packing

Chapter15Packaging Concepts

Developments in food packaging have evolved in response to theneed for protection of the food product from both external andinternal environments and in response to consumer expectations forconvenience and product safety. A recent survey indicated that 72% ofconsumers in the United States are willing to pay extra for guaranteedproduct freshness delivered by the type of packaging. Many newpackaging developments have focused on extending the shelf lifeof the product and on delivering a higher quality product to the con-sumer. These developments would not be possible without significantadvances in the materials used in packaging and the incorporation ofvarious types of sensors into food packaging.

15.1 INTRODUCTIONHistorically, the packaging of foods has evolved in response to a varietyof expectations. The functions of packaging for food have been docu-mented by Yam et al. (1992), March (2001), Robertson (2006), andKrochta (2007). The four basic functions of a food package are:

Containment Protection Communication Convenience

Containment is defined by the food product, with different types ofpackages required for liquids as compared with solids or dry powders.Product protection is a key function for most packages in order tomaintain the quality and safety of the food. The communication

All icons in this chapter refer tothe authors web site which isindependently owned andoperated. Academic Press is notresponsible for the content oroperation of the authors web site.Please direct your web sitecomments and questions to theauthor: Professor R. Paul Singh,Department of Biological andAgricultural Engineering,University of California, Davis,CA 95616, USA.Email: [email protected] 767

function is most obvious in the various types of information presentedon the outside surface of packages, including simple product descrip-tions and details of product composition. The convenience of manyfoods is highly dependent on package design. These four basic func-tions of food packages take on different levels of importance with differ-ent food products. Additional factors that can impact packaging includeefficiency in package manufacturing, the impact of the package on theenvironment, and level of food safety provided by the package.

15.2 FOOD PROTECTIONThe degree of protection required by a food product is a key factor inselecting the packaging material and design. Figure 15.1 summarizesthe role of the food package in this regard. In general, protectionis defined in terms of a variety of factors that can impact the qualityattributes of the food product from the time the product is placedin the container to the time of consumption. Environmental para-meters such as oxygen, nitrogen, carbon dioxide, water vapor oraromas, in direct or indirect contact with the product, are influ-enced by the package properties. Many foods are sensitive to the

Oxidation, color,flavor, respiration

FoodPackagingwall

Environment

Oxygen

Carbon dioxide

Water vapor

Water vapor

Aroma

Light

Respiration,carbonation loss

Dehydration,texture change

Stickiness, texturechange, microbialgrowth

Aroma and/or flavorchange

Color, flavor,nutrient degradation

Aroma and/or flavorchange, toxicity

Aroma and/or flavorloss

Oxygenpermeation

Carbon dioxidepermeation

Water vaporpermeation

Water vaporpermeation

Aromapermeation

Lighttransmission

Packagecomponentmigration

Absorption(scalping)

Figure 15.1 Interactions among the food,the package, and the environment. (Adaptedfrom Linssen and Roozen, 1994)

768 CHAPTER 15 Packaging Concepts

oxygen concentration in the immediate environment due to thedeterioration associated with oxidation. The shelf life of fresh foodcommodities is impacted by concentrations of carbon dioxide indirect contact with the product. In a similar manner, the watervapor concentration in the environment in direct contact with a dryand/or intermediate moisture food must be controlled. In all situa-tions, the properties of the packaging material have a significantrole in establishing the shelf life and quality of the product reachingthe consumer.

15.3 PRODUCT CONTAINMENTThe function of the package in containing the food product is directlyrelated to the packaging material. A variety of materials are used forfood packages including glass, metals, plastics, and paper. Each materialhas unique properties and applications for food packaging.

Glass containers for foods provide an absolute barrier for gases, watervapors, and aromas but do not protect products with sensitivities tolight in the environment surrounding the product package. A majordisadvantage of glass is weight compared with other packagingmaterials.

Metal containers are used for a significant number of shelf-stablefood products such as fruits and vegetables, and offer an excellentalternative to glass containers. The metals used include steel, tin, andaluminum, with each representing a unique application for foods orbeverages. Due to structural integrity, metal containers have beenused for thermally processed foods, with many applications for foodsprocessed in retorts at high temperatures and pressures. Metal con-tainers are relatively heavy, and the container manufacturing processis complex.

