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Drying of sardine muscles: Experimental and mathematical investigations
food and bioproducts processing 8 7 ( 2 0 0 9 ) 115–123
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Drying of sardine muscles: Experimental and mathematical investigations Nadia Djendoubi a,∗ , Nourhène Boudhrioua a , Catherine Bonazzi b,c , Nabil Kechaou a a
Groupe de Recherche Génie des Procédés Agroalimentaires, Unité de Recherche en Mécanique des Fluides Appliquée et Modélisation, Ecole Nationale d’Ingénieurs de Sfax, BP ‘W’ 3038, Sfax, Tunisie b INRA, UMR 1145 Génie Industriel Alimentaire, 1 avenue des Olympiades, F-91300 Massy, France c AgroParisTech, UMR 1145 Génie Industriel Alimentaire, 1 avenue des Olympiades, F-91300 Massy, France
a b s t r a c t The aim of this work was to study the effect of air drying process on the dehydration kinetics of sardine muscles (Sardina pilchardus). Experimental drying kinetics were measured at five air temperatures (40, 50, 60, 70 and 80 ◦ C), two relative humidity and at a constant air velocity of 1.5 m/s. The sardine drying kinetics were accelerated by increasing air temperature and were showed down when increasing air humidity. Moisture desorption isotherms of sardine muscles were determined at three temperatures (40, 50 and 70 ◦ C) by using the static gravimetric method. The equilibrium moisture contents of sardine muscles were used to treat mathematically the experimental drying kinetics. Experimental drying kinetics and desorption isotherms of sardine muscles were described by using empiric models available in the literature. Eight models (GAB, BET, Henderson–Thompson, Modified Chung & Pfost, Modified Halsey, Oswin, Peleg and Adam & Shove models) were compared in order to describe the desorption isotherms. The Peleg model showed the best fitting of experimental data. For the drying kinetics, the Page model allowed a better fitting than the Newton and the Henderson and Pabis models. The Page model was thus used for simulating the drying kinetics of sardine muscles between 40 and 80 ◦ C. © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Air drying; Desorption isotherms; Sardina pilchardus muscles; Equilibrium moisture content; Mathematical treatment
1.
Introduction
Fish and marine products are very important food products, especially in developing Countries. These products are valuable sources of nutrients such as proteins (15–27% wet basis) and lipids and mainly polyunsaturated fatty acids. However, they contain up to 80% of water and are thus highly perishable products, especially in hot countries were cold preservation techniques are often missing (Zakhia, 2002). Preservation is necessary because of high enzymatic and bacterial activity in fresh fish (Sainclivier, 1983). Fishes can thus be valorised by drying which is an efficient technique for improving stabilisation and storage. This increases the availability to consumers and permits the valorisation of many sea and agricultural
∗
products. On the other hand, drying can be responsible for severe quality deterioration in food (Chinnaswamy and Hanna, 1988), especially in fish (Sainclivier, 1985, 1988). Furthermore, studies on drying must take quality indexes into account. The physical, chemical and microbiological stability of a fresh or a processed food product is highly influenced by water activity (aw ). Knowledge of moisture sorption isotherms is therefore essential to determine the equilibrium moisture contents of agricultural crops. This investigation was undertaken in order to examine the effect of drying air (temperature and relative humidity) on drying kinetics of Sardina pilchardus muscles. Experimental drying and desorption isotherms data were measured, and then fitted by using empirical models available in the literature.
Corresponding author. E-mail addresses: djendoubi [email protected] (N. Djendoubi), [email protected] (N. Boudhrioua), [email protected] (C. Bonazzi), [email protected] (N. Kechaou). Received 29 October 2007; Accepted 3 July 2008 0960-3085/$ – see front matter © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.fbp.2008.07.003
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Nomenclature a, b, c polynomial parameters aw water activity A, B, C, D, k, n, a models parameters −dX/dt drying rate kg water (kg dry mater−1 min−1 ) −(dX/dt)0 initial drying rate kg water (kg dry mater−1 min−1 ) f dimensionless drying rate Hv latent heat of vaporization of pure water (kJ mol−1 ) nexp. data number of experimental data nparam number of models parameters qst,n net isosteric heat of desorption (kJ mol−1 ) whole isosteric heat of desorption (kJ mol−1 ) Qst r correlation coefficient R universal gas constant (kJ mol−1 K−1 ) RH air relative humidity (%) S Standard error Ta air temperature (◦ C) Va air velocity (m/s) initial moisture content (kg water kg−1 dry X0 mater) Xeq equilibrium moisture content (kg water kg−1 dry mater) dimensionless moisture ratio Xr
2.
Materials and methods
2.1.
Raw material
Fresh sardines (S. pilchardus) were purchased from a local fish market (Massy, France). Sardines were immediately transported in sealed polystyrene boxes containing ice to the laboratory. Head, scales and viscera were removed, and two fillets were obtained from resulting sardine carcass. Fish muscles were cut in rectangular slabs of 0.06 m length and 0.02 m width. Afterwards, the samples were used for global chemical characterization, measurement of desorption isotherms and drying experiments.
2.2.
Global chemical analysis
In order to characterize the fresh sardine muscles, analyses were realized according to the methods of Association of Offi-
Table 1 – Water activity values of the used saturated salt solutions (Multon et al., 1991). Temperature (◦ C)
Salt
LiCl CaCl2 MgCl2 K2 CO3 Mg(NO3 )2 NaBr SrCl2 KI NH4 Cl NaCl KCl
40 ◦ C
50 ◦ C
70 ◦ C
0.1116 0.1917 0.3159 – 0.4842 0.5317 – 0.6609 – 0.7501 0.8232
0.1105 0.1654 0.3054 0.4091 0.4544 0.5093 0.5746 0.6449 – 0.7484 0.812
0.1075 – 0.2777 0.3737 – – 0.4618 0.6193 0.673 0.7455 0.7949
cial Analytical Chemists (AOAC, 1984). Moisture content was measured using the gravimetric method in an oven at 105 ◦ C up to constant weight (≈24 h). Protein was analyzed according to the Kjeldahl method. The N-total content was determined by using the universal multiplication factor of 6.25. Fat content was determined by the Soxhlet method using petroleum ether as a solvent. Ash content was measured by using a muffle furnace and by heating the dried sample at 550 ◦ C during 4 h. All chemical analyses were performed in triplicate. The results were expressed in wet basis (g/100 g fresh fish) and were presented by calculating the mean value ± standard deviation of repeatability.
2.3.
Desorption isotherms
2.3.1.
Experimental procedure
The desorption isotherms were determined by using the standard static–gravimetric method (Spiess and Wolf, 1983). Eleven saturated salt solutions selected to give different water activities in the range of 0.1–0.9 were used. The salt solutions and their corresponding water activities at different temperatures are taken from literature reported by Multon et al. (1991) and were given in Table 1. Three repetitions were performed (three samples per salt). The glass sorption jars were placed in a cabinet at the controlled temperatures of 40, 50 and 70 ◦ C (±1 ◦ C). Each sample was carefully weighed every week by using an analytical bal-
Table 2 – Equations for describing the desorption isotherms Name of the equation
Equation
No
CABaw (1 − Baw )(1 − Baw + ABaw )
GAB (Guggenhein, Anderson & De Boer) (Van den Berg, 1985)
Xeq =
BET (Brunauer et al., 1938)
Xeq = A
Henderson–Thompson (Thompson et al., 1968)
Xeq =
Modified Chung & Pfost (Chung and Pfost, 1967)
Xeq = A − B ln(aw ) ln(−T + B)
(4)
Modified Halsey (Iglesias and Chirifie, 1976)
Xeq = A −
B ln(aw )
(5)
Oswin (Oswin, 1946)
Xeq = A
Peleg (Peleg, 1993)
Xeq = AaBw + CaD w
Baw 1 − aw
aw 1 − aw
1 − (C + 1)aCw + CaC+1 w 1 + (B − 1)aw −
ln(1 − aw ) −A(T + B)
(1)
1/C
1/C
(BaC+1 w )
(2)
(3)
B (6) (7)
food and bioproducts processing 8 7 ( 2 0 0 9 ) 115–123
ance (Mettler, precision: 10−4 g) until no significant change in weight was observed between two consecutive measurements. Once equilibrium was reached, the moisture content of the sample was determined. The initial mass of the muscle put in each glass sorption jar was of about 2.080 ± 0.055 g. The hygroscopic equilibrium was reached after 3–5 weeks.
