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Experimental and Mathematical Investigations of Apple Slices Convective Drying

The aim of this work was to determine sorption isotherms and thin layer convective drying behavior of apple slices and to compare the experimental and calculated results by using models available in the literature. The sorption isotherm was determined at four temperature levels 40, 50, 60 and 70 °C and at water activity ranging from 0.058 to 0.89, using the static gravimetric method. A non-linear regression procedure was used to fit experimental sorption isotherms and drying curves with most used empirical mathematical models available in literature. It was found that the Peleg model suitably represent the sorption experimental data in the mentioned investigated ranges of temperature and water activities. The Midilli et al. model satisfactorily described the thin layer drying behavior of apple slices. The drying characteristic curve and the thin layer drying rate expression of apple slices have been established from experimental convective drying kinetics. The values of the diffusivity coefficients at each condition were obtained using Fick's second law of diffusion. They varied from 8.51 × 10 -8 to 3.28 × 10 -7 m 2 /s in the temperature range of 40-70 °C and in the relative humidity range of 20%-40%. The activation energies for moisture diffusion were calculated to vary from 26.72 to 35.83 kJ/mol.


Introduction
In order to improve the quality of the dried product, industrial dryers should be used in place of traditional sun drying. Industrial dryers provide uniform dried product, hygiene and also the process is more rapid [1]. An important factor in the loss of quality of dried foods during storage is the water activity (a w ) which influences the biochemical reactions and stability of dried products. Some of these reactions are lipid oxidation, caking, agglomeration and degradation of vitamins and lycopene [2,3]. Knowledge of sorption isotherm and drying behavior are of great importance in food dehydration, especially in the quantitative approach to the prediction of the shelf life of dried foods [4]. Equations for modelling water sorption isotherms are of special interest for many aspects of food preservation by dehydration, including evaluation of the thermodynamic functions of the water sorbet in foods. Knowledge of the thermodynamic properties associated with sorption behavior of water in foods is important to dehydration in several respects, especially in the design and optimization of unit operation, and further help the understanding and interpretation of sorption mechanisms and food-water interactions.
Several thin layer equations available in the literature for explaining drying behavior and sorption isotherms of agricultural products have been used by Diamente and Munro for sweet potato slices [5], Toujani et al. for silverside fish [6], Madamba et al. for garlic slices [7], Midilli for pistachio [8], Yaldız et al. for grape [9], Basunia and Abe for rough rice [10], Panchariya et al. for black tea [11], Dandamrongrak et al. for banana [12], Lahsasni et al. for prickly pear peel [13], Kalpana et al. for betel leaf [14], and Guran and Kamil for hawthorn fruits [15]. The present study were, therefore, undertaken to investigate the sorption isotherms and the thin layer drying characteristics of apple "Golden delicious" slices in a convective dryer and to fit the experimental data to mathematical models available in the literature. In addition, the effective diffusivities and activation energy in the convective drying process of apple slices are calculated.

Materials
Fresh apple "Golden delicious" was purchased from local market. Upon arrival to the laboratory and before drying, apples were washed hand, peeled and cut into rectangle-shaped slices (dimensions in mm: 40 × 10 × 10). The slices were blanched in water at 90 °C during 5 min to prevent enzymatic browning and immediately cooled in water at 15 °C during few minutes to remove excess heat. The water remaining at the surface was removed with a filter paper. In order to characterize the fresh apple, analyses were realized according to the methods of Association of Official Analytical Chemists [16]. Moisture content was measured using the gravimetric method in an oven at 70 °C up to constant weight (≈ 24 h). The mean water content of the fresh product is about 86 ± 3% (dry basis).

Desorption Isotherms
(1) Experimental procedure A static gravimetric method has been used for the determination of the apple sorption isotherms at four temperatures 40, 50, 60 and 70 °C. The salts are dissolved in distilled water at a higher temperature than the working one; a saturated solution is obtained when the liquid phase is in equilibrium with the salt crystals [17]. The prepared solution is then cooled to the working temperatures. To avoid the formation of a concentration gradient in the liquid phase, the salt solution is agitated continuously. Nine saturated salt solutions were prepared corresponding to a range of water activities of 0.058-0.891 (Table 1). These solutions are prepared in hermetic jars and are maintained in a drying room regulated in desired temperature. The sample is suspended in the jar, above salts. The required equilibration time was 15-20 days based on the change in weight expressed on a dry basis, which did not exceed 0.1%. The weight was < 1 mg g -1 dry solids for three consecutive weightings at intervals of minimum 5 days [20]. The equilibrium moisture content is calculated by: where Xe i,exp is the ith experimental equilibrium moisture, Xe i,pre is the ith predicted equilibrium moisture, N is the number of observations, z is the number of constants in the drying model and Xe is the average value of experimental equilibrium moisture was calculated by using this relation: (3) Estimation of sorption isosteric heat The net isosteric heat (q st ) is defined as the total heat of sorption of water from the material minus the heat of water vaporisation at the same temperature.
Conventionally, q st is a positive quantity when heat is evolved during adsorption, and negative when heat is absorbed during desorption. The isosteric heat of sorption plays an important role in the determination of the time and the energy requirements for drying [28]. This parameter can be estimated by using the Clausius-Clapeyron equation, at fixed moisture contents [29,30], as shown in Eq. 5: where q st is the net isosteric heat of sorption (kJ/mol), a w is the water activity (dimensionless), T is the absolute temperature (K), R is the universal gas constant (kJ/mol K) and K is a constant.
In an attempt to describe the relationship between the net isosteric heat of sorption and the moisture content, Tsami et al. proposed an empirical exponential correlation [30], which can be written as Eq. 6: In this expression, Xe is the equilibrium moisture content (kg water/kg dry matter), q 0 is the net isosteric heat of sorption of the first molecule of water in the food (kJ/mol), and X 0 is a characteristic moisture content of the food material (kg water/kg dry matter).

