DRYING KINETICS OF THE SLICED PULP OF BIOFORTIFIED SWEET POTATO ( Ipomoea batatas

Biofortified sweet potato ( Ipomoea batatas ) is one of the foods with the highest contributions of carotenoids in the diet, especially provitamin A carotenoids. Thus, this study aimed to analyze the drying kinetics of the biofortified sweet potato pulp using the Akaike (AIC) and Schwarz’s Bayesian (BIC) information criteria for model selection, as well as determine the effective diffusion coefficient and activation energy under different drying conditions. The biofortified sweet potatoes were sliced into chips and submitted to drying in an air circulation oven at 1.0 m s −1 at temperatures of 45, 55, 65, and 75 °C until constant mass. The mathematical models Wang and Singh, Verma, Thompson, Page, Newton, Midilli et al., logarithmic, Henderson and Pabis, two-term exponential, two-term, diffusion approach, frequently used to predict the drying of vegetal products, were adjusted to the data. The Wang and Singh model was selected to


INTRODUCTION
Sweet potato (Ipomoea batatas Lam.) has a prominent role, as it is one of the most important food crops in the world (Kim et al., 2012). It also has a significant β-carotene content, whose regular intake can prevent and combat blindness and infant mortality caused by vitamin A deficiency, especially in poorer populations that do not have access to other vitamin A sources (Nascimento et al., 2013).
Drying is a process used to preserve food quality by reducing the availability of water to deterioration reactions, increasing food stability, and reducing the volume and mass of the product (Casarin et al., 2016). Reducing the amount of water in agricultural products provides longer shelf life and avoids the degradation of benign substances to the consumer (Tontul & Topuz, 2017). Drying is also the commercial process most used to preserve food and, when compared to other long-term preservative methods, it has a low cost and simpler operation (Alexandre et al., 2013).
The application of reliable mathematical models allows predicting the behavior of the various phenomena that occur during the drying process, which implies the reduction of the operational cost (Dionello et al., 2009). Several criteria can be used to verify the adjustment of mathematical models of drying in plant products. However, some parameters have limitations and it is necessary to adopt additional criteria to reinforce and endorse decision-making, such as the Akaike (AIC) and Schwarz's Bayesian (BIC) information criteria (Gomes et al. 2018).
Chemical composition and physical structure differ from one product to another, making water outlet specific to each material. In drying studies involving water diffusion there are variations in the values of the effective diffusivity coefficient due to the complexity of plant products, such as different prediction methods, type of material, moisture content, drying process, as well as the methodology used to obtain it (Goneli et al., 2007).
Thus, the aim of this study was to analyze the drying kinetics of the biofortified sweet potato pulp using the AIC and BIC criteria for model selection, as well as determine the effective diffusion coefficient and activation energy for the process.

MATERIAL AND METHODS
The experiment was carried out at the Laboratory of Post-Harvest of Plant Products of the Federal Institute of Education, Science, and Technology of Goiás, campus of Rio Verde. An amount of 3 kg of CNPH1210 biofortified sweet potatoes, with the initial moisture content of 3.796±0.018 (decimal dry basis), were manually peeled using metal knives. Subsequently, the pulp was sliced into chips of approximately 4.6 x 4.0 x 0.2 cm (length, width, and thickness), adapted according to Borges et al. (2008), with a domestic grater. The slices of potato pulps were dried in an air circulation oven at 1.0 m s −1 and temperatures of 45, 55, 65, and 75 °C. Samples of 150 g were uniformly distributed in a 0.54 cm layer in rectangular aluminum trays (25 x 10 cm) without drilling, with four replications for each drying temperature.
The reduction of moisture content during the drying was performed by the gravimetric method (loss of mass). The initial moisture content of the product is known and the drying process occurs until reaching a constant mass. The mass reduction was monitored with a 0.01 g resolution scale.
To determine the equilibrium moisture content, samples of biofortified sweet potato were weighed every 24 hours until reaching three weighing measures until constant mass. The moisture contents of the material were determined in an oven regulated at 105 °C for 24 hours.
For determining the moisture content ratios of biofortified sweet potato during drying, [eq. (1)] was used.
Where, RX is the moisture content ratio of the product (dimensionless); X is the moisture content of the product (db); Xi is the initial moisture content of the product (db), and Xe is the equilibrium moisture content of the product (db).
Mathematical models frequently used to represent the drying of plant products (Table 1) were adjusted to the experimental data of biofortified sweet potato drying.
Mathematical models were adjusted from nonlinear regression analysis by the Gauss-Newton method. The significance of model parameters was evaluated by the t-test adopting a 5% significance level. The degree of adjustment of each model was verified according to the magnitudes of the coefficient of determination (R 2 ), relative mean error (P), and estimated mean error (SE). The relative and estimated mean errors were calculated according to eqs (13) and (14), respectively.
Where, n is the number of experimental observations; Y is the value of the moisture content ratio experimentally observed; Ŷ is the value of the moisture content ratio estimated by model, and To select a single model for describing the drying process at each condition, the models with the best adjustments were submitted to the Akaike (AIC) and Schwarz's Bayesian (BIC) information criteria.
The AIC and BIC criteria were used as a counterpart in choosing the best mathematical model to predict the phenomenon. AIC allows using the principle of parsimony in choosing the best model, i.e. according to this criterion, the most parameterized model is not always the best (Burnham & Anderson, 2004).
AIC (Equation 15) is used to compare non-nested models or when three or more models are being compared. Lower AIC values reflect a better adjustment (Akaike, 1974).
Where, p is the number of parameters, and loglike is the value of the logarithm of the likelihood function considering the estimates of parameters.
BIC (Equation 16) also considers the degree of parameterization of the model and, similarly, the lower the BIC value is, the better the model adjustment. It is an asymptotic criterion whose adequacy is strongly related to the magnitude of the sample size. In relation to the penalty applied in the number of parameters, it will be more rigorous than AIC for small samples.
Where, n is the number of observations used to adjust the curve.
The effective diffusivity was determined based on the Fick's second law by assuming the geometric shape of an infinite flat plate, which was calculated by [eq. (17)].
Where, RX is the moisture content ratio (dimensionless), D is the effective diffusion coefficient (m 2 s −1 ), and i is the number of terms.
Volume and surface area of sweet potato slices were determined by measuring with a digital caliper the three orthogonal axes (length, width, and thickness) in fifteen slices of sweet potatoes before drying them. Volume was calculated by [eq. (18)] and surface area by [eq. (19)].

