f e r . Examination of the values reported i n Tables XVI and XVII show that f o r many d u p l i c a t e runs, a decrease i n thermal c o n d u c t i v i t y i s as s o c i a t e d w i t h an increase i n r a d i a n t heat t r a n s f e r c o e f f i c i e n t , and v i c e - v e r s a . Such behaviour must be caused by the erroneous surface temperature readings caused by v a r i a t i o n s i n themocouple placement. O v e r - a l l Thermal C o n d u c t i v i t y The values f o r o v e r - a l l thermal c o n d u c t i v i t y reported i n Tables XVII and X V I I I are f e l t to be q u i t e r e l i a b l e since the surface temperatures are not r e q u i r e d f o r t h i s c a l c u l a t i o n . These values should prove of value f o r c a l c u l a t i o n of heat t r a n s f e r r a t e s f o r other d r y i n g c o n d i t i o n s . 56 SUMMARY OF FINDINGS In t h i s study, the e f f e c t of f r e e z i n g r a t e , system - pressure and heat input on f r e e z e - d r y i n g r a t e s of Macintosh apples and Netted Gem potato t i s s u e were examined. 1. Under constant pressure d r y i n g c o n d i t i o n s the f r e e z e - d r y i n g r a t e of slow f r o z e n apple and potato t i s s u e increased w i t h a temperature increase from 86°F to 104°F. Heat t r a n s f e r was, t h e r e f o r e , the r a t e l i m i t i n g f a c t o r . 2. Chamber pressure had l i t t l e e f f e c t on the f r e e z e - d r y i n g r a t e s of slow f r o z e n apple and potato t i s s u e . Therefore, water vapor d i f f u s i o n was not a r a t e l i m i t i n g f a c t o r . 3. Fast f r o z e n apple and potato t i s s u e could not he f r e e z e - d r i e d under the c o n d i t i o n s of pressure and temperature used i n t h i s study. Water vapor d i f f u s i o n i s r a t e l i m i t i n g i n f r e e z e - d r y i n g of the f a s t f r o z e n t i s s u e s . 4 . The thermal c o n d u c t i v i t y c o e f f i c i e n t s of f r e e z e - d r i e d apple and potato t i s s u e s were found to he 1.0 x 1 0 - 2 and 0.66 x 10"*2 BTU/Hr. F t . 2 °F./Ft. r e s p e c t i v e l y at a d r y i n g pressure of 550 microns of mercury. The c o n d u c t i v i t y of f r e e z e - d r i e d potato was found to increase to O.78 x 10~ 2 BTU/Hr.°F. F t . 2 / F t . at a d r y i n g pressure of 1400 microns of mercury. 5 . The e u t e c t i c p o i n t of Macintosh apples was found to he -10°F and of Netted Gem potatoes, -1°F. REFERENCES CITED 58 LIST OF REFERENCES CITED 1. B a r r e t t , A.S.D., and Beckett, L.G. 1 9 5 L Aspects of the Design of Freeze-Drying Apparatus. F r e e z i n g and Drying. I n s t i t u t e of B i o l o g y , London. 2 . Burke, R.F., and Decareau, R.V. 1964. Recent Advances i n the Freeze-Drying of Food Products. Advances i n Food Research 13, 1. 3 . C a r l , K.R., and Stephenson, K.Q. 1965. E f f e c t s of F r e e z i n g Rate on S t r u c t u r e and Drying Rate of C e r t a i n Freeze- D r i e d Foods. Transactions of the American S o c i e t y of A g r i c u l t u r a l Engineers 8 , 4 l 4 . 