Drying Experiments (1) Experimental set-up
The unit of drying used is a climatic blower available in Energetic and the Mass and Thermo Transfers Laboratory of University of Tunis (Tunisia). A convective dryer by the hot air was used for drying, which could be regulated to any desired drying air temperature, relative humidity and velocity of drying air with high accuracy. Principal elements of this process are a centrifugal blower to aspire the ambient air, an electrical resistance air heating section ensuring the rise in the temperature of the air, heating control unit, a steam air moistening section, measurement sensors and a drying chamber. A balance of high precision located at the lower part of the dryer. Temperature, air velocity and relative humidity inside the vein are adjusted and controlled using an automatic system of regulation. The measurement sensors, the data recording and controlling system coupled with a computer. The hot-air orientation on the samples was vertical. The advantage of this type of flow is to offer optimum conditions for contact air-product and a coefficient of significant heat transfer (Fig. 1).
During drying in the convective dryer, the weight losses of the samples were measured at 10 min This curve type can be used to generalize data for drying kinetics of thin layer of apple slices in a convective dryer. Kouhila et al. [17], Bellegha et al. [32], Timoumi et al. [33] based on the Van Meel transformation [34], have used simply the initial moisture content (X 0 ) instead of the critical moisture content (X cr ) and the initial drying rate (dX⁄dt) 0 instead of the drying rate relative to the constant rate period (dX⁄dt) I , Eqs. 7 and 8.
(3) Empirical drying equations Mathematical modeling using thin layer drying models has been studied in drying of fruits, vegetables, seafood and other agriculture or crop products [9,[35][36][37][38]. The models fall into three categories namely the theoretical, semi-theoretical and empirical. Semi-theoretical models offer a compromise between theory and ease of application [39]. For the present study this approach has been taken. Thus eleven semi-empirical models were applied to describe the convection drying kinetics of thin layer of apple slices Table 3 summarizes the mentioned thin layer drying models used in the data fit analysis of this work. to evaluate the goodness of fit of the models. The lower 2  values and the higher R 2 values, which were chosen as the criteria for goodness of fit. These parameters can be described in Eqs. (9) and (10) [26,27]:   [44] Approximation of diffusion XR= a.exp (-k.t)+(1-a).exp (-k.a.t) [9] Wang and Singh 2 XR= 1+ a.t + b.t [45] Simplified Fick's diffusion

Desorption Isotherms and Modelling
In all cases, the R 2 and 2  values for models changed from 0.98282 to 0.99898, 0.00002 to 0.00033, respectively. Therefore, the Peleg model was the best descriptive model as shown in Table 4, suggested by the highest average R 2 value which equals to 0.99898 and the lowest average χ 2 value which equals to 0.00002. Accordingly, the Peleg model was selected as suitable model to represent the sorption isotherms behavior of apple slices in the water activity range of 0.05-0.9 and the temperature range of 40-70 °C. Apple hygroscopic equilibrium moisture is reached at the end of 15 days. As shown in the sorption curves (Fig. 2), a significant temperature effect was observed on desorption isotherms. At constant temperature, the equilibrium moisture content increased with increasing water activity and at constant water activity, the equilibrium moisture content increases with decreasing temperature. In general, both temperature and water activity have significant effects on experimental equilibrium moisture content values. Similar trends have been observed in several other studies concerning other foodstuffs [17,47].

Isosteric Heat of Desorption
The net isosteric heat can be estimated by plotting the sorption isotherms as ln(a w ) versus. The inverse of temperature (1⁄T) for selected material moisture content, and determining the slope which is (-q st ⁄R), hence q st is determined. The results are given in Fig. 3.
As shown in Fig. 4, the net isosteric heat of sorption was high at lower moisture contents and then decreased reaching a constant value at high moisture content (above moisture content around 0.15 kg kg -1 db). At low moisture content, the net isosteric heat of sorption was high, indicating the highest binding energy for water removal. The decrease in the heat of sorption indicates that the water-solid interactions are weakened at high moisture content levels. The same results were reported by Toujani et al. [6] for silverside fish, Nourhene et al. [48] for olive leaves, Medeni and Fahrettin [28] in the case of pistachio. From Tsami's equation, the q 0 and X 0 values for desorption data were 35.3213 kJ mol -1 and 0.1779 kg kg -1 db respectively, with an R 2 equal to 0.993. Marcel et al. obtained for the Gnetum africanum q 0 value around of 68.523 (kJ mol -1 ) and X 0 value of 0.063 (kg kg -1 db) [49]. Kiranoudis et al. obtained for fruits and some plants, a q 0 value varying between 40 and 115 kJ mol -1 and X 0 varying from 0.08 to 21 (kg kg -1 db) [50].