V= S C 
Where, S is the surface area (m 2 ); A is the largest axis (m), and B is the average axis (m).
The relationship between the diffusion coefficient and the drying air temperature was analyzed by the Arrhenius [eq. (20)]. Where, Def is the effective diffusion coefficient (m 2 s −1 ), Do is the pre-exponential factor (m 2 s −1 ), Ea is the activation energy (J mol −1 ), R is the universal gas constant (8.134 kJ kmol −1 K −1 ), and Ta is the absolute temperature (K −1 ).

RESULTS AND DISCUSSION
The eleven tested models had coefficients of determination (R 2 ) above 0.96 decimal (Table 2), except for the Verma model (3) for a temperature of 65 °C. According to Sozzi & Ramos (2015), the closer to 1 the R 2 value is, the more elucidative the model and the better it will be adjusted to the experimental data.
The models considered satisfactory under all the evaluated temperature conditions were Wang and Singh, logarithmic, and Midilli et al. These three models presented an R 2 higher than 99.15% and P values lower than 10%. Thus, through the joint analysis of statistical parameters (R 2 , P, and SE), these models presented a better adjustment to the drying process of the potato pulp.
In order to select the best model (Wang and Singh, logarithmic, and Midilli et al.), the Akaike (AIC) and Schwarz's Bayesian (BIC) information criteria were adopted as complementary precepts for selection, as shown in Table 3. Thus, the Wang and Singh model was selected to represent the drying kinetics of biofortified sweet potato pulp because it presented the best adjustment for most of the drying conditions. Ribeiro et al. (2014) carried out similar studies with sliced banana and Gomes et al. (2018) with ground jambu mass and also used the AIC and BIC selection criteria to indicate the most suitable model to represent their drying kinetics. Figure 1 shows that different temperatures influenced water loss from the material and drying was faster for higher temperatures. According to Fiorentin et al. (2010), an increased temperature accelerates the drying process, promoting moisture content reduction more quickly at the beginning of the drying process, which consequently results in shorter drying time.
This behavior was expected and was also recorded by other authors when drying pumpkin slices (Borges et al., 2008), fibrous cassava mass (Castiglioni et al., 2013), lemon slices (Wang et al., 2018), and green banana peel and pulp (Gonçalves et al., 2017). In these cases, the highest rates of water vaporization in a shorter drying time was obtained by raising the temperature.  Table 4 shows the coefficients of the Wang and Singh model. The values found for the parameter b increased as temperature increased, while the parameter a decreased as water removal increased. The diffusion coefficient increased linearly as the temperature of the drying air increased and its influence can be described by means of the Arrhenius representation, as shown in Figure 2B. During the drying, the diffusion coefficients showed magnitudes of 7.55 × 10 −11 , 8.9 × 10 −11 , 13.01 × 10 −11 , and 19.24 × 10 −11 m 2 s −1 for temperatures of 45, 55, 65, and 75 °C, respectively. These results are in accordance with those obtained by Fernando et al. (2011), who dried slices of banana, cassava, and pumpkin and found values ranging from 0.69 × 10 −10 to 0.52 × 10 −10 m 2 s −1 for banana, 0.80 × 10 −10 to 1.12 × 10 −10 m 2 s −1 for cassava, and 5.76 × 10 −10 to 5.60 × 10 −10 m 2 s −1 for pumpkin. The activation energy for the liquid diffusion of biofortified sweet potato pulp was 29.18 kJ mol −1 for the temperature range between 45 and 75 °C, which is in accordance with the results obtained by Doymaz (2004b), who studied the drying of sliced carrots with an activation energy of 28.36 kJ mol −1 . According to Corrêa et al. (2010), the lower the activation energy in the drying processes is, the higher the water diffusivity in the product, i.e. the lower the energy required for the physical transformation to occur and for the liquid water pass to steam (drying of the product).

CONCLUSIONS
Among the studied models, the Wang and Singh model was selected to represent the drying kinetics of biofortified potato pulp since it exhibits the best adjustment for most conditions. The AIC and BIC criteria were suitable for selecting a single model. The effective diffusion coefficient increased as the temperature of the drying air increased and the activation energy for the liquid diffusion was 29.18 kJ mol −1 .