Moisture sorption isotherms and heat of sorption of bitter orange leaves (Citrus aurantium)

www.elsevier.com/locate/jfoodeng

Journal of Food Engineering 67 (2005) 491–498

Moisture sorption isotherms and heat of sorptionof bitter orange leaves (Citrus aurantium)

L. Ait Mohamed a,b, M. Kouhila a,*, A. Jamali a, S. Lahsasni a,b, M. Mahrouz b

a Laboratoire d�Energie Solaire et des Plantes Aromatiques et Medicinales, Ecole Normale Superieure, BP 2400, Marrakech, Moroccob Unite de Chimie Agroalimentaire (LCOA), Faculte des Sciences Semlalia, BP 2390, Marrakech, Morocco

Received 3 November 2003; accepted 17 May 2004

Abstract

Moisture adsorption–desorption isotherms (EMC/e.r.h.) of Citrus aurantium leaves were determined at 30, 40, and 50 �C using

the standard gravimetric static method over a range of relative humidity from 0.05 to 0.9. The experimental sorption curves were

fitted by six equations: modified Chung–Pfost, modified Halsey, modified Oswin, modified Henderson, modified BET, and GAB.

The modified Halsey and the modified BET models were found to satisfactorily describe the desorption isotherms of Citrus auran-

tium leaves. For adsorption, GAB and modified BET models were the best fit. The net isosteric heats of sorption of water were deter-

mined from the equilibrium data at different temperatures.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: C. aurantium leaves; Equilibrium moisture content; Isosteric heat of sorption; Modelling; Sorption isotherms

1. Introduction

Bitter orange (Citrus aurantium) is a plant that be-longs to the Rutaceae Family. The peel, flower, leaves,

and fruit are used in both traditional and modern

Chinese medicine. The common uses of C. aurantium

are as a dietary supplement, help relieve stomach upset,

stimulate the appetite, assist with mild insomnia, treat

ringworm infections such as athetes foot and jock itch,

treat inflammation of the eyelid, skin bruising, and mus-

cle pain. Bitter orange is also commonly marketed as aweight loss remedy and as a nasal decongestant. It can

also increase the side effects of many medications

such as: anti-anxiety, cholesterol, decongestant, allergy,

0260-8774/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jfoodeng.2004.05.016

* Corresponding author. Tel.: +212 44 340 125; fax: +212 44 342

287.

E-mail address: [email protected] (M. Kouhila).

fungal, HIV, sedation, anti-nausea, weight loss, steroid,

and erectyl dysfunction medications. The Food and

Drug Administration (FDA) has approved bitter orange(in small amounts) as a flavouring agent. In manufactur-

ing, bitter orange is used in cosmetics and soaps (Jeff,

2002).

During the storage of C. aurantium, some physical,

chemical, and biological reactions (principally, the

transformation of starch to sugars) can happen. These

processes depend on the moisture content of C. auran-

tium. The study of equilibrium moisture content(EMC) was of great importance to know and under-

stand many problems such as the design and optimisa-

tion of processes such as drying, for predicting shelf

life stability and for packaging problems (Gal, 1987;

Spiess & Wolf, 1987). The moisture sorption isotherms

for C. aurantium leaves describe the relationship

between the water activity and the EMC. For determin-

ing the EMC of C. aurantium leaves, the static gravi-metric technique was used.

mailto:[email protected]

Nomenclature

A, B, and C model coefficients

aw water activity (decimal)

B0, C0, h1,

and h2

GAB coefficients

Citrus aurantium C. aurantium

d.b. dry basis

df number of degrees of freedom

EMC equilibrium moisture contente.r.h. equilibrium relative humidity

(decimal)

M equilibrium moisture content

(% d.b.)

Mi,exp ith experimental moisture content

(% d.b.)

Mi,pre ith predicted moisture content

(% d.b.)

Mm monolayer moisture content

(% d.b.)

