Fresh onion bulbs of the variety “Violet de Galmi” were purchased on stalls of fruits and vegetables from the central market, Ouagadougou, Burkina Faso. Fresh onions were sorted, cleaned and peeled by hand from their external layer. These onions were then stored at 4˚C in a refrigerator prior to the experiments [14]. After being stabilized at room temperature for 2 h, some homogeneous samples of onion were sliced 1 - 3 mm thick perpendiculars to the length of the largest semi-spindle of onion using an electric chain saw (model Secotom-10, Struers with precision of 1 - 3 mm). We obtained sliced samples from 30 mm to 50 mm in diameter and 1 - 3 mm thick. The sliced onions were then wrapped by using aluminum foil in an environment having average temperature of 24˚C to prevent all contact of the sample with ambient humidity. This permitted to avoid discrepancy in the composition of onion due to evaporation or to prevent the decay caused by microorganisms [38]. The mass of dry matter was determined by drying the onions at the end of the experiments in an electric oven at 70˚C for 24 h [39]. Experiments were repeated three times to get a reasonable average.

Thin-layer drying experiments were carried out in a wet laboratory dryer with control electronics Mincon 32 (VC0018, otsch Industrie technik Gmbh, German) (Figure 1). Dryer included, among other things, a console, a drying chamber, a cabinet. The relative humidity and the temperature of the drying air were controlled by the control panel and could be varied from 10% to 96% and from 10˚C to 90˚C. The speed of the air was regulated according to temperature and relative humidity determined by the panel. The drying chamber with a capacity of 190 liters was made in polished stainless steel. The maximum load of the

products by tray was 30 kg when the dryer operated in an environment of 25˚C. The fuse of the unit as well as all electrical components and control were integrated in the electrical cabinet. Measurement errors in the temperature according to time and to space in the drying chamber were respectively ±0.1 to ±0.5˚K and ±0.5 to ±1˚K. Measurement errors in the time relative humidity were ±1% to ±3% (Figure 1).

A sliced sample was placed on a tray hanging from an electric balance (Model S4002, DENVER Instrument with precision of 1 - 3 g) which was located at the top of the dryer (Figure 2). The tray was made of nylon mesh allowing the crossing of the air on the surfaces of the sample. Balance is positioned in the center of the circular slot performed above the dryer. Minor vibrations caused by the driving forces of the fan ensuring the forced convection are eliminated by pressing tare of the balance before starting each one of the experiment. The experiments are conducted at temperatures of 40˚C, 50˚C, 60˚C and 70˚C and at 20% RH.

For each drying condition, averages of three repetitions were taken as data. At the end of each experiment, the sample was heated in an oven temperature of 70˚C during 24 h of drying in order to obtain the mass of dry onion skeletal structure [39]. Before performing experiments, dryer was turned on without a loading in order to stabilize at the instruction given by the command board. Heating and cooling rates are 0.6˚C/min and 0.3˚C/min, respectively. The dryer is therefore run for a sufficient period of time to reach the set point. The acquisition system is composed of a data logger (NI USB-6210, National Instruments), a LABview program installed in a computer.

Figure 3 shows the curves of drying for “Violet de Galmi” onions drying at four temperatures (40˚C, 50˚C; 60˚C and 70˚C) and at relative humidity of 20%. On Figure 3, all drying kinetics follows a drying falling-rate period. The absence of a constant drying rate period may be due to the thin layer of product that did not provide a constant supply of water for an applied period of time. Also, some resistance to water movement may exist due to shrinkage of the product on the surface, which reduces the drying rate considerably. The moisture content decreases gradually while the drying time elapsed, exhibiting a smooth downward curve. The dominating mechanism of moisture transfer during this period was moisture diffusion similar to that for most fruits and vegetables as such kiwi-fruit,

