I I ,II II III :5; PREDICTIONS 0F SHELF-LIFE OF ‘ PACKAGED CEREAL BY AN ACCELERATED TEST TECHNIQUE AND A MATHEMATICAL MGDEL Thesis Ior Hm Degree oI M. S MICHIGAN STATE UNIVERSITY Vallop Manathunya I976 This is to certify that the . thesis entitled ‘ PREDICTIONS OF SHELF-LIFE 0F PACKAGED CEREAL BY AN ACCELERATED TEST TECHNIQUE AND A MATHEMATICAL MODEL presented by VALLOP MANATHUNYA ~ has been accepted towards fulfillment of the requirements for M.S. 419mm Packaging ngam (a 96.4% Steven W. Gyeszly, 85:0. Major professor Date June 12, 1976 0-7639 A». -- 7-2 A gig matey [(A4 ‘x.~A:-~f' .3 '{i'i-I.” Vic no": 49W Ian-x /<’:> CL), (4..., \ fl/I /\ ABSTRACT PREDICTIONS 0F SHELF-LIFE OF PACKAGED CEREAL BY AN ACCELERATED TEST TECHNIQUE AND A MATHEMATICAL MODEL BY Vallop Manathunya Ready-to-eat cereals may lose their consumer acceptance for a variety of causes, but one of the most important is the loss of crispness resulting from adsorption of moisture from the atmosphere. To prevent such moisture adsorption, cereals are customarily packed in packages which resist water vapor penetration. The amount of package protection which must be provided depends upon the tine elapsing between manufacture and consumption. This elapsing time is widely named as shelf-life of the product. Shelf-life of a product can presumably be estimated by many methods. The most common method to the food industry is the accelerated test technique. However, shelf-life studies by this method may be expensive and time consum- ing, hence shelf-lives of some products are determined by having actual testing while shelf-lives of some of the "like" products may be estimated to have the same values without testing. Since this way of estimation may give incorrect results, a scientific and theoretical approach to the prediction of shelf—life is proposed in this thesis. A simple mathematical model aiding shelf-life predic- tion of cereals was developed having moisture content as the PREDICTIONS OF SHELF-LIFE OF PACKAGED CEREAL BY AN ACCELERATED TEST TECHNIQUE AND A MATHEMATICAL MODEL BY Vallop Manathunya A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE School of Packaging 1976 DEDICATED TO MY PARENTS AND DEAREST SISTER FOR THEIR ENCOURAGEMENT AND UNQUESTIONING SUPPORT ii ACKNOWLEDGMENTS I wish to express my deepest appreciation to Dr. Steven W. Gyeszly, my advisor, for his guidance, generosity, thoughtfulness and his personal interest to see me through this thesis. Without his kind assistance this thesis would not have been completed. I would like to express my appreciation to Dr. Wayne Clifford who developed the model for this thesis and served as a member of my committee. I wish to thank Dr. James Goff, director of the School of Packaging, and Dr. Gunilla Jonson for their support and encourage- ment. I am grateful to Dr. Richard Nicholas for his willingness to serve as a member of my committee. I also give recognition and thanks to Thomas Bussell who contributed help, assistance and friendship. iii TABLE OF CONTENTS Page LIST OF TABLES O O O O O O O O O O O I 0 O O 0 v LIST OF FIGURES . . . . . . . . . . . . . . . vi INTRODUCTION . . . . . . . . . . . . . . . . 1 Objectives . . . . . . . . . . . . . . . 4 LITERATURE REVIEW . . . . . . . . . . . . . . . 5 DEVELOPMENT OF A MATHEMATICAL MODEL FOR THE PREDICTION OF FOOD PRODUCT SHELF-LIFE . . . . . . . . . . . 9 EXPERIMENTAL . . . . . . . . . . . . . . . . 17 Preparation of Cereal Package Samples . . . . . . 17 Determination of Initial Moisture Content . . . . . 17 Determination of Moisture Gained and Total Moisture Content of the Samples . . . . . . . 17 Determination of Permeability Constant . . . . . . 18 Determination of Volume of Headspace Gas . . . . . 19 Determination of Adsorption Isotherms . . . . . . 20 SAMPLE OF CALCULATION . . . . . . . . . . . . . 39 Example 1. Determination of Moisture Content by Using the Model to Compare the Result With That of the Experimental Test . . . . . . . . 39 Example 2. Prediction of Cereal's Shelf-Life . . . 41 DISCUSSION AND CONCLUSION . . . . . . . . . . . . 43 SUMMARY . . . . . . . . . . . . . . . . . . 48 REFERENCES 0 O O O I O O O O O O O O O O O O 49 iv 10. LIST OF TABLES Data of test conditions . . . . . . . . Data of permeability constant . . . . . . Volume of headspace gas and package surface area Data of adsorption isotherms . . . . . . Data of initial moisture content, adsorption isotherms, intercept and slope . . . . . Increase of moisture content of cereal A in accelerated and room testing conditions . . Increase of moisture content of cereal B in accelerated and room testing conditions . . Increase of moisture content of cereal C in accelerated and room testing conditions . . Time ratio of room and accelerated conditions Percentage difference of moisture content from actual experimental results and model calculated results . . . . . . . . . Page 21 21 21 22 23 24 25 26 27 28 Figure 1. 