A PROCEDURE FOR RAPIDLY DETERMINING TRANSPIRATIUN RATES AND ' , EPIDERMAL PERMEABILITIES 0F FRUITS Thesis for the Degree of Ph. D. ‘ l MICHIGAN STATE UNIVERSITY ' JOE PERRY GENTRY 1970 — W -‘*rfi'3ri‘ NiwI‘ér-lru-semw .- w 1.. . . , , . . . , . ‘ rVIJ;I.v:_.'t"r:1r.‘51-" -‘.x‘.‘“-" #2..“ "F. ”3". H‘ W". _‘ . . , \\\\\\\ \\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\I 3 1293 10385 7839 This is to certify that the thesis entitled A PROCEDURE FOR RAPIDLY DETERMINING TRANSPIRATION RATES AND EPIDERMAL PERMEABILITIES OF FRUITS presented by Joe Perry Gentry has been accepted towards fulfillment of the requirements for Ph.D. degree in Agr. Engr. Major professor Date 0!: [4,1 ’970 0-169 We? LIBRARY Michigan 3t; {43 University L ABSTRACT A PROCEDURE FOR RAPIDLY DETERMINING TRANSPIRATION RATES AND EPIDERMAL PERMEABILITIES OF FRUITS By Joe Perry Gentry Transpiration rates of grapes and cherries as measured by mass— transfer coefficients were evaluated from experimental measurements and a lumped capacity unsteady-state mass-transfer analysis. Parameters to be used in mass-transfer equations to describe the flow of moisture through the epidermis were determined. Effects of mechanical polishing and chemically disturbing the cuticle on the mass-transfer coefficient of grapes were found. Fruits were placed in a small container of dry air, and the dew- point of the air was observed by circulating the air through a hygro— meter. The dew points were converted to vapor pressure and the mass- transfer coefficient and an apparent equilibrium relative humidity were determined by iteratively fitting the vapor pressure ratio to an exponen- tial regression. Permeabilities of the epidermis were determined from the thickness of the tissue, apparent and true convective mass-transfer coefficients. Joe Perry Gentry The true convective mass-transfer coefficient was considered to be the mass-transfer coefficient of the peeled fruit, while the apparent mass— transfer coefficient was the mass-transfer coefficient from the unpeeled fruit. Values of the mass-transfer coefficients were of the order of 8 - -8 0.4 x 10 to 2.0 x 10 grams of H 0 per (minute) (square mm) (mm of 2 mercury). The pedicel with its small surface area in relation to the surface area of the fruit was a significant factor in the total mass transfer. Air flows over a rnage of from one to ten air changes per minute had no significant effect on the convective mass-transfer coefficients. For purposes of predicting epidermal mass transfer, fruits were modeled after a slab. The relationship between vapor pressure and time in a lumped capacity unsteady-state mass-transfer system as predicted by these equations was in close agreement with experimental values. The procedure developed in this study is expected to be quite val- uable in developing systems in which the moisture loss of fresh fruits will be reduced. Approved or Professor Department-Chairman A PROCEDURE FOR RAPIDLY DETERMINING TRANSPIRATION RATES AND EPIDERMAL PERMEABILITIES OF FRUITS By Joe Perry Gentry A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1970 E» ACKNOWLEDGMENTS The author is grateful for the encouragement and assistance of Dr. B. A. Stout (Agricultural Engineering), under whose SUpervision this investigation was conducted. Thanks are also due to Dr. D. R. Heldman (Department of Agricul- tural Engineering), Dr. J. L. Gill (Dairy Department), and Dr. W. M. Urbain (Department of Food Science) for serving on the guidance committee. For the c00perative effort that made this study possible, the author is indebted to many pe0p1e in both the Department of Agricul- tural Engineering, University of California, Davis California, and the Department of Agricultural Engineering, Michigan State University. Recognition must be given to my wife, daughter, and son, without whose devotion and patience this work would not have been completed. ii TABLE OF CONTENTS Page ACKNOWLEDGMENTS. . . . . . . . . . . . . . . . . . . . . . . . . ii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . v LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . . . . . . vi LIST OF SYMBOLS. . . . . . . . . . . . . . . . . . . . . . . . . vii Chapter I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . l 1.1 The Problem. . . . . . . . . . 1 1.2 Objectives . . . . . . . . 3 II. LITERATURE REVIEW . . . , . , , , . . . , 4 2.1 Water as 3 Fruit Component . 4 2.2 Water as a Pedicel Component . . . . . . . . . . . 7 2.3 Types of Transpiration . . . . . . . . . . 7 2.4 Transpiration Models . . . . . . . . . . . . . . . . 7 2.5 Water Potential and Water Activity . . . . . . . . . 10 2.6 Theory of Mass Transfer During Drying. . . . . . . . 12 2.7 Methods for Measuring Permeability . . . . . . . . . 18 III. DEVELOPMENT OF MOISTURE-TRANSFER EQUATIONS. . . . . . . . 19 3.1 Specific-Moisture Coefficient. . . . . . . . . . . . 21 3.2 Epidermal Permeability . . . . . . . . . . . . . . . 23 IV. EXPERIMENTAL STUDIES. . . . . . . . . . . . . . . . . . . 28 4.1 Objectives . . . . . . . . . . . . . . . . . . . . . 28 4.2 Equipment. . . . . . . . . . . . . . . . . . . . . . 29 4.3a General Operational Procedures . . . . . . . . . . . 39 4.3b Operational Procedures for Cherries. . . . . . . . . 39 4.3c Operational Procedures for Grapes. . . . . . . . . . 40 4.4 Analysis Procedures. . . . . . . . . . . . . . . . . 42 4.5 Variability with Locations in Sample Container. . . . . . . . . . . . . . . . . . . . . 44 V. RESULTS OF EXPERIMENTAL STUDIES . . . . . . . . . . . . . 46 5.1 Mass-Transfer Coefficients for Grapes. . . . . . . . 46 5.2 Mass-Transfer Coefficients for Cherries. . . . . . . 54 5 3 Equilibrium Vapor Pressure . . . . . . . . . . . . 57 5.4a Epidermal Permeabilities of Whole Grapes . . . . . . 53 iii Table of Contents (con't.) Page 5.4b Permeabilities of Excised Grape Epidermal Tissue . . O O O . . O . . C . . O O O . O O O O C 59 5.4c Epidermal Permeabilities of Cherries . . . . . . . . 59 5.5 Predicted and Experimental Vapor Pressures . . . . . 60 CONCLUSIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . 62 SUGGESTIONS FOR FURTHER STUDY. . . . . . . . . . . . . . . . . . 64 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 APPENDICES O O O O O O . O O . . . O O O C O O C 0 C O O O . O O 69 iv LIST OF TABLES Table Page 2.1 Resistances to the Diffusive Transfer of Water Vapor Throught the Stomates, the Cuticle, and the Boundary Layer. . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.1 Mass-Transfer Coefficients for Cardinal Grapes . . . . . . 50 5.2 Mass-Transfer Coefficients for Thompson Seedless Grapes. . 51 5.3 Mass-Transfer Coefficients for Bing and Burlat Cherries. . 55 A2.1 Mass-Transfer Coefficients at Different Locations in Sample cylinder. 0 O O O O O I O O O O O O O O C O O O O O 72 A2.2 Analysis of Variance of Mass-Transfer Coefficients at Different Locations. . . . . . . . . . . . . . . . . . . . 