2.3.2.
Mathematical analysis
Moisture sorption isotherms of food products can be described by numerous mathematical models with two or more parameters (Boudhrioua et al., in press-a; Hadrich et al., in press; Kaya and Kahyaoglu, 2007; Jamali et al., 2006; Bellagha et al., 2005; Van der Berg and Bruin, 1981). The experimental desorption data were fitted by using seven equations (with two, three or four parameters) shown in Table 2. Eqs. (1)–(7) (Table 2) were chosen among the most used models in the literature; Xeq is the equilibrium moisture content of S. pilchardus muscles (kg/kg d.b), aw is the water activity, T is the temperature (K) and A, B, C and D are the models parameters. These parameters were estimated by fitting the experimental data using non-linear regression analysis and minimizing the residual sum of squares between experimental and calculated data. The adequacy of each model was evaluated by the correlation coefficient and the standard error coefficient calculated by the software Curve Expert 3.1® . These parameters were calculated as follows:
nexp.data (Xeq i=1
S=
− Xeqcali )
2
r=
nexp.data 1−
i=1
i=1
(Xeq − Xeqi )
2
2
(9)
where Xeqcali is the moisture content calculated by the model, Xeqi the experimental moisture content, nparam the number of model’s parameters and nexp. data the number of experi¯ eq was calculated by using this relation: Xeq = mental data. X nexp.data Xeqi (Boudhrioua et al., in press-a). 1/nexp.data i=1
2.3.3.
Isosteric heat of desorption
The net isosteric heat of desorption qst,n (kJ/mol) was calculated from the experimental desorption isotherms by using the Clausius–Clapeyron equation (Labuza et al., 1985; Igleasias et al., 1989; Tsami, 1991); ln(aw ) = −
qst,n 1 × + Cst R T
(10)
where R is the universal gas constant (kJ/mol K) and T the desorption isotherm temperature (K). The net isosteric heat of desorption was calculated from Eq. (10) by plotting the desorption isosteres as ln (aw ) versus (1/T) for different moisture contents and calculating the slopes which are equal to −qst,n /R (Tsami, 1991; Kiranoudis et al., 1993). This procedure was repeated with different moisture contents in order to determine the dependence of qst on moisture content. The value of the whole isosteric heat of desorption (Qst ) was then calculated by using the following equation: Qst = qst,n + Hv
2.4.
Drying experiments
Drying experiments were performed by using a convective pilot air dryer. The dryer allows carrying out long drying kinetics under strictly defined and well-controlled temperature (20 < Ta < 160 ◦ C), air velocity (0 < Va < 3 m/s) and air humidity conditions (air humidity up to 0.3 kg H2 O kg−1 anhydrous air). The drier works as an open-loop system and is controlled by a computer, with temperature, relative air velocity and relative air humidity as adjustable parameters (Boudhrioua et al., 2002; Boudhrioua et al., 2003). Experiments were performed in order to determine the effect of air temperature and relative humidity on drying kinetics. Five temperatures were investigated (40, 50, 60, 70 and 80 ◦ C). Drying experiments were performed at ambient humidity for drying at 40, 50, 60, 70 and 80 ◦ C and at a relative humidity of 40% for drying at 40 and 50 ◦ C. All experiments were conducted for an air velocity of 1.5 m/s. The sardine muscles samples were hung in a vertical drying channel and the surface of the muscles was held parallel to the airflow direction. The muscles were dried up to a fixed moisture content of 0.25 kg/kg fresh fish (i.e. 0.33 kg/kg dry matter) for further quality comparison. This value was chosen while reported by GRET (1993) as the one at which dried fishes present an acceptable sensorial quality.
2.4.1.
(Xeqi − Xeqcali )
nexp.data
where Hv is the latent heat of vaporization of pure water (Hv is equal to 43.3178, 42.9345 and 42.1269 kJ/mol at 40, 50 and 70 ◦ C, respectively).
(8)
nexp.data − nparam
117
(11)
Characteristic drying curves
Foodstuffs are heterogeneous in structure and in composition, but only the average moisture content is characterized by drying kinetics. The characteristic drying curve method (Lewis, 1921) can be chosen to describe the falling rate period of the drying curves. Based on the Van Meel transformation (Van Meel, 1958), this method consists in normalizing the moisture content (Eq. (12)) and the drying rate (Eq. (13)) as follows: Xr (t) =
f =
X(t) − Xeq X0 − Xeq
(−dX/dt)t (−dX/dt)0
(12)
(13)
where X0 : initial moisture content (kg water/kg dry matter), Xeq : equilibrium moisture content (kg water/kg dry matter), Xr : moisture ratio, (−dX/dt)0 : initial drying rate (kg water/kg dry matter min), f: dimensionless drying rate. The equilibrium moisture content Xeq was determined from the desorption isotherms. The Marquardt–Levenberg non-linear optimization method, using the computer program Curve Expert 3.1® , was then used for fitting the characteristic drying curve f = f(Xr ).
2.4.2.
Empirical drying equations
Semi-empirical and empirical models have been widely used to describe the thin layer drying kinetics of many agricultural products (Jain and Pathare, 2007; Togrul and Pehlivan, 2002; Yaldiz and Ertekin, 2001, Boudhrioua et al., in press-b). The experimental data were presented here by fitting the experimental moisture ratio (Xr ) versus drying time by three of the most widely used models for food and agricultural products (the Newton (Lewis, 1921), the Page (Page, 1949) and the
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Table 3 – Mathematical models applied to the Sardina pilchardus muscles drying curves Model name Newton (Lewis, 1921) Page (Page, 1949) Henderson and Pabis (Zhang and Litchfield, 1991)
Model equation
Parameters
Xr = exp (−kt) Xr = exp(−ktn) Xr = a exp (−kt)
k k, n a, k
Fig. 2 – Comparison between desorption isotherms of sardine obtained in this work and those obtained by Bellagha et al. (2005) and Hadrich et al. (in press). with increasing temperature at a given water activity. For example at aw equal to 0.75, equilibrium moisture content of sardine muscles decreased from 0.274 at 40 ◦ C to 0.141 kg/kg d.b at 70 ◦ C.
3.3. Fig. 1 – Desorption isotherms of sardine muscles obtained at 40, 50 and 70 ◦ C. Henderson and Pabis models (Hendreson and Pabis, 1961)) (Table 3). The description suggested by Lewis is analogous to Newton’s law for cooling when interval resistance to heat transfer can be neglected; Henderson and Pabis and Page’s equation are of similar type, with additional coefficients for a better fitting of experimental data. These models were evaluated, by the Marquardt–Levenberg non-linear optimization method using Curve Expert 3.1® software.
3.
Results and discussion
3.1.
Global chemical composition
Moisture is the most abundant component in fresh S. pilchardus. It varies from 69.32 to 75.00% (w.b). The fresh fish contains 19.65 ± 0.03 g/100 g of proteins and 2.42 ± 0.12 g/100 g of lipids. Abdelmouleh et al., 1980 reported similar results for fresh Tunisian S. pilchardus. Ash content is about 1.19 ± 0.12 mg/100 g and is in the order of magnitude of values published by the FAO (1999).
3.2.
