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Drying kinetics and effective diffusion of buckwheat grains

Cinética de secagem e difusão efetiva de grãos de trigo mourisco

ABSTRACT

Buckwheat has become important in the food sector as its flour does not contain gluten. Since buckwheat is a relatively new crop in the agricultural environment, there is little information available regarding its processing. Drying is one of the most important post-harvest stages of buckwheat. The aim of the present study was to describe the drying process of buckwheat grains. Buckwheat grains with a moisture content of 0.41 ± 0.01 (dry basis, d.b.) were harvested, followed by drying in an experimental dryer at the temperatures of 40, 50, 60, 70, and 80 °C, at an air speed of 0.8 m s-1. The drying rate was determined, and the mathematical models generally employed to describe the drying process of several agricultural products were fitted to the experimentally obtained data. Model selection was based on the Gauss-Newton non-linear regression method and was complemented by Akaike Information Criterion and Schwarz’s Bayesian Information Criterion. It was concluded that the drying rate increased with an increase in temperature and decreased with an increase in drying time. It is recommended to use the Midilli model to represent the drying kinetics of buckwheat grains at the temperatures of 40, 60, and 70 °C, while the Approximation of diffusion model is recommended for the temperatures of 50 and 80 °C. The magnitudes of effective diffusion coefficients ranged from 1.8990 × 10-11 m2 s-1 to 17.8831 × 10-11 m2 s-1. The activation energy required to initiate the drying process was determined to be 49.75 kJ mol-1.

Index terms:
Activation energy; Fagopyrum esculentum Moench; mathematical models; AIC and BIC; gluten

RESUMO

O trigo mourisco tem se destacado na cadeia alimentícia por não possuir glúten em sua farinha. Por ser uma cultura relativamente nova no meio agrícola, faltam informações referentes ao seu processamento, dentre as etapas pós-colheita a secagem é uma das mais importantes. O objetivo do presente trabalho foi descrever o processo de secagem de grãos de trigo mourisco. Os grãos foram colhidos com teor de água de 0.41 ± 0.01 (b.s.) e submetidos a secagem em secador experimental nas temperaturas de 40, 50, 60, 70 e 80 °C, e velocidade do ar de 0.8 m s-1. Determinou-se a taxa de secagem e ajustou-se aos dados experimentais modelos matemáticos frequentemente utilizados para a descrição da secagem de diversos produtos agrícolas. A seleção dos modelos foi baseada no método de regressão não linear de Gauss-Newton e complementada pelo Critério de Informação de Akaike e Critério de Informação Bayesiano de Schwarz’s. Conclui-se que, a taxa de redução da água foi maior para maiores temperaturas e diminuiu com o aumento do tempo de secagem; o modelo de Midilli é recomendado para representar a cinética de secagem dos grãos nas temperaturas de 40, 60 e 70 ºC; para a temperaturas de 50 e 80 ºC recomenda-se o modelo de aproximação da difusão; os coeficientes de difusão efetivo apresentaram magnitude de 1.8990 a 17. 8831 × 10-11 m2 s-1 e; a energia de ativação requerida para iniciar o processo de secagem foi de 49.75 kJ mol-1.

Termos para indexação:
Energia de ativação; Fagopyrum esculentum Moench; modelos matemáticos; AIC e BIC; glúten

INTRODUCTION

In the past few decades, great attention has been focused on the food product to be offered to the consumer, whether in terms of the nutritional value of the food product or the specific requirements of certain individuals. The latter includes the coeliac people, who have a permanent intolerance to gluten, a protein present mainly in wheat, rye, barley, malt, and oats. Since there is no cure currently available for gluten intolerance, the only approach to manage this disorder is to avoid its symptoms by not ingesting gluten.

In this context, buckwheat (Fagopyrum esculentum Moench) could serve as an excellent alternative for people with gluten intolerance who wish to consume flour-based products.

Owing to the economic potential and importance of buckwheat crop, several research works have been focused on improving its yield (Görgen et al., 2016GÖRGEN, A. V. et al. Produtividade e qualidade da forragem de trigo-mourisco (Fagopyrum esculentum Moench) e de milheto (Pennisetum glaucum (L.) R. BR). Revista Brasileira de Saúde e Produção Animal, 17(4):599-607, 2016.), adaptation (Alves et al., 2016ALVES, J. D. C. et al. Potential of sunflower, castor bean, common buckwheat and vetiver as lead phytoaccumulators. Revista Brasileira de Engenharia Ambiental, 20(3):243-249, 2016.), cultivation (Vazhov; Kozil; Odintsev, 2013VAZHOV, V. M.; KOZIL, V. N.; ODINTSEV, A. V. General methods of buckwheat cultivation in Altai region. World Applied Sciences Journal, 23(9):1157-1162, 2013.), and nutritional properties (Zhu, 2016ZHU, F. Chemical composition and health effects of Tartary buckwheat. Food Chemistry, 203:231-245, 2016.). Nonetheless, studies concerning the drying process of buckwheat are scarce.