72 LIST OF FIGURES Figure Page 2.1 Diagram of a Mature Parenchyma Cell. . . . . . . . . . . . 6 3.1 Locations Of Surfaces for Determination of Epidermal Permeability . . . . . . . . . . . . . . . . . . 24 4.1 Apparatus for Determining Mass-Transfer Coefficients . . . 30 4.2 Schematic of Apparatus for Determining Mass-Transfer coefficients 0 O O O O O O O O O O O O O O I O O O O O O O 31 4.3 Principle of Operation of the Dew-Point Hygrometer . . . . 32 4.4 Cutaway Drawings of Fruit Arrangements in Sample cylinder 0 I C O O O O O I O O O O C O O O O O O O O O O O 34 4.5 Sample Cylinder with Cover Removed and Grape in Position for Test on Entire Fuit. . . . . . . . . . . . . . . . . . 35 4.6 Apparatus for Determining Mass-Transfer Coefficient from Cheek Of FrUit O O O O O O O O O O C O O O O I O O O O O O 36 4.7 Preparation of Excised Epidermal Tissue for Permeability Test 0 O O O C C C O O O O O O O O O O C O O I O O O O O O 38 5.1 Typical Dew-Point Values from a Test on a Thompson Seed- less Grape O O O O I O O O O O O O O O O O O I O O O O O O 47 5.2 Predicted and Experimental Vapor Pressures for a Thompson Seedless Grape. . . . . . . . . . . . . . . . . . 48 5.3 Typical Relation Between Vapor-Pressure Ratio and Mass- Transfer Coefficients for Thompson Seedless Grapes . . . . 49 5.4 Computed Relation Between Vapor-Pressure Ratio and Mass- Transfer Coefficients for Thompson Seedless Grapes . . . . 52 5.5 Relation of Mass Transfer Coefficients to Air Flow . . . . 53 5.6 Computed Relation Between Vapor-Pressure Ratio and Mass- Transfer Coefficients for Cherries . . . . . . . . . . . . 56 A1.1 Illustration of How the Equilibrium Vapor Pressure Was Iteratively Determined by the Best Fit- Method . - . . . . 70 vi I!’ I: 52 "U LIST OF SYMBOLS area water activity concentration specific moisture coefficient diffusivity rate of transpiration leaf dimension in direction of air flow air flow rate transpiration constant rate constant empirical constant empirical constant moisture content mass flow rate vapor pressure in the air partial pressure of the air vapor pressure at equilibrium vapor pressure at the surface of fruit total pressure vapor pressure inside the fruit vii ideal—gas constant temperature chemical potential volume partial molar volume leaf dimension perpendicular to air flow humidity ratio linear distance intercept of regression equation slope of regression equation 2.71828 apparent mass-transfer coefficient mass-transfer coefficient true mass-transfer coefficient (i.e., from a fruit with epidermis removed or a water source) heat-transfer coefficient radial distance resistance of component i relative humidity, decimal time velocity water potential epidermal permeability density viii dW dt 99 dt At Ax exp drying rate heat-transfer rate time increment distance increment exponential ix Desicc Quality factc aPPeaI‘arice, t 50~called "ti t0 desiccatic ante which Cc quality frUlt of fruit- n of shrinkage stated that I ienced fI'Uit to whether i, and Data 300} noticeable e PEdicels’ an, perCeut of INTRODUCTION 1.1 The Problem Desiccation (moisture loss) from fresh fruit is an important market quality factor, for the resulting shrivel or shrinkage not only affects appearance, texture, and flavor but also reduces salable tonnage. The so-called "tired" or "dead" look of fruits in the market is due largely to desiccation. As fruits shrivel, they take on a dull lifeless appear- ance which contrasts seriously with the bright fresh condition of high- quality fruit. Desiccation can also drastically affect the stem condition of fruit. The pedicels (stems) of cherries and table grapes show signs of shrinkage before the fruits exhibit signs of water loss. Nelson (1964) stated that the appearance of stems is often used accurately by exper- ienced fruit buyers as a measure of fruit condition and a determination as to whether it has been abused in post-harvest handling. The ASHRAE Guide and Data Book 1964 Applications (1964) states that with grapes the first noticeable effect of moisture loss is drying and browning of stems and pedicels, and this effect becomes apparent with a loss of only 1 to 2 percent of the weight of the fruit. The fruit also loses its turgidity and softens when the loss reaches 3 to 5 percent. As pointed out by Gentry et al.(l964), Lentz et al.(l964), and Lentz (1966) the rate that fruit loses moisture is directly related to the difference in the vapor pressure of the fruit and the vapor pressure of the surrounding air. caus appe ('7 O H) frui lNa beca TESL “Rd dES 1510i Moisture loss causes the crisp, turgid texture of fruit to become soft or rubbery and unpleasant to the touch or taste. Moisture loss also causes packed fruit to settle in the container, which makes the container appear slack or only partly full. This presents an unfavorable appearance to fruit buyers, who are essentially concerned with the amount of salable fruit in the container. Mitchel et al.(1968) report that loose fruits in a container are more subject to injury than are firmly held fruits, because vibrations may cause the loose fruits to move about, which may result in surface scarring. Moisture loss of fruit is an intricate phenomenon in the total handling system. In discussing transitions in produce handling, Roark (1964) made the following statement: "To me, perishable handling is the art or science of bringing the fully matured fresh fruit or vegetable -- at the peak of appearance, flavor, and taste on tree, vine or plant -- right to the dining table. Or coming as close to that objective as conditions, including time, geography, and economic realities permit." The textural prOperties of fresh fruits, commonly referred to as crispness, firmness, and succulence, are all related to the moisture content of the frut. Any loss of moisture from fresh fruit has an undesirable effect on these properties. A better understanding of the desiccation process should help in developing systems in which the moisture loss of fresh fruits will be reduced. In order to improve systems EOiStu: rates I the CO degend bahavi aggrax and a and f mOiSt The C systems, such as these described by Gentry et al.(l968) for reducing the moisture loss of grapes, a procedure for rapidly determining transpiration rates of fruits is essential. Improvements in the appearance and quality of fresh fruits offered the consumer is a worthy goal for such a study. These improvements depend upon a clear understanding of the desiccation process and the behavior of fruit under the influence of physical factors which may aggravate this process. 