Fitting of desorption isotherms
The results in terms of estimated parameters and values of statistics parameters (r and S) are presented in Table 4. It can be seen that the Peleg model presents the smallest S values (0.003 ≤ S ≤ 0.005) and the highest correlation coefficients (r = 0.99). Therefore, it was the best model for fitting the experimental data for water activity ranging from 0.10 to 0.90 and temperature varying from 40 to 70 ◦ C. Fig. 3 shows a comparison between experimental data and Peleg’s model for desorption isotherms of sardine muscles obtained at 40, 50 and 70 ◦ C. In the same figure, it can be noticed that the Peleg model can be recommended for predicting the S. pilchardus muscles desorption isotherms in the range of the investigated temperatures. The variation of Peleg’s model parameters versus temperature was also examined. Peleg’s model parameters (A, B, C and D) showed polynomial variations with temperature (aT2 + bT + c). The calculated coefficients describing
Desorption isotherms
Desorption isotherms of sardine muscles obtained at 40, 50 and 70 ◦ C are shown in Fig. 1. The equilibrium moisture content corresponding to each moisture activity, aw , represents the mean value of three replications. All isotherms follow a sigmoid form and are of type II curves according to BET classification (Brunauer et al., 1938). They describe the sorption of water on an adsorbent with strong water–adsorbent interactions. Similar results were reported by Hadrich et al. (in press) for Sardinella aurita (Fig. 2). Equilibrium moisture content increases with rising moisture activity. A significant temperature effect can be observed on desorption isotherms. In fact the equilibrium moisture content decreases
Fig. 3 – Comparison between experimental and calculated desorption isotherm using Peleg model (dots: experimental values, lines: calculated values).
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Table 4 – Estimated parameters of the eight models used for describing desorption isotherms of Sardina pilchardus muscles and the corresponding statistical parameters T (◦ C)
Equations
Parameters A
B
C
S
r
D
Guggenhein, Anderson & De Boer (Van den Berg, 1985)
40 50 70
0.181 0.200 0.116
1.026 0.799 0.964
0.721 0.759 0.600
0.021 0.046 0.004
0.981 0.997 0.998
BET (Brunauer et al., 1938)
40 50 70
4.200 9.270 1.210
0.021 0.009 0.032
3.000 2.200 3.600
0.026 0.006 0.006
0.970 0.996 0.996
Henderson–Thompson (Thompson et al., 1968)
40 50 70
0.474 0.538 0.513
−25.802 −22.563 −11.133
0.474 0.538 0.513
0.023 0.005 0.009
0.975 0.100 0.990
Modified Chung and Pfost (Chung and Pfost, 1967)
40 50 70
0.383 0.305 0.230
0.070 0.058 0.042
0.048 0.026 0.029
0.868 0.924 0.877
Modified Halsey (Iglesias and Chirifie, 1976)
40 50 70
0.399 0.338 0.311
0.399 0.338 0.311
0.011 0.017 0.007
0.995 0.969 0.994
Oswin (Oswin, 1946)
40 50 70
0.117 0.087 0.059
0.755 0.617 0.782
0.014 0.006 0.004
0.989 0.996 0.997
Peleg (Peleg, 1993)
40 50 70
0.144 0.218 0.046
0.594 6.482 0.569
0.005 0.004 0.003
0.999 0.998 0.998
2.047 2.306 2.448
1.197 0.193 0.274
7.137 1.149 3.450
the dependence on the temperature are summarized in Table 5.
3.4.
Heat of desorption
The values for whole isosteric heat of desorption, Qst , were calculated from desorption data obtained at different temperatures by means of Eq. (11). The whole S. pilchardus muscles desorption heat variation versus moisture content is shown in Fig. 4. The whole isosteric heat desorption decreased from 67.36 to 48.47 kJ/mol as moisture content increased from 0.025 to 0.30 (d.b). At low moisture contents, the desorption heat was higher than at high moisture contents. Tsami (1991) and Lahsasni et al. (2004) suggested that the rapid increase of the whole desorption heat observed at low moisture contents was due to the existence of highly active polar sites on the surface of the food material which are covered with water molecules forming a mono-molecular layer. The whole isosteric heat of moisture desorption of S. pilchardus muscles was successfully described by the following exponential function: Qst = exp(3.91 +
0.032 + 0.114 ln(Xeq )) Xeq
Fig. 4 shows the adequacy between calculated and experimental values of Qst .
with r = 0.98 and S = 1.78
(14)
3.5.
where Xeq is the equilibrium moisture content. Table 5 – Calculated coefficients describing the dependency of desorption isotherms of Sardina pilchardus muscles Polynomial parameters
Peleg model parameters A
a b c
−0.0005 0.0552 −1.2145
Fig. 4 – Variation of the whole isosteric heat of desorption vs. equilibrium moisture content.
B −0.0295 3.2422 −81.921
C
D
0.0035 −0.4139 12.18
0.0238 −2.7402 78.677
Experimental drying curves
The effects of air temperature and relative humidity on the sardine muscles drying kinetics were examined. Figs. 4–8 illustrate the change in moisture ratio of the fish muscles versus drying time (Figs. 5 and 6), and the corresponding drying rates versus moisture ratio (Figs. 7 and 8). The drying rate decreased when moisture content or drying time decreased. No constant drying period was observed and the dehydration of the muscles occurred only in the falling rate period. These results indicated that diffusion is the most likely physical mechanism governing moisture removal from the muscles. Similar results were observed in the drying of
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ing of agricultural products (Lahsasni et al., 2004; Doymaz, 2005a,b). Figs. 7 and 8 show the effect of the relative humidity at 40 ◦ C on drying curves of sardine muscles. The drying time increased with increasing relative humidity at the same temperature. Similar trends have been reported for drying of vegetables products (Viswanathan et al., 2003; Kiranoudis et al., 1993).
3.6. Empirical modeling of the experimental drying curves
Fig. 5 – Variation of the moisture ratio of sardine muscles vs. drying time obtained at different drying temperatures and at ambient relative humidity (Va = 1.5 m/s).
The experimental drying curves (moisture ratio versus drying time) were fitted using three semi-empirical models: the Henderson and Pabis, the Lewis and the Page models. The model evaluation was based on statistical test (r and S values). The corresponding statistical and model parameters are shown in Table 6. In all cases, r-values are higher than 0.90, indicating a good fit of drying curves by all the models. According to the statistical values shown in Table 6, the Page model is the best one for fitting the drying curves over a wide range of temperatures, with corresponding correlation coefficients (r) and standard errors (S) varying between 0.990 and 0.999 and 0.012 and 0.128, respectively. It is important to notice the relation between Fick’s model and Henderson and Pabis’s one. The analytical solution of Fick’s equation (Crank, 1979) for an infinite slab can be written as follows: Ln(Xr ) = Ln
Fig. 6 – Influence of temperature on the variation of drying rate curves of Sardina pilchardus muscles vs. moisture ratio at Va = 1.5 m/s.
8 2
−
2 Dapp t (e/2)
(15)
2
where e is the dimension in the direction of diffusion (m) and Dapp is the apparent diffusivity (m2 /s). With some mathematical transformations, the Fick equation can be written like the Henderson and Pabis model (Xr = a exp (−kt)) (Zhang and Litchfield, 1991): with a = ( 82 ) and k =
2 Dapp 2
(e/2)
.
The values of apparent moisture diffusivity calculated by this way vary between 1.38 × 10−11 and 2.21 × 10−11 m2 s−1 . They are within the general range of 10−11 to 10−9 m2 s−1 reported by Panagiotou et al. (2004) for moisture diffusivity in fish muscles.
Fig. 7 – Variation of the moisture ratio of sardine muscles vs. drying time obtained at different relative humidity and at 40 ◦ C (Va = 1.5 m/s). many biological products (Sainclivier, 1985; Sogi et al., 2003; Desmorieux and Decaen, 2005; Doymaz, 2005a,b; Hadrich et al., 2008). As can be seen from Figs. 5 and 6, one of the main factors influencing the drying kinetics of sardine muscles is the drying air temperature. An increase in drying air temperature caused a reduction in the drying time. Final drying duration (up to 0.33 on a dry basis) takes 3 h 30 min at 80 ◦ C (humidity of ambient air) and 12 h 24 min 40 ◦ C (humidity of ambient air). Different authors reported similar results on dry-
Fig. 8 – Influence of the relative humidity on the drying rate curves of Sardina pilchardus muscles obtained at 40 ◦ C and at Va = 1.5 m/s.