2. 10. ll. 12. Moisture content (3 mil) 0 o 0 Moisture content (1% mil) . Moisture content vs. Moisture content vs. (3 mil) . . . Moisture content vs. (1%,mil) . . . Moisture content vs. Moisture content vs. (3 mil) 0 o 0 Moisture content vs. (1% mil) . . . Moisture content vs. Adsorption isotherms Adsorption isotherms LIST OF FIGURES Page time of cereal A in PE 0 O O O O O O 0 O O O O 33 time of cereal A in PE 0 O O O O O C I O O O O 33 time of cereal A in Saran . . . 33 time of cereal B in PE 0 O O O O I O O O O O O 34 time of cereal B in PE 0 O O O O O O O O O O O 34 time of cereal B in Saran . . . 34 time of cereal C in PE 0 O C O O O O O 0 O O C 35 time of cereal C in PE 0 O O I O C O C O O O O 35 time of cereal C in Saran . . . 35 of cereals at 100°F . . . . 36 of cereals at 76.5°F . . . . . 37 O O O O 0 O O O O 38 Samples in humidity chamber vi INTRODUCTION Basically, the functions of a package are to contain, to carry, to preserve, to communicate and to display. Protection of the product's qualities from the storage environment is the major concern in most cases. The rational selection of packaging materials to insure optimal protection requires knowledge of the functional properties of the packaging materials and the packaging requirements to the food. Cereals may lose their appeal for a variety of causes, but one of the most important is the loss of crispness resulting from adsorption of moisture from the environment. In addition, adsorption of water vapor also indirectly promotes chemical and/or biological changes to the cereals. Permeability of packaging materi- als to water vapor is the most important criterion for this research to follow when assessing the performance of cereal packages; the choice of packaging material will affect the shelf-lives of the cereals directly. Shelf-life is a term generally used to denote the length of time a packaged product will remain useful and of acceptable and salable quality when it is subjected to various factors encountered in its channels of distribution. Shelf-life depends on a large number of factors, such as temperature, relative humidity, water vapor permeation rate of the package, package configuration, water vapor adsorption of the product, etc. For cereals packed in flexible pouches, the rate of water vapor permeation and the adsorption iso- therms of those cereals are the two particular factors responsible for the eventual unacceptability of the product. The adsorption isotherm of a cereal is best described as a plot of the amount of water adsorbed as a function of the equilibrium relative humidity surrounding the material. The amount of water is that which is held after equilibrium has been reached at a constant temperature. Shelf-life of a food product can be determined in different ways. The most popular method, commonly used in the food industry, is the accelerated test technique. Accelerated conditions have a great effect on the product stability, and properties of the packaging material compare to that of room conditions./7Although water vapor adsorption at higher temperature is less than that at lower temperature and the rate of permeation at higher temperature is greater than that at lower temr perature, according to the fact that the permeability constant which is dependent upon temperature increases exponentially with tempera- ture, the reactions which determine shelf-life at one temperature can become significant at another temperature, and vice versa. For example, an enzymatic reaction becomes dominant at higher tempera- ture rather than at lower temperature;& The influence of high and low humidities on shelf-life may have similar effects, too. It is believed that accelerated testing at high temperature and humidity will be rather inconclusive, since room and accelerated conditions might not have similar effects. No attempt has been made in this research to determine what particular factors are responsible for this inconclusive effect.