1.2 Objectives The overall goal of this study was to develop a method for rapid and accurate prediction of the transpiration rates of intact fruit organs and fruit components. Quantitative measures have been made of the moisture loss of some fruits under steady-state mass-transfer conditions. The objectives of this study were: 1) to determine mass-transfer coeffi- cients and epidermal permeabilities for the berry and pedicel of cherries and grapes under specific unsteady-state conditions; and 2) to explain the physical movement of moisture through the epidermal tissue and to the surrounding air during an unsteady-state desiccation process. process the sur: forms a Analysi Standin 8931813] matic f The Ce] Cl38811 II. LITERATURE REVIEW Desiccation or transpiration of fresh fruit is a mass-transfer process in which water vapor moves from the surface of the fruit to the surrounding air. Water, the most abundant compound in fresh fruit, forms a continuous liquid phase through the fruit and pedicel*. Analysis of the transpiration of fresh fruits requires a thorough under- standing of the structure and properties of the fruit. 2.1 Water as 3 Fruit Component Fresh fruits are intact plant organs which, as noted by Esau (1967), generally have structural-type fruit walls, classified as the parenchy- matic fleshy type. The structural unit of the fruit wall is the cell. The cells, grouped together, form tissues, which in fruits may be classified as fundamental or ground tissue and protective tissue. Each cell in the fruit wall is enclosed by its own cell wall. According to Robbins et a1. (1967), adjacent cells are cementéd together by means of the middle lamella, which is composed primarily of a pectic compound. The characteristic softening of fruits during the ripening process is caused by this pectic compound becoming more soluble in the cell— wall water and losing its binding properties. Slatyer (1967) stated that, in turgid cells, most cell-wall water is probably held by surface tension *See Glossary (p.73) for definition of botanical terms such as this. _ A; in the East t1 percent are 1a} 2.1). which, 0f the may be 5 Perc< 93 pe r( in dEs: Slatyer 0f 98 F fOrCeS. in Cree ar .d tn: the Vac in the voids created by the interfibrillar spaces. He also reported that the volumetric water content of turgid cell walls may exceed 50 percent. The ground tissues in fruit are primarily parenchyma cells, which are large, thin-walled, and approximately l4-sided polyhedrons (Figure 2.1). Parenchyma cells are often separated by intercellular spaces, which, according to Reeve (1953), may constitute as much as 25 percent of the total volume of the fruit tissue. These intercellular spaces may be filled with air or water. The protoplast in the fully grown parenchyma cell constitutes about 5 percent of the total cell volume and may have a water content of 95 percent. The protoplast contains proteins, which have a strong affinity for water. The vacuole, as noted by Van Arsdel and Copley (1964), is important in desiccation because it may hold 90 percent of the water in the fruit. Slatyer (1967) states that the vacuole frequently has water-content levels of 98 percent. Water is retained in the vacuole primarily by osmotic forces. The vacuole is also important in fresh fruit because of its role in creating the textural attributes of crispness, firmness, succulence, and turgidity. Turgor is the result of osmotic pressure developed within the vacuole and the pressure exerted by the relatively rigid cell wall. In fruits, the protective tissues, which include the epidermis and periderm tissues, protect the organ from mechanical injury, insects, and microorganisms, and play an important role in desiccation or moisture loss. Part of the epidermal surface of most fresh fruits is made up of .Aqoma .mmadoo mam mamwmu< sm>v Haou mahnucmumm monumz m mo awuwmfia H.N muawfim m_o:oo> 323.8... 4 5332.6 1: I :65 535 \aw \\ 2520. «Mix... oEEmBEmoE \W A. £6.32 3 :03 .CoEtd 3.02032 0:922 . 23:2 mooam 5.2.8.25 1 W 1. “,_ covered tiSSueS While p jetted pediCel 2) Cu: CutiCu] watEr ] have nc microscopic pores or valves, called stomata. There may also be lenticels, which consist mostly of patches of suberized cells. The epidermis is covered with a cuticle, which is a waxlike layer of cutin. 2.2 Water as a Pedicel Component The pedicel contains xylem and phloem conducting tissues. Xylem tissues contain mainly water and mineral salts absorbed from the soil, while phloem tissues contain mainly metabolites produced in leaves. Slatyer (1967) noted that water in these tissues may be sub- jected to tensions in excess of 100 bars during transpiration. Esau (1967) pointed out that tyloses, which are formed in injured pedicel tissue, may effectively block moisture movement through this tissue. 2.3 Types of Transpiration Devlin (1966) classified transpiration of plants as: l) stomatal; 2) cuticular; and 3) lenticular. He stated that water loss through cuticular and lenticular transpiration is insignificant compared with water lost through stomatal transpiration. Some fruits (e.g. grapes) have no stomata on the fruit surfaces but numerous stomata on the pedicels. 2.4 Transpiration Models Raschke (1960) and Gates (1968) have used electrical-circuit models to describe transpiration by leaves. Gates (1968) presented the following T l equation to de E = LPL where E p1 (T1) 1 P l Na r1 ra Gates ( by Gates , (1968 equation to describe the rate of transpiration per unit leaf area: E = Ap/r = [P1 (T1) - Pa (Ta>1 / (r1 + r3), (1) where E = Rate of transpiration per square cm leaf area Pl (Tl) Concentration of water vapor considered at leaf temperature, Tl Pa (Ta) = Concentration of water vapor in the free air at temperature, Ta r1 = Internal resistance to flow r8 = External resistance in the adhering air layer Gates (1968) also developed the following empirical relationships from wind-tunnel studies: where W V (T1) - r.h Pas (Ta)] / [rl + K =% where h’ = True convection coefficient A = Epidermal permeability P3 = Vapor pressure at surface X = Thickness of epidermis Solving for P in equation (24) Which is used in equation (26) to give: 1 h P1 - X (P1 - PS) h dX (25) (26) (27) (28) Using this value to eliminate P in the first part of equation (25), and multiplying both parts of the equation by h, gives: I h K h h P -h' hP +——3———(P1-P S g 1 X S) =—x—(P1- (29) 26 Dividing both sides by (P1- R3) the equation becomes , h’ x in -h hg + LX = i— (30) Solving equation (30) for 1, gives: Xh h (31) from which the epidermal permeability can be determined given an apparent mass-transfer coefficient and a known true-convection coefficient. From equation (25), the vapor pressure at the surface, B3, is: >fl>J "U + 3‘ 'u (32) \ PS = :- + >fl>e The mass-flow rate through the epidermis from equation (25) is ° AA M = 3(— (P1 - PS) (33) Assuming the fruit is placed in a small volume of air, the vapor pressure of the air will be increased by this mass—flow rate in a time interval, At, by {me or - .1 - AMEL. (35 AP x (P1 P3) ( 9%" ) ) 27 Using time notations as a second subscript, the resulting solu- tions for a one-dimensional slab with a constant vapor pressure on one side and with convective mass transfer to an unsteady—state medium on the other are: Pl, t = K for all t (36) at convecting surface 1 I P = i P1, y+1 + hg P , t+1 