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Table 6 – Coefficients and statistical parameters of models fitting drying curves of Sardine pilchardus muscles Models
Drying conditions
Parameters k
◦
a
S
r
n
Newton (Lewis, 1921)
80 C, 2% 70 ◦ C, 3% 60 ◦ C, 4% 50 ◦ C, 6% 50 ◦ C, 40% 40 ◦ C, 14% 40 ◦ C, 40%
−4
1.06 × 10 1.40 × 10−4 8.09 × 10−5 6.42 × 10−5 5.69 × 10−5 7.35 × 10−5 4.90 × 10−5
– – – – – – –
– – – – – – –
0.164 0.045 0.176 0.085 0.067 0.081 0.149
0.960 0.997 0.995 0.987 0.994 0.993 0.978
Page (Page, 1949)
80 ◦ C, 2% 70 ◦ C, 3% 60 ◦ C, 4% 50 ◦ C, 6% 50 ◦ C, 40% 40 ◦ C, 14% 40 ◦ C, 40%
2 × 10−3 1.53 × 10−4 1.70 × 10−5 5.00 × 10−4 4.85 × 10−5 5.90 × 10−5 3.11 × 10−5
– – – – – – –
0.697 0.988 0.6927 0.793 1.01 1.02 1.02
0.025 0.045 0.054 0.044 0.066 0.080 0.012
0.999 0.997 0.996 0.995 0.991 0.993 0.999
Henderson and Pabis (Hendreson and Pabis, 1961)
80 ◦ C, 2% 70 ◦ C, 3% 60 ◦ C, 4% 50 ◦ C, 6% 50 ◦ C, 40% 40 ◦ C, 14% 40 ◦ C, 40%
8.84 × 10−5 1.40 × 10−4 6.70 × 10−5 5.70 × 10−5 5.60 × 10−5 7.21 × 10−5 5.54 × 10−5
0.757 1.009 0.755 0.871 0.977 0.969 1.214
– – – – – – –
0.086 0.045 0.105 0.050 0.066 0.080 0.113
0.989 0.997 0.985 0.995 0.995 0.993 0.987
Plots of the predicted moisture ratios versus drying time using the Page model and the corresponding experimental data are shown in Fig. 9. Page’s model provided a good agreement between experimental and predicted moisture ratios.
3.7.
Determination of the characteristic drying curve
The determination of the characteristic drying curve of S. pilchardus muscles allows to group together all the drying kinetics on a single curve as shown in Fig. 10 which represents the dimensionless drying rate ‘f’ versus moisture ratio ‘Xr ’. The falling rate period is thus represented with a concave curve. A polynomial equation of degree 4 gave the best fit to the dimensionless experimental data.
Fig. 10 – Drying characteristic curves of Sardina pilchardus muscles obtained for different drying experiments.
f = 0.885 Xr − 2.901 Xr2 + 4.513 Xr3 − 1.525 Xr4 (r = 0.972 and S = 0.025)
(16)
40 to 80 ◦ C, a relative humidity varying from 2 to 40%, at an air velocity of 1.5 m/s.
This function allows to characterize the convective drying process of S. pilchardus’ muscles in a temperature ranging from
4.
Fig. 9 – Comparison between experimental and calculated (Page model) drying curves of sardine muscles (dots: experimental values, lines: calculated values).
The moisture desorption isotherms of S. pilchardus muscles were measured at three temperatures (40, 50 and 70 ◦ C) by using the standard gravimetric method. The experimental desorption isotherms of have a sigmoid forms and display the type II in the BET classification. The Peleg model showed the best fit with the experimental desorption data at 40, 50 and 70 ◦ C and for a water activity range from 0.10 to 0.90. The whole isosteric heat of desorption increased with decreasing moisture content and experimental data were well fitted by an exponential equation. The drying kinetics of S. pilchardus’ muscles contained no constant rate period, but only falling rate periods. The effects of air temperature and relative humidity were studied. The drying rate increased when increasing air temperature and decreased when increasing relative humidity.
Conclusion
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The Page model described adequately the drying kinetics of S. pilchardus muscles. The determination of the characteristic drying curve allowed to group together the drying kinetics in a single curve fitted by a polynomial equation.
Acknowledgement The authors gratefully acknowledge the “Agence Universitaire de la Francophonie” for providing financial support.
References Abdelmouleh, A., Katari, M.H. and Hadj Ali Salem, M., 1980, Variations saisonnières de la composition chimique globale de la sardine: Sardina pilchardus de la région de Bizerte (Tunisie). Bulletin De l’Institut National ScientifiqueTechnologique et Océanographique. Pêche Salammbô, 7: 91–101. AOAC, 1984, Official methods of analysis of the association of official analytical chemists, 13th ed. (Association of Official Analytical Chemists, Washington, DC). Bellagha, S., Sahli, A., Glenza, A. and Kechaou, N., 2005, Isohalic sorption isotherm of sardine (Sardinella aurita): experimental determination and modeling. Journal of Food Engineering, 68(1): 105–111. Boudhrioua, Michon, C., Cuvelier, G.P. and Bonazzi, C., 2002, Influence of ripeness and air temperature on changes in banana texture during drying. Journal of Food Engineering, 55: 115–121. Boudhrioua, N., Giampaoli, P. and Bonazzi, C., 2003, Changes in aromatic components of banana during ripening and air drying. LWT—Food Science and Technology, 36: 633–642. Boudhrioua, N., Bahloul, N., Kouhila, M. and Kechaou, N., in press-a, Sorptions isotherms and isosteric heats of sorption of olive leaves (chemlali variety): experimental and mathematical investigations, Food and Bioproduct Processing. Boudhrioua, N., Kouhila, M. and Kechaou, N., in press-b, Experimental and mathematical investigations of convective solar drying of four varieties of olive leaves, Food and Bioproduct Processing. Brunauer, S., Enmett, P.H. and Teller, E., 1938, Adsorption of gases in multimolecular layer. Journal of American Chemists to Society, 60: 309–319. Chinnaswamy, R. and Hanna, M.A., 1988, Expansion, color and shear strength properties of corn straches extrusion-cooked with urea and salts. Strach/Strake, 40: 186–190. Chung, P.S. and Pfost, H.B., 1967, Adsorption and desorption of water vapor by cereal grains and their products. Part I. Heat and free energy changes of adsorption and desorption. Transaction of the ASAE, 10(4): 549–551. Crank, J., (1979). The mathematical of diffusion (2nd ed.). (Claredon Press, Oxford), 414 p Desmorieux, H. and Decaen, N., 2005, Convective drying of spirulina in thin layer. Journal of Food Engineering, 66: 497–503. Doymaz, I., 2005, Drying behaviour of green beans. Journal of Food Engineering, 69: 161–165. Doymaz, I., 2005, Drying characteristics and kinetics of okra. Journal of Food Engineering, 69: 275–279. FAO, 1999, La qualité et son évolution dans le poisson frais. Documents techniques sur la pêche no. 348. Groupe de Recherche et d’Echange Technologique, 1993, Conserver et transformer le poisson (GRET, Paris), 286 p. Hadrich, B., Boudhrioua, N. and Kechaou, N., 2008, Drying of Tunisian sardine (Sardinella aurita) experimental study and three-dimensional transfer modeling of drying kinetics. Journal of Food Engineering, 84(1): 92–100. Hadrich, B., Boudhrioua, N. and Kechaou, N., in press-a. Experimental and mathematical study of desorption isotherms of Tunisian sardine (Sardinella aurita), Food and Bioproduct Processing.