‘ It was a practical experiment to prove that the accelerated test which is used by the food industry to predict shelf-lives of different products is not suitable. Although shelf-life prediction by an accelerated test tech- nique is commonly used by the food industry, most of the time this technique 18.not applied to all the products. Generally, the food industry predicts shelf-lives of "like" products, such as different cereals, without having actual testing of all the "like" products. They usually base their judgments on past accelerated testing of a product to predict shelf-lives of other "like" products. Actual testing of all the "like" products is not commonly performed because to carry out even accelerated tests for all the products is very costly and takes a lot of time. Three cereals were chosen for this research, two of which were sugar-coated. The ring-shaped, sugar-coated cereal was named cereal A. The regular flake-shaped, sugar-coated cereal was named cereal B. Cereal C was the name designated for the nonsugar-coated cereal. Three different cereals were chosen because they have dif- ferent abilities of adsorbing water vapor. Because adsorption of water vapor affects the storage lives of the cereals, different storage lives can be expected. Polyethylene of two thicknesses (3 mil and 1—1/4 mil) and Saran (1 mil thickness) were used as packaging films, even though cereals in the market are not actually packaged in plastic pouches. The purpose of selecting such films was to show that different films have different effects on the storage lives of the products. Polyethylene of different thicknesses will have different rates of water vapor permeation, depending upon the thickness. The thicker film will have a lower rate of perme- ation than the thinner one because the permeation rate is inversely proportional to the thickness. Saran, which has the lowest permeation to water vapor when compared to other films of the same thickness, can be expected to give the longest storage life from the standpoint of protection against water vapor. A mathematical model was developed for the prediction of cereals' shelf-lives. The model includes the theoretical considera- tions that are important to the prediction of cereals' shelf—lives. Those are the rate of water vapor permeation through the packaging film, moisture in the headspace, and water vapor adsorption of the cereals. The model developed was so simple that it enables the rapid prediction of storage life and it is also possible to apply for package design and optimization. Objectives The objectives of this study are: (i) To prove that the accelerated test technique is not accurate for the prediction of cereals' shelf-lives. (11) To show that a simple mathematical model can be used for the prediction of cereals' shelf-lives. LITERATURE REVIEW Prediction of shelf—life in a given food package combination and the related problem of prediction of packaging protection required for a given food to be stored for a specific time are of importance to the food industry. Shelf-life can be determined in different ways. The first, traditional method involves actually testing the product, ‘held under normal conditions, for loss or gain of moisture, loss of flavors, odors or criSpness, and all other factors considered in defining the salability of a product, until it is no longer salable. The major drawback of this method is the time involved before any results are obtained.' To reduce the testing time, an accelerated test technique was introduced. This technique uses high testing temperature and humidity, compared to those of normal conditions. Easter (1953) described how to forecast shelf-life from.an accelera- ted laboratory test. The accelerated test technique assumes the direct relationship of reactions which determine the shelf—life at normal and accelerated conditions. Actual testing of the product is done under normal and accelerated conditions until the product under accelerated conditions is deteriorated or unacceptable. Traditional methods for selection of proper flexible packag- ing materials to insure high quality store for the desired market life of a food product are based essentially on experience and estimation. These methods involved selection of several films which have given good results from previous tests, storage of the food in these films for a number of months, and then subjectively picking the best film from the group. This commonly led to overprotection in many cases and was a very costly procedure in terms of time and manpower expended. These types of studies have been used exclusively in the analysis of storage of foods. A more scientific alternative approach to shelf-life pre- diction and/or packaging protection requirements is the development of a mathematical model to fit all the experimental data. Con- sidering dehydrated foods, since cereals are dehydrated products, dehydrated foods deteriorate through several mechanisms depending on their composition