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doi:10.1016/j.biosystemseng.2006.03.004PH—Postharvest Technology

Biosystems Engineering (2006) 94 (2), 221–228

Equilibrium Moisture Content Models for Maytenus ilicifolia Leaves

D.S. Cordeiro1; G.S.V. Raghavan2; W.P. Oliveira1

1Faculdade de Ciencias Farmaceuticas de Ribeirao Preto, Universidade de Sao Paulo, Av. do Cafe s/n, Bl. Q, CEP 14040-903,Ribeirao Preto, SP, Brazil; e-mail of corresponding author: wpoliv@fcfrp.usp.br

2Department of Bioresource Engineering, McGill University, Macdonald Campus, 21,111, Lakeshore Road, Ste-Anne-deBellevue,Que, Canada H9X 3V9; e-mail: vijaya.raghavan@mcgill.ca

(Received 30 December 2004; accepted in revised form 8 March 2006; published online 11 May 2006)

Knowledge of the relationship between the air relative humidity and moisture content of the test material isessential for the drying and storage process research. The aim of this work was to determine sorptionisotherms of Maytenus ilicifolia leaves and to compare the experimental results with mathematical models inthe literature. The equilibrium moisture content for M. ilicifolia leaves was measured using the static method,at relative humidities and temperatures ranging from 11% to 85% and from 30 to 60 1C, respectively. Theexperimental data were compared with five models available in the literature (Chung–Pfost, modified Halsey,modified Oswin, Henderson–Thompson and Guggenheim–Anderson–deBoer). The adsorption data were bestdescribed by the Chung–Pfost equation, while the desorption data were best fitted by the Henderson–Thomp-son equation. Thus, these models can be used for the estimation of the equilibrium moisture content of M.

ilicifolia leaves.r 2006 IAgrE. All rights reserved

Published by Elsevier Ltd

1. Introduction

Maytenus ilicifolia is a medicinal plant extensivelyused in the Brazilian natural medicine in the treatmentof ulcers, indigestion, chronic gastritis and dyspepsia.The leaf tea is also applied typically to wounds andrashes and to treat skin cancer (Taylor, 1996). Maytenus

ilicifolia is a plant that belongs to the Celastraceaefamily and is a small medicinal shrubby evergreen tree,which grows to 5m in height with leaves and berries. Itis native to many parts of South America and southernBrazil and is commonly known as espinheira santa,cancerosa, cangorosa, maiteno and espinheira divina.In general, the consumption of fresh medicinal plants

guarantees more efficacies of the natural substances withpharmacological activity. However, the sources of freshplant material for immediate use are very restricted,being necessary the utilisation of dehydrated products.Nevertheless, during storage and drying of agriculturalproducts, physical, chemical and microbiological trans-formations can happen. These changes are particularlyinfluenced by moisture content of the material, relative

1537-5110/$32.00 221

humidity of ambient air and the drying and storageconditions.

The equilibrium relationship between the relativehumidity and the moisture content at constant tempera-tures and pressures is expressed by the sorptionisotherms. Sorption isotherms are an extremely valuabletool for scientists because these can be used to predictpotential changes in biological materials stability. Thus,with the knowledge of the moisture sorption isotherm, itis possible to predict the maximum moisture that themedicinal plant can be allowed to gain or lose duringstorage or drying. The adsorption isotherms data can beused for establishing a storage method, while thedesorption isotherms data are useful in the dryinganalysis.

