Experimental and mathematical study of desorption isotherms of Tunisian Sardine (Sardinella aurita)

f o o d a n d b i o p r o d u c t s p r o c e s s i n g 8 6 ( 2 0 0 8 ) 242–247

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Experimental and mathematical study of desorption isotherms of Tunisian Sardine (Sardinella aurita) Bilel Hadrich, Nourh`ene Boudhrioua, Nabil Kechaou ∗ Groupe de G´enie des Proc´ed´es Agroalimentaires de l’Unit´e de Recherche en M´ecanique des Fluides Appliqu´ee et Mod´elisation - Ecole Nationale d’Ing´enieurs de Sfax, B.P ‘W’ 3038, Sfax, Tunisia

a r t i c l e

i n f o

Article history:

a b s t r a c t Desorption isotherms of sardine muscles were determined at three temperatures (25, 35

Received 24 September 2007

and 50 ◦ C) for a water activity range varying from 0.10 to 0.75. Gravimetric static methods

Accepted 4 January 2008

using saturated salt solutions were used (continuous and discontinuous measurements). Six models were taken from the literature to describe experimental desorption isotherms. The OSWIN model shows the best fit of the experimental data.

Keywords:

The net isosteric heat of desorption and the isosteric heat of desorption were determined

Desorption isotherms

by using the CLAUSIUS–CLAPEYRON equation. The isosteric heat of desorption decreases

Gravimetric methods

continuously with the increase of the equilibrium moisture content. A mathematical corre-

Isosteric heat of desorption

lation was established between the isosteric heat of desorption and equilibrium moisture

Modelling

content.

Sardine muscle

© 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

1.

Introduction

Tunisian sardine (Sardinella aurita) has a great importance in Tunisian food customs. In fact, sardine is a cheap source of protein. It can be economically explored in commercial scale. Drying is one of the most common methods of fish preservation. The knowledge of water desorption properties is extremely important in predicting the product behaviour during drying and/or storage at various conditions (Hadrich et al., 2008). In fact, moisture sorption isotherm is an extremely important tool in food engineering because it could be used to predict changes in food stability and to select appropriate package materials (Simal et al., 2007; Bellagha et al., 2005). Desorption data could be used for the proper choice of the end-point of drying process (Gal, 1987). Because of the complexity of solid matrice, it is not possible to predict theoretically desorption characteristics based on knowledge of product composition. Experimental data are always required for each material. A number of mathematical equations having two or more parameters have been developed to model isotherm data. Chirife and Iglesias (1978)

∗

made a review of the different models appearing in the literature, classifying them in linear and non-linear ones. The BET model (modified form of Langmuir isotherm) was developed by Brunauer et al. (1938) to incorporate multilayer adsorption. This model was further modified by Guggenheim-Andersonde Boer (Van den Berg, 1981) and it is always used to describe sorption isotherms of several products. Other types of correlations (logarithmic or power laws) were used to describe sorption isotherms such as Henderson (1952), Chung and Pfost (1967), Halsey (1948) and Oswin (1946) models. These empirical models have also a dependent temperature term and were used to reflect the temperature dependency of equilibrium moisture sorption. Thermodynamic parameter such as net isosteric heat of sorption could be estimated from the curve of water activity versus temperatures. It is possible to predict the moisture desorption isotherm of a product at other temperature conditions by using the CLAUSIUS–CLAPEYRON equation (Kaya and Kahyaoglu, 2007; Simal et al., 2007; Jamali et al., 2006). The paramount objective of the work was to establish desorption isotherms for Tunisian sardine (S. aurita) muscle at three different temperatures (25, 35 and 50 ◦ C). Experiments

Corresponding author. Fax: +216 74275595. E-mail addresses: [email protected] (B. Hadrich), [email protected] (N. Boudhrioua), [email protected] (N. Kechaou). 0960-3085/$ – see front matter © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.fbp.2008.01.003

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Table 1 – Water activities of used saturated salt solutions at 25, 35 and 50 ◦ C