4 . Fennema, 0., and Powrie, W.D. 1964. Fundamentals of Low Temperature Food P r e s e r v a t i o n . Advances i n Food Research 13, 219. 5 . Gane, R. 1951. Freeze-Drying of F o o d s t u f f s . Food Manu- f a c t u r e . 26, 389. 6 . Gane, R., and Wager, H.G. 1958. P l a n t S t r u c t u r e and De- h y d r a t i o n . Fundamental Aspects of the Dehydration of F o o d s t u f f s , p.3 . S o c i e t y of Chemical Industry, London. 7. Hanson, S.W.F. ed. 1961. The Ac c e l e r a t e d Freeze-Drying Method of Food P r e s e r v a t i o n . Her Majesty's S t a t i o n a r y O f f i c e , London. 8 . Harper, J.C., and Tappel, A.L. 1957. Freeze-Drying of Food Products. Advances i n Food Research 7, 171. 9 . Harper, J.C. 1962. Transport P r o p e r t i e s of Gasses i n Porous Media at Reduced Pressures w i t h Reference to Freeze-Drying. American I n s t i t u t e of Chemical Engineering J o u r n a l 3, 298. 59 10. Kramers, H. 1958. Rate C o n t r o l l i n g Factors i n Freeze- Drying. Fundamental Aspects of the Dehydration of Fo o d s t u f f s , p. 57 . S o c i e t y of Chemical Industry, London. 11. K u p r i a n o f f , J . 1958. Bound Water i n Foods. Fundamental Aspects of the Dehydration of F o o d s t u f f s , p. 14. So c i e t y of Chemical Industry, London. 12. Lee, F.A., Gortner, W.A., and Whitcombe, J . 1946. E f f e c t of F r e e z i n g Rate on Vegetables. I n d u s t r i a l and Engineering Chemistry 38, 3 4 l . 13. Lee, F.A., Gortner, W.A., and Whitcombe, J . 1949. E f f e c t of F r e e z i n g Rate on F r u i t . Food Technology 3, 164. 14. Lusk, G., K a r e l , M., and G o l d b l i t h , S. 1964. Thermal C o n d u c t i v i t y of Some Freeze-Dried F i s h . Food Technology l 8 , ( l 0 ) , 1 2 1 . 15. Lusk, G., K a r e l , M., and G o l d b l i t h , S. 1965. E f f e c t of Some Processing Parameters on the Rates of Freeze- Drying of Shrimp. Food Technology 1 9 ( 4 ) , 188. 16. Luyet, B.J. 1962. E f f e c t of Fr e e z i n g Rates on the Str u c t u r e of Freeze-Dried M a t e r i a l s and on the Mechanism of Rehydration. In Freeze-Drying of Foods (F.R. F i s h e r , ed.) p. 194. N a t i o n a l Academy of Sciences, N a t i o n a l Research C o u n c i l , Washington, D.C. 17. MacKenzie, A.P., and Luyet, B.J. 1964. Apparatus f o r the Automatic Recording of Freeze-Drying Rates at C o n t r o l l e d Specimen Temperatures. Biodynamics 9 ( 1 8 4 ) , 193. 18. Meryman, H.T. 1962. I n t r o d u c t o r y Survey of B i o p h y s i c a l and Biochemical Aspects of Freeze-Drying. In Freeze-Drying of Foods (F.R. F i s h e r , ed.) p . l . N a t i o n a l Academy of Sciences, N a t i o n a l Research C o u n c i l , Washington, D.C. 6 0 1 9 . Mink, W.H., and Sachsel, G.F. 1 9 6 2 . E v a l u a t i o n of Freeze-Drying Mechanisms Using Mathematical Models. In Freeze-Drying of Foods. (F.R. F i s h e r , ed.) p. 84. N a t i o n a l Academy of Sciences, N a t i o n a l Research C o u n c i l , Washington, D.C. 2 0 . Reeve, R.M. 1 9 5 3 . H i s t o l o g i c a l I n v e s t i g a t i o n of Texture i n Apples. I I . S t r u c t u r e and I n t e r - c e l l u l a r Spaces. Food Research 1 8 , 6 o 4 . 