avocado, mango, cassava and banana [45] [46] [47] [48]. The drying times onions were obtained at 1.5, 2.0, 2.8 and 3.0 h at 70˚C, 60˚C, 50˚C and 40˚C, respectively. The air temperatures have a major effect on the drying kinetics. The air temperature increase from 40˚C to 70˚C leads to an increase in slope of curve describing the onion drying kinetics. By reducing the drying time of 40˚C to 70˚C, represents nearly 50% of the time of drying at air temperature of 40˚C. The drying air temperature influence water diffusion transport in onion convective drying when the air temperature increment between the different drying conditions is by at least 10˚C. The air drying running at higher air temperature and higher energy power leads to higher temperatures of onion slices implying a larger driving force for mass transfer. The mass transfer rates were higher in the beginning of the drying processes and gradually reduced through the end of the process. Thus more energy was absorbed by the water at the onion surface initially, resulting in faster drying and with the onion surface drying out subsequently, heat penetration through the dried layer decreased thus retarding the drying rates. Also the differences in drying rates caused by different air temperatures levels are higher at the beginning of drying; while by the end of the processes all drying kinetics are closer to each other. During the processes towards the end of drying, the influence of temperature on the drying kinetics is lower than at the beginning and that moisture transport is hindered more and more by internal mass resistances of onion bulb [28]. Because this temperature effect on drying, stepwise changes in temperature from one drying period to another period could be employed so as to avoid a degradation of heat-sensitive natural compounds (antioxidants, color, vitamins) of onion slices and so to save much energy of drying. Similar observations were obtained in a review from Sagar and Kumar [49] on the recent advances in the drying and the dehydration of fruits and vegetables. In literature, our results were generally in agreement with some previous findings on onion drying. It was indicated in a convective drying of yellow onion under drying air temperature of 30˚C to 60˚C. It was visible how the moisture (expressed in dry basis) follows an exponential decay, and how the increase in temperature accelerated this drying process. In this, at 30˚C the drying stabilized after approximately 7 hours whereas at 60˚C 2 hours were sufficient, representing a very important reduction in the drying time (more than 70%) [4]. Three levels of airflow temperature (40˚C - 50˚C - 60˚C) were applied to dry onion by a custom designed fluidized bed dryer equipped with a heat pump dehumidifier, predicting its drying behavior by regression, fuzzy logic and artificial neural network techniques [50]. Drying temperatures exerted a pronounced effect on the quality changes of sliced onion. The drying temperatures up 60˚C did not show any influence on quality changes. However, drying temperatures above 60˚C significantly influenced the color of the dried onion [51]. By using oven drying method (50˚C and 70˚C), the onion drying time up to the moisture content of approximately X_f = 0.818 (dry basis) could be shortened by 11.76% and 79.41%, when compared to sun drying, respectively. For microwave oven drying at 210 W and 700 W, the onion drying times to reach the moisture content of X_f = 0.960 (dry basis) were 10.5 min and 8.33 min, respectively. This was due to the fact that drying at higher temperature and higher energy power which led to higher temperatures implied a larger driving force for heat transfer [6]. The effect of drying temperature on drying kinetics of onion (Allium cepa L.)slices with convective and microwave drying showed that the drying rate increased with increasing in drying air temperature and consequently decreased the required drying time. It is a fact that the higher temperature difference between the drying air and onion slices increases the heat transfer coefficient, which influences the heat and mass transfer rate. Drying of onion slices generally occurred in falling rate period because of quick removal of moisture [52].

The experimental data of onion drying curves obtained at air temperatures of drying (40˚C, 50˚C, 60˚Cand 70˚C) and at relative humidity of 20%, in the form of moisture content ratio, are fitted to Equation (13). The statistical results of fitting are performed by using the MATLAB.7.12.0 (R2011a) installed on the network of the University of Lorraine (France). Table 1 summarizes the statistics and drying parameters for modeling convective onion drying at air temperatures of 40˚C to 70˚C.