Nomenclature aw Lv qst,n Qst r R S T Xeq Xm  relative

water activity latent heat of vaporization of pure water (J/mol) net isosteric heat of desorption (J/mol) isosteric heat of desorption (J/mol) correlation coefficient universal gas constant (J/mol K) standard error absolute temperature (K) equilibrium moisture content (kg/kg d.b.) monolayer moisture content (kg/kg d.b.) relative standard deviation relative = ¯ eq ) (100/X



n (X i=1 eqi

¯ eq ) −X

2



/n − 1

were conducted using the two static gravimetric methods: discontinuous and continuous. The former, i.e. the discontinuous method, is widely favoured because it has the advantage of not being costly and of being simple to use. The latter, i.e. the continuous method, requires computer acquisition of the sample weight. Although the continuous method allows the use of the desorption kinetics to estimate apparent moisture diffusivity, it was used in this paper only for the purpose of validating the results obtained through the use of the discontinuous method. Six mathematical models were tested to fit the experimental data. The variation of the isosteric heat of desorption of sardine was determined as a function of equilibrium moisture content.

2.

Material and methods

2.1.

Studied material

Fresh sardine (S. aurita) was purchased from a local market in Sfax (Tunisia) and transported to the laboratory in a few minutes. Sardine was then eviscerated and cleaned. Parallelepiped samples were prepared from the muscles. These samples were used for desorption experiments.

2.2.

Moisture content

Salt LiCl CH3 COOK MgCl2 K2 CO3 NaBr SrCl2 NaCl

25 ◦ C

35 ◦ C

0.1105 0.2245 0.3300 0.4276 0.5770 0.7083 0.7528

0.1117 – 0.3200 – 0.5455 – 0.7511

50 ◦ C 0.1105 – 0.3054 0.4091 0.5093 0.5746 0.7484

et al., 1991). Table 1 shows water activities of used saturated salt solutions at 25, 35 and 50 ◦ C. The jars were kept 24 h in the oven at a temperature of 25 ◦ C in order to be stabilized. Duplicate samples of 2–4 g of sardine muscle were placed in the hermetically sealed jars which were then placed in a controlled temperature oven (Fig. 1). The samples were weighed at different times. Equilibrium was considered to be reached when the change in weight did not exceed 0.001 g (about 3–4 weeks for every temperature). When the samples reached constant weight, at 25 ◦ C, the temperature of the oven was then increased to the next temperature condition to establish the corresponding desorption isotherms (35 ◦ C then 50 ◦ C). The experiment was stopped when the equilibrium was reached at the temperature of 50 ◦ C and the equilibrium moisture contents of samples were measured.

2.3.2.

Continuous measurement equipment

The continuous measurement was performed at 50 ◦ C and at a relative humidity of 31% obtained by using saturated salt solution of MgCl2 . The equilibrium moisture content was obtained by continuous dehydration of a suspended sample in a drying oven (Fig. 2). The drying oven was equipped with an analytical balance (METTLER-TOLEDO). This balance was related to a personal computer for sample weighting and time acquisition. The experiment was stopped when the equilibrium was reached (weight change less then 0.001 g) and then the equilibrium moisture content of the sample was measured.

2.3.3.

Mathematical treatment

The experimental desorption isotherms data were fitted by using six mathematical models chosen among the most used models in literature (Kaya and Kahyaoglu, 2007; Jamali et al., 2006; Bellagha et al., 2005; Kaleemullah and Kailappan, 2004;

Moisture content was determined by dehydrating the muscle sample during 24 h in an oven at 105 ◦ C (AOAC, 1996). The sample weight was measured by an analytical balance (METTLER-TOLEDO) having a precision of ±0.0001 g. Moisture content was expressed in dry basis (kg/kg d.b.).

2.3.

Desorption isotherms

2.3.1.