MRE mean relative error (%)

N number of data points

Qst net isosteric heat of sorption

(kJ/mol)R universal gas constant

(8.314 J/molk)

SEE standard error of estimate

t temperature in (�C)T absolute temperature (K)

492 L. Ait Mohamed et al. / Journal of Food Engineering 67 (2005) 491–498

The objectives of this work are to:

� determine the effect of temperature on the moisture

adsorption and desorption isotherms of C. aurantium

leaves;

� analyse six sorption isotherm equations available in

the literature;

� find the most suitable model describing the isothermsof C. aurantium leaves;

� calculate the net isosteric heat of water sorption from

the experimental data.

Fig. 1. Apparatus for the sorption isotherms measurement: (1)

thermostatic bath; (2) saturated salt solution; (3) flask containing

product; (4) tripod; (5) glass jar.

2. Material and method

2.1. Experimental procedure

The C. aurantium leaves used in the sorption iso-

therms experiments were grown in Marrakech (histori-

cal town in central Morocco). Harvest was between

May and June 2003.

The sorption method used is the static gravimetric

technique, which is based on the use of saturated saltsolutions (Spiess & Wolf, 1987; Wolf, Spiess, & Jung,

1985) to maintain a fixed relative humidity when the

equilibrium is reached. The water activity of the food

is identical to the relative humidity of the atmosphere

at equilibrium conditions and the mass transfer between

the product and the ambient atmosphere is assured by

natural diffusion of the water vapour.

Six saturated salt solutions (KOH, MgCl2, K2CO3,NaNO3, KCl, and BaCl2) were prepared corresponding

to a wide range of water activities ranging from 0.05 to

0.9 (Greenspan, 1977). The experimental apparatus

(Fig. 1) consisted of six glass jars of 1 l each with an in-

sulted lid. Every glass jar was a quarter filled with a sat-

urated salt solution (Ait Mohamed et al., in press).

Fresh leaves of C. aurantium were used in desorption

experiments. Samples used in adsorption isotherms werepre-dried in an oven at 50 �C for 48 h. Duplicate sam-

ples each of 0.1 g (±0.001 g) for the desorption and

0.04 g (±0.001 g) for adsorption were weighed and

placed in glass jars containing saturated salt solution.

The six samples were weighed every three days. The

EMC was acknowledged when three consecutive weight

measurements showed a difference less than 0.001 g. The

EMC of each sample was determined by a drying ovenwhose temperature is fixed at 105 �C. The temperature

of the thermostatic bath was changed, and the same

L. Ait Mohamed et al. / Journal of Food Engineering 67 (2005) 491–498 493

experiment was conducted for both adsorption and de-

sorption processes at 30, 40, and 50 �C.

2.2. Analysis of sorption data

A large number of models have been proposed in theliterature for the sorption isotherms (Van den Berg &

Bruin, 1981). In the present study, the description of

the relationship between EMC, equilibrium relative hu-

midity (e.r.h.), and temperature for C. aurantium leaves

was verified according to the six following models:

1. Modified Chung–Pfost (Pfost, Maurer, Chung, &

Milliken, 1976):

e:r:h: ¼ exp�At þ B

expð�CMÞ� �

ð1Þ

2. Modified Halsey (Iglesias & Chirife, 1976a):

e:r:h: ¼ exp� expðAþ BtÞ

MC

� �ð2Þ

3. Modified Oswin (Oswin, 1946):

M ¼ ðAþ BtÞ ðe:r:h:Þ1� ðe:r:h:Þ

� �C

ð3Þ

4. Modified Henderson (Thompson, Peart, & Foster,

1968):

1� ðe:r:h:Þ ¼ exp �Aðt þ BÞMC� �

ð4Þ

5. Modified BET (Brunauer, Emmett, & Teller, 1938;

Iglesias & Chirife, 1976b):

M ¼ ðAþ BtÞCðe:r:h:Þð1� ðe:r:h:ÞÞð1� ðe:r:h:Þ þ Cðe:r:h:ÞÞ ð5Þ

Mm ¼ Aþ Bt ð6Þwhere Mm is the monolayer moisture content. The BET

equation is valid for e.r.h.<0.5.

