Edible in Fruit

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    Development ofadvanced edible

    coatings for fruits

    Hyun Jin Park*Graduate School of Biotechnology, Korea University,

    5-Ka, Anam-Dong, Sungbuk-Ku, Seoul 136-701,South Korea (tel: 82-2-3290-3450; fax: 82-2-927-9028;

    e-mail: [email protected])

    Edible coatings can provide an additional protective coating

    for fresh products and can also give the same eect as

    modied atmosphere storage in modifying internal gas

    composition. Recently, several edible coatings for preserving

    fruits such as oranges, apples, and grapefruits were suc-

    cessfully applied. But, in some cases, edible coatings werenot successful. In fact, fruit quality was worse. The success

    of edible coatings for fresh products totally depends on the

    control of internal gas composition. This article is designed

    to help develop a systematic means of selecting edible

    coatings to maximize quality and shelf life of fresh fruits and

    vegetables. Methods will be introduced to select edible

    coatings based on their gas permeation properties relative

    to controlling internal gas composition of target products.

    # 2000 Published by Elsevier Science Ltd. All rights reserved.

    Major losses in quality and quantity of fresh fruitsoccur between harvest and consumption [1]. Savings

    obtained through reduction of postharvest fruit losses is

    regarded as ``a hidden harvest'' [2]. Through a better

    understanding of the respiration process of fresh fruits,

    several techniques have been developed that are suc-

    cessful in extending shelf life. Controlled atmosphere

    storage and modied atmosphere storage have been

    used for preserving fruits by reducing their quality

    changes and quantity losses during storage. Edible

    coatings on fresh fruit can provide an alternative to

    modied atmosphere storage by reducing quality chan-

    ges and quantity losses through modication and con-

    trol of the internal atmosphere of the individual fruits.

    A historical view of edible coatingsWax was the rst edible coating used on fruits. The

    Chinese applied wax coatings to oranges and lemons in

    the 12th and 13th centuries [3]. Although the Chinese

    did not realize that the full function of edible coatings

    was to slow down respiratory gas exchange, they foundthat wax-coated fruits could be stored longer than non-

    waxed fruits. In the 1930s hot-melt paran waxes

    became commercially available as edible coatings of

    fresh fruits such as apples and pears. Erbil and Muftugil

    [4] reported that coating of peach surfaces with wax

    emulsions decreased water vapor and oxygen transmis-

    sion, thus diminishing respiration rate and increasing

    shelf life of the fruit. Nisperos-Carriedo et al. [5] and

    Baldwin et al. [6] observed that oils or waxes and cellu-

    lose had similar eects of preventing spoilage and

    retaining fresh-picked quality for tropical fruits.

    Several attempts have been made to develop other

    materials that could be used to coat, produce and mod-ify internal gas composition for short-term storage. El

    Ghaouth et al. [7] and Zhang and Quantick [8] sug-

    gested that chitin and chitosan (deacetylated chitin)

    from marine invertebrates could be used for making a

    transparent lm for application as an edible coating on

    fruits and vegetables. In 1982, Lowings and Cutts

    reported on an edible coating material that is non-

    phytotoxic, tasteless, odorless, and eective in preser-

    ving fruits. This coating material is a mixture of sucrose

    fatty acid esters (SFAE), sodium carboxymethyl cellu-

    lose, and mono- and di-glycerides. SFAE was originally

    developed as an emulsier. However, it has been estab-lished that the ripening of fruits be retarded by a coating

    of SFAE. SFAE mixtures have been commercially

    available since the 1980s, for coating fruits and vege-

    tables, under the trade names `TAL Pro-long' and

    `Semperfresh' [915]. Park et al. [16,17] applied zein

    coating on the surface of tomatoes and reported that the

    lm coating delayed color change, weight loss and

    maintained rmness during storage.

    Problems associated with edible coatings to beovercome

    Even though some edible coatings have been success-

    fully applied to fresh produce, other applications have

    0924-2244/00/$ - see front matter Copyright # 2000 Published by Elsevier Science Ltd. All rights reserved.P I I : S0924-2244(00)00003-0

    Trends in Food Science & Technology 10 (1999) 254260

    *H.J. Park is also with the Department of Packaging Science,Clemson University, Clemson, SC 29634-0370, USA.