Plastic packaging materials are used for an increasing number andvariety of food products. Most plastic packaging materials are eitherthermoplastic or thermoset polymers. Thermoplastic polymers arethe basic material used for a large number of food products, and pro-vide significant flexibility in package design based on the specificneeds of the food. Plastic films are lightweight and provide anunobscured view of the product within the package. The permeabilityof polymers to oxygen, carbon dioxide, nitrogen, water vapor, andaromas provides both challenges and opportunities in the design ofpackaging materials for specific food requirements.

76915.3 Product Containment

Due to its broad use in all levels of packaging, paper is used for foodpackaging more than any other material. It is the most versatile andflexible type of material. Its key disadvantage is the lack of a barrierto oxygen, water vapor, and similar agents that cause deterioration ofproduct quality.

15.4 PRODUCT COMMUNICATIONThe package of a food product is used to communicate informationabout the product to consumers. This information is presented onthe label and includes both legally required information about theingredients and information needed to market the product.

15.5 PRODUCT CONVENIENCEA variety of designs have been incorporated into food packages in aneffort to increase convenience. These designs include innovation inopening the packages, dispensing the product, resealing the package,and the ultimate preparation of the product before consumption.Convenience will continue to provide innovation in the future.

15.6 MASS TRANSFER IN PACKAGING MATERIALSAn important requirement in selecting packaging systems for foodsis the barrier property of the packaging material. To keep a foodproduct crisp and fresh, the package must provide a barrier to moisture.Rancidity can be minimized by keeping a food protected from light.To reduce oxidation of food constituents, the packaging material mustprovide a good barrier to oxygen. The original aroma and flavor of afood can be maintained by using a packaging material that offers a bar-rier to a particular aroma. Thus, properly selected packaging materialsare beneficial in extending the shelf life of foods. The barrier propertiesof a packaging material can be expressed in terms of permeability.

The permeability of a packaging material provides a measure of howwell a certain gas or vapor can penetrate the packaging material. Inquantitative terms, permeability is the mass of gas or vapor transferredper unit of time, area, and a driving force. In the case of diffusionalmass transfer, the driving force is a difference in concentration or inpartial pressures. If the driving force is a difference in total pressure, themass transfer occurs due to bulk flow of a gas or vapor. A polymericmembrane may be thought of as an aggregate of wriggling worms, with


worms representing the long chains of polymers. The space betweenthe worms is like the interstitial space through which a species passes.The wriggling of worms is representative of the thermal motion ofpolymeric chains.

Mass transport through polymeric materials can be described as astep process. Referring to Figure 15.2, in step 1, the gas vapor or liq-uid molecules dissolve in the polymeric material on the side of thefilm exposed to the higher concentration. In step 2, the gas or vapormolecules diffuse through the polymeric material moving toward theside of the film exposed to the lower concentration. The movementof molecules depends on the availability of holes in the polymericmaterial. The holes are formed as large chain segments of thepolymer slide over each other due to thermal agitation. Finally,step 3 involves the desorption of the gas or vapor molecules andevaporation from the surface of the film.

We can again use Ficks law of diffusion to develop an expression forthe transport process of a gas through a polymeric material. FromEquation (10.11):

_mBA5

DBcB12 cB2x22 x1

15:1

This equation would be sufficient to determine the rate of flux,_mB=A, but the concentrations of a gas at the film surfaces are moredifficult to measure than partial pressures. The concentrations can beconverted to partial pressures by using Henrys law,

c5 Sp 15:2

Polymericfilm

Lowerconcentrationof a gas

Higherconcentrationof a gas

Figure 15.2 Mass transfer of a gas througha polymeric material.

77115.6 Mass Transfer in Packaging Materials

where S is solubility (moles/[cm3 atm]) and p is partial pressure ofgas (atm). Thus, we have

_mB5DBSApB12 pB2

x22 x115:3

The quantity DBS is known as the permeability coefficient, PB.

PB5amount of gas vaporthickness of film

areatimepressure difference across the film 15:4

A wide variety of units are used to report the permeability coefficient(Table 15.1).

Another parameter used by some authors is permeance, which is notcorrected to a unit thickness. Sometimes permeance to water vaporis reported in units that are neither corrected to unit thickness nor tounit pressure, but this value must always be reported with specifiedthickness, humidity, and temperature. For example, water vaporpermeability is defined as grams of water per day per 100 cm2 of

Table 15.1 Conversion Factors for Various Units of PermeabilityCoefficient

cm3 cmscm2 cmHg

cm3 cmscm2 Pa

cm3 cmdaym2 atm

cm3 cms cm2 cmHg

1 7.53 1024 6.573 1010

cm3 mms cm2 cmHg

1021 7.53 1025 6.573 109

cm3 mms cm2 atm

1.323 1022 9.93 1026 8.643 108

cm3 mildaym2 atm

3.873 10214 2.93 10217 2.543 1023

in3 milday100 in2 atm

9.823 10212 7.373 10215 6.463 1021

cm3 cmdaym2 atm

1.523 10211 1.143 10214 1

Source: Yasuda and Stannett (1989)


package surface for a specified thickness and temperature and/ora relative humidity on one side of approximately 0% and on theother side of 95%.

