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ROOM USE ONLY ‘— ABSTRACT THE INFLUENCE OF CUTICULAR WAXES AND SELECTED CATIONS ON THE PERMEABILITY AND ELASTIC PROPERTIES OF TOMATO FRUIT CUTICULAR MEMBRANES by Dorota Haman Burgess The permeability of the cuticular membrane of the tomato fruit influences the water potential of the fruit itself. Since water potential is related to fruit cracking, it is important to understand the influence of certain chemicals on the permeability of the cuticle surrounding the fruit. The strength of the cuticular membrane is another important factor in the cracking of tomatoes. The objectives of this investigation were (1) to show the influence of cuticular waxes (lipids) on the permeability of the cuticular membrane of the tomato fruit, (2) to investigate the influence of selected cations (H+, K+, Ca++, Al+++) on permeability, (3) to investigate the elastic properties of dewaxed and nondewaxed tomato cuticular membranes treated with these cations. Using a modified technique for measuring water permeability, an increase in permeability due to the removal of waxes (lipids) and due to certain treatments (Al+++ for nondewaxed cuticular membranes and Ca++ for both dewaxed and nondewaxed) was found. From the theory developed for a modified experimental tensile test, a decrease in the elastic constant Et, the product of the elastic modulus of the cuticular material and the thickness of the membrane, was found to occur in dewaxed cuticular membranes. Poisson's ratio was also calculated. More investigations on the influence of chemicals on material properties is suggested. THE INFLUENCE OF CUTICULAR WAXES AND SELECTED CATIONS ON THE PERMEABILITY AND ELASTIC PROPERTIES OF TOMATO FRUIT CUTICULAR MEMBRANES By Dorota Haman Burgess A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1983 To my parents: Zofia and Janusz ii ACKNOWLEDGMENTS I would like to thank Dr. George E. Merva, Dr. Martin J. Bukovac (Horticulture), Dr. Larry J. Segerlind and Dr. Hugh C. Price (Horticulture) for serving on the guidance committee. Special thanks to Dr. George E. Merva for his guidance and support during this project. I would like to thank Dr. Martin J. Bukovac for help with the physiological part of this research and Dr. Hugh C. Price for his help with research material. Special thanks to my husband, Gary, for his help with theoretical development, helpful discussions, and corrections. Very Special thanks to my father without whose moral support this never would have happened. TABLE OF CONTENTS DEDICATION ACKNOWLEDGMENTS LIST OF TABLES LIST OF FIGURES Chapter 1. 2. INTRODUCTION AND OBJECTIVES LITERATURE REVIEW 2.1 The Cuticle 2.2 Mechanical Properties of the Tomato Fruit MATERIALS AND METHODS 3.1 Chemical Treatments 3.2 A Procedure for Measuring Water Perme- ability through the Cuticular Membrane 3.3 A Procedure for Measuring the Elastic Properities of the Cuticular Membrane THEORETICAL DEVELOPMENT u.1 Theoretical Solution for the Elastic Properties of the Tomato Cuticle RESULTS AND DISCUSSION 5.1 Results of the Permeability Test iv 20 23 27 27 U4 UH Page Comparison Between Dewaxed and Non— dewaxed Cuticular Membranes UM 5.1.2 Comparison Between Different Chemically Treated Cuticular Membranes and the Con- trol Group 48 5.1.3 Discussion of the Influence of Chemicals on Permeability Coefficients of Cuticular Membranes 50 5.2 Results of the Instron Tensile Test 52 5.2.1 The Influence of Soluble Waxes (Lipids) on the Material Property Et 52 5.2.2 Discussion of the Results for Poisson's Ratio 57 6. CONCLUSIONS 6O 7. RECOMMENDATIONS 62 APPENDICES 1. Appendix A - Calculations for the Theoretical Development in Chapter A A.1 . . . . . . . 63 A 2 . . . . . . . . . 6A A 3 . . . . 65 A u . . . . . . 66 A 5 . 73 A 6 . 7“ A 7 . . . 76 BIBLIOGRAPHY Table Table 5.1 Table 5.2 Table 5.3 Table 5.u LIST OF TABLES The effect of soluble cuticular waxes on water permeability in isolated cuticular membranes for Pik Red tomatoes (set 1) using 4 different chemical treatments and a control group. The effect of soluble cuticular waxes on water permeability in isolated cuticular membranes for Pik Red tomatoes (set 2) using A different chemical treatments and a control group. The effect of soluble cuticular waxes on water permeability in isolated cuticular membranes for "UC 82" processing tomatoes using u different chemical treatments and a control group. The results of the Student's t-test for the comparison between the chemically treated cuticles and the control groups at a significance level of .05 (95% certainty in a difference between the sample and control). Page ”5 146 147 U9 6 ‘ n - iabi37élt Comparison of Et values forgchemically treated subgroups; each subgroup is compared with the control subgroup for a ' given group of cuticles. 56 Table 5.7 Values of Poisson's ratio for different treatments. 58 Table B.1 Additional information for Table 5.“. 86 viii Figure Fig 3.1 3-2 3.3 3.” 3.5 3.6 3.7 4.1 LIST OF FIGURES Procedure for the extraction of waxes from cuticular membranes. Washing procedure for all groups of cuticles. Procedure for the application of ions to cuticular membranes. Final thirty groups of cuticles obtained after chemical treatments. (8) outside surface of the nondewaxed cuticular membrane of the tomato fruit. (b) outside surface of the dewaxed cuticular membrane of the tomato fruit. (8) inside surface of the nondewaxed cuticular membrane of the tomato fruit. (b) inside surface of the dewaxed cuticular membrane of the tomato fruit. The setup for the tensile test on the Instron device. Rectangular section of membrane, forces T1 and T2, and internal pressure p. ix 25 28 “.2 A.” Cross-sectional view of membrane being loaded by spherical indenter. Perspective view of section of membrane under load w. Inverted perspective view of the contact surface and the coordinate system used. Free body diagram of the membrane above the cut in Fig 4.”. Stresses on the element in spherical coordinates. Displacements in spherical coordinates. Displacement of the free surface part of the membrane. Example of output from Instron experiment and graphical explanation of some variables required for PROGRAM QUICK. Page 30 31 34 35 69 7O 77 79 1. INTRODUCTION AND OBJECTIVES The outermost layer of a tomato fruit is the cuticular membrane. The elastic properties of this membrane contribute to the strength of the fruit, in particular, to its resistance to cracking. It is very likely that cracking is induced by a rapid change in water potential in the fruit and since the role of permeability of the tomato fruit cuticle to water vapor influences this water potential, permeability is another factor related to cracking of the tomato fruit. There were two main objectives in this research: 1) to investigate the permeability of cuticular membranes when treated with various cations, and 2) to determine the change in the elastic properties of the membranes as a result of these treatments. Since the application of certain chemicals to the tomato fruit are known to change the permeability of the cuticular membrane (Schonherr, 1976a); H+, K+, Ca++ and Al+++ ions were chosen for investigation in this research. Previous research indicates an increase in permeability with K+ treatment (see Chapter 2) and a change in cracking resistance with Ca++ treatment (Bengerth, 1973). These treatments may also influence the elastic prOperties of the cuticular ‘ - , i i 7 .4, t; :f,‘ the elastic 2. LITERATURE REVIEW 2.1 The Cuticle The cuticle covers the aerial organs of terrestrial plants and serves as a barrier between the tomato fruit and its surrounding environment to limit water loss