Discontinuous measurement equipment

Desorption isotherms of sardine were determined by using the gravimetric static method of saturated salt solutions (Spiess and Wolf, 1987) at 25, 35 and 50 ◦ C. Experiments were performed by using the same samples of sardine muscle for all temperatures, in a range of water activity varying from 0.10 to 0.75. The saturated salt solutions were prepared by dissolving, in a jar, an appropriate quantity of salt in distilled water (Motarjemi, 1988). Each salt solution provides a fixed water activity for each temperature and salt concentration (Multon

Fig. 1 – Experimental apparatus for measurement of desorption isotherms—Static gravimetric method: discontinuous measurement. (1) Thermostated oven; (2) jar containing salt; (3) sample; (4) sample holder; (5) saturated salt solution.

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Table 2 – Models used for fitting the experimental desorption isotherms of sardine muscles Model names

Fig. 2 – Experimental apparatus for measurement of desorption isotherms—Static gravimetric method: continuous measurement.

nexp·data (Xeqi i=1

S=

− Xeqcal,i )

2

(1)

nexp·data − nparam

 r=

nexp·data i=1

1−

(Xeqi − Xeqcal,i )

nexp·data i=1

(Xeq − Xeq,i )

2.3.4.

1



2

(2)

nexp·data

nexp·data

Xeq =

Xm ABaw (1−Baw )(1−Baw +ABaw )

Xeq =

AXm aw (1−aw )(1+(A−1)aw )

HENDERSON (Henderson, 1952)

Xeq = A

CHUNG & PFOST (Chung and Pfost, 1967)

Xeq = − A1 ln −

HALSEY (Halsey, 1948)

Xeq = − ln(a

OSWIN (Oswin, 1946)

Xeq = A(T)



1

ln

T





A(T) w)



1 1−aw

B

T ln(aw ) B

1/B

aw 1−aw

A(T) = exp(A1 + A2 T)

;

B



;

A(T) = A1 + A2 T

The isosteric heat of desorption is important in the analysis and design of equipment for the drying, storage, treatment and protection of dehydrated biological materials. Values of this parameter are used to estimate the minimum energy required for the drying process, as well as for indicating the types of moisture present in the final product (Costa et al., 1998). The obtained values of the isosteric heat of desorption (Qst ) were then correlated to corresponding equilibrium moisture contents by using a mathematical equation (Table 2).

2

where Xeqcal,i denotes the calculated value of equilibrium moisture content by using the regression model, Xeqi denotes the experimental value of equilibrium moisture content, nparam is the parameters number of the particular model and nexp·data is the number of experimental points. The arithmetic average value of the experimental equilib¯ eq ) was simply given by: rium moisture content (X Xeq =

G.A.B. (Van Der Berg and Bruin, 1981) BET (Brunauer et al., 1938)

A and B: models constants; aw : water activity; Xeq : equilibrium moisture content (kg/kg d.b.); Xm : monolayer moisture content (kg/kg d.b.); T: absolute temperature (K).

Kaymak-Ertekin and Gedik, 2004; Lahsasni et al., 2004). A nonlinear regression analysis performed in the computer program CurveExpert (Version 1.37) was used to estimate the parameters of each model. Two statistical parameters were used to determine the quality of the fit: the standard error (S) and the correlation coefficient (r). These parameters were defined as:



Equations expressions

Xeqi

(3)

3.

Results and discussion

3.1.

Desorption isotherms

3.1.1.

Discontinuous measurement

The experimental desorption isotherms obtained at 25, 35 and 50 ◦ C are shown in Fig. 3. The measurements of desorption isotherms determined by calculating the relative standard deviation ( relative ) for all experimental equilibrium moisture contents (two repetitions for each temperature).  relative varies from 0 to 7.3%. It can be seen that the desorption isotherms of sardine behaves like a type II on BET classification (Brunauer

i=1

Isosteric heat of desorption

The net isosteric heat of desorption can be estimated by using the CLAUSIUS–CLAPEYRON equation, for fixed moisture contents (Rizvi, 1986; Tsami, 1991), as shown in Eq. (4): ∂ ln(aw ) qst,n =− R ∂(1/T)

(4)

where qst,n is the net isosteric heat of desorption. The values of ln(aw ) could be plotted against (1/T) for different constant moisture levels. The net isosteric heat of desorption values were determined from the slopes of the straights (−qst,n /R). The isosteric heat of desorption was then estimated by using the following equation: Qst = qst,n + Lv where Lv is the latent heat of vaporization of pure water.