    Review

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    adversely aected quality. Modication of internal

    atmospheres by the use of edible coatings can increase

    disorders associated with high carbon dioxide or low

    oxygen concentration [18]. Smock [19] indicated that

    waxing apples and pears inhibited normal ripening rate

    and if sucient wax was applied respiration was greatlyinhibited and alcoholic avors were developed by anae-

    robic fermentation. Smith and Stow [11] reported that

    apples (cv. Cox's Orange Pippin) coated with sucrose

    fatty acid ester did have reduced detrimental changes in

    terms of fruit rmness, yellowing and weight loss, but

    also had increased core ush incidence. Park et al. [17]

    reported that tomatoes coated with 2.6 mm zein lm

    produced alcohol and o-avors internally which were

    attributable to an internal gas composition too low in

    oxygen and too high in carbon dioxide. Smith et al. [20]

    summarized the eects on physiological disorders asso-

    ciated with modication of internal atmosphere by useof coatings, as core ush, esh breakdown, and accu-

    mulation of ethanol and alcoholic o-avors.

    Wax and SFAE mixtures are the most widely used

    edible coatings for fruits and vegetables. But, they are

    not equally eective on all produce. Another problem is

    that consumers tend to be wary of waxy coatings.

    Therefore, development of alternate edible coatings that

    do not impart a waxy taste are desirable. The eects of

    edible coatings on internal gas composition and their

    interactions on quality parameters must be determined

    for coated fresh produce. For example, color change

    and rmness are very important quality parameters in

    fruits. As Shewfelt et al. [21] stated, color change,rmness loss, ethanol fermentation, decay ratio and

    weight loss of edible lm coated fruits are all important

    quality parameters for some products. Success of edible

    coatings for fruits depends mainly on selecting lms or

    coatings that can give a desirable internal gas composi-

    tion that is appropriate for a specic product. Also, if a

    coating is too thick detrimental eects can result due to

    an internal oxygen concentration below a desirable and

    benecial level and an associated increased carbon

    dioxide concentration above a critical tolerable level.

    Such a condition leads to anaerobic fermentation. This

    is to accomplished by: (a) developing several ediblecoatings, (b) measuring gas permeation properties of

    selected coatings, (c) measuring diusion properties of

    skin and esh of selected fruits, (d) predicting internal

    gas compositions for the fruits coated with edible lms,

    and (e) observing coating eects on the quality changes

    of fruits.

    Gas permeation properties of edible coatingsThere are several possible edible coatings for fruits,

    such as cellulose, casein, zein, soy protein, and chitosan.

    These were chosen since they have the desirable char-

    acteristics of generally being odorless, tasteless and

    transparent. It is not easy to measure the gas permea-

    tion properties of the coatings after being placed on

    fruits. Therefore, separate at lms need to be prepared

    and tested. Two primary known methods of preparation

    of at lm were described by Kamper and Fennema [22]

    and Aydt et al. [23]. An OX-TRAN 1000TM (Mocon

    Modern Control, Inc., Minneapolis, MN) is usuallyused to measure oxygen permeability, and WVP was

    measured using a variation of the ASTM Standard

    Method E 96 (ASTM, 1987), known as the ``cup

    method''. CO2 permeability can be measured using a

    modied permeability cell designed by Gilbert and

    Pegaz [24] . Gas and water vapor permeabilities of the

    coatings can be calculated as shown in Box 1.

    Oxygen, carbon dioxide and water vapor perme-

    abilities of edible coatings reported in the literature are

    presented in Table 1 and compared with other conven-

    tional plastic lms. The oxygen permeabilities of most

    edible coatings was lower than the conventional plasticlms [2932]. Oxygen permeability (OP) of SPE coat-

    ings is 13 times higher than those of polyethylene lm

    and is 410 times higher than those of polypropylene

    lm. OP of SPE coatings are similar to cellulose lm

    values but are higher than those of protein edible coat-

    Box 1. Gas permeability

    The permeation can be described mathematically byFick's rst law. The ux (J) which is proportional to theconcentration gradient can be dened in one direction asfollows:

    t hdgad I

    Where, J is the ux, the net amount of solute that dif-fuses through unit area per unit time (g/m2.s or ml/m2.s),D is the diusivity constant (m2/s), C is the concentrationgradient of the diusing substance and X is the thicknessof the lm (m) [2528].

