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LWT 41 (2008) 18–25

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Water sorption isotherms for lemon peel at differenttemperatures and isosteric heats

J.V. Garcıa-Perez�, J.A. Carcel, G. Clemente, A. Mulet

ASPA Group, Food Technology Department, Polytechnic University of Valencia, Camı de Vera s/n E46022 Valencia, Spain

Received 8 November 2006; received in revised form 6 February 2007; accepted 9 February 2007

Abstract

Lemon peel constitutes a potential source of dietary fiber to formulate new and healthier products, as well as a source of essential oils.

The relationship between moisture content and water activity provides useful information for lemon peel processing, especially for drying

and storage. Water sorption isotherms of lemon peel were obtained using a standardized conductivity hygrometer at four different

temperatures (20, 30, 40 and 50 1C) and wide ranges of moisture content (5.381–0.002 kgwater/kg dry solid) and water activity

(0.984–0.106). One theoretical (GAB) and four empirical equations (Oswin, Henderson, Halsey and Ratti) were used for modelling

sorption isotherms. After evaluating the models according to several criteria, the GAB model appeared as the best option. Isosteric heats

of sorption were assessed from experimental sorption isotherm data using different methods.

r 2007 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved.

Keywords: Sorption isotherms; Modelling; Lemon; Peel; Isosteric heat

1. Introduction

Spain is an important lemon producer in the world, andSpanish output exceeded 50% of total European produc-tion in 2004 (FAOSTAT, 2003). The peel is a by-product oflemon juice processing, with a high potential use. Twodifferent tissues are found in what is colloquially calledlemon peel, flavedo and albedo (Agustı, 2003, Chapter 3).Flavedo is the peel’s outer layer, whose colour varies fromgreen to yellow. It is a rich source of essential oils (Brat,Olle, Gancel, Reynes, & Brillouet, 2001), which have beenused since ancient times by the flavour and fraganceindustry (Vekiari et al., 2002). Albedo is the majorcomponent of lemon peel, and is a spongy and cellulosiclayer laid under flavedo. The thickness of the albedofluctuates according to several variables, among themvariety and degree of ripeness. Albedo has a high dietaryfiber content, and if added to new meat products permits toformulate healthier products like beef burgers (Aleson-Carbonell, Fernandez-Lopez, Perez-Alvarez, & Kuri,2005), bologna (Fernandez-Gines, Fernandez-Lopez,

0 r 2007 Swiss Society of Food Science and Technology. Pu

t.2007.02.010

ing author. Tel.: +34963879365; fax: +34963877369.

ess: jogarpe4@tal.upv.es (J.V. Garcıa-Perez).

Sayas-Barbera, Sendra, & Perez-Alvarez, 2004) and drycured sausages (Aleson-Carbonell, Fernandez-Lopez,Sayas-Barbera, Sendra, & Perez-Alvarez, 2003). Further-more, the presence of associated bioactive compounds(flavonoids and vitamin C) with antioxidant properties infresh lemon albedo involves healthier benefits than othersources of dietary fiber (Marın, Frutos, Perez-Alvarez,,Martınez-Sanchez, & Del Rio, 2002).Dehydration may be a previous, necessary stage in lemon

peel processing. Moisture content reduction is necessary toincrease shelf life and assure all-year-round supply. Dryingalso facilitates handling conditions, reducing storage andtransport costs in lemon peel processing (Aleson-Carbonellet al., 2005), although may affect bioactive compoundspresent on the material like vitamin C. Foodstuffs present aninherent relationship between equilibrium moisture contentand water activity, known as a sorption isotherm, which isdependent on structure and composition of the foodmaterial, as well as pressure and temperature (Mulet,Garcıa-Pascual, Sanjuan, & Garcıa-Reverter, 2002). A soundknowledge of sorption isotherms is essential for dryingprocesses and storage stability (Mayor, Moreira, Chenlo, &Sereno, 2005) and their determination requires experimentalwork, since current prediction methods are not able to

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Nomenclature

aw water activityAH Henderson model parameter, kg dry solid/

kgwater/K (Eq. (5))AHa Halsey model parameter, dimensionless

(Eq. (6))AOS Oswin model parameter, kgwater/kg dry solidAr Riedel model parameter, KBH Henderson model parameter, dimensionlessBHa Halsey model parameter, K�1