from the fruit. However, the cuticle is not impermeable to water and under extreme conditions, wilting may occur (Martin and Juniper, 1970). The cuticle consists of a cutin polymer matrix of non- extractable esters of hydroxylated fatty acids. The main components of the cutin are two families of fatty acid monomers: a C16 and a C18 (Kolattakudy 1981). The cutin matrix is separated from the underlying epidermal cell wall by pectic substances. Extractable lipids (waxes) are deposited on the outside surfaces of cuticular membranes and embedded in the cutin matrix (Martin and Juniper, 1970). The cuticular membrane can be viewed as a two component system; the extractable lipids (waxes), and the non— extractable polymer matrix (Norris and Bukovac, 1968). The permeability of the cuticle to water in an 'in-vitro' system is directly related to the amount of cuticular waxes (Skoss, 1955). Baker and Bukovac (1971) showed that the composition of surface waxes was important in the permeability of the cuticle. Hydrocarbon and aldehyde fractions strongly impeded the passage of water while esters and fatty acids were found to be less restrictive. The composition of the tomato cuticle (cutin and waxes) was studied by Baker, Bukovac and Hunt (1982). For mature tomato fruit, the cutin was found to contain the following monomers: 16 Hydroxyhexadecanoic acid - 4.6% Hydroxyhexadecane-1, 16—doic acid - 4.1% 10,16 — Dihydroxyhexadecanoic acid - 76.8% 9,16 - Dihydroxyhexadecanoic acid - 6.4% 8,16 - Dihydroxyhexadecanoic acid - 6.2% 7,16 — Dihydroxyhexadecanoic acid - 2.2% The constitutents of epicular wax fractions of the mature fruit were as follows: Hydrocarbons 29% Fatty Acids trace a-amyrin 6% B-amyrin 21% Naringenin 32% Chalconaringenin 11% The composition of cuticular wax varied from epicular wax. Cuticular wax was found to consist of: Hydrocarbons 15% Fatty acids 43% a-amyrin 9% B-amyrin 32% Naringenin 0.8% Schonherr (1976a, 1976b) conducted extensive studies on the water permeability of isolated cuticular membranes. By treating the cuticular matrix and cuticular waxes as two resistances acting in series, Schonherr concluded that permeability to water was determined primary by the waxes and that permeability changes with different ionic forms of the membrane; permeability followed the order Li+ < Na+ < K+ < Rb+. The dependence of permeability of cuticular transpiration on water activity was investigated (Schonherr and Schmidt, 1979). They found that the water potential across the membrane was the driving force behind cuticular transpiration. Schonherr, Eckl and Gruler (1979) showed that the permeability coefficient for the cuticular membrane was temperature dependent. The original distribution of soluble cuticular lipids is irreversibly altered above 44°C and is accompanied by an increase in water permeability. Permeability of dewaxed cuticular membranes was shown to be strongly dependent on relative humidity due to the presence of polar functional groups in the polymer matrix. However, for non-dewaxed cuticular membranes the permeability coefficients were only slightly affected by relative humidity, showing that the movement of water was limited by a hydrophobic barrier that lacks dipoles (Schonherr and Merida, 1981). The behavior of the cuticular membrane can also be greatly influenced by the nature and concentration of the fixed charges in the polymer. The fixed charge concentration of the polymer affects sorption and diffusion of water and electrolytes by affecting the water content (swelling) of the polymer and by imparting permselectivity. Schonherr and Bukovac (1973) found that at constant pH and salt concentration, the exchange capacity increased with increasing counter-ion valence and decreasing crystal radius. Swelling of the matrix is a function of its chemical form. The cutin matrix in the Na+ form swelled more than in the Ca++ form (Schonherr, 1976a). Calcium ions associate more closely with fixed charges than sodium ions and reduce swelling because only one half the number of osmotically active particles are present (Schonherr and Bukovac, 1973). An excellent review of the research and literature on water permeability in cuticular membranes was presented by Schonherr (1982) as a relationship between the cuticular membrane structure, membrane composition, and permeability. Certain prOperties of the cuticle can be changed by treatment with different chemicals. The influence of calcium on plant membranes is widely discussed in the literature. Highly disorganized cell membranes can be restored by the addition of calcium (Bangerth, 1979). Ca in the cell walls and the middle lamella appears to play an important role in reducing cracking of fruits due to a strengthening of the constituent of middle lamella. (Bangerth, 1973). Dickinson and McCollum (1964) also pointed out that calcium may be related to fruit crack resistance since it depends on cell wall strength. The distribution of calcium throughout the plant is closely correlated to the distribution of water along the xylem vessels. During the period of rapid growth, very little water enters the tomato fruit through the xylem since the water is supplied by mass flow through the phloem. This mass flow does not carry a significant amount of Ca. Because of this, a non uniform distribution of calcium may occur among different parts of the plant (Wiersum, 1966; Vangoor, 1968). Calcium deficiency in plants can be observed as the cells break down along with loss of turgor which causes the tissues to become water-soaked. Eventually, the tissue may become desiccated, yielding a dry area of necrosis (Simon, 1978). Potassium has been known to enhance the drying of different plants (Dudman, 1962; Chambers and Possingham, 1963; Tullberg, 1978; Dunman and Grncarevic, 1962; Grncarevic, Radler and Possingham, 1968, Columbella (trans. 1945) described a method of making raisins in 60 A.D. by dipping grapes intoa solution ofboiled ashesof vinesmixed witha little oil. This technique, which uses potassium carbonate and oil, has been proven to give good results under laboratory conditions (Dunman, 1962; Dunman and Grncarevic, 1962). It was suggested (Chambers and Possingham, 1963) that air spaces between wax platelets become filled with liquid during dipping and the potassium carbonate in the solution changes the wax from hydrophobic to hydrophilic. However, washing the dipped grapes within two days reduced the increased transpiration to that of undipped grapes (Grncarevic, Radler and Possingham, 1968). One can conclude, therefore, that the potassium was not bound in the cuticular matrix since the K+ ions were removed during washing. Potassium also enhanced the drying of alfalfa (Tullberg, 1978; Tullberg and Angus, 1972) and reduced tomato fruit cracking (Inverson, 1938). Inverson suggested that the decrease in tomato fruit cracking was due to the more fibrous type of root system resulting from an application of potassium permanganate to the soil. 2.2 Mechanical Properties of the Tomato Fruit Mils, Friedley and Jorenzen (1969) suggested that the epidermis was the component of the fruit controlling mechanical strength which is related to cracking and puncture resistance. A number of tests have been developed and performed to describe the rheological properties of agricultural products. (Mohsenin, 1970; Sharma and Mohsenin, 1970; Morrow and Mohsenin 1965, Friedley et aln 1968). A widely accepted method of testing the strength of the tomato epidermis is the puncture test which is also used as an index in relating tomato epidermae strength to fruit cracking (Voisey and Lyall, 1965; Voisey and MacDonald, 1964; Voisey, Lyall