2004. Adsorption Desorptionand Heat of Sorption of Prikly Pear

Energy Conversion and Management 45 (2004) 249–261www.elsevier.com/locate/enconman

Adsorption–desorption isotherms and heat of sorptionof prickly pear fruit (Opuntia ficus indica)

S. Lahsasni a, M. Kouhila b,*, M. Mahrouz a

a Unit�ee de Chimie Agroalimentaire (LCOA), Facult�ee des Sciences Semlalia, B.P. 2390,

Marrakech 40001, Moroccob Laboratoire d’Energie Solaire et Plantes Aromatiques et M�eedicinales, Ecole Normale Sup�eerieure,

B.P. 2400, Marrakech 40001, Morocco

Received 16 December 2002; accepted 24 May 2003

Abstract

The equilibrium moisture contents were determined for prickly pear fruit using the gravimetric static

method at t ¼ 30, 40 and 50 �C over a range of relative humidities from 0.05 to 0.9. The sorption curves of

prickly pear fruit decreased with increase in temperature at constant relative humidity. The hysteresis effect

was observed. The GAB, modified Halsey, modified Chung-Pfost, modified Oswin and modified Henderson

models were tested to fit the experimental data. The GAB model was found to be the most suitable for

describing the sorption curves. The monolayer moisture content values for the sorption at different tem-

peratures are calculated using a modified BET equation. The isosteric heats of desorption and adsorption ofwater were determined from the equilibrium data at different temperatures.

� 2003 Elsevier Ltd. All rights reserved.

Keywords: Equilibrium moisture content; Isosteric heat; Modelling; Prickly pear fruit; Sorption isotherms

* Corresponding author. Tel.: +212-4434-0789; fax: +212-4434-2287.

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

0196-8904/$ - see front matter � 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/S0196-8904(03)00133-X

mail to: [email protected]

Notations

A, B and C model coefficientsaw water activityB0, C0, h1 and h2 GAB coefficientsd.b dry basisdf degree of freedomEMC equilibrium moisture contentM equilibrium moisture content (% d.b)Mi;exp ith experiment 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 pointsQst net isosteric heat of sorption (kJ/mol)R universal gas constant (8.314 kJ/kmolK)RH equilibrium relative humiditySEM standard error of moisturet temperature (�C)T absolute temperature (K)

250 S. Lahsasni et al. / Energy Conversion and Management 45 (2004) 249–261

1. Introduction

The prickly pear cactus (Opuntia ficus indica; Opuntia spp., Cactaceae) is native to the UnitedStates, Mexico and South America, but it grows well in other areas, including Africa, Australiaand the Mediterranean region. The major components of the prickly pear fruit pulp are 85%water, 10–15% carbohydrates and substantial amounts of vitamin C, 25–30 mg per 100 g portion[1]. Its nutritional value lies essentially in its glucose and fructose content (6–8%) [2]. In the foodsector, besides consumption of the fresh fruit, jams, alcoholic soft drinks, syrups, candied fruitand flour can be produced from the plant and oil extracted from the seeds. The vegetable stems(cladode) and fruits of prickly pear are useful to treat diabetes, high blood cholesterol levels,inflammation and obesity [3,4].

The moisture sorption isotherm is an extremely valuable tool for food scientists and techno-logists because it can be used to predict potential changes in food stability. It can be used forstoring method determination, packaging selection and ingredient selection. The relationshipbetween water activity (aw) and the equilibrium moisture content (EMC) in a product is oftenexpressed as a sorption isotherm. The typical shape of an isotherm reflects the manner in whichthe water is bound to the system [5].

Numerousmodels for predicting the relationship between equilibriummoisture, water activity andtemperature have been developed. Iglesias and Chirife [6] reviewed several equations for modellingEMC and reported that some models were adequate to characterize the sorption behaviour ofparticular foods for the given range of temperature and aw or equilibrium relative humidity (Rh).

S. Lahsasni et al. / Energy Conversion and Management 45 (2004) 249–261 251

Chen andMorey [7] evaluated four models: modified Chung-Pfost [8], modified Halsey [6], modifiedHenderson [9] and modified Oswin [10] for their ability to fit data from 18 grains and seed crops.