BOS Oswin model parameter, kgwater/kg dry solid/K

Br Riedel model parameter, kg dry solid/kgwaterC0 GAB model parameter, dimensionless (Eq. (2))C GAB model parameter, dimensionless (Eq. (1))CH Henderson model parameter, KCHa Halsey model parameter, dimensionlessCOS Oswin model parameter, dimensionlessCr Riedel model parameter, kJ/kgd.b. Moisture in dry basis, kgwater/kg dry solid

Hm Monolayer sorption heat, kJ/kgHn Multilayer sorption heat, kJ/kgK0 GAB model parameter, dimensionless (Eq. (2))K GAB model parameter, dimensionless (Eq. (1))ki Ratti model parameter (1pip5)Lr Pure water vaporization energy, kJ/kgPs Saturation vapour pressure, PaQs Isosteric heat of sorption, kJ/kgqsn Net isosteric heat of sorption, kJ/kgR Universal gas constant, kJ/kg/KSy Standard deviation of the sampleSyx Standard deviation of the estimationT Temperature, KW Average equilibrium moisture content,

kgwater/kg dry solidWm Monolayer average equilibrium moisture con-

tent, kgwater/kg dry solidw.b. Moisture in wet basis, kg water/kg solidDHK GAB model parameter, kJ/kgDHC GAB model parameter, kJ/kg

J.V. Garcıa-Perez et al. / LWT 41 (2008) 18–25 19

accurately simulate systems as complex as foods (Kaymak-Ertekin & Saltanoglu, 2001). The final moisture content andthe energy required for drying, as well as the more adequatestorage conditions can be estimated from sorption isotherms,this information being relevant for designing lemon peelprocessing. Due to the complexity of foodstuffs, there is noone model that fits all the cases well. As a consequence, manymodels have been proposed in the literature, and it isinteresting to check how well some of them fit toexperimental data. Moreover, the availability of differentmathematical equations is interesting for optimizationpurposes. The kind of models found have a more or lesstheoretical background. Among the most commonly usedare the GAB model, with a sound theoretical basis, andothers which are more empirical: Oswin, Henderson, Halseyand Ratti. The number of fitting parameters varies accordingto the model.

References about sorption isotherms of lemon peel havenot been found in the literature, despite that the usefulnessof drying and storage has been reported for lemon peelprocessing (Aleson-Carbonell et al., 2003; Fernandez-Gines et al., 2004; Aleson-Carbonell et al., 2005). Theaims of this work were to provide experimental sorptionisotherm data of lemon peel at various temperatures, to testempirical and theoretical sorption models and to assessisosteric heats of sorption.

2. Materials and methods

2.1. Experimental set up

Fresh lemons (Citrus limon v. Fino) were picked in Javea(Alicante, Spain) in an advanced stage of ripeness. The

whole lemons were washed, strained with blotting paperand stored at 4 1C until processing. The average dimensionsof the lemons were: major diameter 74.674.4mm andmajor length 90.176.8mm, while the average weight was220.7722.2 g. The peel reached 4171% of the total weightof the lemon, the albedo being 42.373.2% and the flavedo57.773.2% of total peel weight. The average thickness ofthe peel was 9.971.1mm. The initial moisture content ofthe lemon peel was 5.770.3 (kgwater/kg dry solid).Lemon peel was separated from the pulp by hand and

slightly ground using a kitchen houseware apparatus (TypeD56, Moulinex, Seb Group, France). Ground samples weredried in thin layer at 40 1C using an air forced tray ovenand applying different drying times in order to reach a widerange of moisture contents. To ensure homogenousmoisture content in the material, the sample layer wasperiodically stirred during drying and the dried sample waskept in closed storage jars for 48 h until water activity andmoisture content were measured.Water activity was measured by duplicate using a

standardized conductivity hygrometer NOVASINA TH-500 (Air Systems for Air Treatment, Pfaffikon, Switzer-land). It was previously calibrated using the following salts:LiCl, MgCl2, Mg(NO3)2, NaCl, BaCl2 and K2Cr2O7,according to the calibration procedure of the equipmentmanufacturer. The water activity was measured at fourdifferent temperatures of 20, 30, 40 and 50 1C. The timeneeded to reach equilibrium for measuring was approxi-mately 3 h no matter the temperature or moisture contentconsidered. Once water activity measuring was finalized,sample moisture content was determined by triplicateaccording to AOAC method no. 20.013 (AOAC, 1980).The determination was carried out at 70 1C and 800mbar

ARTICLE IN PRESSJ.V. Garcıa-Perez et al. / LWT 41 (2008) 18–2520

vacuum level until constant weight. Using this experi-mental procedure, more than 30 water activity/moisturecontent experimental points were obtained for each of theexperimental temperatures.