Among these established statistical results, the values of SSE, R² and RMSE obtained for modeling drying have been varied between 0.0288 and 0.0468, between 0.9824 and 0.9931 and between 0.0235 and 0.0370 respectively. The average values of SSE,R²and RMSE are 0.0415, 0.9883 and 0.0301, respectively. This average value of R² is very close to 1 while the average values of SSE and RMSE are close to 0. These statistic parameters of model have been satisfied for modeling drying of this onion variety. To illustrate the quality of model fitting, Figure 4 shows the experimental data compared to those of the model obtained at drying temperatures. In this figure, the results showed a reasonably good agreement between the values predicted from the correlation and the experimental observations. Therefore, the drying parameters obtained from the model reflect the physical and thermal behavior of the process of convective drying of the “Violet de Galmi”onion in thin layers. Due to the fact that drying has an exponentially decreasing trend, two drying parameters like lag factor (G, dimensionless) and drying coefficient (S,s⁻¹) could be introduced for describing this drying. Drying

coefficient shows the drying capability of onion slice and has a direct effect on the moisture diffusivity. In Table 1, the obtained drying coefficient values, S, were 2.856 × 10⁻⁴, 3.322 × 10⁻⁴, 4.794 × 10⁻⁴ and 5.056 × 10⁻⁴ s⁻¹ for drying temperatures of 40˚C, 50˚C, 60˚C and 70˚C, respectively, providing an accurate indication of the drying behavior (Figure 3). This S value range was in concordance with that of other food products such as carrot (1.038 × 10⁻⁴ s⁻¹ at 50˚C), prune (0.70 - 3 × 10⁻⁴ s⁻¹ at 60˚C), potato (0.70 - 9 × 10⁻⁴ s⁻¹ at 40˚C - 80˚C), starch (6 × 10⁻⁴ s⁻¹ at 59˚C), okra (9 × 10⁻⁴ s⁻¹ at 40˚C), broccoli (13 - 24 × 10⁻⁴ s⁻¹ at 50˚C - 75˚C), passion fruit peel (1.83 - 2.74 × 10⁻⁴ s⁻¹ at 50˚C - 70˚C) (Table 2 and Table 3). Kaya et al. [53] reported the drying coefficient for some regularly shape agricultural products such as slab carrot (0.20 - 0.41 × 10⁻⁴ s⁻¹), slab pumpkin (0.16 - 0.33 × 10⁻⁴ s⁻¹) and cylindrical carrot (0.19 - 0.39 × 10⁻⁴ s⁻¹) dried in a convective hot air dryer at temperatures of 30 - 60˚C and constant air flow rate of 1 m·s⁻¹ [53]. Torki-Harchegani et al. [22] were obtained drying coefficient values range 0.027 - 0.24 × 10⁻⁴ s⁻¹ for the whole lemons. The whole lemons were dried in a convective hot air dryer at drying temperatures of 50˚C - 75˚C and a constant air velocity (1 m·s⁻¹) [22]. In infrared thin layer drying of saffron stigmas, Torki-Harchegani et al. [21] found the drying coefficient varied from 4.75 - 16.11 × 10⁻⁴ s⁻¹ at the temperatures from 60˚C to 110˚C [21]. From the obtained results, the drying coefficient increased with increasing drying air temperature. This is due to the fact that an increment in drying temperature increases the heat and mass transfer between the heating media and solid object and consequently, leads to a higher drying capability of the object. Babalis et al. [54] reported the same results for convective hot air drying of figs in the temperature range of 55˚C - 85˚C and the air flow rate in the range of 0.5 - 3 m·s⁻¹ [54].

The lag factor (G) is an indicator of the magnitude of both the internal and external resistance to moisture transfer from the product and has a direct effect on the moisture transfer coefficient as a function of the Biot number [36] [55]. The values of lag factor (1.111, 1.136, 1.150 and 1.162 for air temperatures of 40˚C, 50˚C, 60˚C and 70˚C, respectively) were more than 1 indicating moisture diffusion within the samples is controlled by both internal and external resistance. The variation in calculated values, between 1.111 and 1.162, reflects lumped system specific mass transfer properties. The obtained lag factor values in this study are consistent with reported results for the foods products (Table 4) such as prune (1.0016 - 1.0086) [20] [32] [35] [37], potato (1.0074 - 1.255) [20] [35] [56], broccoli (1.000 - 1.006) [28], passion fruit peel (1.020 - 1.051) [24], eggplant (1.032 - 1.117) [29], lactose powder (1.086 - 1.370) [31], lemons (1.118 - 1.158) [22], saffron (1.096 - 1.104) [21] and apples (1.108 - 1.209) [57].