(5)

Fig. 3 – Experimental desorption isotherms of sardine muscle obtained by the discontinuous measurement at 25, 35 and 50 ◦ C—Standard deviation of measurement.

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Table 3 – Parameter values obtained for the six models used to describe desorption isotherms of sardine muscles at 25, 35 and 50 ◦ C Temperature (◦ C)

Model

Parameters A

GAB

T = 25 ◦ C T = 35 ◦ C T = 50 ◦ C

BET

T = 25 ◦ C T = 35 ◦ C T = 50 ◦ C

HENDERSON

T = 25 ◦ C T = 35 ◦ C T = 50 ◦ C

CHUNG & PFOST

B

14.4698 11.1772 8.5252

r

S × 103

Xm

0.7857 0.8110 0.8875

0.0792 0.0712 0.0552

0.996 1.000 1.000

5.742 3.344 1.983

– – –

0.0498 0.0456 0.0411

0.956 0.973 0.990

16.116 15.939 7.693

3.5978 4.5007 8.7281

0.5571 0.6112 0.7526

– – –

0.994 0.997 0.996

6.048 4.923 4.778

T = 25 ◦ C T = 35 ◦ C T = 50 ◦ C

15.1969 15.5910 16.0877

0.0149 0.0128 0.0097

– – –

0.994 0.996 0.988

6.096 6.209 8.488

HALSEY

T = 25 ◦ C T = 35 ◦ C T = 50 ◦ C

0.0152 0.0177 0.0223

1.7561 1.5971 1.3852

– – –

0.992 0.994 0.996

6.872 7.287 4.727

OSWIN

T = 25 ◦ C T = 35 ◦ C T = 50 ◦ C

0.1183 0.1057 0.0874

0.4028 0.4431 0.5251

– – –

0.996 1.000 1.000

4.804 1.880 1.455

2.1242 × 108 102.8434 25.0447

et al., 1938) and they have a sigmoid form. Besides, it can be also seen that the temperature has a significant effect on the desorption isotherms of sardine. In fact for a water activity of aw = 0.75, the equilibrium moisture content decreased from 0.192 kg/kg d.b. (at 25 ◦ C) to 0.151 kg/kg d.b. (at 50 ◦ C). Initial moisture content of sardine muscle varying from 3 to 4 kg/kg d.b. did not have a significant effect on the form of the isotherm. The results of the non-linear regression analysis of desorption isotherms obtained for the tested models and at 25, 35 and 50 ◦ C were presented in Table 3. It can be observed that all the models have high correlation coefficients r ≥ 0.96 and insignificant standard errors S ≤ 16 × 10−3 . B The OSWIN model (Xeq = A(T)(aw /1 − aw ) ), shows the best fit for all examined temperatures (r ≥ 0.996, 1.455 × 10−3 ≤ S ≤ 4.804 × 10−3 ). This model is always used to describe desorption isotherm of biological products (Bellagha et al., 2005; Kaleemullah and Kailappan, 2004; Motarjemi, 1988). Therefore, the OSWIN model was retained to describe desorption isotherm of sardine muscle at different temperatures. The variations of A and B OSWIN coefficients versus temperature were determined as follows:

3.1.2.

Continuous measurement

Fig. 5 shows the variation of moisture content obtained at different times of a suspended sardine muscle in the drying oven at 50 ◦ C and a relative humidity of 31%. It can be seen that moisture content decreases with drying time to reach an equilibrium moisture value. The experimental value obtained by the continuous measurement was almost equal to the experimental value obtained by discontinuous measurement. Both experimental values were also very close to the calculated value by using the OSWIN model at the same experimental conditions (Table 4).