The drying process involves the simultaneous transfer of heat and mass, which may cause significant changes in food characteristics (Koç; Eren; Ertekin, 2008KOÇ, B.; EREN, I.; ERTEKIN, F. K. Modelling bulk density, porosity and shrinkage of quince during drying: The effect of drying method. Journal of Food Engineering , 85(3):340-349, 2008.). The drying stage exerts a great influence on product quality as well as on the overall production costs. Therefore, this stage requires planning, and if possible, scaling in advance (Siqueira; Resende; Chaves, 2013SIQUEIRA, V. C.; RESENDE, O.; CHAVES, T. H. Mathematical modelling of the drying of jatropha fruit: An empirical comparison. Revista Ciência Agronômica, 44(2):278-285, 2013.).

These concerns could be addressed by the mathematical simulation of the drying process. Drying conditions, particularly the temperature and relative humidity, govern the rate at which water exits the grains (Koua; Koffi; Gbaha, 2019KOUA, B. K.; KOFFI, P. M. E.; GBAHA, P. Evolution of shrinkage, real density, porosity, heat and mass transfer coefficients during indirect solar drying of cocoa beans. Journal of the Saudi Society of Agricultural Sciences, 18(1):72-82, 2019.). High water removal rates during drying could alter the structure and the contents of the product (Lima et al., 2016LIMA, A. G. B. et al. Drying of bioproducts: Quality and energy aspects. In: DELGADO, J. M. P. Q.; LIMA, A. G. B. Drying and energy technologies. Springer International Publishing Switzerland, 2016, p.1-17.). Such high rates could generate internal stresses within the grains that could result in mechanical injuries and reduced product quality (Agrawal; Methekar, 2017AGRAWAL, S. G.; METHEKAR, R. N. Mathematical model for heat and mass transfer during convective drying of pumpkin. Food and Bioproducts Processing, 101(1):68-73, 2017.; Corrêa et al., 2017CORRÊA, P. C. et al. Thermodynamic properties of drying process and water absorption of rice grains. CyTA-Journal of Food, 1(2):204-210, 2017.). In addition, each product exhibits unique behavior during the drying process.

Studies concerning buckwheat post-harvest processes are scarce. Therefore, understanding the behavior of buckwheat during its drying process would lay a foundation for future research in this field. In this context, the present study was conducted with the objectives of fitting mathematical models, describing the behavior of buckwheat grains during drying, and determining the parameters of effective diffusion coefficients, activation energy, and drying rate at different temperatures.

MATERIAL AND METHODS

The study was conducted at the Laboratory of Postharvest Processes of Agricultural Products, Faculty of Agrarian Sciences, Federal University of Grande Dourados.

Buckwheat grains of the cultivar IPR 91-Baili were used in the present study. The grain samples were harvested with the initial moisture content of 0.41 ± 0.01 (decimal, d.b.), which was determined through the oven method as described in the Rules for Seed Analysis (RAS), using an Ethik forced ventilation oven (model 400/D) at 105 ± 1 °C for 24 h, in three replicates (Brasil, 2009BRASIL. Ministério da Agricultura e Reforma Agrária. Secretaria Nacional de defesa Agropecuária. Regras para análise de sementes. Brasília, 2009. 399p.).

Thin-layer drying of the product was performed in an experimental fixed-layer dryer equipped with a system that accurately controlled the drying air flow and temperature. The different temperature and relative humidity conditions used were as follows: 40 °C, 24.42%; 50 °C, 14.61%; 60 °C, 9.05%; 70 °C, 5.78%; and 80 °C, 3.81%. Drying air speed was determined and maintained at 0.8 m s-1 using a digital anemometer (Instrutherm AM-100).

The grains were distributed among four trays (replicates), each with a diameter of 160 mm, fully perforated (33.97% area), and a 7.5-mm high grain layer weighing 89 g. Mass measurement during the drying process was performed using a semi-analytical scale with a resolution of 0.01 g. The drying process was interrupted, for mathematical modeling purposes, when the grain mass reached a value equivalent to 0.13 ± 0.01 (decimal, d.b.) of moisture content.

In order to assess the drying of the buckwheat grains, the drying rate (DR) of the product was determined using Equation 1.

DR = (Mw 0 - Mw i ) / DM . (t i - t 0 ) (1)

Where, DR is the drying rate (kg kg-1 h-1), Mw0 denotes the previous total mass of water (kg), Mai denotes the current total mass of water (kg), DM is dry matter (kg), t0 denotes the previous total drying time (h), and ti denotes the current total drying time (h).

The moisture content values at the beginning, at the end, and during the drying process (calculated) were substituted in Equation 2 to calculate the moisture ratio (RX) of the buckwheat grains during drying.