2 1 . Saravacos, G.D., and Charm, S.E. 1 9 6 2 . A Study of the Mechanism of F r u i t and Vegetable Dehydration. Food Technology l 6 ( l ) , 7 8 . 2 2 . Saravacos, G.D. 1 9 6 5 . Freeze-Drying Rates and Water S o r p t i o n of Model Food Gels. Food Technology 1 9 , 1 9 3 . 2 3 . Weier, T.E., and S t o c k i n g , R. 1 9 4 9 . H i s t o l o g i c a l Changes Induced i n F r u i t s and Vegetables by P r o c e s s i n g . Advances i n Food Research 2 , 2 9 8 . APPENDIX 62 APPENDIX I A. Sample #1 Apple T A = 104OF P A = l400/«.Hg. D.M. = 1 .326 Gms. Time Moisture Drying Grams Centre Surface Hours Grams Rate Hour Temp. °F Temp. °F 0 9.18 8 8 1 6.40 1 .70 9 11 2 4 . 9 0 1 .35 9 15 3 3.63 1.21 9 21 4 2 .52 0 .95 10 27 5 1 .57 0 .82 10 34 6 0 .82 O.65 12 40 7 0 .29 0 .38 20 53 8 0 .08 — 80 88 Sample #2 Apple T A = 104°F P A = l400A H g . D.M. = 1 .506 Gms. 0 9.35 _ ~ 9 9 1 7.64 1.70 9 26 2 5.95 1 .57 11 32 3 4.48 1.40 13 38 4 3.18 1.20 14 44 5 2 .08 1.01 17 50 6 1 .19 0.81 23 56 7 0 .53 0 .50 42 64 8 0 .18 — 75 89 APPENDIX I (Cont'd) Sample #3 Apple T A = 86OP P A = l400/<Hg. D.M. = 1.268 Gms. Time Moisture Drying Grams Centre Surface Hours Grams Rate Hour Temp. °F Temp. °F 0 8.50 — 1 1 1 7 .83 1.84 .1 17 2 6.07 1 .62 2 25 3 4 .60 1 .37 5 31 4 3.34 1 .13 5 35 5 2 .34 0.90 5 39 6 1.53 0 .66 5 4 l 7 0.97- 0.43 8 48 8 0.58 0 .32 11 54 9 0 .32 0.23 27 71 10 0 .13 — 83 86 Sample #4 Apple T A = 860F P A = 1400/cHg. D.M. = 1.409 Gms 0 9.15 9 9 1 8 .05 1.10 8 9 2 6.95 1.10 8 16 3 5.84 1.10 6 20 4 4.75 0.94 5 23 5 3.86 O.83 8 28 6 3.06 0 . 8 0 8 31 7 2 .25 0 .80 8 34 8 1.45 0 . 8 0 9 38 9 O.69 O.63 16 50 10 0 .27 — 53 73 64 APPENDIX I (Cont'd) Sample #5 Apple T A = 104op P A = 5 5 0 ^ Hg. D.M. = 1.520 Gms. Time Moisture Drying Grams Centre Surface Hours Grams Rate Hour Temp, op Temp, op 0 9.80 -16 -16 1 6.26 2.28 -10 + 7 2 4 .30 1.60 - 7 27 3 3.04 1.11' - 6 36 4 2.08 0.91 - 6 47 5 1.29 0.74 + 5 55 6 0.65 0.56 20 65 7 0.24 0.30 75 90 8 0.14 • • — ' 104 104 • Sample #6 Apple TA = 104°P P A = 550/(Hg. D.M. = 1.423 Gms. 0 9.12 -17 Not Recorded l 7.33 1.71 -15 it 2 5.12 1,40 -14 3 3.42 1.08 -13 4 2.11 0.69 -10 5 1.21 0.58 - 5 6 0.50 0.44 12 7 0.14 — 59 65 APPENDIX I (Cont'd) B. Sample #10 Potato T A = 1 0 4 ° F P A = l400_/(Hg. D.M. = 3.322 Gms. Time Moisture Drying Grams Centre Surface Hours Grams • Rate Hour Temp. Q F Temp. Q F 0 11 . 3 — 5 5 1 9.72 1 .53 7 8 2 8.24 1 .36 9 11 3 6 .87 1 .30 10 15 4 5 .65 1.20 11 18 5 4.48 1.10 13 24 6 3.42 1 .06 15 29 7 2 .42 0 .93 17 35 8 1 .56 0 .80 21 39 9 0 .90 0 .63 31 47 10 0.43 0.40 56 67 11 0.33 — 92 94 Sample #11 Potato . T A = 104O F P A = l40Gy<.Hg. D.M. = 2 .979 Gms. 0 10.12 — - 9 - 9 1 9.84 I . 5 8 6 20 2 8.07 1 .37 7 29 3 6.76 1.25 6 35 4 5.57 1 .13 6 42 5 4 .47 1.04 6 48 6 3.52 0 .92 8 53 7 2 .66 O.83 11 58 8 1 .88 0 .71 15 63 9 1 .19 0.62 23 68 10 0 .62 0 .53 42 76 11 0 .15 - - 70 88 APPENDIX I (Cont'd) Sample #12 Potato T A = 104°F P A = 550/cHg. D.M. = 3.848 Gms. Time Moisture Drying Grams Centre Surface Hours Grams Rate Hour Temp. °F Temp. °F 0 12.5 — - 5 - 5 1 8.39 2.96 0 0 2 6.35 1 .58 - 3 + 6 3 5 . 