    With the two assumptions, (1) the diusion is in steadystate and (2) there is a linear gradient through the lm,the ux (J) is given by

    t hgP gIa ae P

    Where, Q is the amount of gas diusing through the

    lm (g or ml), A is area of the lm (m2

    ) and t is the time(s). After application of Henry's law, the driving force isexpressed in terms of partial pressure dierential of gasand a rearrangement of terms yields the following equa-tion in terms of permeability.

    ae hpP pIa pa Q

    Where, S is the Henry's law solubility coecient (mole/atm), p is partial pressure dierence of the gas across thelm (Pa) and P is the permeability ((ml or g) m/m 2.s.Pa).

    Then, the permeabilities of O2, CO2 and H2O vaporcan be calculated from the following equation [2528];

    aep R

    H.J. Park / Trends in Food Science & Technology 10 (1999) 254260 255

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    ings such as zein. CO2/O2 permeability ratios of edible

    coating lms are higher than those of plastic lms. The

    permeability ratios of protein lms are lower than those

    of cellulose lms. SPE coatings present very high water

    vapor barriers compared with other edible coatings [30].

    Water vapor permeability (WVP) of SPE coatings is

    lower than that of polyethylene lm and more than 100

    times lower than the values for cellulose and protein

    lms. These high oxygen and water vapor barrier prop-

    erties will make SPE coatings desirable for fresh pro-duce as a replacement for wax. WVP of other edible

    coating lms are much higher than those of plastic lms

    [33]. WVP of wheat protein lm was 0.6030.630 ng.m/

    m2.s.Pa, which was the highest among all edible lms

    tested [34]. Plastic is the most widely used food wrap,

    but water vapor commonly condenses on the inner sur-

    face of plastic packaging materials thus leading to

    potential microbial contamination in fresh produce [35].

    Thus, a lm with greater WVP is desirable, although an

    extremely high water vapor permeability of a lm is also

    not desirable as it can result in excessive moisture loss of

    fruits during storage.

    Diusivity determination on fruit skin and eshKnowledge of diusivities of gases in bulky plant

    organs is essential in understanding the physiological

    changes, gas exchanges and internal gas composition.

    The internal gas composition of fruits is determined by

    the diusivities of skin, esh and stem [3638]. Burg and

    Burg [36] designed a system to determine gas resistance

    factors that can be used to estimate gas diusivities of

    bulky plant organs as the ratio of internal concentration

    to the ratio of the production of carbon dioxide and

    ethylene at steady state. Diusivities of gases in bulky

    plant tissue can be calculated as shown in Box 2.

    Several reports exist on determining the diusivities of

    the bulky plant organs [3641]. Burg and Burg [36]

    dened a resistance factor (R) which could be estimated

    for bulky plant organs, banana and tomato, as the ratio

    of internal concentration to the ratio of production of

    carbon dioxide and ethylene at steady state. They esti-

    mated that more than 60% of gas exchange takes place

    through the stem scar in tomatoes. But this resistance

    factor is only an empirical value without conventional

    dimensions, and is not constant with changes in thesurface to volume ratio. Cameron and Yang [37] mea-

    sured the eux of a metabolic inert gas, ethane which, is

    neither produced nor metabolized to a signicant degree

    by the tissue. It was shown that over 97% of gas

    exchange of tomato fruits occurs through the stem scar.

    But the measurement of ethane eux introduces several

    uncertainties because they did not measure the diusiv-

    ities of exocarp, pericarp and stem scar separately.

    Solomos [40] , in a review of principles of gas exchange

    in bulky plant organs, considered stationary states for

    carbon dioxide diusion through spherical and cylind-

    rical shaped plant organs and determined diusivities ofesh and skin of apple with the peeled and intact fruit.

    But the eect of the stem for gas transfer was not con-

    sidered in determining the apparent diusivities of

    apple. The wax undoubtedly serves as a gas barrier to

    oxygen, carbon dioxide and water vapor and other

    metabolic gases and also provides protective functions

    (for example, mechanical damage, fungal and insect

    attack). Therefore, it can be assumed that the primary

    factor that regulates the internal concentration of gases

    is the skin in bulky plant organs. In apple, the resistance

    of apple skin to gas diusion was 10 to 20 fold greater

    than that of the esh, depending on the cultivar [40, 41].

