Journal of Food Engineering 61 (2004) 467–470

www.elsevier.com/locate/jfoodeng

Research note

Application of the Guggenheim, Anderson and De Boer modelto correlate water activity and moisture content during

osmotic dehydration of apples

Fr�eed�eeric Prothon, L�ıılia M. Ahrn�ee *

SIK, The Swedish Institute for Food and Biotechnology, Department of Environment and Process Engineering, Box 5401, 40229 G€ooteborg, Sweden

Received 24 September 2002; accepted 6 April 2003

Abstract

Water activity and moisture content are the most valuable characteristics for assessing the stability of dried foods. The aim of this

work was to evaluate if a desorption isotherm model could be used to describe the relationship between the water activity and

moisture content in the product during osmotic dehydration. This model can lead to a better understanding of how water activity of

a product can be reduced during osmotic dehydration. The Guggenheim, Anderson and De Boer (GAB) model was chosen because

it has been proven to best fit the desorption and adsorption of foods over a large range of water activities. The studied material was

apple pieces, and the osmotic medium with a water activity of 0.939 was prepared with sucrose. The osmotic dehydration process

was studied by collecting moisture content and water activity data at different temperatures and times. The model was shown to fit

well the experimental points at temperatures 25, 45 and 55 �C. At 65 �C, however, the model is satisfactory if aw is below 0.970 but

not above. The effect of temperature can be expressed on the C-parameter of the GAB model.

� 2003 Elsevier Ltd. All rights reserved.

Keywords: GAB model; Osmotic dehydration; Water activity prediction; Temperature

1. Introduction

In the context of minimal processing, the measure-

ment and prediction of water activity provide the best

available tool for evaluating the stability of foods. The

sorption isotherm, consisting of a graphic representation

of water activity (aw) against moisture content at con-

stant temperature, is a common way of presenting the

relationship between these two parameters (McLaughlin& Magee, 1998; Rahman & Labuza, 1999). Desorption

isotherms are of particular importance in the design of a

food dehydration process, especially in the determina-

tion of a drying end point. The end point of drying is the

residual moisture content of the final product which

ensures economic viability and microbiological safety,

i.e. a water activity value lower than 0.60. Desorption

isotherms focus therefore on low moisture or interme-diate moisture zones, because this is the range of mois-

ture content of the food product after drying methods

*Corresponding author. Tel.: +46-31-335-56-00; fax: +46-31-83-37-

82.

E-mail address: lia@sik.se (L.M. Ahrn�ee).

0260-8774/$ - see front matter � 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/S0260-8774(03)00119-5

such as air-drying and freeze-drying. The effect of tem-perature on moisture sorption isotherms has also been

reported in many studies (Vel�aasquez de la Cruz, Torres,

& Mart�ıın-Polo, 2001; Wang & Brennan, 1991).

Numerous mathematical models have been proposed

for the study of both adsorption and desorption of

foods, such as the GAB, Iglesias and Chirife, BET,

Oswin, and Ferro Font�aan models (Barbosa-Canovas &

Vega-Mercado, 1996; Crapiste & Rotstein, 1982; Gekas,1992; Wang & Brennan, 1991). There is a lack of

knowledge on how the overall water activity of cellular

material is evaluated near the full turgor state (Crapiste

& Rotstein, 1982). The Guggenheim–Anderson–de Boer

(GAB) model is reported to be the best for fitting

sorption isotherm data for the majority of food products

up to aw levels of approximately 0.9 (Barbosa-Canovas

& Vega-Mercado, 1996; Timmermann, Chirife, & Igle-sias, 2001; Tsami, Krokida, & Drouzas, 1999). At

aw > 0:9, which is the region where cellular material is

still in a quasi-turgor state, the water activity was sel-

dom accurately measured or studied.