The BET equation, developed by Brunauer, Emmett and Teller [11], is the most popular due toits thermodynamic base [12,13]. The BET monolayer concept was found to be a reasonable guidewith respect to various aspects of interest in dried foods, but this equation was known to holdonly for a limited range of water activity 0.1–0.5.

The Guggenhein, Anderson and Boer (GAB) isotherm equation has been widely used to des-cribe the sorption behaviour of foods [14]. The GAB equation has been found to represent ade-quately the experimental data in the range of water activity (0.1–0.9) of most practical interest infood [15].

The net isosteric heat of sorption can be used to estimate the energy requirements for the de-hydration process. The level of material moisture content at which the net isosteric heat of sorptionapproaches the latent heat of vaporisation of water is often taken as an indication of the amount of‘‘bound water’’ existing in the food [16,17]. The heat of vaporisation of sorbed water may increase tovalues well above the vaporisation of pure water as food is dehydrated to low moisture levels [18].

This study aims to:

• determine the effect of temperature on the moisture adsorption and desorption isotherms ofprickly pear fruit in the temperature range 30–50 �C;

• analyse six sorption isotherm equations available in the literature;• find the most suitable model corresponding to the isotherms of prickly pear fruit;• calculate the net isosteric heat of water sorption from the experimental data.

2. Materials and method

2.1. Materials and experimental procedure

The prickly pear fruit used in the sorption isotherms experiments was grown in the region ofBengrir (near the town of Marrakech).

Fresh prickly pear fruits were used in the desorption experiments. Samples used in the ad-sorption isotherms were dried in an oven regulated at a temperature of 50 �C until reachingmaximum dehydration.

The EMC of the prickly pear fruit was determined at 30, 40 and 50 �C. The static gravimetricmethod was applied. This method is based on the use of saturated salt solutions to maintain afixed relative humidity. The salts used were KOH, MgCl2, K2CO3, NaNO3, KCl and BaCl2. Thesesalts have a range of relative humidity of 5–90%. The values of their equilibrium relative hu-midities at different temperatures are given in Table 1 [19].

The experimental apparatus consists of six glass jars of 1 l each with an insulated lid. Each glassjar contains a different salt solution so as to have a relative humidity that varies from 5% to 90%,and they are immersed in a thermostated water bath adjusted to a fixed temperature for 24 h so asto bring the salt solutions to a stationary temperature.

Duplicate samples each of 1 g (±0.001 g) for desorption and 0.1 g (±0.001) for adsorption wereweighed into glass jars. The six samples are weighed every 2 days. EMC was acknowledged when

Table 1

Selected saturated salt solutions and corresponding relative humidities (%) [19]

KOH MgCl2 K2CO3 NaNO3 KCl BaCl2

30 �C 7.38 32.38 43.17 72.75 83.62 89.80

40 �C 6.26 31.59 42.30 71.00 82.32 89.10

50 �C 5.72 30.54 40.91 69.04 81.20 88.23


three consecutive weight measurements showed a difference of less than 0.001 g. The moisturecontent of each sample was determined by a drying oven whose temperature is fixed at 105 �C.

The temperature of the thermostated bath is changed, and the same experiment is repeated forboth adsorption and desorption processes at t ¼ 30, 40 and 50 �C.

2.2. Analysis of data

The description of the relationship between EMC, Rh and temperature was verified accordingto the following models:

Modified Chung-Pfost [8]:

Rh ¼ exp�At þ B

expð�

� CMÞ�

ð1Þ

Modified Halsey [6]:

Rh ¼ exp� expðAþ BtÞ

MC

� �ð2Þ

Modified Oswin [10]:

M ¼ ðAþ BtÞ ðRhÞ1� ðRhÞ

� �C

ð3Þ

Modified Henderson [9]:

1� ðRhÞ ¼ exp½�Aðt þ BÞMC� ð4Þ
GAB [14,15]:
M ¼ ABCðRhÞ½1� BðRhÞ�½1� BðRhÞ þ BCðRhÞ� ð5Þ

whereM is the equilibrium moisture content in % d.b, Rh is the equilibrium relative humidity as adecimal, A, B and C are model coefficients and t is the temperature in �C.