and Kloek, 1970; Johannessen, 1949; Tennes, 1973). Miles, Friedley and Lorenzen (1969) tested tomato fruits Using flat plate compression and internal pressure methods. Three different techniques to determine tomato fruit strength, tensile, puncture and bursting diaphram methods, were used by Voisey and Lyall (1965). Altisent and Sierra (1979) applied quasi-static compression and impact tests to different varieties of processing tomatoes. They also studied the epidermis of processing tomatoes and concluded that epidermal strength depended on the shape of the epidermal cells and cuticle penetration. The correlation between the above properties of the epidermal layer and tomato cracking was also investigated by Conter, Burns and Leeper (1969); however, they could not relate the shape of the cells to tomato skin puncture resistance. They observed that tomato fruits resistant to concentric cracking possessed flattened epidermal cells. Voisey, Lyall and Kloek (1970) suggested that crack resistance can be related to greater cutinization of the epidermal layer and underlying cells. However, they also concluded that the elongated shape of the epidermal cells did not change cracking resistance. Failure and relaxation tests were used to evaluate tomato skin behavior (Hankinson and Rao, 1979). It was concluded that failure occurred in the middle lamella, between cells, andthat theshape ofthe cells andthe degree of deposition of cutin affected cracking. From the above, one can only conclude that there are contradicting 1O opinions about the influence of cell shape on fruit cracking. Since the change in water status of the fruit is thought to be the direct cause of tomato fruit cracking, Murase and Merva (1977) investigated the elastic modulus of the tomato epidermis as affected by water potential. They related mechanical properties with potential characteristics by applying relaxation tests to skin segments with different water potentials. Only a few investigators have attempted to test tomato fruit strength by applying stresses similar to those which occur under natural conditions. Internal pressurization as used by Miles, Friedley and Lorenzen (1968) seems to be closer to the stress which tomatoes undergo in the field. In their experiments, force deformation characteristics were compared with those of an elastic sphere and a spherical membrane filled with water in order to gain insight into the structural composition of the fruit. A preliminary theoretical development using stresses in thin shells was performed by Tennes (1973). The theory of shells has also been used by Considine and Brown (1981) to describe certain aspects of the physics of fruit growth. A theoretical analysis of the forces occurring during the growth period was related to cracking and splitting. The shape of the fruit was found to be a very important factor in determining the stress distribution and region of failure in the cuticular membrane. 3. MATERIALS AND METHODS 3.1 Chemical Treatments Cuticular membranes were enzymatically isolated from two sources (separate fields) of "Pik Red" tomatoes (Lycopersicon esculentum L.) and one source of "UC 82" processing tomatoes. Segments of tomato epidermis were taken from fruits free of visual defects and placed in a solution of 5% pectinase and 0.2% cellulase in 0.2M phosphate citrate buffer, pH 3.7. The pieces of epidermis were then incubated at 370C and the solution was changed every three to four days. After about 10 days, when the cuticular membrane was free from the underlying cells, it was rinsed thoroughly with distilled water. This technique was developed by Orgell (1955) and modified by Yamada (1962). It is generally felt that the morphological and physiological features of the intact cuticular membrane are retained by this procedure (Norris and Bukovac, 1973). The above method was compared by Hoch (1975) to isolation using the zinc chloride—H01 method and ammonium oxalote—oxalic acid reflux procedure for cuticular membrane isolation. It was found that the membrane isolated with pectinase and cellulase appeared most similar to the non- isolated cuticular membrane. Schmidt, Merida and Schonherr 12 (1981) compared fine structures of cuticular membranes and of dewaxed cuticular membranes to non-isolated membranes with a scanning electron microscope and found no harmful effects on the cuticular membrane due to above method of isolation. The separated cuticular membranes from the three sources were divided into two groups. One group was dewaxed by extracting with chloroform for two hours followed by a methanol extraction for two hours. The extraction of waxes was done at 20°C using approximately 1000g of chloroform and 1000g of methanol for 50g of cuticular membrane. (Fig 3A) The other group was not dewaxed. Both groups of the cuticular membranes were washed with 6 N hydrochloric acid (HCl) for three hours twice and rinsed with deionized water after each wash (see Fig 3.2). The procedure was done at 20°C with 1000g of acid for every 50g of cuticular membranes. Each of the two groups (dewaxed and nondewaxed) was divided into five subgroups which were subjected to the following chemical treatments (Fig 3.3): 1 N solutions of hydrochloric acid (HCl), potassium—chloride (KCl), calcium chloride (CaClz), and aluminum chloride (AlCl3); the fifth subgroup in each group of cuticular membranes was left untreatedand usedas thecontrol group. All ofthe treatments were done at 20°C with the cuticular membranes thoroughly submerged in the reagents using a weight proportion of 50g of cuticular membranes for every 1000g of reagent. The reagents were applied twice for 2 hours with a ISOLATED CUTICLE 1 CUTICLE EXTRACTED WITH CHLOROFORM (ZHR) NON-DEWAXED CUTICLE CUTICLE EXTRACTED WITH METHANOL (2HR) EXTRACTED CUTICLE (DEWAXED) Fig 3.1 Procedure for the extraction of waxes from cuticular membranes. ISOLATED DEWAXED AND NON-DEWAXED CUTICLES 1 V HCl WASH (3HR)-6N SOLUTION v DEIONIZED H20 - SEVERAL WASHES (Repeated Twice) Fig 3.2 Washing procedure for all groups of cuticles. WASHED CUTICLE / / / . A1C13 - 1N (2HR) V V AlCl3 — 1N ‘ HCl - 1N KCl - 1N CaC12 - 1N (2HR) (2HR) (2HR) 1 1 DEIONIZED H20 DEIONIZED H20 DEIONIZED H20 DEIONIZED H20 E ’ r ' v‘ ‘v . HCl - 1N KCl — 1N CaC12 - 1N ,(2HR) (2HR) (2HR) (2HR) * v i V DEIONIZED H20 DEIONIZED H20 DEIONIZED H20 DEIONIZED H20 1 v . H+ FORM K+ FORM Ca++ FORM 7 A1+++ FORM Fig 3.3 Procedure for application of ions to cuticular membranes. 16 The two sources of "Pik Red" tomatoes and one source of "UC 82" which were treated separately, yielded 24 sets of chemically treated samples and 6 sets of control samples (3 with and 3 without wax) see Fig 3.4. These samples of cuticular membranes were observed under a scanning electron microscope. There were significant differences between the dewaxed and nondewaxed surfaces of the cuticular membranes (Fig 3.5, 3.6). However, there was no way to distinguish between chemical treatments in the dewaxed and nondewaxed a subgroups. CUTICLES FIELD A FIELD B FIELD C (PIK RED) (PIK RED) (UC-82) NON-DEWAXED DEWAXED NON-DEWAXED DEWAXED NON-DEWAXED DEWAXED H+ H+ H+ H+ H+ H+ K+ K+ K+ K+ x+ K+ Ca++ Ca++ Ca++ Ca++ Ca++ Ca++ A1+++ A1+++ A1+++ Al+++ Al+++ Al+++ CONTROL CONTROL CONTROL CONTROL CONTROL CONTROL Fig 3.4 Final thirty groups of cuticles obtained after chemical treatments. (b) outside surface of the Fig 3.5 (a) - nondewaxed cuticular membrane of the tomato fruit. (b) - outside surface of the dewaxed cuticular membrane of the tomato fruit magnification X600 15KV 65-70O tilt. (b) Fig 3.6 (a) inside surface of the nondewaxed cuticular membrane of the tomato fruit. (b) inside surface of the dewaxed cuticular membrane of the tomato fruit. 