    Chinnan and Park [38] constructed a diusion cell from

    Table 1. O2, CO2 and H2O vapor permeabilities of edible coatings

    PermeabilityFilma

    O2b CO2

    b H2O Vaporc

    SPE 2.100.0001 0.000420.04Chitosan 0.0014 0.49Zein 0.360.16 2.671.09 0.1160.019Wheat gluten 0.200.09 2.131.43 0.6160.013MC (L) 2.170.45 69.019.33 0.0920.003HPC (L) 3.570.03 143.93.76 0.1100.004HPC/Lipid 3.440.06 81.74.58 0.0820.003Cozeen 0.89 5.2526.10 0.407PE 8.30 26.1 PP 0.550.005 0.000650.06PVC 0.0917.99 1.3526.98 0.00071PET 0.130.30 0.671.12

    a SPE is Sucrose Polyester; (L) refers to low level of plasticizer; MC is Methyl cellulose; HPC is Hydroxypropyl cellulose; PE is Polyethylene;PP is Polypropylene; PVC is Polyvinyl chloride; PET is Polyester [22,29,3133]b Unit of permeability is in .m/m2.s.Pa; f is the abbreveation for femto (1015)c Unit of permeability is ng.m/m2.s.Pa; n is the abbreviation for nano (109)

    256 H.J. Park / Trends in Food Science & Technology 10 (1999) 254260

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    PlexiglassTM and an apparatus for diusivity measure-

    ment as shown in Figs. 1 and 2. Gas diusivities of

    exocarp plus pericarp, pericarp and stem scar increased

    as the tomatoes developed from green stage to red stage.

    During the ripening process the progressive loss of

    rmness is the result of a gradual transformation ofprotopectin into pectin which is degraded by enzyme,

    polygalacturonase, in the cell wall [42]. This enzymatic

    degradation of pectin is probably attributed to greater

    diusion of gases in the bulky organs of fruits.

    Measurement of internal gas compositionA cylindrical plug of tissue can be removed from

    individual fruits (orange, apple, tomato, cantaloupe,water melon, and pineapple) using a rubber stopper

    corer. A glass tube can be sealed around the hole in the

    surface of the produce sample. In order to measure

    internal gas composition, gas in the glass tube can be

    allowed to equilibrate with internal gases [16,17,43].

    Then a gas sample can be taken from the glass tube with

    a syringe injected through the sealing stopper. By

    immersing both the produce sample and the attached

    glass tube in water, atmospheric contamination at the

    point of syringe insertion can be prevented. Gas samples

    can be analysed by gas chromatography. Required

    equilibrium times (when gas composition of the insideof the glass tube is constant) need to be determined by

    periodically monitoring gas changes inside the glass

    tube. Equilibrium time can be expected to vary with

    variety, ripeness, temperature and harvesting season for

    various fruits but, two hours is usually enough time [44].

    Prediction of internal gas compositionUsing gas permeation data of edible coatings, diu-

    sivity data of skin and esh of the fruits, and the math-

    ematical models, internal gas composition can be

    predicted for selected fruits. Predictions of internal gas

    compositions with and without coatings will enable

    better matches to be made between individual fruits andindividual edible coatings. The mathematical model

    could be veried by comparing predicted and measured

    internal gas composition for various coating materials

    and thickness on selected fruits.

    Gas diusion models will be determined according to

    physical shape and composition of individual fruits. For

    example, if one dimensional steady state diusion with a

    constant diusion coecient is assumed, the gas diu-

    sion model for a hollow sphere can be used to predict

    internal oxygen composition of some fruits such as

    apples and cantaloupes as follow: In one dimensional

    diusion with a constant diusion coecient, the rate ofgas transfer in the sphere is [2527,40]:

    dgad hdPgadrP Pardgad I

    On substituting u=Cr in the equation (1), we have:

    du/dt=D(d2C/dr2). At steady state, the dierential

    equation of this case is:

    drPdgadradr 0 P

    In a hollow sphere where, r , if gas con-centrations are kept constant at the surfaces such that they

    are C1 at r , and C2 at r , then g g1 r

    Box 2. Diusivity calculation

    Gas exchange in bulky plant tissue can be approxi-mated by Fick's rst law. The ux of a gas of Fick's law isdependent on gradient of concentration and diusivitiesof plant organs. But to determine the gradient of gases,Fick's second law can be employed [2528,40,41]. If dif-fusion is one dimensional and the diusion coecient is

    constant, the rate of transfer through unit area becomes:

    dgad hdgad I

    At non-steady state, all the solutions can be obtainedeither by the method of separation of variables andFourier series or by the Laplace transformation.