The parameters B and C in the GAB equation can be correlated with temperature using thefollowing Arrehenius type equations [20]:

B ¼ B0 exph1RT

� �ð6Þ

C ¼ C0 exph2RT

� �ð7Þ


where B0, C0, h1 and h2 are coefficients, T is the absolute temperature and R is the universal gasconstant.

Modified BET [11,21]

M ¼ ðAþ BtÞCðRhÞð1� ðRhÞÞð1� ðRhÞ þ CðRhÞÞ ð8Þ

Mm ¼ Aþ Bt ð9Þ
Mm: monolayer moisture content.
The correlation coefficient (r) was one of the primary criteria for selecting the best equation to fitthe five models to the experimental data. In addition to r, the statistical parameters, mean relativeerrorMRE as a % and standard error of estimate SEM, were used to determine the quality of the fit.

MRE ¼ 100

N

XNi¼1

Mi;exp �Mi;pre

Mi;exp

�� ð10Þ

SEM ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNi¼1ðMi;exp �Mi;preÞ2

df

sð11Þ

where Mi;exp is the ith experimental moisture content, Mi;pre is the ith predicted moisture content,N is the number of observations and df is the degree of freedom of the regression model.

2.3. Determination of the isosteric heat of sorption

The net isosteric heat of sorption can be determined from moisture sorption data using thefollowing equation, which is derived from the Clausius–Clapeyron equation [22]:

o lnðRhÞoðT Þ ¼ Qst

RT 2ð12Þ

Integrating Eq. (12), assuming that the net isosteric heat of sorption (Qst) is temperature inde-pendent, gives the following equation:

lnðRhÞ ¼ � Qst

R

� �1

Tþ K ð13Þ

The Marquardt–Levenberg nonlinear optimisation method, using the computer programsCurve Expert 3.1 and Origin 6.1, was used to find the best equation for the prickly pear fruitsorption isotherms and the net isosteric heat of sorption.

3. Results and discussion

3.1. Experimental results

The hygroscopic equilibrium of prickly pear fruit is reached in 10 days for desorption and 8days for adsorption.

Fig. 1 gives the experimental data obtained for adsorption and desorption of prickly pear fruit att ¼ 30 �C. The sorption isotherms have an S-shape profile, typical for many food materials [23–31].

0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100

Equ

ilibr

ium

moi

stur

e co

nten

t M %

d.b

Equilibrium relative humidity Rh

adsorption isotherm desorption isotherm

Fig. 1. Desorption and adsorption isotherms of prickly pear fruit at t ¼ 30 �C.


Fig. 1 shows that the desorption and adsorption curves of prickly pear fruit have similar rates.The hysteresis effect was observed. At constant relative humidity, the EMC of desorption is higherthan the adsorption one. Several hypotheses have been put forward to explain hysteresis. Al Hodali[32] explains this hysteresis by considering a rigid structure pore connected to its surrounding by asmall capillary. During adsorption, the capillary begins to fill as a result of the rising in relativehumidity, while the pore is still empty. When the partial pressure of the vapour in air becomesgreater than the vapour pressure of the liquid in the capillary, the moisture will move into the pore.For desorption, the pore is initially full of liquid at saturation. This liquid can escape only when thepressure of the surrounding air becomes lower than the vapour pressure of liquid inside the cap-illary. As the system of pores has generally a large range of capillary diameters, it results thatdifferences between adsorption and desorption are observed.

The adsorption and desorption isotherms of prickly pear fruit obtained for three temperatures(30, 40 and 50 �C) are shown in Figs. 2 and 3. The EMC increases with decreasing temperature atconstant relative humidity. Similar results for many plants and foods materials have been reportedin the literature [23–31].

0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100 Experimental data at t=50˚C

Experimental data at t=40˚C

Experimental data at t=30˚C

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b)


Fig. 2. Influence of temperature on the desorption isotherms of prickly pear fruit.