0 8 1 .04 - 4 11 4 4.12 O.96 - 4 18 5 3.20 O.85 + 4 26 6 2.42 0.73 6 31 7 1 .69 O.65 8 37 8 1 .08 0.54 24 41 9 0 .65 0.42 39 46 10 0 .31 0 .31 54 54 11 0 .15 0,12 72 72 12 0 . 0 8 — 100 100 Sample #13 Potato T A = 104°F P A = 550/<Hg. D.M. = 3.759 Gms 0 12.2 _ _ - 7 - 7 1 8.35 2.66 - 7 - 5 2 6.45 1 .32 - 7 - 5 3 5.40 0.94 - 8 - 2 4 4 .51 0.79 - 9 + 3 5 3 .83 0.67 - 8 9 6 3 .16 0.64 + 9 16 7 2 .56 0 .60 19 24 8 2.03 0.53 29 32 9 1.54 0.41 39 44 10 1 .09 0.38 47 57 11 0.71 0.34 57 74 12 0.45 0 .26 77 88 13 0 .24 0 .19 93 98 14 0 .13 — 103 104 67 APPENDIX I (Cont'd) Sample #14 Potato TA_ = 86°F P A = 5 5 0 A H g . D.M. = 3.306 Gms. Time Moisture Drying Grams Centre Surface Hours Grams Rate Hour Temp. °F Temp. °F 0 -10 -10 1 11.23 1.59 -10 - 7 2 9.65 1.49 -10 - 8 3 8.20 1.36 -10 - 4 4 6.94 1.19 -10 + 2 5 5 .81 1.02 -10 4 6 4 .85 0.93 -10 8 7 3.96 0.79 - 8 13 8 3.30 0.63 + 2 18 9 2.74 0.53 5 23 10 2.25 0.43 8 29 11 1.82 0.40 15 35 12 1.42 0.36 26 39 13 1 . 0 6 0.33 32 44 14 0.76 0.26 39 50 15 0.50 0.23 46 57 16 0.26 0.20 54 62 17 0,13 0.10 64 71 18 0.07 -- 72 78 68 APPENDIX I (Cont'd) Sample #15 Potato T A = 8 6 ° F P A = 550/<Hg. D.M<. = 2.966 Gms. Time Moisture Drying Grams Centre Surface Hours Grams Rate Hour Temp, O F Temp, O F 0 -10 -10 1 _ _ - 4 + 2 2 9.58 -- - 4 6 3 8.23 1.18 _ 4 11 4 7.18 0.95 - 1 14 5 6.29 0.83 + 2 17 6 5.51 0.74 3 20 7 4.84 0.65 4 22 8 4.15 0.62 7 25 9 3.59 0.56 10 29 10 3.02 0.53 14 32 11 2.56 0.50 20 35 12 2.05 0.47 • — -- 13 1.63 0.44 37 47 14 1.25 O.38 47 55 15 O.89 0.33 50 59 16 0.59 0.27 59 65 17 0.36 0.21 69 76 18 0.18 — 78 82 6 9 APPENDIX I (Cont'd) Sample #16 Potato T A = 8 6 ° F P A = 1400/tHg. D.M. 3 . 9 1 5 Gms. Time Hours Moisture Grams Drying Grams Rate Hour Centre Temp. ° F Surface Temp, O F 0 1 1 . 0 4 - 1 0 - 1 0 1 8 . 6 9 1 . 8 0 + 6 + 1 0 2 7 . 2 4 1 . 2 5 6 2 6 3 6 . 0 6 1 . 0 2 6 3 2 4 5 . 0 8 0 . 9 8 6 3 7 5 4 . 1 5 0 . 9 0 6 41 6 3 . 2 8 0 . 8 2 7 4 4 7 2 . 4 6 0 . 7 0 1 0 4 7 8 1 . 8 o 0 . 6 6 1 6 5 0 9 1 . 1 4 0 . 5 9 1 8 5 3 1 0 0 . 6 6 0 . 4 3 2 6 5 7 1 1 0 . 3 1 0 . 2 3 40 6 6 1 2 0 . 1 6 0 . 1 6 6 2 7 6 1 3 0 . 1 2 — 8 1 8 3 70 APPENDIX I (Cont'd) Sample #17 Potato T A = 86QF P A = l400/<»Hg. D.M. = 3 . 1 5 4 Gms. Time ' Hours Moisture Grams Drying Grams Rate Hour Centre Temp. °F .Surface Temp. °F 0 12.0 8 8 1 8.70 1.26 8 • 8 2 7.48 1.17 6 10 3 6.42 1.04 8 14 4 5.51 0.98 8 15 5 4.51 O.85 6 17 6 3.62 0.82 6 20 7 2.90 O.76 8 23 8 2.14 0.66 9 26 9 1.58 0.60 9 28 10 1.07 0.47 11 32 11 0.63 0.38 16 38 12 0.31 0.25 32 50 13 0.13 0.16 58 71 14 0.06 — 82 83 71 APPENDIX I I TERMINATION OF ICE PHASE Sample T l m e . dW LbsT" ' T Q _ T T A - T O BTU Hours dO Hr. a 0 • b HF7 APPLE 1 5.4 1.65 x 10-3 26 68 2.01 2 4,9 2,25 x 10-3 33 55 , 2.74 3 6.4 1.26 x 10-3 39 42 1.54 4 7.75 1.77 x 10-3 28 50 2.16 5 4.2 1.94 x 10-3 54 56 2.37 POTATO 10 6 . 