Hendreson, S.M. and Pabis, S., 1961, Grain drying theory. I. Temperature effect on drying coefficients. Journal of Agricultural Engineering Research, 6: 169–174. Igleasias, H.A., Chirife, J. and Ferro-Fontan, C., 1989, On the temperature dependence of isosteric heats of water sorption in dehydrated foods. Journal of Food Science, 54: 1620–1623. Iglesias, H.A. and Chirifie, J., 1976, Prediction of the effect of temperature on water sorption isotherms of food material. Journal of Food Technology, 11: 109–116. Jain, D. and Pathare, P.B., 2007, Determination of thermal diffusivity of freshwater fish during ice storage by using a one-dimensional fourier cylindrical equation. Biosystems Engineering, 96: 407–412. Jamali, A., Kouhila, M., Mohamed, L.A., Idlimam, A. and Lamharrar, A., 2006, Moisture adsorption-desorption isotherms of Citrus reticulata leaves at three temperatures. Journal of Food Engineering, 77(1): 71–78. Kaya, S. and Kahyaoglu, T., 2007, Moisture sorption and thermodynamic properties of safflower petals and tarragon. Journal of Food Engineering, 78(2): 413– 421. Kiranoudis, C.T., Maroulis, Z.B., Tsami, E. and Marinos-Kouris, D., 1993, Equilibrium moisture content and heat of desorption of some vegetables. Journal of Food Engineering, 20: 55–74. Labuza, T.P., Kaanane, A. and Chen, J.Y., 1985, Effect of temperature on the moisture sorption isotherms and water activity shift of two dehydrated foods. Journal of Food science, 50: 385–389. Lahsasni, S., Kouhila, M. and Mahrouz, M., 2004, Adsorption-desorption isotherms and heat of sorption of prickly pear fruit (Opuntia ficus indica). Energy Conservation and Management, 45: 249–261. Lewis, W.K., 1921, The rate of drying of solid materials. Journal of Industrial Engineering, 5(13): 427–433. Multon, J. L., Bizot, H. and Martin, G., 1991, Mesure de l’eau adsorbée dans les aliments: teneur en eau, activité d’eau, sorption. Techniques d’analyse et contrôle dans les IAA, vol. 4, 2éme ed. (Paris), pp. 41–63. Oswin, C.R., 1946, The kinetics of packing life. III. The isotherm. Journal of Chemical Industry, 65: 419–423. Page, G.E., 1949, Factors influencing the maximum rates of air drying shelled corn in thin layers. Unpublished Master Thesis, Purdue University, Lafayette, IN, USA. Panagiotou, N.M., Krokida, M.K., Maroulis, Z.B. and Saravacos, G.D., 2004, Moisture diffusivity: literature data compilation for foodstuffs. International Journal of Food Properties, 7(2): 273–299. Peleg, M., 1993, Assessment of semi-empirical evaluation of methods to determine moisture sorption isotherms, in Water Activity: Theory and Application to Food, Rocklan, L.B., Beuchut, R.L. (eds). Sainclivier, M., 1983, L’industrie alimentaire halieutique, vol. 1 Le poisson matière première (Sciences Agronomiques, France) 263 p. Sainclivier, M., 1985, L’industrie alimentaire halieutique, vol. 2 Des techniques ancestrales à leur réalisations contemporaines: salage, séchage, fumage, marinage, hydrolysats (Sciences Agronomiques, France) 365 p. Sainclivier, M., 1988, L’industrie alimentaire halieutique, vol. 3 La conservation par des moyens physiques, première partie: Conserverie de poissons (Sciences Agronomiques, France) 297 p. Sogi, D.S., Shivhare, V.S., Garg, S.K. and Bawa, A.S., 2003, Water sorption isotherm and drying characteristics of tomato seeds. Biosystems Engineering, 84(3): 297– 301. Spiess, W.E.L. and Wolf, W., 1983, The results of the COST 90 project on water activity, in Physical Proprieties of Foods, Jowih, R., Escher, F., Halestrom, B., Mefert, H., Spiess, W., & Vos, G. (eds) (Elsievier Applied Science, London), pp. 65–91. Thompson, T.L., Peert, R.M. and Forster, G.H., 1968, Mathematical simulation of corn drying—a new model. Transactions of the ASAE, 11: 582–586.
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Togrul, I.T. and Pehlivan, D., 2002, Mathematical modelling of solar drying of apricots in thin layers. Journal of Food Engineering, 55(3): 209–216. Tsami, E., 1991, Net isosteric heat of sorption in dried fruits. Journal of Food Engineering, 14: 327–335. Van den Berg, C., 1985, Development of B.E.T. like models of sorption of water of foods; theory and relevance, in Properties of Water in Foods, Simatos, D. and Multon, J.L., Multon, J.L. (eds) (Martinus Nijhoff Publishers, Dordrecht), pp. 119–135. Van der Berg, C. and Bruin, S., 1981, Water activity and its estimation in food systems, in Water Activity: Influence on Food Quality, Rockland, L.B. and Stewant, F., Stewant, F. (eds). (Academic Press, New York) Van Meel, D.A., 1958, Adiabatic convection batch drying with recirculation of air. Chemistry Engineering Science, 9: 36–44.
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Contents lists available at ScienceDirect
Food and Bioproducts Processing journal homepage: www.elsevier.com/locate/fbp
Drying of sardine muscles: Experimental and mathematical investigations Nadia Djendoubi a,∗ , Nourhène Boudhrioua a , Catherine Bonazzi b,c , Nabil Kechaou a a
Groupe de Recherche Génie des Procédés Agroalimentaires, Unité de Recherche en Mécanique des Fluides Appliquée et Modélisation, Ecole Nationale d’Ingénieurs de Sfax, BP ‘W’ 3038, Sfax, Tunisie b INRA, UMR 1145 Génie Industriel Alimentaire, 1 avenue des Olympiades, F-91300 Massy, France c AgroParisTech, UMR 1145 Génie Industriel Alimentaire, 1 avenue des Olympiades, F-91300 Massy, France
a b s t r a c t The aim of this work was to study the effect of air drying process on the dehydration kinetics of sardine muscles (Sardina pilchardus). Experimental drying kinetics were measured at five air temperatures (40, 50, 60, 70 and 80 ◦ C), two relative humidity and at a constant air velocity of 1.5 m/s. The sardine drying kinetics were accelerated by increasing air temperature and were showed down when increasing air humidity. Moisture desorption isotherms of sardine muscles were determined at three temperatures (40, 50 and 70 ◦ C) by using the static gravimetric method. The equilibrium moisture contents of sardine muscles were used to treat mathematically the experimental drying kinetics. Experimental drying kinetics and desorption isotherms of sardine muscles were described by using empiric models available in the literature. Eight models (GAB, BET, Henderson–Thompson, Modified Chung & Pfost, Modified Halsey, Oswin, Peleg and Adam & Shove models) were compared in order to describe the desorption isotherms. The Peleg model showed the best fitting of experimental data. For the drying kinetics, the Page model allowed a better fitting than the Newton and the Henderson and Pabis models. The Page model was thus used for simulating the drying kinetics of sardine muscles between 40 and 80 ◦ C. © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Air drying; Desorption isotherms; Sardina pilchardus muscles; Equilibrium moisture content; Mathematical treatment
1.
Introduction
Fish and marine products are very important food products, especially in developing Countries. These products are valuable sources of nutrients such as proteins (15–27% wet basis) and lipids and mainly polyunsaturated fatty acids. However, they contain up to 80% of water and are thus highly perishable products, especially in hot countries were cold preservation techniques are often missing (Zakhia, 2002). Preservation is necessary because of high enzymatic and bacterial activity in fresh fish (Sainclivier, 1983). Fishes can thus be valorised by drying which is an efficient technique for improving stabilisation and storage. This increases the availability to consumers and permits the valorisation of many sea and agricultural
∗
products. On the other hand, drying can be responsible for severe quality deterioration in food (Chinnaswamy and Hanna, 1988), especially in fish (Sainclivier, 1985, 1988). Furthermore, studies on drying must take quality indexes into account. The physical, chemical and microbiological stability of a fresh or a processed food product is highly influenced by water activity (aw ). Knowledge of moisture sorption isotherms is therefore essential to determine the equilibrium moisture contents of agricultural crops. This investigation was undertaken in order to examine the effect of drying air (temperature and relative humidity) on drying kinetics of Sardina pilchardus muscles. Experimental drying and desorption isotherms data were measured, and then fitted by using empirical models available in the literature.