2.2. Modelling

Sorption isotherms of lemon peel were modelled usingtheoretical and empirical equations frequently found in theliterature. In the models, moisture content is described as afunction of temperature and water activity, except for theRatti model in which water activity is a function ofmoisture content and temperature.

The GAB (Leung, 1986; Myhara, Sablani, Al-Alawi, &Taylor, 1998, Chapter 6; Kaymak-Ertekin & Saltanoglu,2001; Timmermman, Chirife, & Iglesias, 2001; Barreiroa,Fernandez, & Sandoval, 2003; Jayendra Kumar, Singh,Patil, & Patel, 2005) theoretical model (Eq. (1)) has beenwidely applied to describe equilibrium moisture isothermsin foodstuffs, and was recommended by the EuropeanProject COST90 (European Cooperation in Scientific andTechnical Research) (Bizot, 1983):

W ¼WmCKaw

ð1� KawÞð1þ ðC � 1ÞKawÞ. (1)

KG and CG can be written as temperature dependentvariables:

C ¼ C0 expDHC

RT

� �where DHC ¼ Hm �Hn, (2)

K ¼ K0 expDHK

RT

� �where DHK ¼ Lr �Hn. (3)

Oswin (Lim, Tang, & He, 1995):

W ¼ Aos þ BosTð Þaw

1� aw

� �Cos

. (4)

Henderson (Leung, 1986):

W ¼ �1

AHðT þ CHÞlnð1� awÞ

� �1=BH

. (5)

Halsey (Lim et al., 1995):

W ¼� expðCHa þ BHaTÞ

lnðawÞ

� �1=AHa

. (6)

Ratti (Khalloufi, Giasson, & Ratti, 2000; Shivhare,Arora, Ahmed, & Raghavan, 2004):

lnðawÞ ¼ �k1W k2 þ k3 expð�k4W lnðPsÞW1þk5 Þ. (7)

Temperature effect is introduced in Eq. (7) through thevapour pressure term, which was calculated from ASAEStandards (ASAE, 2000).

2.3. Determination of isosteric heat of sorption

The net isosteric heat of sorption can be computed fromexperimental sorption isotherm data using the Clausiu-

s–Clapeyron equation (Eq. (8)) (Falade, Adetunji, &Aworh, 2003; Kaur, Abas, Wani, Sogi, & Shivhare,2006). It represents the difference between isosteric heatof sorption (Qs) and vaporization energy of pure water (Lr)(Eq. (9)). Through Eq. (8), qsn may be established byplotting ln(aw) at a specific moisture content vs 1/T andmeasuring the slope (Sanchez, Sanjuan, Simal, & Rossello,1997; Mulet, Garcıa-Reverter, Sanjuan, & Bon, 1999;Kaymak-Ertekin & Saltanoglu, 2001; Mulet et al., 2002;Kaymak-Ertekin & Gedik, 2003).

d ln aw

dT

� �W

¼qsn

RT2, (8)

qsn ¼ Qs � Lr. (9)

The aforementioned procedure assumes that qsn is inde-pendent of temperature (Mittal & Usborne, 1985) andrequires data at least at three experimental temperaturelevels. Estimations of net isosteric heat of sorption havebeen found in literature integrating Eq. (8) between twotemperatures (Eq. (10)) (Mulet et al., 1999, 2002; JayendraKumar et al., 2005).

qsn ¼ RT1T2

ðT2 � T1Þln

aw2

aw1

� �. (10)

It is reported in literature that Riedel equation (Eq. (11))(Riedel, 1977) adequately describes the influence oftemperature on water activity. By combining Eqs. (11)and (10), another expression to estimate net isosteric heatof sorption may be considered (Eq. (12)):

lnaw2

aw1

� �¼ Ar expð�BrW Þ

1

T1�

1

T2

� �, (11)

qsn ¼ Cr expð�BrW Þ, (12)

where Ar and Br are constants of the Riedel equation, Cr

being Ar �R.