and environment. These include lipid oxidation, nonenzymatic browning, enzymatic hydrolysis, degradation of proteins and other structural polymers leading to toughening, loss of crispness, and caking leading to insolubility (Mizhari et al., 1970; Quast et al., 1972; Quast and Karel, 1972; Heiss and Eichner, 1971a and 1971b; Sapers et al., 1974; Labuza et al., 1972; Rockland, 1969). In a package the food is separated from the external environment by the package film barrier. The major function of packaging is to reduce or eliminate the rate of transportation of water vapor or oxygen through the package barrier into the internal environment. This is because the rate of deterioration depends on the conditions of the internal environment in terms of the partial pressure of water vapor or oxygen. The analysis of the properties of food are necessary in order to make any prediction of storage. For example, an equation for the moisture content as a function of water vapor pressure or oxygen pressure in the package is necessary, as well as an equation for the rate of transport of water vapor pressure or oxygen pressure in the package, and also an equation for the rate of tranSport of water vapor or oxygen across the package barrier as a function of the vapor pressure difference across the barrier. Many studies have been done in the past in which storage life and/or packaging protection requirements have been calculated on the basis of certain properties of the food or package. Oswin (1946), Heiss and Eichner (1971b), Caurie (1970 and 1971), and Iglesias et al. (1975) developed some models for prediction of shelf-life on the basis of adsorption of water by the food to some critical level of moisture content. Labuza et a1. (1972) reviewed some mathematical models which could be used to predict packaging requirements on the basis of film properties, and the basic physical/ chemical properties of several space rations. Similar types of models were develOped by many experts, not only for dehydrated foods but for other foods as well. Quast et al. (1972) and Quast and Karel (1973) developed a mathematical model simulating shelf-life of potato chips. Quast and Karel (1972) developed a computer simulation of storage life of foods undergoing spoilage by two interacting mechanisms. Mizhari et a1. (1970) and Karel et a1. (1971) developed a computer model for dehydrated cabbage. Henig-(1975) developed a mathematical model representing the changes in reSpiratory gas con- centrations within fresh potato packs. However, according to the author's knowledge, no article has been found which describes the comparison of the cereal shelf-life determination method of accelera- ted testing to that of prediction by a mathematical model. The use of mathematical models is significantly better than a hit-or-miss type of study and allows much more confidence in choos- ing a package. The use of the models also takes much less time than packaging study methods previously used, being economical as well as a good tool. DEVELOPMENT OF A MATHEMATICAL MODEL FOR THE PREDICTION OF FOOD PRODUCT SHELF-LIFE Permeation of gas and vapor through glass and metal is con- sidered to be negligible, while paper has extremely high permeation to both gas and vapor. In contrast, all plastics are permeable to gas and vapor in some degree, depending upon the nature of the per- meant, nature of the film, temperature, partial pressure difference, and so on. Because a number of excellent reviews exist on perme- ation (Lebovits, 1966; Major and Kammermeyer, 1962; Reeves and Kil- gore, 1964; Rogers, 1964), this will be briefly described. Permeation may be described as a gas or vapor dissolving into one side of a membrane under pressure or concentrated driving force, diffusing across the membrane under a concentration gradient and desorbing from the low-pressure side. The rate of water vapor permeation through_the packaging material at a given time is inversely proportional to the thickness and directly proportional to the per- mability constant, package surface area and pressure difference (Gyeszli, 1971). This can be expressed as a“; = 133090“? (1) where M = amount of water vapor permeated across the film, gm, t = time, sec, 10 P = permeability constant of the film, 2 , (sec)(cm )(Aatm) A = surface area of the film, cmz, x = film thickness, cm. Assumptions were made when the equation was derived. (1) Permeability constant is independent of the filmis thickness and water vapor partial pres- sure difference between the two sides of the film. (ii) Thickness of the films was assumed constant; the films did not swell upon