Corresponding author. E-mail addresses: djendoubi [email protected] (N. Djendoubi), [email protected] (N. Boudhrioua), [email protected] (C. Bonazzi), [email protected] (N. Kechaou). Received 29 October 2007; Accepted 3 July 2008 0960-3085/$ – see front matter © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.fbp.2008.07.003
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Nomenclature a, b, c polynomial parameters aw water activity A, B, C, D, k, n, a models parameters −dX/dt drying rate kg water (kg dry mater−1 min−1 ) −(dX/dt)0 initial drying rate kg water (kg dry mater−1 min−1 ) f dimensionless drying rate Hv latent heat of vaporization of pure water (kJ mol−1 ) nexp. data number of experimental data nparam number of models parameters qst,n net isosteric heat of desorption (kJ mol−1 ) whole isosteric heat of desorption (kJ mol−1 ) Qst r correlation coefficient R universal gas constant (kJ mol−1 K−1 ) RH air relative humidity (%) S Standard error Ta air temperature (◦ C) Va air velocity (m/s) initial moisture content (kg water kg−1 dry X0 mater) Xeq equilibrium moisture content (kg water kg−1 dry mater) dimensionless moisture ratio Xr
2.
Materials and methods
2.1.
Raw material
Fresh sardines (S. pilchardus) were purchased from a local fish market (Massy, France). Sardines were immediately transported in sealed polystyrene boxes containing ice to the laboratory. Head, scales and viscera were removed, and two fillets were obtained from resulting sardine carcass. Fish muscles were cut in rectangular slabs of 0.06 m length and 0.02 m width. Afterwards, the samples were used for global chemical characterization, measurement of desorption isotherms and drying experiments.
2.2.
Global chemical analysis
In order to characterize the fresh sardine muscles, analyses were realized according to the methods of Association of Offi-
Table 1 – Water activity values of the used saturated salt solutions (Multon et al., 1991). Temperature (◦ C)
Salt
LiCl CaCl2 MgCl2 K2 CO3 Mg(NO3 )2 NaBr SrCl2 KI NH4 Cl NaCl KCl
40 ◦ C
50 ◦ C
70 ◦ C
0.1116 0.1917 0.3159 – 0.4842 0.5317 – 0.6609 – 0.7501 0.8232
0.1105 0.1654 0.3054 0.4091 0.4544 0.5093 0.5746 0.6449 – 0.7484 0.812
0.1075 – 0.2777 0.3737 – – 0.4618 0.6193 0.673 0.7455 0.7949
cial Analytical Chemists (AOAC, 1984). Moisture content was measured using the gravimetric method in an oven at 105 ◦ C up to constant weight (≈24 h). Protein was analyzed according to the Kjeldahl method. The N-total content was determined by using the universal multiplication factor of 6.25. Fat content was determined by the Soxhlet method using petroleum ether as a solvent. Ash content was measured by using a muffle furnace and by heating the dried sample at 550 ◦ C during 4 h. All chemical analyses were performed in triplicate. The results were expressed in wet basis (g/100 g fresh fish) and were presented by calculating the mean value ± standard deviation of repeatability.
2.3.
Desorption isotherms
2.3.1.
Experimental procedure
The desorption isotherms were determined by using the standard static–gravimetric method (Spiess and Wolf, 1983). Eleven saturated salt solutions selected to give different water activities in the range of 0.1–0.9 were used. The salt solutions and their corresponding water activities at different temperatures are taken from literature reported by Multon et al. (1991) and were given in Table 1. Three repetitions were performed (three samples per salt). The glass sorption jars were placed in a cabinet at the controlled temperatures of 40, 50 and 70 ◦ C (±1 ◦ C). Each sample was carefully weighed every week by using an analytical bal-
Table 2 – Equations for describing the desorption isotherms Name of the equation
Equation
No
CABaw (1 − Baw )(1 − Baw + ABaw )
GAB (Guggenhein, Anderson & De Boer) (Van den Berg, 1985)
Xeq =
BET (Brunauer et al., 1938)
Xeq = A
Henderson–Thompson (Thompson et al., 1968)
Xeq =
Modified Chung & Pfost (Chung and Pfost, 1967)
Xeq = A − B ln(aw ) ln(−T + B)
(4)
Modified Halsey (Iglesias and Chirifie, 1976)
Xeq = A −
B ln(aw )
(5)
Oswin (Oswin, 1946)
Xeq = A
Peleg (Peleg, 1993)
Xeq = AaBw + CaD w
Baw 1 − aw
aw 1 − aw
1 − (C + 1)aCw + CaC+1 w 1 + (B − 1)aw −
ln(1 − aw ) −A(T + B)
(1)
1/C
1/C
(BaC+1 w )
(2)
(3)
B (6) (7)
food and bioproducts processing 8 7 ( 2 0 0 9 ) 115–123
ance (Mettler, precision: 10−4 g) until no significant change in weight was observed between two consecutive measurements. Once equilibrium was reached, the moisture content of the sample was determined. The initial mass of the muscle put in each glass sorption jar was of about 2.080 ± 0.055 g. The hygroscopic equilibrium was reached after 3–5 weeks.
2.3.2.
Mathematical analysis
Moisture sorption isotherms of food products can be described by numerous mathematical models with two or more parameters (Boudhrioua et al., in press-a; Hadrich et al., in press; Kaya and Kahyaoglu, 2007; Jamali et al., 2006; Bellagha et al., 2005; Van der Berg and Bruin, 1981). The experimental desorption data were fitted by using seven equations (with two, three or four parameters) shown in Table 2. Eqs. (1)–(7) (Table 2) were chosen among the most used models in the literature; Xeq is the equilibrium moisture content of S. pilchardus muscles (kg/kg d.b), aw is the water activity, T is the temperature (K) and A, B, C and D are the models parameters. These parameters were estimated by fitting the experimental data using non-linear regression analysis and minimizing the residual sum of squares between experimental and calculated data. The adequacy of each model was evaluated by the correlation coefficient and the standard error coefficient calculated by the software Curve Expert 3.1® . These parameters were calculated as follows:
nexp.data (Xeq i=1
S=
− Xeqcali )
2
r=
nexp.data 1−
i=1
i=1
(Xeq − Xeqi )
2
2
(9)
where Xeqcali is the moisture content calculated by the model, Xeqi the experimental moisture content, nparam the number of model’s parameters and nexp. data the number of experi¯ eq was calculated by using this relation: Xeq = mental data. X nexp.data Xeqi (Boudhrioua et al., in press-a). 1/nexp.data i=1
2.3.3.
Isosteric heat of desorption
The net isosteric heat of desorption qst,n (kJ/mol) was calculated from the experimental desorption isotherms by using the Clausius–Clapeyron equation (Labuza et al., 1985; Igleasias et al., 1989; Tsami, 1991); ln(aw ) = −
qst,n 1 × + Cst R T
(10)
where R is the universal gas constant (kJ/mol K) and T the desorption isotherm temperature (K). The net isosteric heat of desorption was calculated from Eq. (10) by plotting the desorption isosteres as ln (aw ) versus (1/T) for different moisture contents and calculating the slopes which are equal to −qst,n /R (Tsami, 1991; Kiranoudis et al., 1993). This procedure was repeated with different moisture contents in order to determine the dependence of qst on moisture content. The value of the whole isosteric heat of desorption (Qst ) was then calculated by using the following equation: Qst = qst,n + Hv
2.4.
Drying experiments
Drying experiments were performed by using a convective pilot air dryer. The dryer allows carrying out long drying kinetics under strictly defined and well-controlled temperature (20 < Ta < 160 ◦ C), air velocity (0 < Va < 3 m/s) and air humidity conditions (air humidity up to 0.3 kg H2 O kg−1 anhydrous air). The drier works as an open-loop system and is controlled by a computer, with temperature, relative air velocity and relative air humidity as adjustable parameters (Boudhrioua et al., 2002; Boudhrioua et al., 2003). Experiments were performed in order to determine the effect of air temperature and relative humidity on drying kinetics. Five temperatures were investigated (40, 50, 60, 70 and 80 ◦ C). Drying experiments were performed at ambient humidity for drying at 40, 50, 60, 70 and 80 ◦ C and at a relative humidity of 40% for drying at 40 and 50 ◦ C. All experiments were conducted for an air velocity of 1.5 m/s. The sardine muscles samples were hung in a vertical drying channel and the surface of the muscles was held parallel to the airflow direction. The muscles were dried up to a fixed moisture content of 0.25 kg/kg fresh fish (i.e. 0.33 kg/kg dry matter) for further quality comparison. This value was chosen while reported by GRET (1993) as the one at which dried fishes present an acceptable sensorial quality.
2.4.1.