The traditional method for measuring sorptionproperties is the static method. The advantage of thestatic method is its ability to maintain constantconditions easily (Arnosti Junior et al., 1999; Barrozoet al., 1994). In this method, samples are placed in anenvironment set to relative humidity and temperature.When the change in the mass of the sample is

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Notation

a, b, c, b0, c0, h1,h2,

constants

MRE mean relative error, %HR relative humidity, decimalM equilibrium moisture content, d.b.md dry sample mass, gmf sample mass at equilibrium condi-

tion, gN number of samplesR2 determination coefficientRg universal gas constant;

kJ kmol�1K�1

RSS residual sum of squaresT temperature, 1CTk absolute temperature, K

Subscripts

ads adsorptiondes desorptionest estimatedexp experimentali sample number

D.S. CORDEIRO ET AL.222

insignificant, the moisture of the samples is measuredand adopted as the equilibrium moisture content (EMC)value.Several empirical and semi-empirical equations have

been proposed to correlate the sorption isotherms valuesof agricultural and food products, including aromaticand medicinal plants (ASAE, 1996; Belghit et al., 2000;Kouhila et al., 1999; Park et al., 2002; Zanoelo, 2005).However, no single equation is general enough topredict the relationship between the EMC of agricultur-al and food products and the relative humidity over awide range of temperature (Brooker et al., 1974; Soysal& Oztekin, 1999; 2001; Park et al., 2002; Lahsasni et al.,2004).The Henderson–Thompson (Thompson et al., 1968)

and Chung–Pfost equations (Chung & Pfost, 1967; Pfostet al., 1967) are satisfactory models for most starchygrains and fibrous materials. The Halsey equation is anadequate model for products having a high oil andprotein content (Halsey, 1985). The modified Oswinequation (Chen, 2000) has served as a good model forpopcorn, maize cobs, peanut pods and some varieties ofmaize and wheat. According to Soysal and Oztekin(2001), the Guggenheim–Anderson–deBoer (GAB)equation is considered as the most versatile model forvarious materials such as inorganic and food productsover a wide range of water activities.However, few studies have been conducted to

determine and to model the EMC data for M. ilicifolia

leaves.The objective of this study was to determine the

adsorption and desorption isotherms of M. ilicifolia

leaves at relative humidities and temperatures rangingfrom 11 to 85% and from 30 to 601C, respectively. Fivemodels presented in the literature (Chung–Pfost, mod-ified Halsey, modified Oswin, Henderson–Thompsonand GAB) were fitted to the experimental data in order

to verify their adequacy to describe the EMC of the M.

ilicifolia leaves.

2. Materials and methods

The M. ilicifolia leaves used in the sorption experi-ments were grown in the nursery of medicinal plants ofUniversity of Ribeirao Preto (Ribeirao Preto, Brazil)and harvested between May and June, 2002. Leaves withsizes between 3 and 5 cm were used in the experiments.Damaged leaves were discarded. Fresh leaves were usedin desorption experiments. The leaves used in theadsorption experiments were dried during 48 h in anoven with air circulation, being the air temperatureadjusted at 40 1C. Fresh and dried plants sufficient forall experiments were vacuum-packed in plastic bags andstored in a cold chamber at 471 1C. The initial moisturecontent of the fresh and dried leaves, determined by theoven drying method at 105 1C for 24 h (AOAC, 1990),were respectively 75�0% (w.b.) and 8�4% (d.b.).

The samples used in the sorption studies were sealedup in small glass cylindrical containers with basediameter of 80mm and height of 125mm. Each of thesevessels contained a different saturated salt solution ofLiCl, CH3COOK, MgCl2�6H2O, K2CO3, NaNO2, NaCland KCl, corresponding to a range of relative humidityof 11–85% (Greenspan, 1976; Labuza et al., 1985). Theleaves were placed on a perforated tray, arranged 50mmfrom the base of the vessel to avoid any contact betweenthe saturated salt solutions and the samples of M.

ilicifolia leaves. The initial leaf mass used in eachreservoir was of about 3 g in the desorption experimentsand 1 g in the adsorption experiments. The vessels werethen placed in an oven at controlled temperatures of 30,40, 50 and 60 1C (maximum variation of 0�5 1C), andkept under constant thermodynamic conditions during

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Maytenus ilicifolia leaves

support

saturated

salt solution

80 mm

70 m

m

125 m

m

Fig. 1. Schematic diagram of the hermetic glass cylindrical containers

Table 1Equilibrium moisture content models used in this work

Equation Model References

Chung–Pfost M ¼ �1aln � ðTþbÞ

clnðHRÞ

h iPfost et al. (1976)