S, t+1 I l (37) h+— g X in the unsteady-state medium _ Mm: P ,t+1_ Pt + XCmVD 1, t s, t (38) IV. EXPERIMENTAL STUDIES 4.1 Objectives Moisture loss from fruit is not only of interest in preserving fresh fruit but is an important factor in fruit dehydration. The interest is on limiting moisture flow in one application and on increasing moisture flow in the other. Both are concerned with mass transfer and have many common physical parameters. In raisin making, grapes are often treated to speed moisture flow from the berry. The experimental studies were done to determine: a) the magni— tudes of convective mass-transfer coefficients of the intact grape and cherry fruits, with and without pedicels under specific unsteady- state conditions; b) the magnitudes of the convective mass-transfer coefficient of the grape berry with epidermis removed; c) the relative magnitudes of the epidermal permeability of the grape and cherry; d) the effect of a cold-water-emulsified oil dip, used in raisin making on the mass-transfer coefficient of Thompson Seedless grapes, and e) the effect on the mass-transfer coefficient of mechanically polishing the surface of Thompson Seedless grapes. 28 29 4.2 Equipment The equipment used consisted of treatment equipment and instru- mentation. IMuch of the equipment was designed and built especially for these studies. The equipment (Figures 4.1, 4.2) consisted of an air pump, con— trol valves, sample cylinder for fruit, desiccant bed, dew point instru- ment, and recording potentiometer. The air pump was a diaphragm—actuated Neptune Dyna-Pump, model number 54904-006, with a rated capacity of 225 cubic inches per minute at a pressure of two pounds per square inch. In the system, the pump output was normally 3600 cc/min. The control valves were stainless-steel needle valves. Stain- less-steel tubing was used for connecting practically all of the compon— ents together. The dew point was measured by an industrial dew point hygrometer, Model 992-C1 (Figures 4.1, 4.2, 4.3), a product of Cambridge Systems Inc., which utilized the well-known thermoelectric or “Peltier” cooling effects to cool a stainless-steel mirror to the dew point. A scattering type of optical system sensed the dew point of the air sample and tracked it continuously. The basic sensing unit of this instrument (Figure 4.3) contained the thermoelectric dew-point sensor, its associated amplifier and power-supply circuitry, and a gas sampling system. This unit could measure dew points between the ambient temperature of the installation down to 100° F lower. The accuracy of this instrument was specified to be plus or minus l.0° F, with a response time of 2—3° F/second. n.- ~nl~§ s-u.~ A.R.-~n«~, a..~vl .,...‘-~ -,..~ <...-§v\.4..mi ;.y n...§uto Io-..!Ic--.1 o-A . ub.n-Q'.U Q nv..§v. I 1h~l--§-§I. I f V‘luohlll : 30 mwmcam b.~ >uumnwncm men Umnmnawawsm zmmm anusmmmn nommmwoumsnm. roams Hmmn. men been“ comma Hmmn. ammwnnmnn.no:nmwsmn. nonnmn Hmmn mum nonnmn now. nonnnow oaom Ho>oo nufi3 “mocwaxo oHnEmm n .q 8:5 Figure 4.6 a? Apparatus for Determining Mass-Transfer Coefficient from Cheek of Fruit. Top, grape being placed in position; bottom, grape during test. 37 to at most :_0.5 degree. Air flow rates were measured with Fisher and Porter Tri-Flat Var- iable Area Flowmeters. Air flow rates were adjusted by means of a stainless-steel needle valve (Number 1, Figure 4.2). To measure epidermal permeability of excised epidermal tissue, a cylindrical aluminum container was made from l-inch by l/2-inch round stock by drilling and reaming to 0.250 inch by 3/4 inch deep. A 3/16- inch-deep cylindrical cap with a 0.250-inch—diameter hole in the center was made for this container from the same material. The container and cap were sealed together during epidermal permeability tests by means of a l/2-inch-inside-diameter neoprene tube (Figure 4.7). The desiccant used was Sovabead ( a product of Socony-Vacuum Oil Company), which is a chemically inert solid siliceous material in the form of beads (4-to-8 mesh). The desiccant was frequently reactivated by placing it in an open container in an oven at 300° F. The reactivated desiccant was placed in a Number 10 steel can which had fittings attached near the botton and top (Figure 4.1). The air entered the bottom of the desiccant bed by means of a plenum chamber formed from woven wire. The top of the container was covered with a plastic cap. Plastic tubing connected the desiccant container to the diverting valves. In the laboratory the equipment was operated in a chamber in which air temperature was controlled to i_1° F. Early in the grape— growing season the equipment was taken to Southern California, where it was operated in an air-conditioned motel room. Here the equipment was maintained at a relatively constant temperature by air cooled with an ice chamber, fan and duct arrangement. 38 Figure 4.7 Preparation of Excised Epidermal Tissue for Permeability Test. Top, sample prepared ready to insert in holder; bottom, sample inserted in holder. 39 4.33 General Operational Procedures All tests were conducted according to the following procedure: 1) The dew-point instrument and air pump were turned on. 2) Valves 2 and 3 (Figure 4.2) were opened and valve 1 was closed. This caused the air in the system to flow through the desiccant, removing moisture from the air. The air was circulated through the desic- cant for thirty minutes to insure that all moisture was removed from all internal parts of the apparatus. 3) The air pump was st0pped, and the fruit or fruit component was put into the sample chamber. In tests where the chamber top was removed, this procedure was done very rapidly (2 to 3 seconds) to keep excessive moisture from entering the system from the ambient air. 4) The air pump and the recording potentiometer were turned on, and the air in the system was circulated through the desiccant for three additional minutes. This permitted the dew-point instrument to stablize. 5) The desiccant was removed from the system by opening valve 1 and closing valves 2 and 3 (Figure 4.2). 6) Dew-point temperature, system temperature and time were recorded by a potentiometer. 4.3b Operational Procedures for Cherries Bing and Burlat varieties of fresh cherries were harvested daily from selected trees in the orchard of the Pomology Department, University 40 of California, Davis, California. The harvested fruits were transported in polyethylene bags to the temperature—controlled test chamber, where they were stored for approximately 18 hours before tests were conducted. This procedure provided uniform fruit temperature. Tests on both varieties were conducted on the intact fruit and pedicel, which were placed in the test chamber as illustrated in Figure 4.4 (bottom). The surface areas of the cherries were determined by assuming that the fruit had the same surface area as a sphere of diameter equal to the average of the three axial diameters of the fruit. The surface areas of the pedicels were assumed to equal the surface of a cylinder of equal length and a diameter the average of three measurements of the diameter of the pedicel. The area of the pedicel tip was assumed to be negligible. 