15.6.1 Permeability of Packaging Materialto Fixed Gases

Gases such as oxygen, nitrogen, hydrogen, and carbon dioxide, whichhave low boiling points, are known as fixed gases. They show similarideal behavior with respect to permeability through packaging materi-als. The permeability of O2, CO2, and N2 for several polymeric materi-als is shown in Table 15.2. It is evident that for any given gas there existmaterials with widely differing permeabilities. For example, Saran is

Table 15.2 Permeability Coefficients, Diffusion Constants, and Solubility Coefficients of Polymersa

Polymer Permeant T[8C] P3 1010 D3 106 S3 102

Poly(ethylene) (density 0.914) O2 25 2.88 0.46 4.78CO2 25 12.6 0.37 25.8N2 25 0.969 0.32 2.31H2O 25 90

Poly(ethylene) (density 0.964) O2 25 0.403 0.170 1.81CO2 25 1.69 0.116 11.1CO 25 0.193 0.096 1.53N2 25 0.143 0.093 1.17H2O 25 12.0

Poly(propylene) H2 20 41 2.12N2 30 0.44O2 30 2.3CO2 30 9.2H2O 25 51

Poly(oxyethyleneoxytere-phthaloyl) (Poly(ethylene terephthalate)) crystalline

O2 25 0.035 0.0035 7.5N2 25 0.0065 0.0014 5.0CO2 25 0.17 0.0006 200H2O 25 130

Cellulose acetate N2 30 0.28O2 30 0.78CO2 30 22.7H2O 25 5500

(Continued)


Table 15.2 (Continued)

Polymer Permeant T[8C] P3 1010 D3 106 S3 102

Cellulose (Cellophane) N2 25 0.0032O2 25 0.0021CO2 25 0.0047H2O 25 1900

Poly(vinyl acetate) O2 30 0.50 0.055 6.3

Poly(vinyl alcohol) H2 25 0.009N2 14

b , 0.00114c 0.33 0.045 5.32

O2 25 0.0089CO2 25 0.012

23b 0.001 19023d 11.9 0.0476

ethylene oxide 0 0.002

Poly(vinyl chloride) H2 25 1.70 0.500 2.58N2 25 0.0118 0.00378 2.37O2 25 0.0453 0.0118 2.92CO2 25 0.157 0.00250 47.7H2O 25 275 0.0238 8780.0

Poly(vinylidene chloride) (Saran) N2 30 0.00094O2 30 0.0053CO2 30 0.03H2O 25 0.5

Poly[imino (1-oxohexamethylene)](Nylon 6)

N2 30 0.0095O2 30 0.038CO2 20 0.088

30b 0.1030e 0.29

H2O 25 177

Poly[imino(1-oxoundecamethylene)](Nylon 11)

CO2 40 1.00 0.019 40

Source: Yasuda and Stannett (1989)Notes: See overleaf.aUnits used are as follows: P in [cm3 (STP) cm cm22 s21 (cm Hg)21], D in [cm2 s21], and S in [cm3 (STP) cm23 atm21]. To obtain correspondingcoefficients in SI units, the following factors should be used: P3 7.53 10245 [cm3 (STP) cm cm22 s21 Pa21]; S3 0.9873 10255 [cm3 (STP)cm23 Pa21]bRelative humidity 0%.cRelative humidity 90%dRelative humidity 94%eRelative humidity 95%


100,000 times less permeable to oxygen than silicone rubber.Moreover, there are certain regularities in the transmission of differentgases through the same material. For example, carbon dioxide perme-ates four to six times faster than oxygen, and oxygen four to six timesfaster than nitrogen. Since carbon dioxide is the largest of the three gasmolecules, we would expect its diffusion coefficient to be low, and it is.Its permeability coefficient is high because its solubility S in polymersis much greater than that for other gases.

Fixed gases also show ideal behaviors:

1. Permeabilities can be considered independent of concentration.

2. The permeabilities change with temperature in accordancewith the following relation:

P5 Poe2Ep=RT 15:5where Ep is the activation energy for permeability (kcal/mol).