20 3.2 A Procedure for Measuring Water Permeability Through the Cuticular Membrane The transpiration chambers were manufactured from 28.6 mm outside diameter aluminum rods. The chambers were 38.1 mm tall and were milled to contain a well in the chamber which was 9.5 mm in diameter and 31.8 mm deep, over which a circular membrane could be placed. A rubber o-ring 12.5 mm in diameter servedas aseal between themembrane andthe chamber. It was embedded in a 1.5 mm groove surrounding the center well. An aluminum cover with a center opening 8.3 mm in diameter was placed over the membrane and fastened with three screws. These chambers were very similar to the ones used by Schonherr and Lendzian (1981L Schonherr and Merida (1981) showed that for the dewaxed membranes, permeability was strongly dependent on humidity due in their opinion to the presence of polar functional groups in the polymer matrix. For the nondewaxed cuticular membranes, changes in humidity did not influence permeability significantly. The permeability of the cuticular matrix is also a function of temperature and it changes drastically at about 44°C (Schonherr, Eckl and Gruler, 1979). For these reasons, the transpiration chambers were also stored in desiccators over blue silica gel. The desiccators were placed in a constant temperature water bath (25 1 .SOC). Under these conditions, the air in equilibrium with the silica gel contained only about 3 x 10‘ 11 kg—m‘3 water (Kolthoff et al., 1969), so for all 21 practical purposes, the activity of the water vapor at the surface of the silica gel was zero and theldumidity and temperature in the desiccators were held constant. Therefore, the relative effects of humidity and temperature on permeability were eliminated. At the beginning of each experiment, 1 cm3 of distilled water was placed in every chamber. The membrane was then placed over the chamber opening followed by the aluminium cover which was secured by screws. The chambers were placed over silicagel upsidedown(membranecnithebottom)anda paper filter was inserted between the chambers and the silica gel. The upside down position is believed to be closest to the situation in vivo since the inner surface of the cuticular membrane on a fruit is in contact with liquid and the outer surface with dry air (Schonherr and Schmidt, 1979). The chambers were taken from the desiccators and weighed every two hours for dewaxed cuticular membranes and every 12 hours for non-dewaxed, after which, they were quickly returned to the desiccators. From this, the transpirational flux across the membrane was obtained from the equation; Jtr = R/Ap (3.1) where A is the area of the membrane exposed to water and air, and p is the density of water at 25°C (996.5 kg/m3). Note that Jtr is expressed in (m/s). Since there was more than one sample for each group of cuticular membranes, the rate R (in kg/s) of water from the chamber in the presence 22 of the membrane was calculated by a modified least squares method which is presented in Appendix C. Then permeability coefficients (P) were obtained as the ratio of the flux Jtr per unit driving force. The driving force for the transpiration process is the water activity difference which was calculated assuming that the water activity inside the chambers was 1 (distilled water) and outside the chambers was zero by assumption (due to silica gel). The difference was therefore assumed to be unity. Since permeability coefficients obtained using chambers without membranes are not infinite due to the distance of the water surface from the silica gel and duetx>the unstirred layer effect, permeability coefficients in the absence of cuticular membranes had to be determined. For this purpose, silica gel was placed in a screen basket above the water filled chambers. A paper filter was placed between the screen and the silica gel. The chambers were filled to the rim which was the position of the membrane during the experiment in the upside down position. The value of the permeability coefficient without the membrane was found to be 1.07 x 10’7 m/s (average of 10 chambersL The permeability coefficient for the membrane itself was calculated using the assumption that the membrane acts as resistance in series with the boundary layer resistance so that 23 1 1 1 —-—- = -~~a~~~ - -—— (3.2) Pmembrane Ptot Po where: Pmembrane - permeability coefficient for the membrane Ptot — permeability coefficient obtained from the experiment for the chamber in the presence of the membrane. Po - permeability coefficient obtained from the experiment for the chamber in the absence of the membrane. 3.3 A Procedure for Measuring Elastic Properties of the Cuticular Membrane The chemical treatments described earlier in of "Materials and Methods" yielded 30 different groups of cuticles. Since different ions in the polymer matrix could influence the elastic properties of the matrix, a tensile test was performed using the Instron tensile tester to determine the effect of chemical treatments on material properties. However, since the cuticle of the tomato is nearly spherical and therefore cannot be unfolded into a strip without introducing initial stresses, a modification of the tensile test was introduced and is presented in Figure 3.7. The edge of the cuticle was clamped between two plates with a opening of radius .79 cm. A force was applied to the surface of the membrane using a sphere with a radius of .48 cm. This arrangement did not introduce the initial stresses thatwould occurin usinga thinstraight stripof tomato skin and performing a classical tension test. 21: Two experiments were performed for each of the 30 groups of cuticles. In one experiment, it was made sure that there was friction between the sphere and the cuticular membrane. Several samples from a group were then selected and the tensile test was performed under these conditions. 25 Fig 3-7 The setup for the tensile test on the Instron device. 26 In the second experiment, the contact surfaces were made frictionless using a lubricant vegetable oil between the membrane and the sphere. The tensile test was again performed on the remainder of the samples in the group under the new conditions. The reason for this separation is explained in detail in the theory chapter. For now, it is sufficient to say that the calculation of the material properties, Et and v, is made easier by this separation into "slip" and "no-slip" groups. From the experiment described above, curves of force versus displacement were obtained. Using the equations developed in the next chapter and the computer program QUICK shown in Appendix B, the elastic properties of the cuticles were calculated. 