2.4. Parameter estimation

The identification of model parameters was carried outfor each of the models using the generalized reducedgradient optimization method. The objective functionselected to be minimized was the squared differencesbetween experimental and calculated average moisturecontent except in the Ratti model in which it was theexperimental and calculated average water activity. Thecloseness of the fit was assessed by computing the explainedvariance (VAR) (Eq. (13)) (Lipson & Sheth 1973) and theplots of the residuals:

VAR ¼ 1�S2

yx

S2y

!100. (13)

The VAR represents the relative variance explained by themodel with respect to the total variance, and it varies from0% to 100%. Plotting residuals (Wexp�Wcalc oraWexp�aWcalc) against the independent variable may also

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Table 1

Estimated GAB model parameters at constant temperature

Ta Wmb Cc Kd VARe

20 0.064 4.88 1.0 98.9

30 0.069 1.37 1.0 99.7

40 0.062 2.30 1.0 99.0

50 0.049 4.50 1.0 98.8

aTemperature (1C).bMonolayer average equilibrium moisture content (kg water/kg dry

solid).cGAB model parameter (dimensionless).dGAB model parameter (dimensionless).eExplained variance (%).

J.V. Garcıa-Perez et al. / LWT 41 (2008) 18–25 21

contribute to evaluate the closeness of the fit (Kaleemullah& Kailappan, 2004). If the model fits well, then theresiduals should only be random independent errors with azero mean (Pagan & Mascheroni, 2005). Modelling withlow VAR and/or clear patterns in the residual plots shouldbe rejected.

3. Results and discussion

3.1. Modelling sorption isotherms

Experimental sorption isotherms of lemon peel deter-mined at 20, 30, 40 and 50 1C are plotted in Fig. 1. Theexperimental data ranged between 5.381 and0.002 (kgwater/kg dry solid) for average moisture contentand between 0.984 and 0.106 for water activity. Isothermslook like a type III pattern (Brunauer, 1945) characteristicof products holding small amounts of water at low wateractivity levels and large amounts at high relative humiditylevels.

In order to analyse the temperature influence, sorptionisotherms were modelled using the GAB equation for eachtemperature (Eq. (1)). The parameters identified are shownin Table 1 and the calculated curves are plotted in Fig. 1.The observed behaviour is typical of foodstuffs, wateractivity increases as temperature rises at constant moisturecontent (Jayendra Kumar et al., 2005). It seems that

20 °C

0.0

0.5

1.0

1.5

2.0

0 0.25 0.5 0.75 1

aw

W (

d.b

.)

40 °C

0.0

0.5

1.0

1.5

2.0

0 0.25 0.5 0.75 1

aw

W (

d.b

.)

Fig. 1. Experimental (~) sorption isotherms of lemon peel at 20, 30, 4

monolayer moisture content (Wm) remained quite constantat the lower temperatures, but dropped at 50 1C. Actually,the usual hypothesis is that active adsorption sites are fixed,although some authors believe that water molecules maytake more than one active site by increasing kinetic energyat high temperatures (Diosady, Rizvi, Cai, & Jagdeo,1996). The decrease of active sites may be also explainedconsidering more intense interactions among them throughhydrogen and/or sulphur bonds due to shrinkage at hightemperatures. The K values obtained were nearly constantand equals to 1, which indicates that GAB equation hasbecome BET model. Garau, Simal, Femenia and Rossello

30 °C

0.0

0.5

1.0

1.5

2.0

0 0.25 0.5 0.75 1

aw

W (

d.b

.)

50 °C

0.0

0.5

1.0

1.5

2.0

0 0.25 0.5 0.75 1

aw

W (

d.b

.)

0 and 50 1C and estimated curves (—) with GAB model (Eq. (1)).