For some materials there is a break in the permeability temperaturecurve, and above a critical temperature the material is much morepermeable. For polyvinyl acetate, that temperature is around 308Cand for polystyrene it is around 808C. Breaks are due to a glasstransition temperature T 0g , below which the material is glassy, andabove which it is rubbery.

Example 15.1The permeability coefficient for a 0.1-mm polyethylene film is being mea-sured by maintaining a moisture vapor gradient across the film in a sealedtest apparatus. The high moisture vapor side of the film is maintained at 90%RH and a salt ZnClU12H2O maintains the opposite side at 10% RH. The area offilm exposed to vapor transfer is 10 cm by 10 cm. When the test is conductedat 308C, a weight gain of 50 g in the desiccant salt is recorded after 24 h.From these given data, calculate the permeability coefficient of the film.

GivenFilm thickness5 0.1 mm5 13 1024 mHigh relative humidity5 90%Low relative humidity5 10%Temperature5 308CFilm area5 10 cm3 10 cm5 100 cm25 0.01 m2

Moisture rate of flow5 50 g/24 h5 5.7873 1024 g water/s


ApproachWe will use Equation (15.4) to calculate the permeability coefficient (PB) aftervapor pressures are expressed in terms of moisture contents of air.

Solution1. By using Equation (9.16) modified with vapor pressures,

5pwpws

3 100

2. From Table A.4.2,

pws5 4:246 kPa at 308C

3. From steps 1 and 2, at 10% relative humidity,

pw 5 4:2463 10=100

5 0:4246 kPa

At 90% relative humidity,

pw 5 4:2463 90=100

5 3:821 kPa

Using Equation (15.4) and solving for permeability coefficient,

PB5(5:7873 1024 g water=s)(13 1024 m)

(0:01 m2)(3:821 kPa2 0:4246 kPa)(1000 Pa=kPa)

PB5 1:73 1029 [(g water m)=(m2 Pa s)]

4. The permeability coefficient of the film is calculated to be1.73 1029 [(g water m)/(m2 Pa s)]; the units may be converted to anyother form desired using Table 15.1.

15.7 INNOVATIONS IN FOOD PACKAGINGInnovations in food packaging have created an array of new termsassociated with the role of packaging in the improvement of safety,shelf life, and convenience of the food product. There are three broadcategories of packaging for foods: passive, active, and intelligent. Thetwo types of active packaging systems include simple and advanced.Intelligent packaging systems are simple and interactive.


15.7.1 Passive PackagingA passive packaging system is a system that serves as a physical barrierbetween the product and the environment surrounding the package.

Most conventional packaging used for food products would bedescribed as passive packaging systems. Metal cans, glass bottles, andmany of the flexible packaging materials provide a physical barrierbetween the product and the environment. These packaging systemsensure that most properties of the environment and the agents con-tained in the environment are prevented from making contact withthe food. In general, these packages are expected to provide maximumprotection of the product but are not responsive to any of the changesthat might occur within the container.

Innovations in passive packaging systems continue with the develop-ment of new barrier coatings for polymer containers and films. Thesenew materials reduce or control permeability of agents that could impactthe safety or shelf-life of the food product within the container.

15.7.2 Active PackagingAn active packaging system is a system that detects or senses changeswithin the package environment, followed by modification of packageproperties in response to the detected change.

15.7.2.1 Simple ActiveA packaging system that does not incorporate an active ingredientand/or actively functional polymer is referred to as a simple activesystem. An active packaging system responds in some manner tochanges occurring within the package. One of the earliest activepackaging systems was Modified Atmosphere Packaging (MAP).The package materials for MAP have properties that attempt to con-trol the atmosphere within the package in contact with the foodproduct. A simple example is packaging films that help maintaindesired concentration of oxygen and carbon dioxide in a packagecontaining respiring fruits and vegetables.

15.7.2.2 Advanced ActiveA packaging system that contains an active ingredient and/or anactively functional polymer is an advanced active system. Advancedactive packaging systems can be divided into two categories. Theincorporation of an oxygen scavenger into the package is an exampleof a system that absorbs an unwanted agent within the environment

77715.7 Innovations in Food Packaging

of the package and in contact with the product. Usually, scavengers areincluded as small sachets inserted into the package to reduce the levelof oxygen within the package. An alternative to the sachets is the inte-gration of an active scavenging system into packaging materials, such asfilms or closures.