The lag factor is an indicator of magnitude of both internal and external resistances of a solid object to the heat and/or moisture transfer during drying process as a function of the Biot number (Equation (14)). There are three cases of the Biot number: B_i < 0.1, 0.1 < B_i < 100 and B_i > 100. The case of B_i < 0.1 indicates that minor internal resistance and major surface resistance across the boundary layer (external resistance) to moisture transfer and moisture gradient inside the product are so small while, B_i > 100 means that internal resistance is much more than external resistance. The case of 0.1 < B_i < 100 indicates the existence of both finite internal and surface resistances and is known as the most common case for the drying applications [36] [55]. The calculated Biot number values were in the range of 0.9797 - 2.9397 at drying temperature range 40˚C - 70˚C (Table 2), indicating the presence of the both internal and external resistances to moisture transfer, which is consistent with reported results for foods on literature (Table 4) such as potato (0.0851 - 1.1280, at 40˚C - 80˚C) [20] [35] [56], broccoli (0.2299 - 0.3228, at 50 - 75˚C) [28], passion fruit peel (0.1018 - 0.3199, at 50˚C - 70˚C) [24], lemon (0.361 - 2.894, at 50˚C - 75˚C) [22] and lactose powder (0.185 - 1.370, at 20˚C - 40˚C) [31]. The variation in calculated Bi numbers suggests that it was a function of the product and drying process parameters. During onion convective drying, the B_i number was found to increase

with increasing temperature indicating internal mass transfer control (Table 2). The results are in agreement with those reported for the convective drying of lemon slices [22], broccoli [28], eggplant slices [29] [58], potato [56] [59], passion fruit peel [24], saffron [21] and banana [60]. McMinn et al. [56] found that the microwave and combined microwave-convective drying of potato slices and cylinders were controlled by power levers. Thus the Bi number increased with power level (slab, 0.521 and 0.650 for 90 and 650 W, respectively) [56]. This is why a number of Biot number correlations for mass transfer, namely Bi-S, Bi-Re, Bi-G and Bi-Di were proposed according the medium and product parameters for use in practical drying applications [20] [35] [36] [37].

Analysis of moisture transfer mechanism in the falling rate period, based on the procedure described by [61], confirmed the diffusive nature of moisture movement. The non-linear pattern of moisture ratio and time on a semi-log plot also indicated the diffusive nature of moisture transport rather than capillary. It may be attributed to shrinkage in the product, non-uniform distribution of initial moisture and temperature coupled with variation of moisture diffusivity with moisture content [62]. The mass diffusivity in the diffusion model is a fundamental property based on molecular interactions and on the physical structure of the material [63]. All of the various phenomena of mass diffusion are represented by the effective diffusion coefficient. Using the values of μ₁ and S, effective diffusion coefficient D_eff of “Violet de Galmi” onion drying is calculated from Equation (15). The calculated values of D_eff at onion drying conditions are found between 0.2798 × 10⁻⁹ m²·s⁻¹ and 0.8121 × 10⁻⁹ m²·s⁻¹ (Table 2). The magnitude range of these D_eff values is close to those proposed for air convective drying of onion obtained by the conventional solution of Fick’s second law of diffusion developed by Crank (Table 3) such as the range 3.33 - 8.559 × 10⁻⁹ m²·s⁻¹, at 30˚C - 60˚C obtained by [4], the range 0.025 - 0.032 × 10⁻⁹ m²·s⁻¹, at 30˚C - 60˚C obtained by [5], the range 0.747 - 1.554 × 10⁻⁹ m²·s⁻¹, at 50˚C - 70˚C obtained by [6], the range 34.9 - 94.4 × 10⁻⁹ m²·s⁻¹, at 50˚C - 70˚C obtained by [9], the range 1.96 - 14 × 10⁻⁹ m²·s⁻¹, at 50˚C - 70˚C obtained by [10], the range 2.084 - 2.271 × 10⁻⁹ m²·s⁻¹, at 40˚C - 60˚C obtained by [13]. The small difference range of D_eff for onion convective drying are due to the diffusivities dependence of the drying characteristics (air velocities, combination of Infrared, vacuum, microwave drying techniques with convective drying) and product characteristics (thickness, pretreatment namely water blanching and blanching-steaming). Dincer and Hussain [35] explained that the variation of moisture diffusivity data of the foods was often due by structure complexity of foods [35]. Pathare and Sharma [5] noted that the diffusivities are negatively correlated with air velocity. The increase in air velocity accelerated the cooling effect, which reduced the temperature of the product and water vapor pressure [5]. Concerning the temperature parameter, the temperature level had a considerable influence on the magnitude