    If surface concentrations are constant, the followingboundary and initial conditions may apply:

    g g1Y x 0Y ! 0

    g 0Y x vY ! 0

    g 0Y 0 ` x ` vY 0

    The solution in the form of a trigonometrical series is:

    gxY g11 xav

    2apI

    n1

    g1an sinnxavxphn2p

    2av2 P

    As t approaches innity the terms involving theexpoential vanish and we simply have the linear con-centration distribution. The rate at which the gas emergesfrom unit area of the face x=L of the test sample is givenby hdgadxv, which is easily deduced from equa-tion (2). By integrating them with respect to t, we obtainthe total amount of diusing substance Qt which haspassed through the membrane in time t as follows:

    avg1 hav2 1a6 2p

    I

    n1

    1xphn2p2av2 Q

    As t approaches innity, equation (3) approaches theline:

    hgIav vPaTh R

    This has a intercept L on the t-axis given by:

    v vPaTh S

    The intercept Lt is referred to as the `time lag'. Thus,the measured values of concentration of the diusionconstant from the linear portion of the plot [38,39].

    H.J. Park / Trends in Food Science & Technology 10 (1999) 254260 257

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    g2r ar . By integrating with respect to timet over the surface area, the total amount of diusing gas

    Qt passing through the wall can be determined by:

    RphppgP gIa Q

    Where: Dapp is apparent diusivity of the hollow

    sphere and a and b are constants for individual fruits

    [2527,40].

    However, at steady state the ux of oxygen passing

    through the spherical fruit wall should equal the rate of

    gas consumption, thus:

    RphppgP gIa yP R

    where: R(O2) is respiration rate of oxygen per fruit and

    W is weight of the fruit.

    Internal oxygen composition, C1, can be predicted

    using equation (4). Correlation factors will be calculatedfrom actual measurement of internal gas composition.

    Also, predicted internal gas composition of edible lm

    coated fruits will be veried by measuring internal gas

    composition [40,41,45]. Also optimum edible coating

    thickness can be calculated for each produce-coating

    combination as shown in Box 3.

    Fig. 2. Apparatus for diusivity measurement: (1) diusion cell, (2) water bath, (3) ask, (4) mineral oil, (5) test gas inlet, (6) nitrogen inlet, (7)three-way valve, (8) three-way connector, (9) two-way valve, (10) sampling chamber, (11) silicone septum, (12) gas owmeter, (13) brass tub-ing. Diusivity measurement can be done by the following procedures in [38]. Each of the cored and sliced sample prepared for the studycan be placed in the diusion cell, and a pre-mixed gas (9.9% O 2, 10.1% CO2, 80.0%, N2) can be introduced to the supplying chamber. Theamount of CO2 and O2 diused through the sample in time t into the sampling chamber can be measured by gas chromatography. Thesampling interval is 5 min, and the total sampling period is 2 hr. The diusion cell is immersed in a water bath maintained at 21 C. All

    equipment for determining gas diusivities are placed in a heat-insulated chamber, and the temperatures at several places inside thechamber monitored.

    Fig. 1. Diusion cell: (1) sample holder, (2) gas chamber, (3) sample, (4) sample retainers, (5) threaded bush, (6) sealing O-ring, (7) tubingadapters, (8) thumb nuts, (9) thread rods. The diusion cell was constructed from PlexiglassTM for determining diusivities [38,39]. The cell iscomposed of three main parts: the sample holder, supplying chamber and sampling chamber. The face of each part be tooled for an O-ring

    which provides a tight connection.

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    Measurement of quality and shelf life changeQuality criteria for edible lm coated fruits must be

    determined carefully, and the quality parameters must

    be monitored throughout the storage period. For

    example, color change and rmness are very important

    quality parameters in some fruits. Color change, rm-

    ness loss, ethanol fermentation, decay ratio and weight

    loss of edible lm coated fruits need to be monitored

    [21]. Color change can be monitored by the change in

    hue angle. An Instron universal test machine can be

    used to measure rmness with a non-destructive method

    [45]. Sensory evaluation and consumer acceptabilitytests need to be examined during storage.