the exposure of high relative humidity or moisture content. (iii) When a film was determined to have any defi- nite thickness, it was assumed that the film of the same roll has the same thickness, even though unevenness of the film's thickness can occur. (iv) Water vapor was performing as an ideal gas. Due to the many assumptions applied to the equation, errors were expected when compared to the actual test data. It was con- sidered that these assumptions are appropriate since the purpose of this research is to develop a model that is simple and practically useful and at the same time gives adequate prediction. Generally, it is easier to measure the percent relative humidity than to measure the water vapor pressure. Relation between the water vapor pressure and the percent relative humidity is given by Equation (2). 11 where P = water vapor pressure at a temperature, atm, PS = saturated water vapor pressure at a temperature, atm, H = percent relative humidity. Assume that the temperature inside and outside the package is the same; the rate of permeation can be expressed by Equation (3), P . %=§-%-1—6§5(H0-ni) (3) where HO = percent relative humidity outside the package, Hi = percent relative humidity inside the package. The amount of water vapor transported across the package film will spread out in the headspace of the package and equilibrate with the food. The water vapor is then adsorbed by the food. The amount of water adsorbed depends on the internal water vapor pres- sure or the equilibrium relative humidity inside the package. When the amount of water adsorbed is plotted against the equilibrium relative humidity, this is called the adsorption isotherm of the food. Labuza (1968) described the theoretical fundamentals of iso- therm equations in the analysis of packaging kinetics. The simplest equation of all is the equation of straight line. Since the data of adsorption isotherms within the range of 10-50% RH on Figures 10 and 11 can be fitted relatively well by straight lines, a straight line equation was then applied for this model. The straight line equa- tion is expressed as, 12 m=a+bH (4) where m = water vapor adsorbed/dry solid, Z, a = intercept of the straight line on Y-axis, Z water vapor adsorbed, water vapor adsorbed relative humidity ’ b = slope of the straight line, i H = percent relative humidity. If W is the amount of dry solid weight of the product, the amount of water vapor adsorbed (m1) can be expressed as m1 = (a + NH) I36 (5) Labuza et a1. (1972) assumed that all of the water vapor transported across the package was solely adsorbed by the food material because the water vapor will rapidly equilibrate with the food. One must not ignore that there is water vapor distributed in the headspace, too, even though this is a very small amount. The amount of water vapor in the headspace is the number of water mole- cules. This can be determined by using the Ideal Gas Law, n = -1- (6) where :1 ll number of water vapor molecules in the headSpace, P. = water vapor pressure inside the package, atm, < ll volume of the headspace gas, c.c., l3 _ _ (c.c.)(atm) R gas constant, - 82.06 (°C)(moles) , T = absolute temperature, °K. Since 1 mole of water vapor weighs 18 gm, and the water vapor pres- sure can be expressed in terms of relative humidity, Equation (6) can be expressed as — o 1 O V m2 ‘ 18 Ps 100 RT (7) where m2 = amount of water vapor in the headspace, gm, P = saturated water vapor at temperature inside the package, atm, percent relative humidity inside the package. :1: II The total amount of water vapor (M) inside the package is the sum of the amount of water vapor adsorbed by the product and water vapor in the headspace. Dr, M = m1 + m2 (8) From Equations (5) and (7), W PS V M = (a + bHi) 1'66"}- 18 ' T66 ' Hi ° E] (9) The rate of water vapor permeation equals the changes in water vapor content inside the package with time, or, 14 Rate of = :1_ (total amount of H O permeation dt inside the package) From Equations (3) and (9), we have, P P - A s d W s V P x 100 (Ho-H1) ’ dt (3+bH1) 100 + [18 100 Hi RT (10) In Equation (10), relative humidity inside the package is the only factor that varies with time; the others remain constant, so, §.A._Ps_(H_H)= 18.Ps.1+.1>1fl x 100 0 i 100 RT 100 dt Or P — A s dHi P E’ 100 = (H - H ) dt P o i 180—..s_.c_v_+.l)y_ 100 RT 100 Let p . A...jEL x 100 J = P s V bW [18 100 RT + 100] So dHi 'PET = J (H0 - H1) dH 1 - H _ H - J dt Integrate Hi or where 2!: ll Equation (12) can be content which can be 15 from 0 to t sec, t J dt 0 eJt (11) H - H 1 o 1 l J 1n H (12) O - H1(t)J percent relative humidity outside the