Osmotic dehydration is characterized by a more com-

plex mass transfer process than air-drying. The transport

Table 1

Some characteristics of mutsu apple

Dry matter (%) 13.9� 0.8

�Brix 12.8� 1.0

Density (g/cm3) 0.839� 0.014

468 F. Prothon, L.M. Ahrn�ee / Journal of Food Engineering 61 (2004) 467–470

of water out of the tissue is completed by a counter-cur-rent diffusion of the osmotic agent from the solution to-

ward the tissue. These two simultaneous transports have a

depressing effect on the aw of the samples. Osmotic pro-

cesses are often evaluated in terms of water loss (WL) and

solid gain (SG) (Bolin, Huxsoll, Jackson, & Ng, 1983;

Erba, Forni, Colonello, & Giangiacomo, 1994; Garrote,

Silva, & Bertone, 1992; Hawkes & Flink, 1978). Mathe-

matic models have been reported in the literature to de-scribe thewater transport during osmotic drying (Azuara,

Beristain, & Garcia, 1992; Fito & Chiralt, 1997; Pana-

giotou, Karathanos, & Maroulis, 1998; Toupin, Mar-

cotte,&LeMaguer, 1989).However, only few studies aim

at representing kinetics of water activity changes (Hough,

Chirife, & Marini, 1993; Monsalve-Gonzalez, Barbosa-

C�aanovas, & Cavalieri, 1993). Marcotte and Le Maguer

(1991) developed a model based on the equality of awbetween the osmotic solution and potato material.

A mathematical model, based on the principles of

desorption isotherms, can be a suitable way to predict the

aw of a product during osmotic dehydration using the

moisture content data. A reduction of the experimental

work can therefore be reached. In addition, this model

can be included in the mathematical models for des-

cription of water transport during dehydration allowingthe direct prediction of the water activity in the product.

The aim of this study was to evaluate if the GAB

model can be used (1) to describe the relationship be-

tween aw and moisture content in the particular case of

osmotic dehydration and (2) to study the effect of tem-

perature on the parameters of this model.

2. Materials and methods

2.1. Sample preparation

A Swedish apple variety (Mutsu) produced in the

Kivik region was purchased from a local market and

stored at 4 �C at a relative humidity of around 95%. In

the experiments two batches of apples were used. It was

always ensured that apples of satisfying and equivalent

quality in terms of firmness, colour and size were cho-

sen. In order to evaluate the quality of the apples, the

degree Brix was always measured and only apples withBrix 12.8� 1.0 were used. A cork borer was used to

extract the samples. Only radial orientation was used,

i.e. the samples were cut equatorially from the surface

into the core so as to sample the parenchymatic tissue.

From each radial cylinder one apple sample was pro-

duced with the help of a cutting device by cutting at the

point were the vascular tissue is at its densest, thus ob-

taining a sample from the periphery of the parenchyma.The cutting device was specially built in order to cut

cylinders without applying compression forces to the

samples during the preparation stage. The blades that

were used were suitable for the microtome. The samples

were disks with an average diameter of approximately

13 mm and average width of approximately 10 mm. The

samples were placed on wet paper to prevent dehydra-

tion until all the samples were cut.

Since the composition of foodstuffs greatly influences

sorption isotherms, some characteristics ofMutsu apples

are gathered in Table 1.

2.2. Experimental set-up and sampling procedure

A 50% w/w sucrose solution corresponding to a water

activity value of 0.939� 0.001 at 24 �C was prepared by

mixing grade sucrose with distilled water. Bottles with a

volume of 250 cm3 were filled with both samples and

osmotic solution. In each bottle six samples were im-

mersed in 125 ml osmotic medium, which corresponds

to a 1:8 volume ratio. Since the apple samples have alower density than the osmotic solution, a net was used

in order to keep them immersed in the solution.

The bottles were placed in a shaking water bath with

80 rotations per min (rpm). Experiments were carried

out at temperatures of 25, 45, 55 and 65 �C. The osmotic

treatment took place over a period of up to 24 h.

2.3. Measurements during processing

After removal from the osmotic medium, the sampleswere washed with distilled water, to remove excess so-

lution, and blotted with absorbent tissue to remove ex-

cess water, after which their weight, Brix and water

activity were measured. Water activity was measured

with a water activity meter (AquaLab Series 3 TE) with

temperature control and an accuracy of �0.003. Sam-

ples were cut to tiny discs in order to fill the surface of

the cups, and the water activity was measured at 24 �C.The moisture content was determined by drying the two

samples in a 70 �C vacuum oven at 100 mmHg until a

constant weight was reached (AOAC, 1995).

2.4. Moisture isotherms model

The GAB equation was used to describe the dry basis

moisture content (X ) as a function of water activity (aw):

X ¼ CkX0aw½ð1� kawÞð1� kaw þ CkawÞ�

ð1Þ

where C and k are constants and X0 is described in the

literature as the monolayer moisture content on dry

basis (kg/kg).