Modified Oswin M ¼ ða� bTÞ HR=ð1�HRÞ� �c Oswin, (1946)

Modified Halsey M ¼ expða� bTÞ=� lnðHRÞ� �1=c Iglesias and Chirife (1976)

Henderson–Thompson M ¼ lnð1�HRÞ=ð�aðT þ cÞÞ� �1=b Thompson et al. (1968)

Guggenheim–Anderson–deBoer (GAB) M ¼ abcHR

ð1�bHRÞð1�bHRþbcHRÞChen (2002)

whereb ¼ b0e h1=RgTk

� �Labuza et al. (1985)

c ¼ c0e h2=RgTk

� �Labuza et al. (1985)

Equilibrium moisture content M ¼ 100ðmf �md Þ=md

M, equilibrium moisture content; HR relative humidity; T and Tl temperature in 1C and K, respectively; md and mf, mass in g of dry sample and at

equilibrium condition; Rg, universal gas constant in kJ kmol�1K�1 ; a, b, c, b0, c0, h1 and h2, coefficient specific to individual equations.

EQUILIBRIUM MOISTURE CONTENT MODELS 223

30 days to ensure that the equilibrium was reached.Each sample was weighed on an analytical balance withprecision of 1mg. It was assumed that the equilibriumconditions had been attained when three subsequentmeasurements of the sample mass at intervals of 1 daygave identical results. The equilibrium moisture contentof each sample was determined by the oven dryingmethod at 105 1C for 24 h (AOAC, 1990). The assayswere performed in two or three containers containingthe same salt solution, depending on the relativehumidity, to verify the reliability of the experimentalprocedure. Figure. 1 shows the schematic diagram of thehermetic vessel used in the isotherms experiments.

2.1. Data analysis

In this work, the relationship between the equilibriummoisture content data and the relative humidity andtemperature for M. ilicifolia leaves was evaluatedaccording to the models of Chung–Pfost, Halsey, Oswin,Henderson–Thompson and GAB. These models arepresented in Table 1. A non-linear estimation packageSTATISTICA 5�0 was used to find the model para-meters. The regression analysis was repeated severaltimes with different initial values above and below thosecalculated to confirm the validity of the regressionparameters (Park et al., 2002; Peleg, 1993). The mean

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D.S. CORDEIRO ET AL.224

relative error (MRE), the determination coefficient (R2),the residual sum of squares (RSS), and residualdistributions plots were used to evaluate the fittingquality. The residual sum of squares RSS, the meanrelative error MRE, and the determination coefficientR2, are given by

RSS ¼XN

i¼1

Mi;exp �M� �2

(1)

MRE ¼100

N

XN

i¼1

Mi;exp �Mi;est

Mi;exp

�������� (2)

R2 ¼

PNi¼1

Mi;est �M� �2

PNi¼1

Mi;exp �M� �2 (3)

where: Mi and M are the equilibrium moisture contentsin dry basis (d.b) for the ith sample and for the average

TablExperimental equilibrium moisture content (EMC) results obtained

relative humidities

Salt Relative humidity, decimal� Temperature, 1

LiCl 0�113 30CH3COOK 0�216 30MgCl2�6H2O 0�324 30K2CO3 0�432 30NaNO2 0�635 30NaCl 0�751 30KCl 0�836 30

LiCl 0�112 40CH3COOK 0�204 40MgCl2�6H2O 0�316 40K2CO3 0�432 40NaNO2 0�616 40NaCl 0�747 40KCl 0�823 40

LiCl 0�111 50CH3COOK 0�192 50MgCl2�6H2O 0�305 50K2CO3 0�433 50NaNO2 0�597 50NaCl 0�744 50KCl 0�812 50

LiCl 0�111 60CH3COOK 0�175 60MgCl2�6H2O 0�293 60K2CO3 0�421 60NaNO2 0�565 60NaCl 0�745 60KCl 0�803 60

ads, adsorption; des, desorption; d, standard deviation.�Source: Greenspan (1976); Labuza et al. (1985).

of N samples, with subscripts exp and ext denotingexperimental and estimated values.