6. GAB (Van den Berg, 1984):

M ¼ ABCðe:r:h:Þ½1� Bðe:r:h:Þ�½1� Bðe:r:h:Þ þ BCðe:r:h:Þ� ð7Þ

where M is the equilibrium moisture content in % d.b.,e.r.h. is the equilibrium relative humidity as a decimal,

A, B, and C are model coefficients, and t is the temper-

ature in �C.

The parameters B and C in the GAB equation can be

correlated with temperature using the following Arre-

henius-type equations (Labuza, Kaanane, & Chen,

1985):

B ¼ B0 exph1RT

� �ð8Þ

C ¼ C0 exph2RT

� �ð9Þ

where B0, C0, h1, and h2 are coefficients, T is the absolute

temperature, and R is the universal gas constant.

The statistical parameter mean relative error MRE as

a %, and standard error of estimate SEE were used to

determine the quality of the fit.

MRE ¼ 100

N

XNi¼1

Mi;exp �Mi;pre

Mi;exp

�� ð10Þ

SEE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNi¼1

ðMi;exp �Mi;preÞ2

d

vuuutð11Þ

where Mi,exp is the ith experimental moisture content,

Mi,pre is the ith predicted moisture content, N is thenumber of data points, and df is the number of degrees

of freedom of regression model.

2.3. Determination of the net isosteric heat of sorption

The heat of sorption can be explained by the

Clausius–Clapeyron equation (Iglesias & Chirife,

1976c; Okos, Narsimhan, Ingh, & Weitmauuer, 1992)as follows:

o lnðe:r:h:ÞoðT Þ ¼ Qst

RT 2ð12Þ

Integrating Eq. (12), assuming that the net isosteric heat

of sorption (Qst) is temperature independent gives the

following equation:

lnðe:r:h:Þ ¼ � Qst

R

� �1

Tþ K ð13Þ

The Marquardt–Levenberg non-linear optimisationmethod, using the computer programs Curve Expert

3.1, and Origin 6.1 were used to find the best equation

for sorption isotherms of the C. aurantium leaves (Ait

Mohamed et al., in press).

3. Results and discussion

3.1. Experimental results

The hygroscopic equilibrium of C. aurantium leaves

was reached in 10 days for desorption, and nine days

for adsorption. The results of the experiments are pre-

sented in Figs. 2 and 3. These figures show that theEMC increases with decreasing temperature at constant

e.r.h. This result may be explained by the higher excita-

tion state of water molecules at higher temperature thus

decreasing the attractive forces between them. Further-

more, at constant temperature, the EMC increases with

increasing equilibrium relative humidity. Similar results

have been reported in the literature (Aregba, 2001;

Basunia & Abe, 2001; Belghit, Kouhila, & Boutaleb,2000; Ertekin & Sultanoglu, 2001; Kouhila, Belghit,

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b.)

Equilibrium relative humidity e.r.h.

Desorption data Adsorption data

Fig. 4. Desorption and adsorption isotherms of C. aurantium leaves at

t=50 �C.

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b.)


Experimental data at t=30°C Experimental data at t=40°C Experimental data at t=50°C

Fig. 3. Influence of temperature on the adsorption isotherms of

C. aurantium leaves.

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50E

quili

briu

m m

oist

ure

cont

ent M

(%

d.b

.)

Equilibrium relative humidity e.r.h

Experimental data at t=30°C Experimental data at t=40°C Experimental data at t=50°C

Fig. 2. Influence of temperature on the desorption isotherms of



Daguenet, & Boutaleb, 2001; Kouhila, Kechaou,

Otmani, Fliyou, & Lahsasni, 2002; Lahsasni, Kouhila,

Mahrouz, & Fliyou, 2003; Lahsasni, Kouhila, Mahrouz,

& Kechaou, 2002; Menkov, 2000; Menkov, Paskalev,

Galyazkov, & Kerezieva-Rakova, 1999; Stencl, Otten,

Gotthardova, & Homola, 1999).