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

70

80

90

100

Equ

ilibr

ium

moi

stur

e co

nten

t M (

%d.

b)


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

Fig. 3. Influence of temperature on the adsorption isotherms of prickly pear fruit.


3.2. Fitting of sorption models to experimental sorption data

The results of nonlinear regression analysis of fitting the sorption equations to the experimentaldata are shown in Table 2 for desorption, and in Table 3 for adsorption. The parameters for theGAB model are presented in Table 4. The moisture content models were compared according totheir correlation coefficient (r), mean relative error (MRE) and standard error of estimate (SEM).

Table 2

Parameters estimation, r, MRE and SEM of the four equations fitted to the desorption isotherms of prickly pear fruit

A B C r MRE% SEM

Modified Henderson 0.0005 )28.8195 1.7241 0.9922 13.67 3.7672

Modified Chung-Pfost 188.6934 9.2432 0.0453 0.9861 11.82 5.0116

Modified Oswin 55.9235 )0.5301 0.4227 0.9944 9.62 3.1456

Modified Halsey 12.3481 )0.1527 1.8807 0.9932 6.91 3.4732

Table 3

Parameters estimation, r, MRE and SEM of the four equations fitted to the adsorption isotherms of prickly pear fruit

A B C r MRE% SEM

Modified Henderson 0.0005 0.1991 1.1195 0.9839 15.31 5.2440

Modified Chung-Pfost 472.1636 108.6252 0.0485 0.9631 27.13 7.7591

Modified Oswin 29.5784 )0.1426 0.5051 0.9934 10.79 3.2897

Modified Halsey 5.8588 )0.0338 1.4528 0.9967 9.76 2.7683

Table 4

Parameters estimation, r, MRE and SEM of the GAB equation fitted to the sorption isotherms of prickly pear fruit

A B0 C0 h1 h2 r MRE% SEM

Desorption 19.1677 3.1818 0.0004 )3403 28696 0.9967 5.89 2.7795

Adsorption 12.9642 1.4753 0.0002 )1163 32752 0.9976 5.89 2.2733

0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100

t=40˚C

t=30˚C t=50˚C

t=40˚C

t=40˚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

20

40

60

80

100

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

20

40

60

80

100

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b)

Equilbrium relative humidity Rh

Experimental data Modified Chung-Pfost model

0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100E

quili

briu

m m

oist

ure

cont

ent M

(%

d.b

)


Experimental data Modified Henderson model

0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

b)


Experimental data GAB model

Fig. 4. Desorption isotherms of five models of prickly pear fruit.


0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100

t=30˚C t=50˚C

t=30˚C t=30˚C

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

20

40

60

80

100

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 1.0

0

20

40

60

80

100

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 1.0

0

20

40

60

80

100E

quili

briu

m m

oist

ure

cont

ent M

(%

d.b

)

Equlibrium relative humidity Rh

Experimental data Modified Henderson model

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

70

80

90

100

Equ

ilibr

ium

moi

stur

e co

nten

t M (

% d

.b)


Experimental data GAB model

Fig. 5. Adsorption isotherms of five models of prickly pear fruit.


Table 5

Parameters estimation, r, MRE and SEM of the modified BET equation fitted to the sorption isotherms of prickly pear

fruit

A B C r MRE% SEM

Desorption 10.6385 )0.0063 )136.6911 0.9466 14.60 9.7594

Adsorption 8.0978 0.0141 )94.4504 0.9864 11.13 4.4081


However, the GAB model had the highest r value and the lowest MRE and SEM values fordesorption and adsorption compared to the other models.

Figs. 4 and 5 show that there is a slight difference between the experimental data and thedifferent models. To compare the performances of the five models, the GAB model gave the bestresults for the isotherms for both desorption and adsorption of prickly pear fruit. Consequently,the GAB model was selected to describe better the sorption isotherms of prickly pear fruit. Themodified Halsey is the second best model.