In general, larger values of R2, and small values ofRSS and MRE, associated with randomly residualdistributions indicate good fitting ability.

3. Results and discussion

The hygroscopic equilibrium of M. ilicifolia leaveswas reached almost in 20 days for desorption studiesand in 30 days for adsorption tests. Table 2 reports theexperimental EMC data obtained for the adsorptionand desorption assays (dry basis), at different relativehumidities and temperatures used. The small standarddeviations between replicate or triplicate assays per-formed at identical conditions confirm the reliability ofthe experimental methodology.

The results presented in Table 2 indicate that bothtemperature and relative humidity have significant effect

e 2for the adsorption and desorption assays (dry basis), at different

and temperatures

C EMC, ads, % d, ads, % EMC, des, % d,des, %

8�3 0�03 14�0 0�0510�4 0�13 19�2 0�1913�0 0�10 29�1 0�2814�6 0�08 37�1 0�3714�4 0�09 39�3 0�3316�7 0�52 53�7 1�0526�0 0�43 63�7 1�55

5�7 0�02 10�5 0�0511�0 0�08 11�6 0�0913�0 0�06 19�6 0�2415�0 0�05 27�1 0�3314�6 0�09 29�3 0�2815�5 0�22 37�9 0�9722�5 0�26 39�4 0�88

3�3 0�07 7�6 0�274�1 0�08 10�5 0�229�2 0�17 13�2 0�487�7 0�15 15�6 0�5511�5 0�33 19�9 0�6415�0 0�28 28�4 0�6922�4 0�30 30�3 0�86

2�9 0�02 3�9 0�174�0 0�35 6�0 0�256�9 0�03 9�8 0�227�2 0�04 12�4 0�4411�4 0�33 17�0 0�3713�5 0�28 19�3 0�4618�9 0�31 25�9 0�95

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EQUILIBRIUM MOISTURE CONTENT MODELS 225

on experimental EMC values. In a general way,increasing the temperature reduces the EMC both inadsorption and desorption data. According to Mo-hamed et al. (2005), this effect may be related with thehigher excitation state of water molecules at highertemperatures, leading to a reduction in the attractiveforces between them— an effect more pronounced in thedesorption data. An opposite behaviour is caused by theequilibrium relative humidity HR. The EMC data(sorption and desorption) follow a sigmoidal curve,typical of the most biological products. The EMC washigher for desorption data than for adsorption data,presenting the typical hysteresis effect. Similar effectshave been observed in several other studies withagricultural and food products such as tarragon steamsand leaves (Arabhosseini et al., 2005), orange leaves(Mohamed et al., 2005), Moroccan Eucalyptus globulus

Tabl

Model parameters, determination coefficients and mean relative err

Parameters

Chung–Pfost Oswin Halse

a 16�355 0�183 �3�85b �7�214 1�39� 10�3 0�024c 188�624 0�346 2�093b0 — — —c0 — — —h1 — — —h2 — — —R2 0�880 0�834 0�817MRE, % 14�3 21�4 22�8RSS 0�011 0�013 0�013Residual distribution Random Random Rando

a, b, c, b0, c0, h1, h2, model parameters; R2, determination coefficient; M

Tabl

Model parameters, determination coefficients and mean relative err

Parameters

Chung–Pfost Oswin Halse

A 7�809 0�543 �0�67B �23�287 6�98� 10�3 0�0641C 81�157 0�370 2�013B0 — — —C0 — — —h1 — — —h2 — — —R2 0�923 0�931 0�925MRE, % 19�3 12�4 14�1RSS 0�043 0�025 0�024Residual distribution Random Systematic Systema

a, b, c, b0, c0, h1, h2, model parameters; R2: determination coefficient; M

(Kouhila et al., 2002) and prickly pear peel (Lahsasmi et

al., 2002).The adsorption isotherms are essential to select the

adequate storage conditions. To guarantee the productquality, in general is recommended a relative humidityin the storage chamber of 60% as the upper limit inorder to avoid the mold growth. In this case, the resultsof this paper indicates that the M. ilicifolia should bedried to a minimum moisture content of 0�170 at 30 1C,0�148 at 40 1C, 0�132 at 50 1C and 0�119 at 60 1C.