A hysteresis effect was observed for C. aurantium

leaves (Fig. 4). This phenomenon is not fully under-

stood, although there is general agreement that some

thermodynamically irreversible processes must occur

during desorption or adsorption or both. Many expla-

Table 1

Model parameters estimation, MRE, and SEE of the six equations fitted to

Modified Chung–Pfost Modified Halsey Modified O

A 69.4254 5.8303 17.8822

B �18.8773 0.0275 0.1217

C 0.0965 2.3305 0.3288

B0

C0

h1h2MRE % 9.6968 8.7538 9.4282

SEE 4.6380 2.9955 3.6616

nations for this phenomenon have been reported (Kou-hila et al., 2002; Lahsasni et al., 2002). One theory

used to explain hysteresis suggests that in the wet con-

dition the polar sites onto which water is sorbed are

not entirely satisfied. Upon drying the water holding

sites are drawn close enough together with shrinkage

to satisfy each other. This results in a reduction of

the water binding capacity during adsorption (Moshse-

nin, 1986).

3.2. Fitting of sorption models to experimental

sorption data

The coefficients of the modified Chung–Pfost, modi-

fied Halsey, modified Oswin, modified Henderson, mod-

ified BET, and GAB models with their statistic mean

relative error MRE and standard error of estimateSEE are presented in Tables 1 and 2. As seen in these ta-

bles, the modified Halsey model gives the best fit to the

experimental data with MRE of 8.7538 and SEE of

2.9955 for desorption isotherms for a wide range of

water activity (0.05–0.9). For adsorption, the GAB

model gives the lowest MRE (8.8361) and SEE

(2.1356) values. The modified BET equation gives the

lowest MRE 1.6876 and 3.9611 and the lowest SEE0.2102 and 0.3930 for desorption and adsorption iso-

therms respectively for the range of water activity

the desorption isotherms of C. aurantium leaves

swin Modified Henderson Modified BET GAB

0.0011 3.1122 6.887

�28.7585 0.1013

1.9834 119.2306

2.63·1016

22.12

�28823.7

�8206.84

13.6476 1.6876 14.3455

5.301 0.2102 3.9723

Table 2

Model parameters estimation, MRE, and SEE of the six equations fitted to the adsorption isotherms of C. aurantium leaves

Modified Chung–Pfost Modified Halsey Modified Oswin Modified Henderson Modified BET GAB

A 126.1807 3.9356 13.3114 0.0080 �11.5245 4.1061

B 13.9369 �0.0335 �0.0857 �9.3124 0.4363

C 0.0971 1.4010 1.6874 0.5270 68.0089

B0 8.4697·1016

C0 3.007

h1 �32807.2

h2 �2845.91

MRE % 30.0883 13.312 31.005 47.0067 3.9611 8.8361

SEE 6.7111 2.5969 3.6496 5.1197 0.3930 2.1356

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

t=30°C

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b.)


Experimental data Modified Chung - Pfost model

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

t=30°C

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b)

Equilibrium relative humidity e.r.h

Experimental data Modified Hasley model

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

t=30°C

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b.)


Experimental data Modified Oswin model

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

t= 30°C

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b.)


Experimental data Modified Henderson model

0.0 0.1 0.2 0.3 0.4 0.50

5

10

15

20

t= 30°C

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b.)


Experimental data Modified BET model

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

t=30°C

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b.)


Experimental data GAB model

(c)

(a) (b)

(d)

(f)(e)

Fig. 5. Desorption isotherms of C. aurantium leaves fitted by six models.


0.05–0.45. The observed and predicted sorption iso-

therms using six models are shown in Figs. 5 and 6.

Consequently, the modified Halsey model describes

better the desorption isotherms and the GAB equation

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

t=30°CE

quili

briu

m m

oist

ure

cont

ent M

(%

d.b

)


Experimental data Modified Chung- Pfost model

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

t=30°C

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b.)


Experimental data Modified Halsey model

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

t=30°C

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b.)


Experimental data Modified Oswin model

0.0 0.2 0.4 0.6 0.8 1.0

0

10

20

30

40

50

60

t=50°C

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b.)