A second example of the absorbing type of system is an ethylenescavenger. Ethylene triggers ripening, accelerates senescence, and reducesthe shelf life of climacteric fruits and vegetables. By incorporating anethylene-absorbing material into the packaging system, the shelf life ofthe product can be extended.

Moisture content or water activity becomes a shelf life limitingfactor for many foods. For these products, the incorporation ofwater-absorbing material into the package can be beneficial. Moresophisticated control may be required within packages for productsrequiring regulation of humidity levels.

Another example of an advanced active packaging system would beMAP with barrier properties in combination with gas flushing to achievea desirable steady-state atmosphere composition around the product.Other active absorbing packaging systems are available to controlconcentrations of undesirable flavor constituents or carbon dioxide.

Advanced active packaging systems are continuing to evolve with thedevelopment of systems designed to release agents in response to unde-sirable activity within the package. For example, in response to microbialgrowth, the release of antimicrobial agents can be used to extend theshelf-life of refrigerated foods. Similarly, antioxidants can be incorpo-rated into packaging films to protect the film and the product within thepackage from degradation. The potential for incorporation of flavorcompounds into a package represents a significant opportunity. Therelease of these compounds during the shelf life of a food product couldmask off-odors or improve the sensory attributes of the product.

15.7.3 Intelligent PackagingA packaging system that senses changes in the environment andresponds with corrective action is defined as an intelligent packagingsystem. Four objectives for intelligent packaging systems have beenidentified:

1. Improved product quality and product value

2. Increased convenience


3. Changes in gas permeability properties

4. Protection against theft, counterfeiting, and tampering

15.7.3.1 Simple IntelligentA packaging system that incorporates a sensor, an environmentalreactive component, and/or a computer-communicable device is asimple intelligent system. Quality or freshness indicators are exam-ples of simple intelligent packaging systems and are used to commu-nicate changes in a product quality attribute. These internal orexternal indicators/sensors may indicate elapsed time, temperature,humidity, time-temperature, shock abuse, or gas concentration. Theprimary function of the sensor is to indicate quality losses duringstorage and distribution. Other sensors are available for changes incolor, physical condition (damage), and microbial growth.

A second type of simple intelligent package system is the time-temperature indicator (Taoukis et al., 1991). Temperature-indicatinglabels are attached to the external surface of the package and reportthe maximum temperature to which the surface has been exposed.Time-temperature integrators provide more refined information byintegrating the impact of time and temperature at the package surface(Wells and Singh, 1988a,b; Taoukis and Labuza, 1989). The disad-vantage of both types of indicators is that the output may not revealthe actual impact on the product.

Internal gas-level indicator sensors are components of a simple intelli-gent packaging system. These sensors are placed in the package tomonitor gas concentrations and provide rapid visual monitoringbased on color changes. In addition to monitoring food product qual-ity, the sensor can detect package damage. Indicators are available formonitoring oxygen (O2) and carbon dioxide (CO2). A variation onthese types of indicators may be used for detecting microbial growthby monitoring for increased CO2 levels.

Simple intelligent package systems for supply chain managementand traceability use automatic data capture during distribution andwith connection to the Internet. Examples include systems to tracecontainers of fruits from the fields to the point of delivery to thecustomer. Currently, Radio Frequency Identification (RFID) tags areattached to bulk containers to provide information on content,weight, location, and times throughout the distribution channels.It is possible that in the future RFID labels will be placed onindividual food packages.

77915.7 Innovations in Food Packaging

Another convenience-type of simple intelligent packaging systemmay be incorporated into intelligent cooking appliance systems.These systems carry essential information about the food productand the package on a bar code and assist appliances by providingpreparation instructions, maintaining food product inventories, andidentifying expiration dates.

15.7.3.2 Interactive IntelligentInteractive intelligent packaging systems incorporate mechanisms torespond to a signal (sensor, indicator, or integrator). For example, aninteractive intelligent packaging system can change permeability proper-ties to accommodate changes in freshness and quality of the packagedfood product during storage and distribution. New and improved intelli-gent breathable films change permeability in response to different freshproduce or changes in temperature of the produce. These packagingfilms have been developed based on knowledge of respiration rates as afunction of temperature. The systems are ideal for high-respiratory-ratefresh and fresh-cut produce.