The experimental adsorption and desorption EMCdata were fitted to the five models presented in Table 1.Tables 3 and 4 show the models parameters, EMR,MRE, R2, and the RSS, obtained respectively, for theadsorption and desorption data. The residuals distribu-tions of the EMC generated by the fitted models wereplotted against the predicted values. The distributions

e 3

ors in fitting of adsorption isotherms of Maytenus ilicifolia leaves

Sorption models

y Henderson–Thompson Guggenheim–Anderson–deBoer

8 1�057 0�3882�034 —1�635 —— 0�010— 0�126— �51078�3— 68914�8

0�823 0�83021�3 18�30�015 0�019

m Random Systematic

RE, mean relative error; RSS, residual sum of squares.

e 4

ors in fitting of desorption isotherms of Maytenus ilicifolia leaves

Sorption models

y Henderson–Thompson Guggenheim–Anderson–deBoer

3 0�510 2�2731�822 —�21�678 —

— 4�94� 10�3

— 4�09� 10�3

— �35 488�0— 60 312�5

0�960 0�9589�8 12�80�015 0�031

tic Random Systematic

RE, mean relative error; RSS, residual sum of squares.

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0.05 0.10 0.15 0.20 0.25

0.08

0.06

0.04

0.02

0.00

−0.02

−0.04

−0.06

−0.08

Res

idual

EM

C v

alues

, g [

wat

er]

/g [

dry

lea

ves

]

Predicted EMC values, decimal (d.b.)

Fig. 3. Residual plots for the Chung–Pfost equation fitted toadsorption equilibrium moisture content data for Maytenusilicifolia leaves at various temperatures (T): , T ¼ 30 1C; ,,

T ¼ 40 1C; J, T ¼ 50 1C; ’, T ¼ 60 1C

0.3

0.4

0.5

0.6

0.7

[w

ater

] /g

[dry

lea

ves

]

D.S. CORDEIRO ET AL.226

were considered either randomly or systematicallydistributed, being the results presented in Tables 3 and4. Models presenting systematic distribution wereconsidered inadequate.As seen in Table 3, for a wide range of temperature

and relative humidity, the adsorption EMC data werebest fitted by the Chung–Pfost model, with an MRE of14�3%, R2 of 0�880 and RSS of 0�011. The residual plotdistributions showing scattered data points centred onzero confirm no typical systematic tendencies towards aclear pattern (Drapper & Smith, 1981). The comparisonbetween experimental and calculated adsorption EMCdata of M. ilicifolia leaves and, the residual plotsobtained by the Chung–Pfost model are presented,respectively, in Figs 2 and 3. For desorption EMC data,the Henderson–Thompson model gives the smallestMRE (9�8%) and RSS of 0�015, with a random residualdistributions. This model presents an R2 of 0�960, beingable to describe 96% of the data variation due toalterations in the temperature from 30 to 60 1C and/orrelative humidity from 0�11 to 0�83. Figures 4 and 5

show, respectively, the comparison between experimen-tal and calculated adsorption EMC data of M. ilicifolia

leaves and, the residual plots distributions obtained bythe Henderson-Thompson model. Although the GABmodel gives a high value for the determinationcoefficient R2 of 0�958, this model was consideredunacceptable, since it gives systematic residual plotdistributions, as can be seen in Fig. 6. These resultscorroborate the importance of applying several decisionparameters to evaluate the fitting adequacy of models.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

EM

C,

g [

wat

er]

/g [

dry

lea

ves

]

Relative humidity HR, decimal (d.b.)