4.3c Operational Procedures for Grapes Early-season Cardinal variety grapes were studied by setting up the apparatus in a motel room in Indio, California. Cardinal grapes were obtained fresh daily from the vineyeards of the Harlan Kettle Ranch and placed in polyethylene bags immediately upon harvest. Tests on the intact fruit and pedicel and on the pedicel end of the fruit were conducted with the early-season Cardinal grapes. Some of the early grapes were packed in lug boxes, shipped in a refrigerated truck to Davis, California and stored two weeks before tests were conducted. This was to determine the effects of storage on transpiration. 4l Later-season Cardinal and Thompson Seedless varieties of table grapes were obtained from vineyards of the Department of Viticulture and Enology, University of California, Davis, California. The grapes were harvested daily from a selected area of the vineyard, placed in polyethylene bags, and transported to the controlled-temperature test chamber, where samples were prepared and held for approximately eighteen hours before tests were conducted. This permitted the cut on the pedicel to callus over, effectively blocking moisture transfer from the end of the pedicel. For determination of epidermal permeabilities, selected grapes were prepared by cutting the pedicel close to the berry, allowing the cut to callus over, testing the berry, and then peeling the epidermis from the berry and testing it again without the epidermis. Excised epidermal tissue was tested by peeling large areas of the grape epidermis, cutting circular segments of this tissue with a cork bore, and sealing the tissue segment to a container filled with water (Figure 4.7). This provided a reservoir of water with a steady vapor pressure on one side of the epidermal tissue. The effect of an oil emulsion dip on the transpiration of Thompson Seedless grapes was determined by selecting grapes, cutting the pedicel close to the berry, allowing the cut to callous over, testing the berry, and then dipping the grape in the oil emulsion for 3 minutes and testing the berry again. The dipping emulsion consisted of 2.5 percent potassium carbonate in water and 2 percent dipping oil (Shelltana, a product of Shell Oil Company). 42 The surface areas of the nearly spherical Cardinal grapes were assumed to be the same as a Sphere with the diameter equal to the average of three perpendicular diameter measurements. The surface areas of the Thompson Seedless grapes were assumed to be the same as that of a cylinder whose diameter was the average of two perpendicular measurements across the sides of the grape and whose length was the length of the berry. The surface area of the pedicel was assumed to be the same as the surface area of a tapered cylinder as long as the pedicel and with end diameters the same as those at the ends of the pedicel. The end area of the pedicel was assumed to be effectively sealed, and hence not contributing to moisture transfer. 4.4 Analysis Procedures Data from the tests were analyzed using equation (18), and on the basis of a transpiration constant, J, defined by P - P 1 0 E where h A J = —3— (40) VPCm Equation (39), somewhat similar to the drying equation given by Hall (1957), is, according to Draper and Smith (1966), a non—linear model that is intrinsically linear. The transpiration constant, J, was found as the regression coefficient of an exponential curve. An apparent equilibrium vapor pressure was determined iteratively to give the least error. All of these functions were performed by a computer program. 43 The computer program, designated TRANSP, was used to analyze all data. At the start of the program an array was read into the computer to convert dew-point readings to vapor pressures (mm of mercury) for each half degree from 0.5 to 90° F. For each test, the data were read into the computer from three cards. The first card of a test set had the number of data points, the vapor pressure that corresponded to the ambient temperature, the test number, and surface area of the sample. After the first card was read, the number of data points was checked. It was programmed to terminate when given a card with the number of data points listed as minus one. So that each test would be summarized on a single output page, the test number and number of data points were printed at the top of an output page. The second card in a set had the times of the dew-point readings that were on the third card. Dew points were read to the nearest half degree. Dew-point readings were converted to vapor pressures and printed out along with corresponding time values. Starting with PE equal to the vapor pressure for the ambient temper- P - PE ature values for §——:f§' were calculated for all vapor pressures. Natural O E logarithms of these values were summed and squared, and the squares summed. The time values were summed and the products of each time value and its corresponding vapor pressure were summed. The time values were also squared and summed. 44 The parameters of the curves were found from the equation P - P P - P nzt In (——-E) - 21:: 1n (——5) P0" PE Po' PE J = 2 (41) nZt - (St)2 A correlation coefficient was determined by P - P P - PE nEt In (-—————) - XtZ 1n»(-——-——) P0- PE P0- PE r: (42) P - P P - P [nit2 - (2t)2] n2 (ln-f-:jF-)2 (Zln-F—:—§§)2 0 E O E The values of J and r were stored, PE was reduced by 0.1, and new values of J and r were calculated. The new value of r was compared with the old value, and as long as r was approaching - 1.0 this itera- tive process was repeated. When the correlation coefficient stopped approaching —l.0, the values of r, j, PE, Intercept, and Mass-transfer Coefficient were printed. The next set of data was then processed. An illustration of this iterative procedure is presented in Appendix 1- 4.5 Variability With Locations in Sample Container To determine the variability of results with the location in the sample chamber, mass-transfer coefficients were made for a cylinder filled with water placed at three locations on an axis of the chamber which was perpendicular to the axis of the air Openings. The tests were made with water-filled cylinders positioned at each end and at the center of the axis. An analysis of variance of three tests at each location gave an observed F value of 1.17, with a required F(0.lO) of 3.46 (Appendix II). 