The values of the monolayer moisture content obtained using modified BET model are shown inTable 5. The Mm values decreased with the increase in temperature for desorption. For adsorption,theMm values decrease with decrease in temperature. There is also a hysteresis effect with respect tothemonolayermoisture content. This decrease inmonolayer moisture contents for desorption can beexplained by considering the structural changes in the plant at increased temperatures. It was sug-gested that at increased temperature, some water molecules are activated to energy levels that allowthem to break away from their sorption sites, thus decreasing the equilibrium moisture content [27].

3.3. Heat of sorption

The isosteric heat of sorption, Qst, values were calculated from the slope of the plot between thevalues of lnðRhÞ and 1=T at constant moisture content as shown in Figs. 6 and 7. The relativehumidities at different temperatures and at constant moisture content were obtained from Figs. 2and 3. The variations of the heats of adsorption and desorption of the prickly pear fruit withmoisture content are shown in Figs. 8 and 9, respectively. The isosteric heats of adsorption and

0.00310 0.00315 0.00320 0.00325 0.00330 0.00335

0.4

0.6

0.8

1.0

1.2

1.4

ln(R

h)

1/T

M=25% M=30% M=35% M=40% M=45%

Fig. 6. lnðRhÞ vs 1=T graphs for calculating the heat of desorption of prickly pear fruit.

0.00310 0.00315 0.00320 0.00325 0.00330 0.00335

0.2

0.4

0.6

0.8

1.0

ln(R

h)

1/T

M=25% M=30% M=35% M=40% M=45%

Fig. 7. lnðRhÞ vs 1=T graphs for calculating the heat of adsorption of prickly pear fruit.

30 35 40 45

6

8

10

12

14

Hea

t of

deso

rptio

n Q

st (

kJ/m

ol)

Equilibrium moisture content M (% d.b)

Experimental data Curve fit

Fig. 8. Net isosteric heat of desorption for different moisture contents.


desorption of prickly pear fruit decrease with increase in material moisture content. The heat ofdesorption is greater than that of adsorption. This indicates that the energy required in the de-sorption process is greater than that in the adsorption process as stated by Hossain et al. [30] andErtekin and Sultanoglu [31]. At low moisture contents, the heat of sorption is higher than at highmoisture contents. Tsami [33] suggested that the rapid increase in the heat of sorption at lowmoisture content was due to the existence of highly active polar sites on the surfaces of the foodmaterial, which are covered with water molecules forming a mono-molecular layer. The netisosteric heat of desorption and adsorption of water in prickly pear fruit can be expressedmathematically as a polynomial function of moisture content:

Qst ðdesorptionÞ ¼ 207:5376� 13:8130M þ 0:3220M2 � 0:0025M3 ðr ¼ 1Þ ð14ÞQst ðadsorptionÞ ¼ 6:5183þ 0:0267M � 0:0032M2 ðr ¼ 1Þ ð15Þ

30 35 40 450

1

2

3

4

5

6

Hea

t of

adso

rptio

n Q

st (

kJ/m

ol)

Equilibrium moisture content M (% d.b)

Experimental data Curve fit

Fig. 9. Net isosteric heat of adsorption for different moisture contents.


4. Conclusions

The moisture adsorption and desorption isotherms of prickly pear fruit at three temperatures (30,40 and 50 �C) and different relative humidities were determined using the gravimetric static method.The EMC increases with decrease in temperature at constant relative humidity. It has been furtherdemonstrated that the temperature dependence of sorption isotherms could be predicted withreasonable accuracy. The hysteresis phenomenon was observed.

Among the sorption models chosen to fit sorption curves, the GAB equation describes better thesorption isotherms of prickly pear fruit. The monolayer moisture content values for adsorptionand desorption at different temperatures were determined using a modified BET equation.

The heat of sorption of prickly pear fruit decreases with an increase in moisture content and isfound to be a polynomial function of moisture content.

Acknowledgements

This study was financed by the CNRST (Morocco) for a project PROTARS III (Ref. D12/34)on Solar Drying and Quality of Medicinal and Aromatic plants.

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2004. Adsorption Desorptionand Heat of Sorption of Prikly Pear

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