Fig. 2. Comparison of the adsorption equilibrium moisturecontent data for Maytenus ilicifolia leaves at various tempera-ture (T) with the estimates obtained by the Chung–Pfost model:

, T ¼ 30 1C; ,, T ¼ 40 1C; J, T ¼ 50 1C; ’, T ¼ 60 1C; —,predicted

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.1

0.2

EM

C,

g

Relative humidity HR, decimal (d.b.)

Fig. 4. Comparison of the desorption equilibrium moisturecontent data for Maytenus ilicifolia leaves at various tempera-tures (T) the estimates obtained by the Henderson–Thompsonmodel: , T ¼ 30 1C; ,, T ¼ 40 1C; J, T ¼ 50 1C; ’,

T ¼ 60 1C; —, predicted

Based on the results reported in this paper, theChung–Pfost model can be recommended for predictionof the adsorption isotherms of Maytenus ilicifolia leavesin the temperature range of 30–60 1C and relativehumidity from 11–85%. This relationship for theEMC, is given by:

M ¼�1

aln �

ðT þ bÞ

clnðHRÞ

� �(4)

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0.08

0.06

0.04

0.02

0.00

−0.02

−0.04

−0.06

−0.08

Res

idual

EM

C v

alues

, g [

wat

er]

/g [

dry

lea

ves

]

Predicted EMC values, decimal (d.b.)

0.1 0.2 0.3 0.4 0.5 0.6

Fig. 5. Residual plots for the Henderson–Thompson equationfitted to desorption equilibrium moisture content data forMaytenus ilicifolia leaves at various temperatures (T): ,

T ¼ 30 1C; ,, T ¼ 40 1C; J, T ¼ 50 1C; ’, T ¼ 60 1C

0.08

0.06

0.04

0.02

0.00

−0.02

−0.04

−0.06

−0.08

Res

idual

EM

C v

alues

, g [

wat

er]

/g [

dry

lea

ves

]

Predicted EMC values, decimal (d.b.)

0.10.0 0.2 0.3 0.4 0.5 0.6

Fig. 6. Residual plots for the Guggenheim–Anderson–deBoermodel fitted to desorption equilibrium moisture content data forMaytenus ilicifolia leaves at various temperatures (T): ,

T ¼ 30 1C; ,, T ¼ 40 1C; J, T ¼ 50 1C; ’, T ¼ 60 1C

EQUILIBRIUM MOISTURE CONTENT MODELS 227

where: a, b and c are coefficients; T is the temperature in1C; and HR is the relative humidity as a decimal. Thevalues of parameters fitted to experimental adsorptionEMC data were: a ¼ 16�355, b ¼ �7�214 andc ¼ 188�624.In the same way, the statistical analysis performed on

adsorption EMC data showed that the Hender-son–Thompson model can be recommended for char-acterising the desorption isotherms of M. ilicifolia leaves

in the temperature range of 30–60 1C and relativehumidity from 11% to 85%. The Henderson–Thomp-son equation is presented by the following equation:

M ¼ ½lnð1�HRÞ=ð�aðT þ cÞÞ�1=b (5)

The values of parameters (specific to individualequations) found in this work were: a ¼ 0�510, b ¼ 1�822and c ¼ �21�678.

4. Conclusion

The equilibrium moisture content of Maytenus

ilicifolia leaves at four temperatures and relativehumidities in the range of 11–85%, were determined.From the results, it is concluded that the sorptionisotherms of medicinal plants can be measured by agravimetric static method with sufficient accuracy forpractical purposes. The experimental data were used todetermine the best model for predicting the adsorptionand desorption isotherms of fresh and dried M. ilicifolia

leaves for known levels of temperature and relativehumidity. Mathematical models that best fitted theexperimental data were found by statistical analysis ofthe experimental data: the Chung–Pfost model foradsorption isotherms and the Henderson Thompsonequation for desorption isotherms. The equilibriummoisture content (EMC) was higher for desorption datathan for adsorption data, presenting the typical hyster-esis effect commonly observed for biological materials.

Acknowledgements

This work was supported by a grant from The State ofSao Paulo Research Foundation, FAPESP.

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