45 This indicated that there was no real difference in mass-transfer coefficients between the different locations in the sample chamber. V. RESULTS OF EXPERIMENTAL STUDIES 5.1 Mass-Transfer Coefficients for Grapes Figure 5.1 presents the results of a typical test run on Thompson Seedless grapes. This shows the dew—point temperatures which were normally read from the strip chart for each three-minute interval. The computer converted these dew-point temperatures to vapor pressures, which are shown as the experimental values in Figure 5.2. The computer iteratively determined the equilibrium vapor pressure and correlation coefficient, and the results of analysis of this typical test run are illustrated in Figure 5.3. The results with Cardinal grapes are summarized in Table 5.1, and the results with Thompson Seedless grapes are summarized in Table 5.2 and Figure 5.4. A test on the means of the mass-transfer coefficients for the whole grapes With pedicel indicated a significant difference (0.001 level) in mass-transfer coefficients between the Cardinal and Thompson Seedless grapes, confirming observations that Cardinal grapes do not store as well as Thompson Seedless grapes. With Cardinal grapes there was a significant difference in mass- transfer coefficients between the whole grape plus pedicel and the pedicel end of the grape plus pedicel. With both Cardinal and Thompson Seedless grapes there was no significant difference in mass-transfer coefficients between fresh and stored grapes. Figure 5.5 illustrates mass—transfer coefficients determined at different air flows for Cardinal and Thompson Seedless grapes. 46 47 ow .oamuu mmmaoomm commsozH m co umoH m Boum monam> ucflomlzon Hmoflame mm._.32_s_ .mEE. mm Om mm ON 9 O. H.m.mnswnm . _ A _ _ _ _ 050 .oz 33. Eat :22, .oEoEtuaxw .- 9 O N 0 r0 0 c On ' 3801V83d|~31 .LNIOd M30 :lo 48 .oamuo mmoaooom GOmQEOLH m pow wousmmoum uomm> Hmucoawpoaxm cam oouoflooum ~.m muswfim mUPDzi . NE: m? 0? on On mm ON 0. 0. n O A i _ _ _ _ _ 0:062 32 ES. 339, .2coEtoqul o 83932.3 22.33 52. 3362a 6H :0 ww ‘aanssaaa aoawx 49 0.4 ~— 0.” an: I l n. (1.0 0.3 ~— 0 Computed valuu from Tu? No. O3IO 0.2 ~— 01 1 1 1 1 ' 0 IO 20 30 4O 50 TIME , MINUTES Figure 5.3 Typical Relation Between Vapor Pressure Ratio and Time for a Thompson Seedless Grape. Table 5.1 Mass-Transfer Coefficients for 50 Cardinal Grapes* Average Standard Test condition No. of tests (hg x 108)** Deviation x 108 Whole grapes 11 0.874 0.185 with pedicel Pedicel and 9 1.94 1.13 pedicel end of grape Whole grapes 4 0.889 (Air flow 350 cc/min) Grapes (stored 2 weeks) No pedicel (unpeeled) 5 0.987 0.036 No pedicel (peeled) 5 20.5 3.3 Excised epidermal tissue (68°) 2 4.78 Excised epidermal tissue (45°) 2 6.17 * All air flows were 3600 cc/min unless otherwise stated, ** Units of hg are grams of H20 per (minute) (square mm) (mm of mercury). 51 Table 5.2 Mass—Transfer Coefficients for Thompson Seedless Grapes* Average8 Standard Test condition No. of tests (hg x 10 )** Deviation x 10 Whole grapes with pedicel 4 0.415 0.143 Whole grapes with pedicel 4 0.637 0.111 Air flow (350 cc/min) Whole grapes with pedicel (polished) 4 0.813 0.139 Grape (stored 2 weeks) No pedicel 9 0.583 0.179 Dipped (no pedicel) 5 0.847 0.307 Peeled (no pedicel) 5 23.9 0.95 Excised epidermal tissue 4 15.94 14.77 * All air flows were 3600 cc/min unless otherwise stated. ** Units of hg are grams of H 2 0 per (minute) (square mm) (mm of mercury) 52 I.0 <19 (18 0.7 -— Untreated ”€58.35 -08 CLG~~ (15*- (14~- of] TN Dipped @7847 E -08 I 0- n-° 031—» Pbfiehed by! .BIJE-OB Peeled "9" 239 E - 06 (lZ- 0., 1 1 1 1 1 1 0 IO 20 30 40 50 60 TIME , MINUTES Figure 5.4 Computed Relation Between Vapor-Pressure Ratio and Mass- Transfer Coefficients for Thompson Seedless Grapes. A surface area of 1200 square mm and a value for pCmV of 0.0003532 were used. E-08 = 10‘8. 53 CON? .BOHm uw< Ou mucmwofiwmoou umwmamqummmz mo cowumaom m.m ounwwm .2335 .30.; «.4 con» ooow oo_~ 00¢. 00» o a A i _ _ _ . . .1 \ 1\__ .320 3.33m c0362; .1 e . _ _ T, D 17“ 1 A.“ :35 .3630 W ”I .01! “'11 saves/w “2 0.. 54 Although the mass-transfer coefficient should decrease with reduced air flow a tftest on the results of this study indicated that evidence was insufficient to say that the mass-transfer coefficients with air flow of 3600 cc per minute were different from those with air flow of 350 cc per minute. Air flows below 350 cc per minute could not be used since the dew-point instrument required enough air to function. Polishing Thompson Seedless grapes for three minutes with burlap fragments on a rotary vibrator increased the mass-transfer coefficient significantly (0.001 level). (Table 5.2 and Figure 5.4). Thus, rough handling or vibratory damage of loosely packed grapes can reduce resis- tance to moisture transfer through the epidermis, thereby damaging the quality of fresh fruit. For raisin making, mechanical polishing of grapes may be an alter- native to dipping. Thompson Seedless grapes dipped in an oil emulsion dip (made of 2.5% potassium carbonate and 2% "dipping oil”), used in Australia to increase moisture transfer through the epidermis in raisin making, gave a mass—transfer coefficient significantly higher than that for untreated grapes, though not significantly higher than that for polished grapes. 5.2 Mass-Transfer Coefficients for Cherries Table 5.3 and Figure 5.6 present results of studies on cherries. A E-test on the means of the mass-transfer coefficients for the whole fruit indicated a significant difference (0.001 level) in the mass-transfer 55 Table 5.3 Mass-Transfer Coefficients for Bing and Burlat Cherries Averagg Variety Fruit component No. of tests (bg X 10 )* Bing Whole 11 0.879 (0.215)** Pedicel 9 4.783 (1.504) Burlat Whole 8 1.995 (0.360) Pedicel ' 7 15.671 (2.985) 20 per (minute) (square mm) (mm of mercury). ** Standard deviations are in parentheses. * Units of hg are gram of H LO 0.9 0.8 0.7 0.6 0.5 0.2 0.] Figure 5.6 56 \ \ Bing (Pedicel) _ \ V \ __ \ \ \ Bing (Whole) \ \ Burlat L— (Wholo) \ \ Burlat (Pedicel) l L l l 0 IO 20 30 4O 50 TIME , MINUTES Computer Relation Between Vapor Pressure Ratio and Mass-Transfer Coefficients for Cherries. A surface area of 1700 square mm was used for the whole cherries, and a surface area of 170 square mm was used for the pedicels. 57 coefficients between Bing and Burlat cherries. This confirmed observa- tions that the Burlat variety loses moisture and deteriorates faster in storage than does the Bing variety. In both cases the pedicels lost moisture significantly (0.001 level) faster than the whole fruit. The pedicel of the Burlat variety, which was a very important factor in moisture loss from this variety, had a significantly (0.001 level) larger mass—transfer coefficient than the pedicel of the Bing variety. Assuming that the pedicel has a surface area one-tenth the surface area of the whole fruit, as in Figure 5.6, the convective mass—transfer coefficient for the epidermis of the fruit for the Bing cherry was calcul- ated to be 0.446 x 10.“8 grams of H20 per (minute) (square mm) (mm of mercury); and the convective mass-transfer coefficient for the epidermis of the Burlat cherry was calculated to be 0.476 x 10-8 grams of H20 per (minute) (square mm) (mm of mercury). 