package, initial percent relative humidity inside the package, percent relative humidity inside the package at time t see, time for the relative humidity inside the package to reach the value of Hi(t)’ sec, constant. used to find the time to reach a given unisture expressed in percent relative humidity as well from the adsorption isotherm of that food. Once the critical mois- ture content or critical relative humidity of the package product is established shelf-life of the product can then be determined. Inversely, if the shelf-life and critical moisture content of the product are established, this equation can be used to select the 16 appropriate packaging material as well. By inserting the estab- lished valueszhathe equation, J-value can be determined. Once the J-value is known, the permeability constant can be determined. Then one can find out if there is any packaging material that possesses the same permeability constant as determined. The pack- aging material that possessed the same permeability constant as determined should be selected as the packaging material for the product. By using this technique, the packaged product will have a shelf-life as established without being overprotected. EXPERIMENTAL Preparation of Cereal Package Samples Cereal samples weighing from 20 to 30 gm were packed in three films having the same size of 14-1/2 X 17 cm pouches and heat sealed. Thirty samples of each product in each film were prepared. Determination of Initial Moisture Content Initial moisture content of the three cereals was determined by using the Cenco Moisture Balance. Approximately 5 g of cereal sample were exposed to infrared radiation which provides temperatures of varying degrees. Cereal A.was exposed to infrared radiation at 300°F while cereals B and C were exposed at 240°F for 11, 10, and 12 min, respectively. The percentage of moisture content was determined by reading of the loss of weight of the sample due to the loss of moisture content. Moisture content was expressed in the unit of g. moisture 100 g. dry solid . Results are in Table 5. Determination of Moisture Gained and Total Moisture Content of the Samples Half of the prepared samples were hung in a walk-in control- lable chamber. Temperature and humidity of the chanber'were set at 100°F and 70% RH. This was designated as the accelerated testing conditions. The other half of the samples were hung in a chamber having a temperature of 76.5°F and 50% RH by average. This was 17 18 assigned as the room testing conditions. The samples were hung in such a manner that they would not touch each other or the chamber walls. This was to insure that each package had full exposure to the testing conditions. (See Figure 12.) Measurement of weight gained was made periodically. Weight gain of samples was the average of fifteen samples and expressed in g. moisture 100 g. dry solid. periods was the sum of the initial moisture content and the averaged Total amount of moisture at different the unit of weight gain of those periods. Results are in Tables 6-8. The total moisture content of the samples and the time were plotted. The plots of moisture content and time of the same cereal packed in the same film but stored in the two testing conditions were made on the same figure so that the time ratio of the two conditions can be determined (see Figures l-9). The time ratio was determined by drawing a straight line from the axis of moisture content parallel to the axis of time passing the curves of accelerated and room conditions. The straight line drawn must pass the curves of accelerated and room conditions. At the points where the straight line passes the curves, the time of accelerated and room conditions was read. By dividing the time at room condition by the time at accelerated conditions, the time ratio can be obtained. Results are in Table 9. Determination of Permeability Constant Dow Chemical Company which was the film supplier provided the water vapor transmission rates of the three films. Water vapor trans- mission rates were determined by using standard method ASTM E96-66, 19 for both room and accelerated conditions. These rates were con- 2 ’ (sec)(cm )(A atm) verted to permeability constant, having the unit of by assuming that the partial pressure of water vapor inside the test dish is 0 atm. The assumption was based on the fact that adsorption of moisture by the desiccant at partial condition is much greater than the diffusion of moisture through the barrier. Results are in Table 2 . Determination of Volume of Headspace Gas The method used resembles that of Griffin (1972). The cereal package was weighed