ARTICLE IN PRESSJ.V. Garcıa-Perez et al. / LWT 41 (2008) 18–2522

(2006) found similar values of GAB parameters forsorption isotherms of orange peel determined at 25 1C(Wm ¼ 0.085 kgwater/kg dry solid, C ¼ 2.374, K ¼ 0.982).In the literature, references to the sorption isotherms of thepeel of other citrus fruits have not been found. Lahsasni,Kouhila, Mahrouz, and Kechaou (2002) determineddesorption and adsorption isotherms of prickly pear peel,from the GAB model a monolayer moisture content ofbetween 0.027 and 0.022 (kgwater/kg dry solid) was found,slightly lower than the figures found in this work.

Sorption isotherms were also modelled by consideringthe influence of temperature being described by Eqs. (2)and (3). Estimated model parameters and statistical resultsare shown in Table 2. In order to evaluate the models someoutputs should be checked, among those are the explainedvariance, the number of parameters involved as well astheir physical meaning and residual distribution. The idealmodel would have a high VAR, a low number ofparameters to be identified simultaneously, physical mean-ing of those parameters, and a random residual plot. TheGAB and Ratti models reached the highest VAR values,higher than 99% and random residual distribution (Figs. 2and 3). Poorer fits between experimental and calculateddata were found for the Oswin and Henderson modelslower than 97.5% explained variance. These two modelsalso showed patterned residuals (Fig. 2). The Halsey modelcame between both groups (VAR ¼ 98.4%). The useful-ness of models may also be assessed considering thenumber of parameters involved. The Halsey model onlyuses three against the five parameters on GAB (Wm, C0,DHC, K0 and DHK) and Ratti models, when temperature isincluded as independent variable. A small amount ofparameters for modelling not only simplifies the calculationprocedure, but also contributes to obtain more reliablevalues, since decrease the degrees of freedom on theidentification procedure. This may be interesting when themodel is used for process design. For modelling sorptionisotherms of lemon peel, it seems that the GAB model wasthe best option. It provided a high explained variance, arandom residual distribution and useful information maybe extracted from its parameters. Its only drawback was

Table 2

Modelling sorption isotherms of lemon peel

Model Parametersa

GAB Wm C0 DHC

0.065 1.0 118.8

Oswin AOS BOS COS

0.1 �8.6� 10�5 1.1

Henderson AH BH CH

6.7� 10�4 0.3 3502.0

Halsey AHa BHa CHa

0.8 8� 10�3 �5.1

Ratti k1 k2 k3

8.4� 10�2 �0.9 1.2� 10�3

aModel parameters (units, see nomenclature).bExplained variance (%).

the high number of parameters to be identified. Thus, inthose cases in which a small amount of parameters isrequired, the Halsey model would be the best choice. TheOswin and Henderson models were not adequate.The physical meaning of the GAB model parameters

constitutes a basis allowing to compare different materials(Timmermman et al., 2001). The positive value of DHC

(111.8 kJ/kg) indicates that the binding energy betweenwater molecules in the monolayer and the solid matrix washigher than for water molecule binding energy in themultilayer. A negative DHK value (�14.84 kJ/kg) wasfound, but it was very close to 0, which suggests that thebinding energy in the multilayer was slightly higher thanwater vaporization energy. A further analysis will beachieved through isosteric heats.

3.2. Isosteric heats of sorption

Isosteric heat of sorption for lemon peel was determinedfrom experimental sorption isotherms. The errors asso-ciated to experimental work, also linked to naturalvariability, constitute the main disadvantage of thistechnique as compared to those based on calorimetricmethods (Chirife & Iglesias, 1992), which are a goodalternative if proper instrumentation is available (Muletet al., 1999). The isosteric heat was assessed from theClausius–Clapeyron equation using differential (Eq. (8))and integral procedures (Eq. (10)). Sorption isothermsestimated using the GAB model for each temperature (Fig.1, Table 1) were used to obtain by interpolation wateractivity values at the different experimental temperaturesfor a constant moisture content. Fig. 4 shows the influenceof moisture content on isosteric heat of sorption fordifferential and integral methods (using data at 20 and50 1C). Both curves were very close; at high moisturecontents the figures were almost equal, whereas there werelarger differences as moisture content reduced. Theseresults agree with those reported in literature about thecloseness between both methods for estimating isostericheats of sorption (Mulet et al., 1999, 2002). Isosteric heatvalues decreased as moisture content increased, and were

VARb Residual plot

K0 DHK 99.3 Random

1.1 �14.9

97.4 Patterned

96.4 Patterned

98.4 Random

k4 k5 99.8 Random

42.5 �0.9

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GAB

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.2 0.4 0.6 0.8 1

aw

Wexp -

Wcalc

(d

.b.)