4. THEORETICAL DEVELOPMENT 4.1 Theoretical Solution for Elastic Properties of Tomato Cuticle A tomato fruit cracks due to the water status change in the fruit (Frazier (1934, 1947)). An increase in water potential of the fruit will cause an increase in pressure on the cuticular membrane surrounding the fruit. We can simulate this state in the laboratory by applying a pressure to the membrane using a smooth spherical indenter. The experimental procedure was described in the previous chapter and presented in Figure 3.7. Since the surface of the sphere can be made very smooth, nearly frictionless slip can be made to occur between the cuticular membrane and the spherical indenter. Then the cuticular membrane can be treated as a thin membrane under pressure. Higdon et al. (1976) gives the following equation for a thin membrane under pressure; (p/t) = (01/73) + (02432) (4.1) where p is the pressure applied to the membrane, t is the thickness of the membrane, p1 and p2 are the principal radii of curvature in two perpendicular directions, and O1 and 02 are the corresponding "in-plane" membrane stresses. (See Figure 4.1) 27 28 Fig 4.1 Rectangular section of membrane-forces T and internal pressure p. 1 and T2 29 Equation (4.1) can be rewritten in the following form, p = (T1/o1) + (T2/o2) (4.2) where T1 and T2 are forces per unit length in the same directions as (a and 02 respectively. The complete state of tension (T1, T2) at any point on the membrane for this particular experiment will now be determined. An examination of Figure 4.2 which describes the configuration of the membrane used in the experiment during deformation shows that the only parameter which is difficult to measure is the "contact angle", 90. Fortunately, 60 can be expressed in terms of the other parameters R, h and a. In Appendix A-1 it is shown that sineo = (aR - (R - h) (h2 + a2 - .2Rh)‘/2)/(R2 + (R — m?) (4.3) The state of stress in the upper portion of the membrane above the contact line can now be determined by "making a horizontal cut" 2 units from the top and drawing afree bodydiagramcfl‘themembrane andindenter belowthis cut as shown in Figure 4.3. With W equal to the downward force exerted on the spherical indenter and b equal to the radius of the horizontal circle formed by the cut, the balance of forces in the vertical direction requires that ”vert = 2m) - T1 cos(9o°— eo) - w = o (4.1:) From the geometry of Figure 4.2, it can be shown that b sineo : a sineO - z coseO (4.5) Substituting this into equation (4.4) gives T1 = W/(2n (a sineo - z c0360), 0523h—R+R coseo (4.6a) 30 Fig 4.2 \i\\\\ I X g A A CLAMP MEMBRANE l T CONTACT LINE n j :2 CONTACT SURFACE v UNDER PRESSURE Q / Crossectionai view of membrane being loaded by Spherical indenter. 31 Fig 4.3 Perspective view of section of membrane under load W. 32 (for details see Appendix A-2(a)). With T1 determined for any value of 2 above the contact line, T2 may be found using Equation (4.2). Since 91 = w and p = 0, Equation (4.2) reduces to 0 = (T1/m) + (TE/p2) (4.6.b) and, therefore, T2 = 0 for any 2 5 h - R + R cos 60 Now that the tensions (T1, T2) at any point on the free surface of the membrane have been found, it remains only to calculate (T1, T2) for those points on the contact surface. The contact surface is defined to be that part of the membrane which is directly in contact with the sphere (below the contact line). Here, the situation is a little more difficult; the pressure, p, exerted by the sphere on the membrane varies from point to point on the contact surface as do T1 and T2. Under the assumption of frictionless slip, Equation 0L2) still applies but it alone is not sufficient to determine all three unknowns, p, T1 and T2. It will be necessary, therefore, to derive two additional equations. For any point on the contact surface, p1 : 92 : R where R is the radius of the sphere so that Equation (4.2) can be written as T1 + T2 : pR (4.7) This equation relates the tensionsT} and T2 in two perpendicular directions to p. An equilibrium equation involving'T1and palone canbe obtained bymaking a horizontal cut through the membrane parallel to and just 33 below the contact line and drawing a free body diagram of the membrane below this cut. After having done this, in order to simplify matters, the entire free body diagram will be flipped upside down and a spherical coordinate system (R, d, ¢) with its origin at C, the center of the sphere, will be used. See Figure 4.4. Since all points on the membrane are equidistant from C and since axisymmetry of the stress field eliminates any dependence on the coordinate a, only 9 will appear in the equilibrium equation. Note that in this free body diagram,¢ may assume values in the range, 0 g¢ge , where 6 marks the cut in the membrane. By summing forces in the vertical direction on Figure 4.5 we can obtain a second independent equilibrium equation n zrvert = -T1 cos(9o°—a )(27TR sine) + 3) (p(¢>)cos¢)dA ogoge (48) where dA = (2nR sin¢)(Rd¢) = the element of area corresponding to the thin band shown in Figure 4.5. This equation can be rearranged to produce (dT1/d9) tane + 2T1 : Rp(9) (4.9) (for details see Appendix A-3) There are now two independent relations, 0L7) and 0L9), in three unknowns obtained from the two available equilibrium equations. The third equation must come from elasticity considerations. From Sokolnikoff (1956), in the three dimensional formulation of elasticity theory there are 3 equations of equilibrium, 6 stress-strain relations and 6 R 90r—0 CONTACT LINE Fig 4.4 Inverted perspective view of the contact surface and the coordinate system used. JV ..---.. r...- lm-ti‘ C-- CENTER OF THE SPHERE Fig 4.5 Free body diagram of the membrane above the cut in Fig 4.4. 36 strain-displacement relations. These equations are given in spherical coordinates in Appendix A-4. All variables here are functions of eonly since the assumption of axisymmetry immplies that a/aa : 0 and u :0. Axisymmetry also implies that there are no in-plane shear stresses. For this particular problem there are no body forces. These considerations are justified by the fact that one can obtain the same equilibrium Equations 0L7) and (4.9) by using them. (For details, see Appendix A-4). The advantage in taking the elasticity approach is that it yields the third equation in T1, T2 and p necessary for a solution; this equation comes in the form of a compatibility equation. Applying the axisymmetry conditions to the strain- displacement equations gives only two nontrivial equations, see: (1/R)( &%/89) (4.10) Eda: (1/R) ue cote (4.11) Solving Equation (4.11) for ue , differentiating and substituting into Equation (4.10) gives a compatibility equation cec052 : Eda + ( Beau/89) SiJ19 cose (4.12) These strains can now be expressed in terms of the stresses which in turn can be expressed in terms of the tensions. %e: 01 : T1/t (4.13.a) and odd: 02 = T2/t (4.13.b) The third stress, 0 can be taken to be zero since it is FY" 37 small in comparison withoGe This is justified in the following way: andoda. Orr : -p on the inside of the membrane Orr = O on the outside of the membrane (4.14) It is expected then that Orr is on the same order of magnitude as p everywhere along the thickness of the membrane. But p : (T1 + T2)/R from Equation (4.7), so using Equation (4.2) p = (Ceet +00“, t)/R = (t/R)(Oee+oaa ). rr is therefore on the order of t/R timeso or o 99 ac and since t/R << 1, Orr ((069 and qé = W/(2nR sinZeo) (4.22) (See Appendix A-2(b)) Now that|T1 is completely determined for any value of 9 in the range 0 56560 in terms of known parameters, T2 can be determined from equations (4.7) and (4.9), T2 = pR - T1 = (2T1 + (dT1/de)tan0) - T1 39 = T, + (dT1/d6)tan6 (4.23) This can be rewritten as: T2 cosG : T1 c056 + (dT1/d6)sin6. (4.24) Substituting (4.19) into (4.24) one obtains: sinne T2 c056 = 0059 k E b VIIO n - ” - n-1 + Sine coso k 2) n bn 51n 0 n:o Dividing through by c039 which is never zero since 00593900, Q _ n T2 = k z (n+1) bn Sin 9 (4.25) h=0 where bn and k are the same as in Equations ULZO) and (4.21). It can be seen that T1(0) = k : T2(0) as expected since at 9: 0, T1 is physically indistinguishable from T2. An examination of the coefficients bn in Equation (4.20) shows that b0 :1 is the only positive one since 92 = —(1-v)/8, and n2 +ii- 1 + V is positive for the remaining values of n : 2,4, 6,“.This means that the expressions for T1 and T2 in Equations (4.19) and (4.25) are monotonically decreasing functions of9 . This renders both T, and T2 maximized at 9 : 0 with Timax = T2max : k. The strainse1 and 62 can be calculated using