5.3 Equilibrium Vapor Pressures The average equilibrium vapor pressure for 14 tests on Thompson Seedless grapes was 13.693 mm of mercury, with a standard deviation of 2.475 mm. Using the saturated vapor pressure for the ambient temperature, an average equilibrium relative humidity of 75.5% was calculated. This equilibrium relative humidity is significantly lower than the static equilibrium relative humidity normally expected for grapes. 58 Measurements with a 40-gage thermocouple placed just below the surface of a container filled with water showed a temperature drop of three degrees below ambient early in the test. Since there must be a temperature gradient at the epidermis of the fruit, use of the saturated vapor pressure at the ambient temperature is questionable. The equili- brium vapor pressure determined by the procedure used in this study should probably be designated as an apparent equilibrium vapor pressure. 5.4a Epidermal Permeabilities of Whole Grapes Equation (31) gives the epidermal permeability as I Xh h A=F'g‘-F‘ 8 The average thickness of ten excised epidermal tissue samples of both Cardinal and Thompson Seedless grapes was determined by a micro~ meter to be 0.305 mm. The value of the mass-transfer coefficient of the peeled grapes was considered to be the true convective mass—transfer coefficient. Using the values for the apparent mass—transfer coefficients as those for grapes without pedicels (Tables 5.1 and 5.2), the epidermal -9 permeability for Thompson Seedless grapes was 1.82 x 10 gram H 0 per 2 (minute) (square mm) (mm of mercury) per mm of thickness, and the epidermal —9 permeability of Cardinal grapes was 3.16 x 10 gram H 0 per (minute) 2 (square mm) (mm of mercury) per mm of thickness. 59 5.4b Permeabilities of Excised Grape Epidermal Tissue Tests of the excised epidermal tissue were made with water contained below the tissue in the cylindrical holder (Figure 4.7). To obtain a true convective mass-transfer coefficient for this study, test runs were made with water in the test cylinder and no epidermal tissue in the cylinder. The average mass-transfer coefficient for three tests was 0.213 x 10"6 , and the value therefore, used as the true convective mass- transfer coefficient for this study. This value compared favorably with the values for peeled Cardinal grapes (0.205 x 10-6) and peeled Thompson Seedless grapes (0.239 x 10—6). Using the mass-transfer coefficient values from Table 5.1, the epidermal permeability for excised epidermal Cardinal grape tissue was 2.24 x 10"8 gram H 0 (minute) (square mm) (mm of mercury) 2 per mm of thickness. The epidermal permeability of excised epidermal Thompson Seedless tissue was 1.93 x 10.7 gram H20 per (minute) (square mm) (mm of mercury) per mm of thickness. With both varieties, permeability was greater for the excised tissue than for the whole fruit. Because of the large standard deviation in the mass-transfer coefficients of the excised tissue, this procedure appears to be excessively injurious to the epidermal tissue. 5.4c Epidermal Permeabilities of Cherries Cherries being difficult to peel were not tested without skins. The average thickness of both Bing and Burlat epidermal tissues was approximately 0.305 mm. Using a value of 0.210 x 10”6 for a true 6O convective coefficient, the epidermal permeability was calculated to be 1.37 x 10—9 gram of H20 per (minute) (square mm) (mm of mercury) per mm 9 of thickness for Bing cherries and 1.49 x 10 gram H20 per (minute) (square mm) (mm of mercury) per mm of thickness for Burlat cherries. 5.5 Predicted and Experimental Vapor Pressures Assuming that the vapor pressure inside the fruit was equal to PE equations (37) and (38) were used to predict the system vapor pressure during a typical run with Thompson Seedless grapes. Values for the variables, chosen to correspond with those for the Thompson Seedless grape used in test number 0310, were as follows: PE = 13.843 hg = 0.394 x 10‘8 hé = 0.239 x 10‘6 A = 1385 square mm At = 3 minutes p = 0.0012 grams of dry air per cubic centimeter Cm = 0.000841 grams of H20 per gram of dry air per mm of mercury V = 350 cubic centimeters Pa = 1.000 at t = 0 Since Xh h’ A — h’ -h 61 :3" 23“ then Nb) u 3' =1. and equation (37) becomes h h’ E7tfifi PE + hg P ,t P = g .1 go. 1,1: h h, . I ____E hg + h’-h and equation (38) becomes h h’ = __a AAL - P , t+l P ,t. + hé-h pcmv (PE PS,t) Figure 5.2 shows the value predicted from these equations along with the corresponding experimental values. From the above equations it can be noted that epidermis thickness need not be known if both a true and an effective mass-transfer coefficient is known. The good agreement between predicted and experimental values indicates that use of the slab equations was justified on the basis that the epidermis is a thin layer relative to the radius, and that there is little if any vapor pressure gradient in the flesh of the fruit. CONCLUSIONS The following conclusion can be drawn from this study: 1) Transpiration rates as measured by the mass-transfer co- efficient can be determined from experimental measurements and an unsteady-state mass-transfer analysis. 2) The mass-transfer coefficient and an apparent equilibrium vapor pressure can be determined by iterative least-squares fitting of the data to an exponential equation. 3) The permeability of the epidermis can be determined from the thickness of the tissue and apparent and true convective mass—transfer coefficients. 4) Air flow changes over a range of one to ten air changes per minute in the system had no significant effect on mass—transfer 'coefficients. 5) Values of the mass-transfer coefficients are of the order of 0.4 x 10—8 gram H20 per (minute) (square mm) (mm of mercury) for Thompson Seedless grapes 0.9 x 10—8 gram H 0 per (minute) (square mm) 2 (mm of mercury) for both Cardinal grapes and Bing cherries and 2.0 x 10 gram of H 0 per (minute) (square mm) (mm of mercury) for Burlat 2 cherries. 6) The pedicel, with its small surface area, contributed over one-half of the total mass transfer for Bing cherries, and over three—fourths of the total mass transfer for Burlat cherries. 7) The effects of different surface treatments on transpiration rates can be rapidly determined. Transpiration rates of individual fruits can be determined, the fruits treated so as to either increase or 63 decrease transpiration, and the transpiration rate on the same fruit determined again. 8) Prediction equations for a fruit with known apparent and true mass-transfer coefficients and equilibrium vapor pressure can accurately determine what the vapor pressure in relation to time will be for a lumped capacity unsteady-state mass-transfer system. 