Henderson

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.2 0.4 0.6 0.8 1

aw

We

xp -

Wcalc

(d

.b.)

Halsey

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.2 0.4 0.6 0.8 1

aw

We

xp -

Wcalc

(d

.b.)

Oswin

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.2 0.4 0.6 0.8 1

aw

We

xp -

Wcalc

(d

.b.)

Fig. 2. Residuals plots for GAB, Oswin, Henderson and Halsey models.

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.25 0.5 0.75 1 1.25 1.5

W (d.b.)

aw

ex

p -

aw

calc

Fig. 3. Residuals plots for Ratti model.

2000

2200

2400

2600

2800

0 0.25 0.5 0.75 1

W (d.b.)

Qs (

kJ/k

g)

Differential

Integral

Riedel

GAB

Lr

Fig. 4. Influence of moisture content on isosteric heat of sorption.

J.V. Garcıa-Perez et al. / LWT 41 (2008) 18–25 23

close to water vaporization energy for moisture contenthigher than 1 (kgwater/kg dry solid). This fact may beexplained assuming that sorption occurs at low moisturecontents on the most active sites, hydrophilic groups, while,as moisture content increases water molecules bind withless active sites resulting in lower isosteric heats of sorption(Jayendra Kumar et al., 2005; Iglesias & Chirife, 1976).

Net isosteric heat of sorption was also calculated fromthe Riedel equation (Eqs. (11) and (12)). The identifiedparameters of Eq. (11) were Br ¼ 8.02 (kg dry solid/kgwater) and Ar ¼ 1532.08 (K), and the fit was accurateto 97.7%. Mulet et al. (2002) estimated similar figures forMorchella esculenta mushrooms. Isosteric heats determinedfrom Eq. (12) using Ar and Br were close to the values from

ARTICLE IN PRESSJ.V. Garcıa-Perez et al. / LWT 41 (2008) 18–2524

differential and integral methods. However, isosteric heatvalues obtained with the Riedel equation approached thefigure for water vaporization energy at a lower moisturecontent than differential and integral methods (Fig. 4).

From the GAB model, the monolayer moisture content(Wm ¼ 0.065 kgwater/kg dry solid) and the energy asso-ciated to this moisture content (Hm ¼ 2389 kJ/kg) (Fig. 4)were estimated, as well as the net isosteric heat of sorptionin monolayer, 133.6 (kJ/kg). This figure for the net isostericheat differed 66.773.2% from those found using theClausius–Clapeyron and Riedel equations at the samemoisture content. Chirife and Iglesias (1992) reported that,on the precision of net isosteric heat of sorption obtainedusing the Clausius–Clapeyron equation, only the varia-bility of experimental data may introduce fluctuations inthe estimations from 24% to 63%. In order to assessisosteric heat of sorption from sorption isotherms, highlyaccurate experimental work would be desirable due to theerrors associated to inaccuracies on sorption data (Chirife& Iglesias, 1992). This is quite difficult due to thevariability of natural products.

4. Conclusions

Sorption isotherms of lemon peel were experimentallyperformed at 20, 30, 40 and 50 1C, in a wide range of wateractivity and moisture contents. Several equations were usedfor modelling and the usefulness of each was evaluatedaccording to several criteria. The GAB model was chosenas the best equation for describing sorption isotherms oflemon peel, due to the high explained variance attained, thephysical meaning of its parameters and the fact that itpresented a random residual distribution. The Halseymodel was also well rated for adequately estimatingisotherms (VAR ¼ 98.4%) using a small number ofparameters, which may be interesting in some applications.The Ratti model will be useful when a explicit form forwater activity is sought, Oswin and Henderson models willbe disregarded.

Isosteric heat of sorption was assessed considering theClausius–Clapeyron equation, using differential and inte-gral procedures, and the Riedel equation. The estimationswere all similar, especially for differential and integralmethods. A figure of the net isosteric heat of sorption wasalso estimated from the GAB parameters for the mono-layer moisture content.

Acknowledgement

The authors would like to acknowledge the financialsupport of MCyT project (Ref: AGL2005-08093-C02-01/ALI)

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