Equation (4.15), e : (1/Et)(T - vT ) = (k/Et) E (1-v-nv) b Sin 6 i i 2 rut n (4.26) 7 w e = (1/Et)(T - vT ) = (k/Et) z (n+1-v) b sinne 2 2 1 V.:O n Since (n+1-v ) > O for all n, the sign considerations for the bnmentionedabove areunchangedso thate2 ismaximizedat 9 = 0 with €2max : k(1 -\z)/Et. But since (1-v-nv) 40 changes sign for n >(1 - v)/v, so do the terms in the series and a determination of the point at which 61, is maximized and the value of that maximum cannot easily be made. From the graph of load versus displacement obtained from the experiment described earlier (see Fig 3.7) in "Materials and Methods" it is possible to determine the material properties v and Et. This is done by comparing the actual displacement to the theoretical one for a given load. The total vertical displacement u is composed of two parts: 2 the part below the contact line “2b and the part above the contact line u The first step is to relate the 28' vertical displacement below the contact line to 60 and W. From the strain - displacement relation (Appendix A-4), cad: uG (cote /R) (4.27) so, u6 = R taneeaa (4.28) From the stress-strain relations (Appendix A—4), Eom.=(1/E)(Ucm- vow) (4.29) Using Gad: T2/t and o 60: T1/t we obtain EGG: (1/Et)(T2 -' VT‘l) so that U6 2 (R tan9 /Et)(T2 - VT1) (H.30) This correctly predicts that ue : 0 when 6: 0. The vertical component of the displacement below the Contact line is the component of ue evaluated at 6 :90 in the vertical direction, 41 uzb = (R tan eo/Et)(T2(90)- T1((%))sin60 (4.31) Now thatuzb hasbeen calculatm in termsof known parameters and the material properties, uza can be determined. For the free surface part, T2 = 0 and T1 : W/(2r(a sin 60 - z coseo)) from Equation (4.6a). From Hooke's law, ‘01 : T1/t = E31 so that 61 = T1/Et (4.32) From Appendix A-7, du = 61 dz After integration this gives the second part of the vertical displacement, u : (W/2nEt) (ln(a/Rsin90)/coseo) (4.34) 2a The total vertical displacement is uz : uza + uzb which from (4.31) and (4.34) is uz = (Rsin290(T2—vT1)+(W/2n)ln(a/Rsin90))/(Et cos 90) (4.35) The term T2 — v T1, evaluated at 9: 60 can easily be replaced~in Equation (4.35) using Equations (4.21), (4.22) and (4.25). T2—vT1zk §;(n-1)bnsinn60 -v(W/2nR sin290) (4.36) 2 w o m n T2-VT1=(W/2WR sin 90)(('§((n-1)bnsin00/r2ébnsin 90)-v) (4.37) Using this in equation UM35) the total vertical displacement becomes uZ:(W/2rEt coseo)(( i;R so o°<9o< 90° h = AB + BD : BP tan9o + BD : (a - Rsin0O ) tanoo + (R - Rcoseo) hcoseo : asiné)O - RsineeO + Rcost?O - RcoszeO (h - R)cos£?O .-. asinBO - R (h - R)2 c0326O : a2sin200 -2aRsin6O + R2 (n - R)2 (1 - sin260) = a231n290 - 2aRsin90 + R2 (a2 + (R-h)2)sin290 - 2aR sinOo + R2 - (R-h)2 = o sineO = (2aR:(4a2R2_4(a2R2-a2(R-n)2+R2(R-n)2-(R-n)”))V2/(2(a2+(R—n)2)) sineo = (aRi((R-h)2(a2-R2+(R-h)2)1/2)/(a2+(R-h)2) sinQO = (aR:(R-n)(62+a2-2hR)1/2)/(a2+(R-n)2). When azR, 90 : 900 provided h>2R. Then, 1 = (R2i(R-h)1R-h1/(R2+(R-h)2). Choose (-) since h>2R. sinGO = (aR—(R-h)(h2+a2—2Rh)1/2)/(R2+(R-h)2) Check; when h:0, sineO : (aR—aR)/a2+R2) : 0 which meanseO :0. 63 64 APPENDIX A-2 (a). From Fig 4.3, ESPY = 2wa1cos(9O° -eo ) - w = 0. From Fig 2.4, x/z : tan (90O - 00) x = 2 tan (90O - 90) b : a-ztan (90O - BO) : a-zcoteO T,cos(90° -ao)2n(asin60 -zcoseO)/sin9O : W T,(asin90-zcos€7O ): W/2n T, : W/(271(asin9O -zcos€b)) ngSh-R+Rcoseo (b). at 0:00 z:h-R+Rcoseo T, = W/(27r(asineO - (h-R+Rcoseo)cosQD)) T, : W/(27r(asin6O - (h-R)cos€O—R(1-sin260))). Fran Equation A.1 (Appendix A—1), asineO - (h-R)cosQO:R Substituting, T, = W/(2w(R-R(1-sin2eo))) = W/2nRsin200. 65 APPENDIX A—3 Using spherical coordinates and summing forces in Fig 4.5 in the vertical direction, ZZFy : —T,cos(90°—9)(2 Rsine) + % (p(¢)cos¢) dA:0 0 565’s where dA : 2nRsin¢Rd¢. e T,sine2nRsine : 1 p(¢)cos¢2ngsin¢d¢. o 21rRT,sin26 = 2er2 p(¢)oososin¢d¢. 0LT"'fi (D 9 T,sin23 : R j p(¢)cos¢sin¢d¢. Taking the ogrivative with respect toéfiof both sides, (dT,/09)sin0 + 2Tsin0cose : Rp(€)cosésiné. (dT,/dé)tané + 2T, : Rptfl. 66 APPENDIX A-4 In three dimensional elasticity using spherical coordinates (see Figure A.4-1, A.4-2) there are 3 equations of equilibrium: 80m '1 86:57 +l 801.6 + 8r name 80: 1‘ 30 80m + 1 80-14“ _ _1_ 80-69 _ 8r raine Ba r 80 .895; + _1__,6985. 1_ .8, -_ _ 3r re‘ré 8a V“ 65 and 6 stress—strain relations: err €66 = (Gee ‘ V (Orri-odgj1/ E a“ = (“w - v‘cwweart Yre = Ute/G Yoe = Gee/G Y = “.._/C = (of? "V (596+0-xd11/E 20'1-r- 0211 — (Tee '1' 03-9 Cdt e r Bow + ZUae Cote r + Eb Acne +1511... :gxngii 1‘" +Fr= 67 and 6 strain-displacement relations: err = 811,. /3‘F 668 = 1; 1/17,(au5,/89, + 1 (Jr/1" ,. m ll 3,, (I/rsireflaud /aa‘, +(Urg’r1—1—(Ueto‘19/F) 6.. = -;11/151r9)(au./eo) - sou/r) + (an. 5111/2 e..= ((1/r)(au./ae)-(ue/r) + (we/MN/Z e..=((1/r)(au./ae)—(meow/11+(i/rsine)(eu./aa)1/2 (see Sokolnikoff, 1956) In order to relate the elasticity variables to p, T,, and T2, consider the definitions of T,, and T2 in relation to Figure A-4.1. 5.4 = T24 069A : T11.” But A:L't, so T2 :a'cm t + 00.0.: (1/t)T2 T, :096 t '* 0'99: (1/t)T1. Now, if one assumes that both shear stresses and body forces are zero, it can be shown that the three equilibrium equations of elasticity reduce to the two equilibrium equations corresponding to equations (7) and (9) in the text. For the 68 axisymmetric case (3/3a:0) with no shear stresses or body forces, the equivalent equations of elasticity are (Barr/8r) + (1/r) (20”. «ran, "’99 )=0 0:0 (809,, /ae) + (0’Ge ~oaa)cot6:0. The first equation can be rewritten as (r2(ao,.,./ar) + 2w”) = r(aee we“, ) OI” (a/ar)(r26,,) = ro'e6 + rqmg. 69 H Fig A4.1 Stresses on the element in spherical coordinates. .1 N 70 Fig A4.2 Displacement in spherical coordinates. 71 Integrating R+1 11*". R+t 1 (a/ar)(r2orr)dr : 1 robedr +.1 rqdadr P R R r26” 1:: (117,03) + 1172(9)) (R+t)2'0 - R2(-p) : RT, + RT2, T, + T2 = pR (same as (7)). The third equilibrium equation of elasticity is (d/de) (T1/t) + (T,/t - T2/t)cote : 0 (dT,/de) + (T, - (pR - T,))cote : 0 (dT,/de) tane + 2T, = pR (same as (9)). This means that the 'no shear stress, no body force' assumptions applied to 3—D elasticity in spherical coordinates are compatible with the membrane equations obtained by equilibrium considerations alone. The advantage in taking the elasticity approach is that it yields the third equation in T1, T2 and p necessary for a solution; this equation comes in the form of a compati- bility equation. Using the stress-strain relations, the no shear stress assumptions require that erm :%e=(L In view of the axisymmtry conditions, the strain- displacement equations for 511 and €09 are satisfied automatically. The remaining equation requires that Ere: 0 : ((1/r)(8ur/86) - (ue/r) + (Bug/8r))/2. It was assumed that the change in thickness during deformation is negligable. As a result ur< R, ln (a/Rsineo) > 0, so that u > 0. Z 76 \\\\\\\ Fig A7.1 Displacement of the free surface part of the membrane. APPENDIX A—8 Equation (4JH) in the text represents the deflection over load result for no slip conditions. Solving (4.41) for Et, Et = (W/uz)(ln(a/Rsin90))/21rcoseO (A8.1) Since W and uz from the Instron experiment were read off of the graph in inches with a full scale load of 10 inches : 1kg for W and with a 2 inch displacement on the paper corresponding to a 1 inch displacement of the indenter, W/uZ : force/displacement : W/WcotB :(W[in] * 9.81[N]/10[in])/(Wcot8 [in]*(1[in indenter]/2[in N/m chart]* .0254[m]/1[in]) : 77.244 tanB[N/m] where B is the angle from the graph shown on Figure A8.1. Using Equation (A8.2) in Equation (A8.1), Et:(12.294 tans /coseo)(ln(a/Rsineo)) (A8.3) for the no-slip part of the experiment. Let MNSbe thenumber ofsamples ineach groupof cuticular membranes which were tested under "no-slip" conditions and MS the number under slip conditions. Since 8 and 00 change for each<3fthe MNS samples, from Equation (A8.3). Etavg = (12.294 :2 tanen ln (a/(Rsian))/cosen)/MNS (A8.4) In program QUICK, two vectors were generated, 78 DEFLECTION 79 PAPER MOTION OPE ISL/ I ‘3 1 I l l I l l ¥ W FORCE where: H - initial distance from the horizontal plane to the point of taut membrane (Figure 4.2) HF - final distance H from the horizontal plane to the point of break 0 — "Instron angle"; ANG in program QUICK W - load applied to the membrane Figure A8.1 Example of graph from Instron experiment and graphical explanation of some variables required for PROGRAM QUICK (W and U2 were read in inches from the graph). 