—: not measured, CD: characteristic dimensions.

of the diffusivity during convective drying (0.2798 × 10⁻⁹ m²·s⁻¹ for 40˚C and 0.8121 × 10⁻⁹ m²·s⁻¹ for 70˚C, respectively). Such results from this analysis are in accordance with the experimental observations (Figure 3). They are also similar with the results for onion convective drying reported by Mota et al. [4], by Demiray et al. [9], by Asiah and Djaeni [13] and with the results for the food convective drying such as potato [56], lemon [22], spirulina [39], blackwood passion fruit [24] and banana [64]. Torki-Harchegani et al. [21] obtained in saffron drying that any increment in the drying temperature leaded to an increment in the diffusivity. In fact, an increase in temperature caused a decrease in water viscosity and increased the activity of water molecules. These phenomena facilitated diffusion of water molecules in object capillaries and consequently, increased the moisture diffusivity [21]. Sharma et al. [8] reported that the moisture diffusivity of food material was affected by its moisture content, temperature as well as its composition and porosity. This may indicate that as the moisture content decreased, the permeability to water vapor increased as it provided more pore structure open. The temperature of the product would have risen rapidly in the initial stages of drying due to more absorption of convective heat. This increased the water vapour pressure inside the pores resulted into pressure induced opening of the pores. Furthermore, Süfer et al. [10] concluded in their study that slice thickness and pretreatment application affected Deff adversely, whereas temperature increase enhanced the moisture diffusivities at high temperatures, any augmentation in energy of heating causes an increase in the molecular activity of water, thus generating higher diffusivity. In addition, high salt concentrations in vegetable cells may reduce or prevent moisture removal from food system [10] [65].

Knowing both the moisture diffusivities and mass transfer coefficients for the various systems is essential, as more complex mathematical models and correlations which can provide a more in depth understanding of the drying operations require data on specific mass transfer parameters. This is an important drying parameter that depends on mass diffusivity, viscosity, velocity of the fluid, and geometry of the transfer system [63]. The mass transfer coefficient values of “Violetde Galmi” onion drying in thin layers are obtained from Equation (17) using the Biot number and effective moisture diffusivities. Mass transfer coefficients hm are presented in Table 2. The values of hm obtained for drying conditions of “Violet de Galmi” onion slice vary between 3.37 × 10⁻⁷ m·s⁻¹ and 13.38 × 10⁻⁷ m·s⁻¹. These results were found in the range (0.16 - 8725.60 × 10⁻⁷ m·s⁻¹) of those available in the existing literature for different foods and drying conditions (Table 4), such as the convective drying of potato (0.16 - 391.02 × 10⁻⁷ m·s⁻¹, at 40˚C - 80˚C) [20] [35] [56], broccoli (1921.5 - 8725.6 × 10⁻⁷ m·s⁻¹, at 50˚C - 75˚C) [28], passion fruit peel (4.530 - 8.702 × 10⁻⁷ m·s⁻¹, at 50˚C - 70˚C) [24], lemon (0.163 - 9.008 × 10⁻⁷ m·s⁻¹, at 50˚C - 75˚C) [22], saffron (2.6433 - 8.7203 × 10⁻⁷ m·s⁻¹, at 60˚C - 110˚C) [21] and eggplant (6.478 - 2.190 × 10⁻⁷ m·s⁻¹, at 50˚C - 70˚C) [29]. Ours results were also in accordance with those from Markowski [66] who determinates an average mass transfer coefficient value of 1.371 × 10⁻⁷ m·s⁻¹ during drying of fresh carrot slices, those by Elbert et al. [67] with a value of 4.81 × 10⁻⁷ m·s⁻¹ during parboiled rice drying, those by Tsami and Katsioti [68] with 4.026 × 10⁻⁷ m·s⁻¹ during drying of prune slices, and those by Ruiz-Cabrera et al. [69] with 6.608 × 10⁻⁷ m·s⁻¹ during carrot drying. Examination of the relative magnitude of the mass transfer coefficient for onion showed a variation