Drying Curves
The drying curves obtained were fitted with 11 different moisture ratio models (Table 4). For results of moisture ratio obtained in experiments for thin-layer

Characteristic Drying Curve
Marquardt-Levenberg nonlinear optimization method, using the computer program Origin 6.0, was used to find the best equation for apple slices characteristic drying curve. According to our results, the characteristic fitting of the drying curves drying curve of thin layer of apple slices is depicted in Fig. 5. The best fitting of this curve is carried out by a polynomial equation of degree 3: 3 2 f=0.9622XR 1.2354XR 1.2659XR 0.0583    The criterion used to evaluate goodness of fit was the correlation coefficient (R 2 = 0.99). This function (Eq. 12) characterizes the convective drying process of apple slices dried in single layer in a temperature ranging from 40 to 70 °C, a relative humidity varying from 20% to 40%, at an air velocity of 2 m s -1 .

Fitting of the Drying Curves
The results of statistical analysis on the eleven drying models relating the drying time and moisture ratio with the experimental condition for drying temperatures of 40, 50, 60 and 70 °C and relative humidity of 20%, 30% and 40% (  Table 6. According to the results of thin layer drying of apple slices, Midilli et al. model could be used to predict the moisture ratio of the product at any time of drying process (Figs. 6-8).

Calculation of Effective Diffusivity and Activation Energy
The thin layer drying of apple slices occurs in the falling rate period only and liquid diffusion controls the process. Fick's second law can be used to describe the thin layer drying of apple slices. General series solution of Fick's second law in Cartesian coordinates is given below (Eq. 13). 2 2 e e f f 2 2 2 0 e n 1 X -X -(2n +1) .π .D .t where D eff is the effective diffusivity and L is the thickness of thin layer of apple slices.
This equation was applied assuming one-dimensional moisture movement without volume change; a constant diffusivity, uniform moisture distribution and negligible external resistance [51].
The Eq. (13) can be simplified by taking the first term Eq. (14): The effective diffusivity was obtained when ln(XR) was plotted versus t  The effective diffusivity was calculated by Eq. (15), using slopes Eq. (16) derived from the linear regression of ln(XR) against time data shown in Figs. 9-11. Generally an effective diffusivity is used due to limited information on the mechanism of moisture movement during drying and complexity of the process. The effective diffusivity (D eff ) during thin layer drying of apple slices varied from 8.51 × 10 -8 to 3.28 × 10 -7 m 2 /s in the temperature range from 40 to 70 °C and in the relative humidity range from 20% to 40% (Table 7). The obtained values are in the suitable range for various products reported in the literature [52,53]. The effective diffusivities increased with temperature as expected.
Where D eff is the effective diffusivity, D 0 is the constant equivalent to the diffusivity at infinitely high temperature, E a is the activation energy, R is the universal gas constant (8.314 × 10 −3 ) and T is the absolute temperature (in K). The logarithm of D eff as a function of the reciprocal of the temperature is plotted and fitted by linear regression. The activation energy was calculated from the slope of the straight line described by the Arrhenius equation is varied from 26.72 to 35.83 kJ mol -1 . These values are in the range to the values (12.7 to 110 kJ mol -1 ) reported by Troncoso and Pedreschi for various foods [55].

Conclusions
Experimental desorption isotherms of apple slices were determined at 40, 50, 60 and 70 °C, using a static gravimetric methods. The experimental data were successfully fitted by the Peleg model in the investigated temperature and water activity ranges. Tsami's equation was applied to correlate the net isosteric heat of sorption as function of equilibrium moisture content with satisfactory results. From the experimental drying curves obtained, it is noted that only the falling drying rate period exists. Also, the drying air temperature was found to be the main factor influencing the drying kinetics. In this study, the results show that the Midilli et al. model give the best fit. Due to higher number of parameters, this model give better results from the other proposed models based on the solution of the liquid diffusion equation. Midilli et al. model is suitable to predict best the moisture ratio of apple slices in a thin layer dryer at the air temperature T ranges of 40-70 °C, 20%-40% relative humidity range and 2 m s -1 drying air velocity. The calculated effective diffusivities and activation energy ranged from 8.51 × 10 -8 to 3.28 × 10 -7 m 2 s -1 and 26.72 to 35.83 kJ mol -1 respectively. The effective diffusivities increased with temperature following the Arrhenius type relationship.