80 1 ‘ r 7' 1 1 ‘thl’ipl I 1656} ‘ Mus 11“ Being, I MNS _ SEEP: - -ill_ X" tose; 1 Y" In RQrEu : (A8°5) ,tangm £+ME M5 , C , 1 1‘45 :— cos 0 Mus+M5 .5 , n Pen/16M“, M5 1 1. Using the above two vectors, (A8.4) can be written as Mus Etan = (12.2911 11?, Xnyn)/MNS (A8.6) The only unknown in (A8.6) is Etavg since everything on the right hand side is known. For "slip" conditions, Equation (4.40) in the text should be used. Solving (4.40) for Et, Et:(W/(2ncoseouz))(1 —v + ln(a/Rsin00)) (A8.7) Since the same conversion factors used in Equation (A8.1) apply to Equation (A8.7) as well, Et:(12.294 tanB/coseo)(1 -\)+ ln(a/Rsin90)) (A8.8) andtheaverageEt fin‘all"slip"samplesin agivengroupof cuticles can be calculated as V Etavg = 12.294 ((1-v) hi; (taan/cosen) + MS n3(tan81/cosen)ln(a/Rsin0n))/MS (A8.9) or in terms of the vectors in (A8.5) MNs‘I'Ms “95*".‘1‘: Etavg = 12.294 ((1-0) 2 xn + 2 xnyn)/MS (A8.10) h=MNb+I "=l’v;g+l Now, since Equations (A8.6) and (A8.10) both give Etavg’ the right hand sides can be equated and the resulting expression can be solved for the only remaining unknown, Poisson's ratio. 81 Mu MN:*M5 MwiM v = -(Hlfiy/M~Q zjxpx-2M ,xnyn1/ 2 5 x") (A8.11) h: r: N5+ n=MM+I Et and v for each group of cuticular membranes were calculated using Equations (A8.6) and (A8J1) and program QUICK listed in Appendix B. In the same program, the standard deviation for Et was calculated using the value of from Equation (A8.11) and generating an additional number (MS) of Et's from Equation (A8.8). In this way, the standard deviation applied to all samples in the group, "slip" and "no-slip", not just to the "no-slip" ones. 02: 5, (Et(“) - Etavg)2/(MNS + MS) (A8.12) This can be expanded as 2 - n 2 n 2 a - 5 ((Et( l) - 2Et( )Etavg + Etavg )/(MNS + MS) (A8.13) It ill now be sh n th t z Et(n): M M t where w ow a m ( NS+ S)E avg Etavg was calculated using only MNS samples. From Equation (A8.4) MM (n) 5. Et - MNSEtavg (A8.14) From Equation (A8.10) ”S ( ) 2 Et 9 - MSEtavg (A8.15) “=1 But, a (81.01))2 = z (Et(n>)2 + 2 (Et("))2 (A8.16) 0 M5 NS 82 Using (A8.14) and (A8.15) in (A8.16) (,7, (81:91))? = (MNS + MS)(Etan)2 (A8.17) Substituting the right hand side of (A8.17) into (A8.13) 2 _ (n 2 2 2 o - ( .1? (Et 1) - 2(MNS + MS)Etavg + (MNS . MS)Etavg )/ (MNS‘I—MS) , OT‘ (,2 = ( .7 (Et(n))2 - (Mus . MS) 12t,.,,,g2)/(MNS + MS) or 2 _ (n) 2 2 o .(1/(11NS + 115)) (5, (Et ) ) - 81;an (A8.18) Separating the sum into groups, 02 = (1/MNS + MS)) ( 2 mm)? + 34:81:90)?) - Etavg2 MN5 5 (A8.19) Using the expressions (A8.3) and (A8.8) for the "no-slip" and "slip" parts respectively, 02 = ( 2 (12.294 §?4%e— 1n —Ji——— 2 + MNS D‘r\ RSll’len (A8.20) 19088. _ __aL__I 2 _ 2 ri(12.294COSen (1 v+ lnRsmen ) )/(Mns + Ms) Etavg Using the vectors in (A8.5), (A8.20) can be simplified to a2 = (12.294)2( M2 (xnyn)2 + 2 xn2(1- +yn)2)/ 45 M5 (MNS + Ms)-Etavg2 (A8.21) and the standard deviaticniis equalixnthe square root of (A8.20). APPENDIX B PROGRAM DEWAX D T R F. U ' Pr- . vl P, 3 F x ‘ T5 M l. 5 E \I U1. 5 ‘ E ' R 2 UV R Hw R s 3 T t :E r. C 7. T 1 t 20 VI 8 B 1 O Y CI ED L H F. 0M” E 5 L 5 PT L 5 A M 6‘ E pr. P 1 L I\ As A L H A ’4- N N o F. ‘ v T O C C C 5 \IC A A L O C E 9’ 531 L \I R R s t 1 D T5 TE” A E E 3H 8 B 3 H D U‘ NVE - T H H ’c M M E G F. T PG .LIHI a. 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KCl .127 17 1.220 16 115-: CaC12 -.135 17 -.310 17 AlCl3 1.238 17 -.599 17 f\ HCl -1.131 9 -.681 17 ég-g) KCl -1.22N 7 .717 16 g g CaC12 -.564 6 2.273 17 (**) E; AlCl3 -.3H9 7 -1.195 16 d.f - degrees of freedom (**) - samples found to be significantly different from the control group at the uncertainty level c2: .05 (5%) APPENDIX C Each of the ten chambers was weighed three times. It is easy to show thatii‘the standard least square technique is used, the line fitted to three points has a slope M = (w3 — w.)/u and y-intercept b = (5W1 - W2 + 2W3)/6 where W1, W2, W3 are the consecutive weights of each chamber at O, 2 and U hours for dewaxed samples. This means that the slope of the line depends onlyron the first and last measurements and that the y-intercept is not W1. This is unacceptable since at t : O, the weight must be W1. For this reason, a modified least square method which forces the line to pass through the first point is used. With this method, the slope is dependent on all three measurements; it takes into account the second measurement, W2, as it should. In general, ifone wants to fit a straight line to Npoints while atthe sametime forcing itto pass through the first point (x1,y1), an equation of the form y : y1 + M (x - x1) is used. Here we want to minimize the variance N E2 = z (yk — (y1 + M (xk _ x1)))2 k=1 87 88 This requries that 8E2/8M = o O!" N -2 z (yk - (y1 + M (xk - x1))) (xk - x1) = o (c-1) k=1 Solving (C-1) for M, N M = 2, N (x - x )(y - y )/ 2 (x - x )2 (c—2) k k 1 k 1 k:2 k 1 2 For three points; (W1,O), (w2,2), (W3,4) for dewaxed and (W110), (W2112), (W3,2H) for nondewaxed Mdewaxed = (-3w1 + w2 + 22w3)/1o (c-3) Mnondewaxed = ('3w1 ' W2 + 22 W3)/6O (c-u) The slope of the line represents the permeability rate R for a given chamber in (kg/h). The permeability rate was converted to (kg/s) and the flux Jtr was calculated, Jtr : R/Ap where Jtr - transpirational flux for the chamber (m/s) R - rate of permeability for the chamber (kg/s) A - surface area of the exposed membrane (m2) p - density of water at 250C (996.5 kg/m3) Then permeability coefficients for each chamber were obtained as the flux Jtr per unit driving force (Aa:1), where Aa is the difference in water activity between the inside and outside of the membrane. The permeability coefficient for the membrane itself was calculated using Equation (3.2) in Chapter 3. Finally the average value for the permeability coefficient for each subgroup of membranes BIBLIOGRAPHY Altisent M.R. and J.G. Sierra 1979 - Relation between Resistance of Fruit, and Skin Characteristic in Tomato Varieties - ASAE Paper, #79-3085, St. Joseph, MI. Baker E.A. and M.J. Bukovac 1971 - Characterization of the Components of Plant Cuticles in Relation to the Penetration of 2, u-D. Ann. Appl. Biol 67, 2H3- 253. Baker E.A., M.J. Bukovac and G. M.Hunt (182 - Composition of Tomato fruit Cuticle as Related to Fruit Growth and Development - The Plant Cuticles. P. F. Cutler, K. L. Ellvifi? C.—ET'Price;”AEademic Press, London. Bangerth F. 1973-Investigation Upon Ca Related Physiological Disorders - Phytopath. A. 77:20—37. Bangerth F. 1979 — Calcium Related Physiological Disorders of Plants. Ann. Rev. Phytopath - 17:97-122. Chambers, T.C. and J.V. Possingham - 1963, Studies of the Fine Structure of the Wax Layer of Sultana Grapes - Aust. Journal Biol. Sci. 16:818-825. Columbella, IHJ.H Husbandry in Twelve Books, 60. AJL, Translated by Pliny et al., London, printed for A. Miller, M. DC6.XLV 17MB pp. 520-521 (Chapter XVI) - of making dried raisins or raisins of the sun. Considine J., K. Brown 1981 - Physical Aspects of Fruit Growth - Theoretical Analysis of Distribution of Surface Growth Forces in Fruit in Relation to Cracking and Splitting - Plant Physiol. 