An evolving expectation for interactive intelligent packaging systemsincludes detection of theft, counterfeiting, and tampering. To accom-plish this, simple intelligent packaging systems could include labelsor tapes that are invisible before tampering but change color perma-nently if tampering occurs. More complex devices would respond tocounterfeiting and theft by using holograms, special inks and dyes,laser labels, bar codes, and electronic data tags.

15.8 FOOD PACKAGING AND PRODUCT SHELF-LIFEThe packaging provided for a food product may have a significantimpact on its shelf-life. These impacts are closely related to the typesof protection provided by the package, as mentioned earlier. Theimpact of the package can be quantified using information on thedeterioration of the product in combination with the type of protec-tion provided by the package. We will first develop mathematicalrelationships that are useful in describing the deterioration of foodproducts during storage.

15.8.1 Scientific Basis for Evaluating Shelf LifeThe scientific basis for evaluating shelf life of a food product relies onprinciples of chemical kinetics (Labuza, 1982; Singh, 2000). In this


section, we will examine changes in a quality attribute, Q, measuredover time. The general rate expression for the quality attribute may bewritten as

6dQdt

5 kQn 15:6

where6 indicates that the quality attribute may increase or decreaseduring storage, k is the pseudo forward rate constant, and n is theorder of reaction. We will first assume that the environmental factorsthat influence shelf life such as storage temperature, moisture, andlight are kept constant.

If the quality attribute decreases with time, then we may writeEquation (15.6) as

2dQdt

5 kQn 15:7

15.8.1.1 Zero-Order ReactionIn Figure 15.3, the measured amount of a quality attributeremaining at different storage times is plotted. The plot is linear,suggesting that the rate of loss of quality attribute remains con-stant over the entire period. This type of behavior is observed inmany shelf life studies, including quality changes due to enzymaticdegradation and non-enzymatic browning. Similar behavior isobserved for lipid oxidation, which often causes the developmentof rancid flavors.

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20

Time, weeks

Qua

lity

attr

ibut

e

Figure 15.3 A linear decrease in theremaining quality attribute plotted against time.

78115.8 Food Packaging and Product Shelf-Life

The linear plot in Figure 15.3 represents a zero-order reaction. Therefore,if we substitute n5 0 in Equation (15.7), then we get

2dQdt5 k 15:8

We can solve this equation using the procedure of separation of vari-ables to obtain an algebraic solution. We will consider that initiallythe amount of quality attribute is represented by Qi and after somestorage time, t, it is Q.

Then,

2

QQi

dQ5 kt0dt 15:9

Integrating, we get,

2jQjQQi5 kt 15:10

or

Qi2 Q5 kt 15:11

In Equation (15.11), the left-hand side denotes the extent of reac-tion, , for a reaction that follows a zero-order kinetics. Thus,

5 kt 15:12

if we specify that the end of shelf life of a food product, ts, is reachedwhen the quality attribute, Q, reaches Qf. Then, from Equation(15.11),

Qf 5 Qi2 kts 15:13

or, the shelf life of a food product based on a quality attribute thatfollows zero-order kinetics is

ts5Qi2 Qf

k15:14

15.8.1.2 First-Order ReactionLet us consider another shelf life study where the measured qualityattribute follows a profile as shown in Figure 15.4. This plot shows


an exponential decrease of the quality attribute. In this study,the rate of loss of quality attribute depends upon the amountof remaining quality attribute. Food deterioration reactions thatshow an exponential decrease include loss of vitamins and protein,and microbial growth as we learned in Chapter 5. The exponentialdecrease in a quality attribute is described by the first-orderkinetics, where the rate of reaction, n5 1. Thus we may rewriteEquation (15.7) as

2dQdt

5 k Q 15:15

We again use the method of separation of variables to integrate thisequation as

2dQQ 5 kdt 15:16

Again, we assume that initially the quality attribute is [Qi] and aftertime t it decreases to [Q], then

2

QQi

dQQ 5 k

t0dt 15:17

Integrating, we get,

2jlnQjQQi5 kjtjt0 15:18

0102030405060708090

100

0 5 10 15 20

Time, weeks

Qua

lity

attr

ibut

e

Figure 15.4 An exponential decrease in theremaining quality attribute plotted against time.


or

lnQi2 lnQ5 kt 15:19

Thus for a first-order reaction, the extent of reaction is determined as

5 lnQi2 lnQ 15:20

We may also rewrite Equation (15.19) as

lnQQi

52kt 15:21

To determine the fraction of quality change after a certain storageperiod, Equation (15.21) may be rewritten as

QQi

5 e2kt 15:22

In Equation (15.21), [Q] is the amount of quality attribute remainingafter a storage time t.