F. Prothon, L.M. Ahrn�ee / Journal of Food Engineering 61 (2004) 467–470 469

2.5. Data analysis

Equation parameters were estimated by the general-

ized reduced gradient algorithm (Microsoft Excel Sol-

ver) for nonlinear problems. It allows optimizing the

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.940 0.945 0.950 0.955 0.960 0.965 0.970 0.975 0.980 0.985aw

X (g

moi

stur

e/ g

DM

)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.940 0.945 0.950 0.955 0.960 0.965 0.970 0.975 0.980 0.985aw

X (g

moi

stur

e / g

DM

)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.940 0.945 0.950 0.955 0.960 0.965 0.970 0.975 0.980 0.985aw

X (g

moi

stur

e / g

DM

)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.940 0.945 0.950 0.955 0.960 0.965 0.970 0.975 0.980 0.985aw

X (g

moi

stur

e / g

DM

)

65°C

55°C

45°C

25°C

Fig. 1. Comparison of experimental (r) and predicted (full line) water

‘‘desorption’’ data of apple samples subjected to osmotic dehydration.

The GAB model is described in Eq. (1).

three parameters by minimizing the sum of the residualerror. The regression coefficient (R2) was calculated for

model fit at each temperature. Because of the difficulty

in getting a unique solution, the regression procedure

was repeated with different initial values and different

upper and lower limits until stable and reproducible

values were reached.

3. Results and discussion

Desorption isotherm graphs of apples during osmoticdehydration with sucrose solution at four different

temperatures are presented in Fig. 1. As it can be ob-

served the fit of the GAB model is good and it is

quantified with the regression coefficient R2 (Table 2). At

65 �C, however, the model is satisfying below 0.970 but

not above.

The GAB parameters at each temperature are also

gathered in Table 2. The so-called monolayer value X0

looses here its original meaning since it was derived from

desorption–adsorption theories and not in the special

case of osmotic dehydration. Thus, in this approach all

GAB parameters can be called empirical constants.

Table 2 shows that only the C constant increases with

the temperature and this correlation is also demon-

strated by the principal components plot in Fig. 2. The

fact that the C-point and T -point are very close to eachother means that they are correlated.

Whenever required the correlation between C and Tcan be described by a second-order polynom:

C ¼ �0:0014 � T 2 þ 0:1545 � T � 1:6754 ð2Þ

In the prediction of parameters X0 and k it is recom-

mended to use an average value. It is important to point

out that any comparison of the osmotic ‘‘desorption’’

with sorption isotherms developed for traditional drying

must be very carefully verified. In fact, in the case oftraditional sorption isotherms, samples are put in a

chamber with known vapour pressure and constant

temperature until equilibrium is reached (Labuza, 1968).

Sample moisture content is then measured and plotted

against the corresponding water activity. In our study the

samples were surrounded with a liquid osmotic media at

different temperatures, for different times, and the water

Table 2

GAB parameters and regression coefficients for moisture desorption of

apple in osmotic medias at different temperatures

Tempera-

ture (�C)GAB parameters

X0 C K R2

25 0.051 1.322 1.009 0.9497

45 0.057 2.563 1.007 0.9821

55 0.039 2.606 1.011 0.9855

65 0.051 2.614 1.007 0.9199

Fig. 2. Principal component analyses showing correlation level of

temperature (T ) with the three GAB parameters (C, k, X0).

470 F. Prothon, L.M. Ahrn�ee / Journal of Food Engineering 61 (2004) 467–470

activity measurements of the pieces were made separatelyat 24 �C. In the case of traditional desorption the water

activity equilibrate with the surrounding atmosphere.

4. Conclusions

The GAB model showed a good fit with experimental

data at nearly all the studied temperatures, and at 65 �Cit was suitable for water activities below 0.970. A strong

correlation was found between the C constant in the

GAB model and temperature. It should, however, be

borne in mind that the model is only an empirical model,

which was not derived from any set of physical laws or

diffusion theories. Accordingly, despite its demonstrated

success, therefore, its general applicability cannot be

taken for granted and it needs to be established inde-pendently for any system where its use is considered.

The model could, however, be used to compare the be-

haviour of different food products, sugar solutions and

processing methods in decreasing the water activity of

the product during osmotic dehydration, leading to a

better understanding of the osmotic process.

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