(Xeqi − Xeqcali )
nexp.data
where Hv is the latent heat of vaporization of pure water (Hv is equal to 43.3178, 42.9345 and 42.1269 kJ/mol at 40, 50 and 70 ◦ C, respectively).
(8)
nexp.data − nparam
117
(11)
Characteristic drying curves
Foodstuffs are heterogeneous in structure and in composition, but only the average moisture content is characterized by drying kinetics. The characteristic drying curve method (Lewis, 1921) can be chosen to describe the falling rate period of the drying curves. Based on the Van Meel transformation (Van Meel, 1958), this method consists in normalizing the moisture content (Eq. (12)) and the drying rate (Eq. (13)) as follows: Xr (t) =
f =
X(t) − Xeq X0 − Xeq
(−dX/dt)t (−dX/dt)0
(12)
(13)
where X0 : initial moisture content (kg water/kg dry matter), Xeq : equilibrium moisture content (kg water/kg dry matter), Xr : moisture ratio, (−dX/dt)0 : initial drying rate (kg water/kg dry matter min), f: dimensionless drying rate. The equilibrium moisture content Xeq was determined from the desorption isotherms. The Marquardt–Levenberg non-linear optimization method, using the computer program Curve Expert 3.1® , was then used for fitting the characteristic drying curve f = f(Xr ).
2.4.2.
Empirical drying equations
Semi-empirical and empirical models have been widely used to describe the thin layer drying kinetics of many agricultural products (Jain and Pathare, 2007; Togrul and Pehlivan, 2002; Yaldiz and Ertekin, 2001, Boudhrioua et al., in press-b). The experimental data were presented here by fitting the experimental moisture ratio (Xr ) versus drying time by three of the most widely used models for food and agricultural products (the Newton (Lewis, 1921), the Page (Page, 1949) and the
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Table 3 – Mathematical models applied to the Sardina pilchardus muscles drying curves Model name Newton (Lewis, 1921) Page (Page, 1949) Henderson and Pabis (Zhang and Litchfield, 1991)
Model equation
Parameters
Xr = exp (−kt) Xr = exp(−ktn) Xr = a exp (−kt)
k k, n a, k
Fig. 2 – Comparison between desorption isotherms of sardine obtained in this work and those obtained by Bellagha et al. (2005) and Hadrich et al. (in press). with increasing temperature at a given water activity. For example at aw equal to 0.75, equilibrium moisture content of sardine muscles decreased from 0.274 at 40 ◦ C to 0.141 kg/kg d.b at 70 ◦ C.
3.3. Fig. 1 – Desorption isotherms of sardine muscles obtained at 40, 50 and 70 ◦ C. Henderson and Pabis models (Hendreson and Pabis, 1961)) (Table 3). The description suggested by Lewis is analogous to Newton’s law for cooling when interval resistance to heat transfer can be neglected; Henderson and Pabis and Page’s equation are of similar type, with additional coefficients for a better fitting of experimental data. These models were evaluated, by the Marquardt–Levenberg non-linear optimization method using Curve Expert 3.1® software.
3.
Results and discussion
3.1.
Global chemical composition
Moisture is the most abundant component in fresh S. pilchardus. It varies from 69.32 to 75.00% (w.b). The fresh fish contains 19.65 ± 0.03 g/100 g of proteins and 2.42 ± 0.12 g/100 g of lipids. Abdelmouleh et al., 1980 reported similar results for fresh Tunisian S. pilchardus. Ash content is about 1.19 ± 0.12 mg/100 g and is in the order of magnitude of values published by the FAO (1999).
3.2.
Fitting of desorption isotherms
The results in terms of estimated parameters and values of statistics parameters (r and S) are presented in Table 4. It can be seen that the Peleg model presents the smallest S values (0.003 ≤ S ≤ 0.005) and the highest correlation coefficients (r = 0.99). Therefore, it was the best model for fitting the experimental data for water activity ranging from 0.10 to 0.90 and temperature varying from 40 to 70 ◦ C. Fig. 3 shows a comparison between experimental data and Peleg’s model for desorption isotherms of sardine muscles obtained at 40, 50 and 70 ◦ C. In the same figure, it can be noticed that the Peleg model can be recommended for predicting the S. pilchardus muscles desorption isotherms in the range of the investigated temperatures. The variation of Peleg’s model parameters versus temperature was also examined. Peleg’s model parameters (A, B, C and D) showed polynomial variations with temperature (aT2 + bT + c). The calculated coefficients describing
Desorption isotherms
Desorption isotherms of sardine muscles obtained at 40, 50 and 70 ◦ C are shown in Fig. 1. The equilibrium moisture content corresponding to each moisture activity, aw , represents the mean value of three replications. All isotherms follow a sigmoid form and are of type II curves according to BET classification (Brunauer et al., 1938). They describe the sorption of water on an adsorbent with strong water–adsorbent interactions. Similar results were reported by Hadrich et al. (in press) for Sardinella aurita (Fig. 2). Equilibrium moisture content increases with rising moisture activity. A significant temperature effect can be observed on desorption isotherms. In fact the equilibrium moisture content decreases
Fig. 3 – Comparison between experimental and calculated desorption isotherm using Peleg model (dots: experimental values, lines: calculated values).
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Table 4 – Estimated parameters of the eight models used for describing desorption isotherms of Sardina pilchardus muscles and the corresponding statistical parameters T (◦ C)
Equations
Parameters A
B
C
S
r
D
Guggenhein, Anderson & De Boer (Van den Berg, 1985)
40 50 70
0.181 0.200 0.116
1.026 0.799 0.964
0.721 0.759 0.600
0.021 0.046 0.004
0.981 0.997 0.998
BET (Brunauer et al., 1938)
40 50 70
4.200 9.270 1.210
0.021 0.009 0.032
3.000 2.200 3.600
0.026 0.006 0.006
0.970 0.996 0.996
Henderson–Thompson (Thompson et al., 1968)
40 50 70
0.474 0.538 0.513
−25.802 −22.563 −11.133
0.474 0.538 0.513
0.023 0.005 0.009
0.975 0.100 0.990
Modified Chung and Pfost (Chung and Pfost, 1967)
40 50 70
0.383 0.305 0.230
0.070 0.058 0.042
0.048 0.026 0.029
0.868 0.924 0.877
Modified Halsey (Iglesias and Chirifie, 1976)
40 50 70
0.399 0.338 0.311
0.399 0.338 0.311
0.011 0.017 0.007
0.995 0.969 0.994
Oswin (Oswin, 1946)
40 50 70
0.117 0.087 0.059
0.755 0.617 0.782
0.014 0.006 0.004
0.989 0.996 0.997
Peleg (Peleg, 1993)
40 50 70
0.144 0.218 0.046
0.594 6.482 0.569
0.005 0.004 0.003
0.999 0.998 0.998
2.047 2.306 2.448
1.197 0.193 0.274
7.137 1.149 3.450
the dependence on the temperature are summarized in Table 5.
3.4.
Heat of desorption
The values for whole isosteric heat of desorption, Qst , were calculated from desorption data obtained at different temperatures by means of Eq. (11). The whole S. pilchardus muscles desorption heat variation versus moisture content is shown in Fig. 4. The whole isosteric heat desorption decreased from 67.36 to 48.47 kJ/mol as moisture content increased from 0.025 to 0.30 (d.b). At low moisture contents, the desorption heat was higher than at high moisture contents. Tsami (1991) and Lahsasni et al. (2004) suggested that the rapid increase of the whole desorption heat observed at low moisture contents was due to the existence of highly active polar sites on the surface of the food material which are covered with water molecules forming a mono-molecular layer. The whole isosteric heat of moisture desorption of S. pilchardus muscles was successfully described by the following exponential function: Qst = exp(3.91 +
0.032 + 0.114 ln(Xeq )) Xeq
Fig. 4 shows the adequacy between calculated and experimental values of Qst .
with r = 0.98 and S = 1.78
(14)
3.5.
where Xeq is the equilibrium moisture content. Table 5 – Calculated coefficients describing the dependency of desorption isotherms of Sardina pilchardus muscles Polynomial parameters
Peleg model parameters A
a b c
−0.0005 0.0552 −1.2145
Fig. 4 – Variation of the whole isosteric heat of desorption vs. equilibrium moisture content.