If [Qf] represents the amount of quality attribute at the end of shelflife, then from Equation (15.21) we obtain

ts5lnQiQf k

15:23

Equation (15.23) can easily be modified if we want to knowtime for half-life of a quality attribute. We substitute Qf5 0.5Qi toobtain

t1=25ln 2k5

0:693k

15:24

Equations (15.14) and (15.24) have been used to predict shelf life ofa food product, or the time that would elapse from when the productis placed in storage until the quality attribute deteriorates to anunacceptable level [Qf]. The rate constant (k) has been establishedfor key deterioration reactions in foods, or it can be determined dur-ing shelf life evaluations.


The impact of environmental conditions during product storage isexpressed through the magnitude of the rate constant (k). The mostevident environmental variable is temperature, and the influenceof temperature on the rate constant is expressed by the Arrheniusequation (Eq. (5.9)):

k5Be

2

EARTA

15:25

where the activation energy constant (EA) quantifies the influence oftemperature on the rate of product quality deterioration during stor-age. This expression is used primarily during accelerated shelf lifetesting, when elevated temperatures are used under experimentalconditions to accelerate the deterioration of the product. Theseapproaches allow us to quantify shelf life in a relatively short periodof time (days or weeks) at elevated temperatures, whereas the actualshelf life may be much longer (1 to 2 years).

In most situations, the impact of the package on product shelf lifeis a function of environmental parameters other than temperature.As indicated earlier, the concentrations of oxygen, water vapor,nitrogen, carbon dioxide, and other environmental parameters mayinfluence the deterioration reactions in foods. In order to incorpo-rate the impact of these parameters into the prediction of shelf life,we will need to know the influence of these variables on rate con-stants. These additional relationships are then used in combinationwith expressions describing the transport of the agent across thepackage barrier. These expressions, as based on Equation (15.1) andappropriate permeability coefficients, were presented earlier in thischapter.

Example 15.2A dry breakfast cereal has been fortified with ascorbic acid (Vitamin C).The degradation of ascorbic acid during storage of the cereal is a functionof water activity of the product. The package used for the cereal mustensure that the water activity is maintained at a sufficiently low level topreserve the desired level of Vitamin C.The initial water activity of the cereal is 0.1, and the moisture content is3.0% (d.b.). The relationship between product moisture content and wateractivity was established as

w5 0:175 aw1 0:0075


The rate constant (k) for degradation of ascorbic acid is 1.7013 1025/minat a water activity of 0.1, and the rate constant increases with increasingwater activity according to the following relationship:

k5 2:7333 1025 aw1 1:4283 1025

The package dimensions are 20 cm3 30 cm3 5 cm, and there is 0.5 kg ofproduct in the package. Select the package film permeability, with 1 mmthickness, to ensure that 60% of the original ascorbic acid is retained inthe product after 14 days of storage in an environment with a relativehumidity of 60% and 308C.

GivenProduct initial moisture content (w)5 3.0% (d.b.)Product initial water activity (aw)5 0.1Storage environment relative humidity5 60%Ascorbic acid degradation rate constant (k)5 1.7013 1025/minShelf-life expectation5 14 daysPackage surface area5 0.17 m2

ApproachThe key expression used in the solution is Equation (15.3), with the permeabil-ity (PB)5DBS. The degradation rate of ascorbic acid is used to establish themaximum product water activity allowed to prevent degradation beyond 60%within the 14-day shelf life. Given the maximum allowable water activity, wecan determine the total amount of water that can be added to the productover the 14 days of storage, and the permeability of the package film with agiven thickness.

Solution1. Use Equation (15.22) to determine the average rate constant for the

time period of product shelf life:

0:65 exp [2(kave)(14 days)(24 h=day)(60 min=h)]

kave5 2:533 1025=min

2. Given the relationship between water activity and the rate constant:

2:533 10255 2:7333 1025 aw 1 1:4283 1025

aw 5 0:4


3. In order to determine the amount of moisture change needed toincrease the water activity to 0.4, the water activity must be convertedto moisture content. The typical relationship is given by Equation (12.1),but the relationship for this product for the range of water activitiesbetween 0.1 and 0.4 is

w5 0:175aw 1 0:0075

Given this relationship, the product moisture content at a water activityof 0.4 is

w5 0:175(0:4)1 0:00755 0:0775 or 7:75%(d:b)