    References

    1 Sparks, W.C. (1976) `Losses in Potatoes and Lesser Fruits andVegetables' in Proc. of National Food Loss Conf., M. V. Zaeh-ringer and J. O. Early (eds.), College of Agriculture, Universityof Idaho, Moscow

    2 Spurgeon, D. (ed). (1976) `Hidden Harvest'. International Devel-opment Research Center, Ottawa, Canada

    3 Hardenburg, R.E. `Wax and Related Coatings for HorticulturalProducts' in A Bibliography. Agricultural Research Service Bul-letin 5155, United States Department of Agriculture,Washington, DC

    4 Erbil, H.Y. and Muftugil, N. (1986) `Lengthening the PostharvestLife of Peaches by Coating with Hydrophobic Emulsions' in J.Food Pro. and Pre 10, 269279

    5 Nisperos-Carriedo, M.O., Show, P.E. and Baldwin, E.A. (1990)`Changes in Volatile Flavor Components of Pineapple andOrange Juice as Inuenced by the Application of Lipid and

    Composite Films' in J. Agri. Food Chem. 38, 138213876 Baldwin, E.A., Nisperos-Carriedo, M.O., Show, P.E. and Burns,

    J.K. (1995) `Eect of Coatings and Prolonged Storage Condi-tions on Fresh Orange Flavor Volatiles, Degrees Brix, andAscorbic Acid Levels' in J. Agric. Food Chem. 43, 13211331

    7 El Ghaouth, A., Ponnampalam, R., Castaigne, F. and Arul, J.(1992) `Chitosan Coating to Extend the Storage Life of Toma-toes' in Hort. Science 27, 10161018

    8 Zhang, D.L. and Quantick, P.C. (1997) `Eects of ChitosanCoating on Enzymatic Browning and Decay During Post-harvest Storage of Litchi Fruit' in Postharvest Biology andTechnology 12, 195202

    9 Banks, N.H. (1984) `Some Eects of TAL Pro-long Coating onRipening Bananas' in J. Exper. Bot. 35, 127137

    10 Chu, C.L. (1986) `Poststorage Application of TAL Pro-long on

    Apples from Controlled Atmosphere Storage' in Hort. Science21, 267268

    11 Smith, S.M. and Stow, J.R. (1984) `The Potential of a SucroseEster Coating Material for Improving the Storage and Shelf-lifeQualities of Cox's Orange Pippin Apples' in Annu. Appl. Biol.104, 383391

    12 Santerre, C.R., Leach, T.F. and Cash, J.N. (1989) `The Inuenceof the Sucrose Polyester, SemperfreshTM, on the Storage ofMichigan Grown ``McIntosh'' and ``Golden Delicious'' Apples'in J. Food Pro. and Pre. 13, 293305

    13 Tasdelen, O and Bayindirli, L. (1998) `Controlled AtmosphereStorage and Edible Coating Eects on Storage Life and Qualityof Tomatoes' in J. Food Pro. and Pre. 22, 303320

    14 Lau, O.L. and Meheriuk, M. (1994) `The Eect of Edible Coatingson Storage Quality of ``McIntosh'', ``Delicious'' and ``Spartan''Apples' in Can. J. Plant Sci. 74, 847852

    15 Park, H.J., Rhim, J.W. and Lee, H.Y. (1996) `Edible CoatingEects on Respiration and Storage Life of ``Fuji'' Apples and``Shingo'' Pears' in Food and Biotechnology 5, 5963

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    21 Shewfelt, R.L., Prussia, S.E., Resurreccion, A.V.A., Hurst, W.C.and Campbell, D.T. (1987) `Quality Changes of Vine-ripenedTomatoes Within the Postharvest Handling System' in J. FoodSci. 52, 661672

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    Box 3. Optimal thickness for edible coating

    The hollow sphere model can be used also to determinethe edible coating optimal thickness in some fruits, suchas apple and cantaloupe. In the edible lm coated appleand cantaloupe, the ux of oxygen passing through thespherical fruit wall from the center to the interface of thelm coating and the fruit surface should equal the ux ofoxygen passing throguh the edible coating from theinterface of the lm coating and the fruit surface to theatmosphere, and should equal the rate of oxygen con-sumption of the edible lm coated apple and cantaloupeat steady state [40,41,45].

    4phppg2 g1a

    4phzg2 gxa2 y2 I

    Where: Rc(O2) is the oxygen consumption rate ofcoated fruits, D

    czis the diusivity of edible coatings and

    X is the thickness of the edible coating. Cx is oxygenconcentration at the surface between the edible coatingand the surface fruits.

    Optimal coating thickness which will create a desirablerange of internal oxygen concentrations (C1) in apples,(i.e., 23%), and cantaloupe, (35%) will be calculatedfrom the following equation:

    RphzgP gxPayP P

    Where b+X becomes b when X is very small. Cx isdetermined from equation (1) with C2=Cx.

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