with the temperature parameters under the drying operations providing further comprehension of the mass transfer characteristics. For our onion drying experimentation, the value of h_m (3.37 × 10⁻⁷ m·s⁻¹ at 40 - 5.69 × 10⁻⁷ m·s⁻¹ at 50 - 8.46 × 10⁻⁷ m·s⁻¹ at 60 - 13.38 × 10⁻⁷ m·s⁻¹ at 70˚C) varied positively with drying temperature. It showed that the value of hm increased with drying temperature of onion. This is a confirmation of results obtained for drying constant S and diffusivity D_eff. This dependence result of temperature was also similar to that from McMinn [31] for dying lactose powder, form Torki-Harchegani et al. [22] for drying lemon, from Mrkić et al. [28] for drying broccoli, from Torki-Harchegani et al. [21] for drying saffron and Bezerra et al. [24] for drying passion fruit peel.

The values of the diffusivity for “Violet de Galmi” onion drying at drying temperature are used to estimate the values of the diffusivity for an infinite temperature and the average activation energy E_a by Equation (18). Thus, the natural logarithm of the diffusion coefficient is represented according to the absolute temperature reciprocal (Equation (17)) [24]. The values obtained for the water diffusion coefficient at infinite temperature D0 and the average activation energy E_a for “Violet de Galmi” onion drying are respectively 1.372 m²·s⁻¹ and 31.73 kJ·mol⁻¹ with R² = 0.99, SSE = 2.666 × 10⁻⁶ and RMSE = 0.001633. The values obtained for the average activation energy are close to those obtained in the literature of convective drying of onion (Table 3) such as E_a = 26.4 kJ·mol⁻¹ from Mota et al. [4], E_a = 10.93 - 34.13 kJ·mol⁻¹ from Süfer et al. [10] and E_a = 45.6 kJ·mol⁻¹ from Demiray et al. [9]. The range of energy activation of 5.06 kJ·mol⁻¹ to 10.63 kJ·mol⁻¹ is reported for infrared convective drying of onion slices under air temperature conditions of 35˚C - 45˚C [5]. Ours E_a values are in the range of E_a = 12 - 110 kJ·mol⁻¹ of food and agricultural products were, hence findings were in agreement with literature [70]. The differences between the values reported in the present work and the values highlighted in the literature are related with the dependence of the diffusion coefficient of a food with the conditions within the material on drying [24]. For Baia Periforme variety, the activation energy for convective drying of onion was E_a = 34.081 kJ·mol⁻¹ at temperature range of 40˚C - 60˚C [71]. Ours Ea of onion slices were also close to green beans (E_a = 35.43 kJ·mol⁻¹, convective drying; [72]), radish (E_a = 15 - 40 kJ·mol⁻¹, vacuum drying; [73]), carrot (E_a = 22.43 kJ·mol⁻¹, infrared drying; [74]) and mulberry (E_a = 21.2 kJ·mol⁻¹, convective drying; [75]). These values can be interpreted as an energy barrier that must overcome the drying mechanism to remove moisture. This vision of the drying energy barrier is to advantage developed by other approach theory for drying modeling [76] [77] [78].