Experimental data Modified Henderson model

0.0 0.1 0.2 0.3 0.40

5

10

t=40°C

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b.)


Experimental data Modified BET model

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

t=50°C

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b)


Experimental data GAB model

(a)

(c)

(e)(f)

(d)

(b)

Fig. 6. Adsorption isotherms of C. aurantium leaves fitted by six models.

310 315 320 325 330

0.4

0.8

1.2

1.6

2.0

ln (

e.r.h

.)

(1/T). 105 K-1

M=15% M=20% M=25% M=30%

Fig. 7. ln (e.r.h) vs 1/T graphs for calculating the heat of desorption of



is satisfactory in predicting the EMC for adsorption ofC. aurantium leaves. The modified BET was an adequate

model for describing the sorption isotherms at relative

humidity lower than 0.5.

3.3. Heat of sorption

The values of Qst were calculated from the slope of

the plot between the values of ln(e.r.h) and 1/T at con-stant moisture content as shown in Figs. 7 and 8.

The representation of the net isosteric heats of sorp-

tion for different moisture contents is shown in Fig. 9.

It can be observed that the net isosteric heat decreases

when the moisture content increases for sorption

(Ait Mohamed et al., in press). These trends are similar

in both food and pharmaceutical products (Acosta,
Nuevos, Rodriguez, Pardillo, & Ramos, 2000; Ertekin
& Sultanoglu, 2001; Hossain, Bala, Hossain, & Mondol,

12 16 20 24 28 32

0

20

40

60

80

100

Hea

t of

sorp

tion

Qst

(kJ

/mol

)

Equilibrium moisture content M (% d.b.)

Experimental data of desorption Curve fit of desorption Experimental data of adsorptionCurve fit of adsorption

Fig. 9. Net isosteric heat of adsorption and desorption for different

moisture contents.

310 315 320 325 330

0.2

0.3

0.4

0.5

0.6ln

(e.

r.h.)

(1/T). 105 K-1

M=15% M=20% M=25% M=30%

Fig. 8. ln (e.r.h.) vs 1/T graphs for calculating the heat of adsorption

of C. aurantium leaves.


2001; Myhara, Taylor, & Al-Bulushi, 1996; Tsami,

1991). The net isosteric heats of desorption and adsorp-

tion of water in C. aurantium leaves can be expressed

mathematically as a power function of moisture content:

QstðdesorptionÞ ¼ 241:284� 15:8364M

þ 0:2624M2 ðr ¼ 0:9990Þ ð14Þ

QstðadsorptionÞ ¼ 2:6478þ 10M�7:8881 ðr ¼ 0:9996Þð15Þ

These mathematical relationships may be used to calcu-

late the heat of sorption of C. aurantium leaves for var-

ious moisture contents.

4. Conclusions

The sorption curves of C. aurantium leaves obtained

at three temperatures (30, 40, and 50 �C) showed a sig-

moid shape, as expected from previous studies. Adsorp-

tion–desorption equilibrium moisture data have been

collected for a range of temperatures and relative humi-

dities commonly used in drying and storage of C. auran-tium leaves. The experimental data were fitted to six

isotherm models. The modified Halsey equation gives

the best fit for desorption isotherms for a wide range

of water activity (0.05–0.9). The GAB model describes

well the isotherms of adsorption of this product. The

BET equation gives also the best fit for both adsorption

and desorption for the aw range of 0.1–0.5. The EMC

decreases with increasing temperature and a hysteresis

effect was observed. By applying the Clausius–Clapey-

ron concept, the net isosteric heats for adsorption anddesorption were evaluated as a power function of mois-

ture content.

Acknowledgment

The authors gratefully acknowledge the CNRST

(Morocco) for providing financial support of a projectPROTARS III (No. D12/34) entitled: Convective solar

drying and quality control of medicinal and aromatic

plants of the Moroccan traditional medicine.

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Documents

Moisture sorption isotherms and heat of sorption of bitter orange leaves (Citrus aurantium)