1) 3) 4) 5) SUGGESTIONS FOR FURTHER STUDY Further studies should be made in the following areas: The effects of treatments for increasing or decreasing moisture transfer through the epidermis should be evaluated. This should include the effect of different types and amounts of waxes on both the fruit and pedicel. The relation of the convective mass-transfer coefficient to the moisture content of grapes during the raisin-making process should be determined. The effect of including a temperature gradient in the epidermis, and a variable permeability in the vapor—pressure distribution equations, should be examined. Further study should be undertaken to develop this procedure so that equilibrium relative humidities can be predicted rapidly and accurately. A more precise non-destructive method is needed for determining the surface areas of fruits and pedicels. 64 REFERENCES ASHRAE Guide and Data Book 1964 Applications. 1964 ASHRAE, New York. p. 616 ASTM Book of Standards. 1968 Standard Methods of Test for Water Vapor Transmission of Materials in Sheet Form. Part 27. ASTM Designation: E-96-66. ASTM, Philadelphia. pp. 815-822. Cooke, J. R. 1966 Some theoretical considerations in stomatal diffusion: A field theory approach. Acta Biotheroetica 17, pp. 95-124. Devlin, R. M. 1966 Plant Physiology. Reinhold Publishing Company, New York. Draper, N. R. and H. Smith 1966 Applied Regression Analysis. John Wiley and Sons, New York. Durbroff, E. B. and D. P. Webb 1968 A Modified Denny Osmometer for Permeability Studies with Plant Membranes. Canadian Journal of Botany 46:1601- 1603. Esau, K. 1967 Plant Anatomy. John Wiley and Sons, New York. Gates, D. M. 1968 Transpiration and leaf temperature. Annual Review of Plant Physiology, ed. L. Machlis. Annual Reviews, Palo Alto. 19:211-238. Gentry, J. P., F. C. Mitchell, and K. E. Nelson 1963 Weight loss of grapes and nectarines as related to humidity and air velocity of storage. Trans. ASAE. 6(3):254-266. Gentry, J. P. and K. E. Nelson 1964 Conduction Cooling of Table Grapes. American Journal of Enology and Viticulture. l4(2):41-46. Gentry, J. P., and K. E. Nelson 1968 Device and Method for Treating Picked Grapes. U.S. Patent No. 3,409,444, November 5. 65 Gorling, P. 1958 Hall, C. W. 1957 Henderson, S. M. 1952 Henderson, S. M. 1955 Hoffman, G. J., 1968 Jason, A. C. 1958 Physical phenomena during the drying of foodstuffs. In: Fundamental Aspects of the Dehydration of Foodstuffs. Society of Chemical Industry. Metchim & Son, London, pp. 42-53. Drying Farm Crops. Agricultural Consulting Associates, Ann Arbor. Basic concept of equilibrium moisture. Agricultural Engineering 33:(1) 29-32. , and R. L. Perry Agricultural Process Engineering. John Wiley and Sons, New York. and W. E. Splinter Instrumentation for measuring water potential of an intact plant-soil system. Trans. ASAE. 11(1):38-40. A study of evaporation and diffusion processes in the drying of fish muscle. In: Fundamental Aspects of the Dehydration of Foodstuffs. Society of Chemical Industry. Metchim & Son, London, pp. 103-135. Lentz, C. P. and E. A. Rooke 1964 Lentz, C. P. 1966 Rates of Moisture Loss of Apples Under Refrigerated Storage Conditions. Food Technology 18(8):ll9-121. Moisture Loss of Carrots Under Refrigerated Storage. Food Technology. 20(4):201-204. Mitchell, F. G., N. F. Sommer, J. P. Gentry, R. Guillou, and G. Mayer 1968 Nelson, K. E. 1964 Newman, A. B. 1931 Tight-Fill Fruit Packing. California Agricultural Experi- ment Station Extension Service. Davis, California, Circular 548, pp. 23. Fruit shrivel, cooling and storage. Proceedings of Fruit and Vegetable Perishables Handling Conference. University of California, Davis, pp. 63-64. The drying of porous solids: diffusion calculations. Trans. AIChE. 27:310-333. 66 Ozisik, M. N. 1968 Perry, J. H. 1963 Raschke, K. 1960 Reeve, R. M. 1953 Roark, J. 1964 Robbins, W. W., 1967 Rockland, L. B. 1969 Sherwood, T. K. 1929a Sherwood, T. K. 1929b Sherwood, T. K. 1930 Slatyer, R. O. 1967 Tuwiner, S. B. 1962 Boundary Value Problems of Heat Conduction. International Textbook Company, Scranton, Pennsylvania. Chemical Engineers' Handbook, Fourth Edition. McGraw-Hill Book Company, New York. Heat transfer between the plant and the environment. Annual Review of Plant Physiology. ed. L. Machlis, Annual Reviews, Palo Alto. 11:111-126. Histological Investigations of Texture in Applies. II. Structure and Intercellular Spaces. 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S. Department of Agriculture, Agri- cultural Marketing Service, Market Quality Research Division. Marketing Research Report No. 539. pp. 15. 68 APPENDIX I ILLUSTRATION OF HOW THE EQUILIBRIUM VAPOR PRESSURE WAS ITERATIVELY DETERMINED BY THE BEST-FIT METHOD 0.4 I» d? I I CLO 0.3 — o 0.2 - PE , b a h, 1: 10° 0 20 -0.99968 -0.0298 0.9886 .6I84 0 I9 -0.99990 -0.0325 0.9932 .6752 0 l8 - LOOOOO -0.0359 LOOOO .7459 o I? -0.99985 -0.040I LOIOZ .833I 01 1 1 1 1 1 1 0 5 l0 I5 20 25 30 TIME, MINUTES Figure A1.1 Illustration of How the Equilibrium Vapor Pressure 70 0.9 0.8 0.7 0.6 0.5 was Iteratively Determined by the Best Fit Method. The surface area was 1700 square mm and the value used for pCmV was 0.0003532. APPENDIX II ANALYSIS OF VARIABILITY IN LOCATIONS IN SAMPLE CONTAINER 72 APPENDIX II ANALYSIS OF VARIABILITY IN LOCATIONS IN SAMPLE CONTAINER Table A2.1 Mass-Transfer Coefficients at Different Locations in Sample Cylinder Location hg x 106 Center .879 .687 .730 Top .674 .754 .742 Bottom .640 .665 .731 Table A2.2 Analysis of Variance of Mass-Transfer Coefficient at Different Locations Source of Degrees of Sum of Mean Observed Required Variation Freedom Squares Square F F (0.10) Total 8 .0398 Locations 2 .0112 .0056 1.167 3.46 Error 6 .0286 .0048 APPENDIX III GLOSSARY berry cuticle cytoplasm epidermis lenticel middle lamella nucleolus nucleus osmosis parenchyma pedicel phloem plasmalemma plastid protoplasm stoma (p1. stomata) tonoplast turgor 74 a simple, fleshy fruit in which the ovary wall remains succulent a waxy layer formed on the outer layer of epidermal cells the protoplasm of a cell exclusive of the nucleus and membranes the outermost cell layer of the plant body a pore consisting of cells covered with a waxy material the cementing substance between adjoining cells a spherical body found in the nucleus a protoplasmic body found in the cytOplasm and thought to be the metabolic center of the cell diffusion of solvent molecules through a differentially permeable membrane a tissue made up of living thin-walled cells the stalk (stem) of an individual flower or fruit the conducting tissue concerned primarily with the movement of food materials in the plant outer protoplast membrane a specialized body found in the cytoplasm the generalized living substance in a cell an opening between two guard cells inner protoplast membrane the result of osmotic pressure developed within the vacuole and the pressure exerted by the cell wall tylos vacuc xylem tyloses vacuole xylem 75 callus like protrusions from parenchyma cells into adjacent passageways often numerous enough to fill passageway completely a cavity in the protoplasm filled with a watery fluid the conducting tissue, concerned primarily with the movement of water in the plant "71111111'1‘1111111“