3.2.

The net isosteric heat of desorption

The isosteric curves determined for sardine muscles by using CLAUSIUS–CLAPEYRON equation are shown in Fig. 6. The absolute values of the slopes of the isosters decrease to zero when moisture content increases. This observation is similar to those obtained by Simal et al. (2007) for pineapple.

A(T) = 0.4885 − 0.0012T B(T) = −1.0693 + 0.0049T The new form of the modified OSWIN model determined for sardine muscles was thus obtained for a water activity varying from 0.10 to 0.75: Xeq = (0.4885 − 0.0012T)

 a ( −1.0693+0.0049T) w 1 − aw

(6)

A comparison between experimental and calculated (OSWIN model) values of desorption isotherms of sardine muscles obtained at 25, 35 and 50 ◦ C was shown in Fig. 4. The OSWIN model could thus be used to predict desorption isotherms of sardine muscles at any temperature between 25 and 50 ◦ C.

Fig. 4 – Desorption isotherms of sardine muscle obtained at 25, 35 and 50 ◦ C (♦, , ): experimental data (discontinuous measurement). (–): Predicted values using OSWIN model.

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Fig. 5 – Moisture content variation of sardine muscle (a temperature of 50 ◦ C and a relative humidity of 31%) obtained by using gravimetric method (continuous measurement). Table 4 – Comparison between calculated and experimental equilibrium moisture content values obtained by continuous and discontinuous method (T = 50 ◦ C, aw = 0.31) Equilibrium moisture content value Xeq (kg/kg d.b.)

Continuous method

0.057

Discontinuous method

0.056

Calculated (OSWIN model)

Fig. 7 – Isosteric heat of desorption for sardine muscle.

Furthermore, Fig. 7 shows a comparison between calculated isosteric heat of desorption (Eq. (5)) and the mathematical correlation describing the isosteric heat of desorption (Eq. (7)). This equation could be used to determine the isosteric heat of desorption for temperatures and equilibrium moisture contents varying respectively from 25 to 50 ◦ C and from 0.01 to 0.19 kg/kg d.b. Qst =

1 −3

8.047 × 10

2 + 0.134Xeq − 0.322Xeq

(7)

0.055

4. The variation of the isosteric heat of desorption versus equilibrium moisture content is shown in Fig. 7. The curve shows a continuous decrease of the value of isosteric heat of desorption with the increase of equilibrium moisture content. At moisture content of 0.19 kg/kg d.b., the isosteric heat of desorption was close to the mean value of latent heat of vaporization of pure water. The last observation indicates that there were small water–solid interactions (Medeni and Gogus, 1997). The variation of isosteric heat of desorption versus equilibrium moisture content was similar to those observed by Kaya and Kahyaoglu (2007) for safflower petals and tarragon, Jamali et al. (2006) for Citrus reticulate leaves, Schmalko and Alzamora (2005) for bark and xylem desorption and Wang and Brennan (1991) for potatoes desorption.

Conclusion

Experimental desorption isotherms of sardine muscle were determined at 25, 35 and 50 ◦ C by using a static gravimetric discontinuous method. Another experimental device allowing continuous measurement of the muscle weight was also used to determine desorption isotherm at 50 ◦ C. The results obtained by both discontinuous and continuous systems were similar. The experimental desorption isotherms of sardine have a sigmoid form. The equilibrium moisture content decreased with the increase of temperature. Six models were tested to describe the experimental sardine desorption isotherms. The OSWIN model was the most suitable for describing the relationship between the equilibrium moisture content, the water activity and temperature. The isosteric heat of desorption of sardine muscle increased with decreasing moisture content. An empirical equation was established to describe this variation between 0.01 and 0.19 kg/kg d.b.

Acknowledgment This work was done in the context of the AUF project (Ref. P2-2092RR513).

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Fig. 6 – Isosteric curves determined for sardine muscles by using CLAUSIUS–CLAPEYRON equation.

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