B −0.0295 3.2422 −81.921
C
D
0.0035 −0.4139 12.18
0.0238 −2.7402 78.677
Experimental drying curves
The effects of air temperature and relative humidity on the sardine muscles drying kinetics were examined. Figs. 4–8 illustrate the change in moisture ratio of the fish muscles versus drying time (Figs. 5 and 6), and the corresponding drying rates versus moisture ratio (Figs. 7 and 8). The drying rate decreased when moisture content or drying time decreased. No constant drying period was observed and the dehydration of the muscles occurred only in the falling rate period. These results indicated that diffusion is the most likely physical mechanism governing moisture removal from the muscles. Similar results were observed in the drying of
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ing of agricultural products (Lahsasni et al., 2004; Doymaz, 2005a,b). Figs. 7 and 8 show the effect of the relative humidity at 40 ◦ C on drying curves of sardine muscles. The drying time increased with increasing relative humidity at the same temperature. Similar trends have been reported for drying of vegetables products (Viswanathan et al., 2003; Kiranoudis et al., 1993).
3.6. Empirical modeling of the experimental drying curves
Fig. 5 – Variation of the moisture ratio of sardine muscles vs. drying time obtained at different drying temperatures and at ambient relative humidity (Va = 1.5 m/s).
The experimental drying curves (moisture ratio versus drying time) were fitted using three semi-empirical models: the Henderson and Pabis, the Lewis and the Page models. The model evaluation was based on statistical test (r and S values). The corresponding statistical and model parameters are shown in Table 6. In all cases, r-values are higher than 0.90, indicating a good fit of drying curves by all the models. According to the statistical values shown in Table 6, the Page model is the best one for fitting the drying curves over a wide range of temperatures, with corresponding correlation coefficients (r) and standard errors (S) varying between 0.990 and 0.999 and 0.012 and 0.128, respectively. It is important to notice the relation between Fick’s model and Henderson and Pabis’s one. The analytical solution of Fick’s equation (Crank, 1979) for an infinite slab can be written as follows: Ln(Xr ) = Ln
Fig. 6 – Influence of temperature on the variation of drying rate curves of Sardina pilchardus muscles vs. moisture ratio at Va = 1.5 m/s.
8 2
−
2 Dapp t (e/2)
(15)
2
where e is the dimension in the direction of diffusion (m) and Dapp is the apparent diffusivity (m2 /s). With some mathematical transformations, the Fick equation can be written like the Henderson and Pabis model (Xr = a exp (−kt)) (Zhang and Litchfield, 1991): with a = ( 82 ) and k =
2 Dapp 2
(e/2)
.
The values of apparent moisture diffusivity calculated by this way vary between 1.38 × 10−11 and 2.21 × 10−11 m2 s−1 . They are within the general range of 10−11 to 10−9 m2 s−1 reported by Panagiotou et al. (2004) for moisture diffusivity in fish muscles.
Fig. 7 – Variation of the moisture ratio of sardine muscles vs. drying time obtained at different relative humidity and at 40 ◦ C (Va = 1.5 m/s). many biological products (Sainclivier, 1985; Sogi et al., 2003; Desmorieux and Decaen, 2005; Doymaz, 2005a,b; Hadrich et al., 2008). As can be seen from Figs. 5 and 6, one of the main factors influencing the drying kinetics of sardine muscles is the drying air temperature. An increase in drying air temperature caused a reduction in the drying time. Final drying duration (up to 0.33 on a dry basis) takes 3 h 30 min at 80 ◦ C (humidity of ambient air) and 12 h 24 min 40 ◦ C (humidity of ambient air). Different authors reported similar results on dry-
Fig. 8 – Influence of the relative humidity on the drying rate curves of Sardina pilchardus muscles obtained at 40 ◦ C and at Va = 1.5 m/s.
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Table 6 – Coefficients and statistical parameters of models fitting drying curves of Sardine pilchardus muscles Models
Drying conditions
Parameters k
◦
a
S
r
n
Newton (Lewis, 1921)
80 C, 2% 70 ◦ C, 3% 60 ◦ C, 4% 50 ◦ C, 6% 50 ◦ C, 40% 40 ◦ C, 14% 40 ◦ C, 40%
−4
1.06 × 10 1.40 × 10−4 8.09 × 10−5 6.42 × 10−5 5.69 × 10−5 7.35 × 10−5 4.90 × 10−5
– – – – – – –
– – – – – – –
0.164 0.045 0.176 0.085 0.067 0.081 0.149
0.960 0.997 0.995 0.987 0.994 0.993 0.978
Page (Page, 1949)
80 ◦ C, 2% 70 ◦ C, 3% 60 ◦ C, 4% 50 ◦ C, 6% 50 ◦ C, 40% 40 ◦ C, 14% 40 ◦ C, 40%
2 × 10−3 1.53 × 10−4 1.70 × 10−5 5.00 × 10−4 4.85 × 10−5 5.90 × 10−5 3.11 × 10−5
– – – – – – –
0.697 0.988 0.6927 0.793 1.01 1.02 1.02
0.025 0.045 0.054 0.044 0.066 0.080 0.012
0.999 0.997 0.996 0.995 0.991 0.993 0.999
Henderson and Pabis (Hendreson and Pabis, 1961)
80 ◦ C, 2% 70 ◦ C, 3% 60 ◦ C, 4% 50 ◦ C, 6% 50 ◦ C, 40% 40 ◦ C, 14% 40 ◦ C, 40%
8.84 × 10−5 1.40 × 10−4 6.70 × 10−5 5.70 × 10−5 5.60 × 10−5 7.21 × 10−5 5.54 × 10−5
0.757 1.009 0.755 0.871 0.977 0.969 1.214
– – – – – – –
0.086 0.045 0.105 0.050 0.066 0.080 0.113
0.989 0.997 0.985 0.995 0.995 0.993 0.987
Plots of the predicted moisture ratios versus drying time using the Page model and the corresponding experimental data are shown in Fig. 9. Page’s model provided a good agreement between experimental and predicted moisture ratios.
3.7.
Determination of the characteristic drying curve
The determination of the characteristic drying curve of S. pilchardus muscles allows to group together all the drying kinetics on a single curve as shown in Fig. 10 which represents the dimensionless drying rate ‘f’ versus moisture ratio ‘Xr ’. The falling rate period is thus represented with a concave curve. A polynomial equation of degree 4 gave the best fit to the dimensionless experimental data.
Fig. 10 – Drying characteristic curves of Sardina pilchardus muscles obtained for different drying experiments.
f = 0.885 Xr − 2.901 Xr2 + 4.513 Xr3 − 1.525 Xr4 (r = 0.972 and S = 0.025)
(16)
40 to 80 ◦ C, a relative humidity varying from 2 to 40%, at an air velocity of 1.5 m/s.
This function allows to characterize the convective drying process of S. pilchardus’ muscles in a temperature ranging from
4.
Fig. 9 – Comparison between experimental and calculated (Page model) drying curves of sardine muscles (dots: experimental values, lines: calculated values).
The moisture desorption isotherms of S. pilchardus muscles were measured at three temperatures (40, 50 and 70 ◦ C) by using the standard gravimetric method. The experimental desorption isotherms of have a sigmoid forms and display the type II in the BET classification. The Peleg model showed the best fit with the experimental desorption data at 40, 50 and 70 ◦ C and for a water activity range from 0.10 to 0.90. The whole isosteric heat of desorption increased with decreasing moisture content and experimental data were well fitted by an exponential equation. The drying kinetics of S. pilchardus’ muscles contained no constant rate period, but only falling rate periods. The effects of air temperature and relative humidity were studied. The drying rate increased when increasing air temperature and decreased when increasing relative humidity.
Conclusion
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The Page model described adequately the drying kinetics of S. pilchardus muscles. The determination of the characteristic drying curve allowed to group together the drying kinetics in a single curve fitted by a polynomial equation.
Acknowledgement The authors gratefully acknowledge the “Agence Universitaire de la Francophonie” for providing financial support.
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