suspended in water at atmospheric pres- sure. Then it was transferred and sunk in a vacuum desiccator carrying water. The pressure in the desiccator was then reduced until the gases in the package expanded sufficiently to create a condition of neutral buoyancy. The volume of the gas was then cal- culated from the difference in pressure (atmospheric vs. neutral buoyancy) and the weight of the package suspended in water at atmospheric presSure. Result is in Table 3. Some errors can be expected from this method, because the volume of headspace gas was determined when the packages were in full expansion, while the package for actual storage test did not expand. Although the error can be relatively high, this will have little effect on the result of the calculation, because most of the water vapor in the package will be adsorbed rapidly by the cereal compared to the very small amount of water vapor left in the 20 headspace gas of the package. This can be seen in the sample of cal- culation, Example 1. Moisture content of the headspace is 0.000046 gram, while the amount of moisture adsorbed by the cereal is 0.0167 gram. Headspace moisture content accounts for less than lZ of the moisture adsorbed by the cereal. In addition, this method is the only practical method available to the author's knowledge. Determination of Adsorption Isotherms The adsorption isotherm of each product was determined by using saturated aqueous solutions of salts in contact with an excess of the definite solids phase. Samples of cereals weighing approxi- mately 7 g were placed in an enclosed container over a saturated aqueous solution of a salt maintained at a definite Z RH and temp perature. Saturated aqueous solutions were prepared to obtain dif- ferent Z relative'humidities. (See Table 4.) When equilibriumwwas reached, the moisture content of the samples was determined using Cenco Moisture Balance. To obtain the adsorption isotherms the moisture contents were plotted against the corresponding Z relative humidities. Adsorption isotherms of the three cereals were determined for both temperatures: 100°F and 76.5°F. Results are in Table 4. The plots of adsorption isotherms of the cereals are in Figures 10 and 11. DATA Table 1.——Data of test conditions. Accelerated Room Condition Condition Temperature (°F) 100 76.5 Relative Humidity (Z) 70 50 Saturated vapor pressure (atm.) 0.065 0.031 Table 2.--Data of permeability constant. Test Conditions Packaging Films Permeability constant __ (g. H20)(cm) } P, 2 (A atm)(sec)(cm )J' Accelerated PE (3 mil) 4.87 X 10.-10 PE (1% mil) 5.24 x 10’10 Saran 9.53 x 10"11 -10 Room PE (3 mil) 1.41 X 10 PE (11 mil)’ 1.41 x 10’10 Saran 2.35 X 10-11 Table 3.-4Volume of headspace gas and package surface area. The average value of headspace gas was 200 c.c. The average package surface area was 493.084 cm.2 21 Table 4.——Data of adsorption isotherms. 22 Moisture Content g. moisture ] (100 g. dry solid] Test Condition Chemical Z RH Cereals A B‘ c 100°F LiC2(l) 11.1 2.04 1.21 2.56 (l) K0211302 20.4 2.61 1.83 3.52 MgC£2(l) 31.9 3.09 2.46 4.11 Cr03(1) 40.2 3.31 2.97 5.04 KN02(2) 45.9 3.90 3.30 5.54 (2) Na20r207 50.0 4.00 3.84 6.10 NaN02(2) 61.8 6.04 5.93 -- o (2) 76.5 F ZnCRz 10.0 2.25 1.52 2.56 LiC£(2) 15.0 2.30 1.68 2.75 (2) K02H302 20.0 2.67 2.25 2.99 CaC£2(2) 32.3 3.09 2.67 3.90 Cr03(2) 35.0 3.47 2.97 5.04 KN02(2) 48.6 4.07 3.57 5.26 (2) NaZCrZO7 54.1 4.38 3.83 6.61 NaN02(2) 64.8 7.18 6.61 9.53 (l) Wink and Sears 1950. (2) International Critical Tables. 23 Table 5.--Data of initial moisture content, adsorption isotherms, intercept-and slope. Initial Moisture Content Intercept Slope Test Condition Cereal ‘ g. moisture a b 100 g. dry solid Accelerated A 3.44 1.49 0.051 B 2.69 0.44 0.066 C 1.85 1.67 0.083 Room A 3.44 1.66 0.049 B 2.69 0.995 0.054‘ C 1.85 1.71 0.071 waw.m Ho.N on.c Ho.m «OH.¢ Ho.N 24 mow.m NN.H Num.¢ NN.H moo.q NN.H NNo.m oo.H mom.q oo.a omu.m oo.a oom.m Nu.o Hoo.¢ mm.o mmo.m Nu.o mmq.m o nmq.m o nmq.m o ZOHHHQZOU ome¢mmamou< wqw.m No.mm mmo.q ON.mm oan.m mo.wm qmq.q Nm.mm me.m mo.w~ oom.m om.NN NH<.¢ oo.mH oqm.m Nm.NN qa~.m oo.©H Hmm.m om.m wow.m 00.0H mmq.m o qu.m o umq.m o 6:8 NS .w 02 6:8 .36 .w 02 III! 336, he .w d2 H chaumHoE .wg Amxmmv fl musumfioa .wg Amxmov H mhsumwoa .wH Amzmov ucmucoo musumflos MEHH ucmucoo mpsumfioa mZHH ucmucoo mudumwofi mZHH H 836m - as 8.3 mm SE 3 mm ZOHHHQZOU Zoom .mcoauaocoo wcfiummu Eoou was omumuoawoom ca < Hmmumo mo ucwucoo wuaumwoa mo mmmmuucHnl.o mHQmH mao.m oo.~ ~ma.m . co.~ Hum.m oo.~ 25 «No.m HN.H oqw.m Hm.H oam.m HB.H www.~ oo.H onm.m oo.H «No.m oo.H o~w.~ Hm.o nnH.m Hm.o mqm.N Hw.o mme.~ o wwo.~ o wwe.N o ZOHHHQZOU ame