0 2.23 x 10-3 15 75 2.72 11 4.75 2.32 x 10-3 41 58 2.83 12 5.75 1.67 x 10-3 24 75 2.04 13 5.6 1.49 x i o - 3 19 92 1.82 14 7.8 1.51 x 1 0 - 3 23 69 1.85 15 8 .1 1.35 x 10-3 18 60 1.65 16 5 .9 1.82 x 10~ 3 38 42 2.22 17 9 . 8 1.15 x 10-3 21 55 1.41 72 APPENDIX I I I THERMOCOUPLE HEAT CONDUCTION Conduction along the thermocouple wire was b e l i e v e d to be r e s p o n s i b l e f o r an erroneous temperature r e a d i n g . Sub- sequent t e s t s w i t h slow f r o z e n m a t e r i a l suggested that t h i s was not the case, and th a t a r e l i a b l e temperature measurement was being obtained. A sample c a l c u l a t i o n to determine the, heat conduction along the thermocouple wire under the worst c o n d i t i o n s was made: Assume a 1.0 i n c h length of wire = -40° to 122° = l62°P diameter of copper wire = 0 .003 inches Area - * f ' = _ J L ^ ^ = 4 . 9 x 1 0 " 8 FT 2 . Q = ( 2 2 0 ) ( 4 . 9)(I0 - 8 ) ( 1 6 2 ) = 2 > 1 x 1 0 - 2 B T U / H r < , 1 2 " Conduction along a 0.010 i n c h diameter constantan wire the same leng t h w i t h the same temperature d i f f e r e n c e : Area = JL^L_ = ^ = 5 . 4 3 x 10 FT 2 Q = kA^T 73 APPENDIX I I I (Cont'd) Q = ( 1 ^ ) ( 5 . 4 3 ) ( 1 0 ^ ) ( 1 6 2 ) = 1 M x 1 0-2 BTU/Hr. 12 T o t a l = 3 .6 x 10-^ = 0.036 BTU/Hr. Latent heat of sub l i m a t i o n at -40°F = 1221 BTU/Lb. = 1221 BTU/454 Grams, 0.036 BTU ( ° - ° ^ ( 4 5 4 ) = 0.0135 Orams^r. The sub l i m a t i o n which could be caused by heat conducted along the thermocouple wire i s i n s i g n i f i c a n t when compared to the a c t u a l s u b l i m a t i o n r a t e s . In p r a c t i c e heat l o s s e s along the wire would tend to reduce the heat conducted to the thermo- couple j u n c t i o n and reduce the e r r o r f u r t h e r . 74 APPENDIX IV Load Ring Design M i l d s t e e l r i n g : f o i l s t r a i n gauges width w = 0.375 i n . gauge f a c t o r = 3 . 0 depth d = 0.015 i n . o r i g i n a l r e s i s t a n c e 1000 ohms ra d i u s r = 1.0 i n . allowable s t r e s s S = 40,000 PSI Young's modulus E = 30 x 1 0 6 PSI Maximum load P = ffiaj— 6 ( 0 . 3 l 8 ) r - 40,0 0 0 ( 0 . 3 7 5 ) ( 0 . 0 1 5 ) 2 6 ( 0 . 3 1 8 ) ( 1 ) = 1.77 Lbs. S t r a i n p = change i n length o r i g i n a l length n„,,„~ n change i n r e s i s t a n c e . Gauge f a c t o r G = — : — ? — - :—- «• s t r a i n o r i g i n a l r e s i s t a n c e Assuming 10"3 ohms i s l e a s t detectable change S t r a i n = 0.33 x 10~ 6 S = E C = 30 x 1 0 6 x .33 x 10~ 6 = 10 PSI S = wd* M = ( 1 0 ) ( 0 . 0 1 5 ) 2 ( 0 . 3 7 5 ) = 0.000140 6 Minimum load P . jfagj; - (o°°iB)(i) " ° - 0 0 ° 4 4 L t e - P = 0 . 2 Grams. to recorder APPENDIX IV (Cont'd) calibration switch 75 alancing esistance 4 micro-switch 12 volt battery FIGURE 12. LOAD CELL WIRING DIAGRAM Maximum power dissipation i n air i s 0 .25 watts per gauge power input at 12 volts: 2 P = I 2R = E_ 12' 1000 = 0.144 watts over 4 gauges Due to poor heat dissipation in the freeze-drying chamber, intermittent rather than continuous operation was used.

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