4. During the 14 days of storage, the moisture content can increase from3% to 7.75% or

0:07752 0:035 0:0475 kg water=kg product solids

and 0:02375 kg water per package

is the amount of moisture transfer through the package film over aperiod of 14 days. Then the transfer rate becomes

50:02375 kg water

(14 days)(24 h=day)(60 min=h)

5 1:1783 1026 kg water=min

5. Using Equation (15.3):

PB5(1:1783 1026 kg water=min)(13 1023 m)

(60 s=min)(0:17 m2)(2:54762 0:4246 kPa)(1000 Pa=kPa)

where: pws5 4:246(0:6)5 2:5476

pw 5 4:246(0:1)5 0:4426

PB5 5:443 10214 kg m=(m2 Pa s)

6. By converting to units consistent with Table 15.1:

PB5 6:443 10210 cm3 cm=(cm2 s cm Hg)

7. Based on information presented in Table 15.2, polyvinylidene chloridewould be the appropriate package film to ensure the desired shelf life.


15.9 SUMMARYRecent innovations in packaging for foods and food products haveresulted in an array of developments that improve the safety, conve-nience, shelf life, and overall quality of the products. New packagingprovides opportunities for detection of changes in the product duringstorage and distribution and the potential for corrective action basedon package design. Future developments will provide more sophisti-cated packaging to extend shelf life and improve quality attributes ofthe food product.

The evolution of nano-scale science has potential impacts for futurepackaging innovations. The outcomes from nano-scale research willlead to nano-materials with unique properties for protection of foodsfrom all types of harmful agents. These materials will provide suchopportunities as antimicrobial surfaces and sensing of microbiologicaland biochemical activities for all packaging systems. The applicationof nano-scale science will lead to packaging materials that will adjustto changes in pH, pressure, temperature, and light as well as to otherbyproducts of reactions occurring within the package.

PROBLEMS15.1 A dry food product is contained in a 1 cm3 4 cm3 3 cm

box using a polymer film to protect the oxygen sensitivity ofthe product. The concentration gradient across the film isdefined by the oxygen concentration in air and 1% withinthe package. The oxygen diffusivity for the polymer film is33 10216 m2/s. Estimate the film thickness needed to ensurea product shelf life of 10 months. The shelf life of theproduct is established as the time when oxidation reactionswithin the product have used 0.5 mol of oxygen.

*15.2 A dry food product is being stored in a package with a0.75 mm polypropylene film. The dimensions of the packageare 15 cm3 15 cm3 5 cm, and the amount of product in thepackage is 0.75 kg. The initial water activity of the productis 0.05, and the initial moisture content is 2% (d.b.). A keycomponent of the product is sensitive to water activity,and the rate constant for degradation of the componentis described by

k5 53 1025 aw1 1:5

* Indicates an advanced level in solving.


The relationship of the product water activity to moisturecontent is described by the following GAB constants

K5 1:05

C5 5:0

wo5 1:1%

The product is stored in a 258C environment with 50% relativehumidity. Predict the shelf life of the product when the shelflife is established by the time period for the intensity of the keycomponent to decrease to 50% of the original amount.

LIST OF SYMBOLSA area (m2)aw water activityB Arrhenius constantC GAB constantc concentration (kg/m3 or kg mole/m3)D mass diffusivity (m2/s)EA activation energy for temperature (kJ/kg)Ep activation energy for permeability (kcal/mole)K GAB constantk rate constant for quality change (1/s)m mass flux (kg/s)n order of reactionp partial pressure of gas (kPa)P package film permeabilityQ amount of quality attributeR gas constant (m3 Pa/kg mol K)S solubility (moles/cm3 atm) extent of reactionT temperature (8C)TA absolute temperature (K)t time (s)ts shelf life (s)t1/2 half life (s)w moisture content (%, d.b.)wo monolayer moisture content (%, d.b.)x distance coordinate (m)

Subscripts: B, component B; i, initial condition; f, final condition;o, standard condition; w, water vapor; ws, water vapor at saturation;1, location 1; 2, location 2.

789List of Symbols

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791Bibliography

CoverFront matterContentsAuthorsForewordPreface1. Introduction2. Fluid Flow in Food Processing3. Resource Sustainability4. Heat Transfer in Food Processing5. Preservation Processes6. Refrigeration7. Food Freezing8. Evaporation9. Psychrometrics10. Mass Transfer11. Membrane Separation12. Dehydration13. Supplemental Processes14. Extrusion Processes for Foods15. Packaging ConceptsAppendicesIndex

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