68:371- 376. Conter S.D” E.E.Burns and PAL Leeper 1969 - Pericarp Anatomy of Crack-resistant and Susceptible Tomato Fruits - Journal American Soc. Hort. Science 9u:135—137. 9O 91 Dickinson D.B. and J.P. McCollum 196M - The Effect of Calcium on Cracking in Tomato Fruits - American Soc. Hort. Science, 8H2A85-H90. Dunman W.F. 1962 — The Dipping of Sultanas - (letters to editor) - Aust. Journal Science October, 168-169. Dunman W.F. and M. Grncarevic 1962 - Determination of the Surface Waxy Substances of Grapes - Journal Science Food Agric 13: 221-224. Frazier, W. A. 1934 - A Study of Some Factors Associated with the Occurrencenof Cracks in a Tomato fruit - Proc. Am. Soc. Hort. Sci. 32:519—523. Frazier, W. A. and J. L. Bowers. 19U7 - A Final Report on Studies of Tomato fruit Crocking in Maryland - Proc. Am. Hort. Sci. u9:2u1—55. Fridley, R.B” R.A.Bradley, J.W.Rumsey and P.A.Adrian 1968 - Some Aspects of Elastic Behavior of Selected Fruits - ASAE Trans. pp. H6-u9. Grncarevic M., F. Radler and J.V. Possingham 1968 - The Dipping Effect Causing Increased Drying of Grapes Demonstrated with an Artifical Cuticle — American Journal Enol. 19:27—29. Hankinson B., V. N. M. Ras. 1979 - Histological and Physical Behavior of Tomato Skins Susceptible to Cracking, J. Amer. Soc. Hort. Sci. 10H(5):577-581. Higdon A., E.}L Ohlsen, W. B.13tilles, J. A. Weese, W. F. Riley. 1976 - Mechanics of Materials - John Wiley & Sons, Inc., New York; London, Sydney, Toronto. Hoch, H. C. 1975 - Ultrastructural Alterations Observed in Isolated Apple Leaf Cuticles. Iverson, V.E. 1938 — Fruit Cracking of Tomatoes as Influenced by Applying Potassium Permangamate Note to Soils in which Transplants are Grown - Hort. Agr. Exp. Sta. Bul. #362. Johannessen, G.A. 19A9 - Skin Puncture Studies on Red—ripe Tomatoes - Proc. American Soc. Hort. Science 5A:272-276. Kolattukudy P. E. 1981 - Structure, Biosynthesis and Biodegradation of Cutin and Suberin - Ann. Rev. Plant Physiol. 92 Kolthoff I.M.,EL B.Sandell, E..L Meehan, S.Bruckenstain — 1969 - Quantitative Chemical Analysis - Nth edition - New York — Macmillan. Krogman, D.W. 1973 - "The Biochemistry of Green Plants" Foundation of Modern Biochemistry Series. Martin, J.T” and B.E. Juniper 1970 - The Cuticles of Plants - Edward Arnolds. Miles, .LA., R. B. Friedley and C. Lorenzen 1969 - "Strength Characteristics of Tomatoes Subjected to Quasi- Static Loading", ASAE Transaction 12:G27-63. Morrow, C.T” and N.N. Mohsenin 1965 - Considerations of Agricultural Products as Viscoelastic Bodies - ASAE paper #65-810, St. Joseph, MI. Mohsenin, N.N. 1970 - "Physical Properties of Plant and Animal Materials", Vol. 1, Gordon and Breach, N.Y. Murase, H” and G.E. Merva 1977 - "Static Elastic Modulus of Tomato Epidermis as Affected by Water Potential", ASAE Transaction 20:59U-97. Noris, R.F” and M.J. Bukovac 1968 - Structure of the Pear Leaf Cuticle with Special Reference to Cuticular Penetration - American Journal Botany, 55:975-983. Oktaba, W. 197” - "Elementary Statystyki Matematycznej i Metodyka Doswiadczalnictwa - Warszawa PWN. Orgell, W.H” 1955 - Isolation of Plant Cuticle with Pectic Enzymes - Plant Physiology 30:78-80. Schmidt, H.Wq T. Merida and J. Schonherr 1981 - "Structure of Cuticular Membranes Isolated Enzymotically from Leaves of Clivia Miniata" - Reg. International Journal of Plant Physiology. 105:A1-51. Schonherr, J. 1982 - "Resistance of Plant Surfaces to Water Loss: Transport Properties of Cutin, Suberin and Associated Lipids" - In: Encyclopedia of Plant Physiology; Physiological Plant Ecology, Vol. B: 153—179. Schonherr, J. 1976a - Water Permeability of Insulated Cuticular Membranes: the effect of pH and cations on diffusion. Hydrodynamic permeability and size of polar pores in the cutin matrix - Planta 128:113-126. 93 Schonherr, J. 1976b - Water Permeability of Insulated Cuticular Membranes: The Effect of Cuticular Waxes on Diffusion of Water - Planta 131:159-16”. Schonherr J, T. Merido. 1981 - Water Permeability of Plant Cuticular Membranes: The Effects of Humidity and Temperature on the Permeability of Non-isolated Cuticles of Onion Bulb Scales. Schonherr, J” J. M. Bukovac 1973 - Ion Exchange Properties of Insulated Tomato Fruit Cuticular Membrane & Exchange Capacity, Nature of Fixed Charges and Cation Selectivity - Planta 109:73-93. Schonherr, J.; K. Eckl and H. Gruber 1979 - Water Permeabi- lity fo Plant Cuticles: The effect of Temperature on Diffusion of Water - Planta 1u7z21-26. Schonherr, J. and K. Lendzian 1981 - A Simple and Inexpen- sive method of Measuring Water Permeability of Isolated Plant Cuticular Membranes - Z. Pylanzenphysiol. Bd. 102.8. 321-327. Schonherr, J., H.W. Schmidt 1979 - Water Permeability of Plant Cuticles - Planta 1AU:3A1-AOO. Sechler, E.E. — Elasticity in Engineering - John Wiley and Sons, Inc. Simon, E.W. 1978 - The Symptoms of Calicum Deficiency in Plants - New Phytol 80:1-15. Sharma, M.G., N.N. Mohsenin 1970 - Mechanics of Deformation of a Fruit Subjected to Hydrostatic Pressure - Journal Agriculture Eng. Res. 15:65-7“. Skoss, J.D. - 1955 - Structure and Composition of Plant Cuticle in Relation to Environmental Factors and Permeability - Bot. Gazette 117:55-72. Sokolnikoff I. S. 1956 - Mathematical Theory of Elasticity - Second Edition McGraw-Hill Book Company, Inc” N.Y.Toronto,London. Tennes, B.R. 1973 - Physical Properties of Fruit Related to Cracking — Ph.D. Dissertation, M.SJL Tullburg, J.N. 1978 - The Effect of Potassium Carbonate Solution on the Drying of Lucerne - Journal of Agriculture Science. Camb. 91:551-556, ($.3J8u) Tullburg, J.N. and D.E. Angus 1972 - Increasing the Drying Role of Lucerne by use of Chemicals - Aust. Inst. Ag. Sci.7:21U-215. 9M VanGoor, BHL 1968 - The Role of Calcium and Cell Permeability in the Disease Blossom-end Rot of Tomatoes. Physiol. Planetarium 21:1110-1121. Voisey, P.Wq and L.H. Lyall 1965 - Methods of Determining the Strength of Tomato Skins in Relation to Fruit Cracking - Proc. American Science for Hort. Sciences, Vol. 86:597-609. Voisey, P.Wq IMH. Lyall and M. Kloek 1970 - Tomato Skin Strength - Its Measurement and Relation to Cracking - Journal of American Soc. Science 95:”85-“88. Voisey, P.W. and D.C. MacDonald 196A — An Instrument for Measuring the Puncture Resistance of Fruits and Vegetables - Proc. American Soc. Hort. Science 8H:557-563. Wiersum, L.K. 1966 - Calcium Content of Fruits and Storage Tissuesin Relationto theMode ofWater Supply- Acta. Bot. Neerlandica 15:”06-“18. Yamada, Y. 1962 - Studies of the Joliar absorption of Nutrients by Using Radioisotopes - Ph.D. Dissertation, University of Kyoto, Japan. Yamada, Y., S.H. Wittwer and M.J. Bukovac 196M - Penetration of Ions Through Insulated Cuticles - Plant Phys. 39:28-32. '“vwr --...~...l..-... .- l ._ MICHIGANTATE NIVERSITYIL'BRAR'ES » - 111111111111111111111» ~ M11111 1 H 111 11‘ 11 , _; 31293 03082 3045 ~ ,» _ .: 1,1 . .1»; . :3}. ..... .-. ‘ 'ut. «a... _ "sq.“ _ “111"" “we. .1. . ‘ ‘12.“ ,.‘.,.,H:~.. WHH‘“ ’4. y-—.. u.-.» u... -._. “I V... .~--, ..~...-.. M. _— ‘7 _ -<.- ‘ ' an“-.. ___. H“, __ 1»..._-~ -- A c“ W L”..‘."‘. ~..-..l‘; _fi~_;\_.,,:':«~__m V _ “‘~‘~-a~ «' ""~-« .0‘ _~_ V... I» - ... .‘C. ,_ . H ” '1 , - .. .. "‘~~\......._ . ............ H V . 2““- ~~~.... ~. IV ':-~“~~..~._. . H .:;:u«.....“ “L - ._.,. . ‘ r up-.. w.-. .. .z. _ ~~ 7‘“ l'u'.‘ “A\v«.‘ "F'- ~s.~-..-‘ m. k‘\ 4 .- ‘ “a...“ q ‘ ‘ :‘3~'~‘.‘.‘::'N‘-v.n. ~ .. mu...“ .... . u‘. , ~‘ 4 n-usi- . ~< . 3:339" -.'.:~,:,‘.» .:.l _ ”_ I“ Jaunnaayn