RX = X - X e / X i - X e (2)

Where, RX is the moisture content ratio of the product (dimensionless), Xe denotes the equilibrium moisture content of the product (decimal, d.b.), X denotes the moisture content of the product (decimal, d.b.), and Xi denotes the initial moisture content of the product (decimal, d.b.).

The equilibrium moisture content of the buckwheat grains was determined experimentally by performing the drying process inside the experimental dryer under the same conditions until a constant mass was reached.

Mathematical models (Equations 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13) generally used to represent the drying process of agricultural products were fitted to the experimentally obtained data for the drying of buckwheat grains (Table 1).

Table 1:
Mathematical models used for representing the drying process of agricultural products.

The drying kinetics experimental data were subjected to non-linear regression analysis using the Gauss-Newton method. The mathematical models were fitted to the experimental data using the program Statistica 7.0®. The selection of the drying models was based on the relative mean error (P) values, standard deviation of the estimate (SE), and the coefficient of determination (R²). The values for relative mean error and standard deviation of the estimate were calculated using Equation 14 and 15.

P= 100 / n i = 1 n Y - Y ^ / Y (14)

SE = i = 1 n Y - Y ^ 2 D F (15)

Where n is the number of experimental observations, Y is the experimental value, Ŷ is the value estimated using the model, and DF denotes the degrees of freedom of the model (i.e., the difference between the number of observations and the number of parameters).

In order to further refine the selection process of the model for representing the drying process of buckwheat grains under different conditions of drying air temperature, the models presenting best fits in the Gauss-Newton method were subjected to Akaike Information Criterion (AIC) and Schwarz’s Bayesian Information Criterion (BIC), using R 3.6.1® software in function nls. According to Wolfinger (1993WOLFINGER, R. D. Covariance structure selection in general mixed models. Communications in Statistics, 22(4):1079-1106, 1993. ), lower AIC and BIC values indicate a better fit of the selected model, thereby representing a more accurate decision making. These criteria could also be included in the selection of drying models (Gomes et al., 2018GOMES, F. P. et al. Drying kinetics of crushed mass of ‘jambu’: Effective diffusivity and activation energy. Revista Brasileira de Engenharia Agrícola e Ambiental , 22(7):499-505, 2018.). AIC and BIC values were determined using Equation 16 and 17.

AIC = - 2 l o g L + 2 p (16)

BIC = - 2 l o g L + p l n ( N ) (17)

Where, p is the number of parameters of the model, N is the total number of observations, and L represents the maximum likelihood.

The effective diffusion coefficient of the buckwheat grains under different drying conditions was calculated using Equation 18, which is based on the theory of liquid diffusion and represents an analytical solution for Fick’s second law, by considering the geometric form of the product to be spherical and with eight-term approximation.

RX = X X e X i X e = 6 π 2 n t = 1 1 n t 2 exp n t 2 π 2 D i t 9 3 R e 2 (18)

Where, Di is the liquid diffusion coefficient (m2 s-1), Re denotes the equivalent sphere radius and nt is the number of terms.

The equivalent sphere radius used in the effective diffusion model was determined by randomly selecting 50 buckwheat grains and measuring the three orthogonal axes of each grain using a digital micrometer.

The volume of each grain was calculated on the basis of perpendicular diameters, using Equation 19 and 20 (Jain; Bal, 1997JAIN, R. K.; BAL, S. Properties of pearl millet. Journal of Agricultural Engineering Research, 66(2):85-91, 1997.). The approximation of the actual volume determined through the method of displacement using a low-density fluid was considered as the basis for this calculation.

V g = π D 2 D 1 2 6 (2 D 1 D ) (19)

D = ( D 2 D 3 ) 1 / 2 (20)

Where, Vg denotes the volume of the grain (mm3), D1 denotes the length of the longest axis (mm), D2 is the length of the medium axis (mm), D3 is the length of the shortest axis (mm), and D denotes the diameter of the spherical part (mm).

Arrhenius Equation (Equation 21) was used for evaluating the effect of temperature on the effective diffusion coefficient.

D i = D 0 exp E a R T a (21)

Where, Di is the pre-exponential factor (m2 s-1), R is the universal gas constant (8.314 kJ kmol-1 K-1), Ta denotes the absolute temperature (K), and Ea is the activation energy (kJ mol-1).

RESULTS AND DISCUSSION

The buckwheat grains were dried until a moisture content of 12 ± 0.05% was reached, on a wet basis, which required drying times of 6.00, 2.25, 1.25, 0.83, and 0.50 h at the drying air temperatures of 40, 50, 60, 70, and 80 °C, respectively. These differences could be attributed to the drying conditions, physical and chemical characteristics, cultivation conditions, and the initial moisture contents of the grains (Diógenes et al., 2013DIÓGENES, A. M. G. et al. Cinética de secagem de grãos de abóbora. Revista Caatinga , 26(1):71-80, 2013.). The average drying rate for the buckwheat grains throughout the drying process tended to decrease as the drying time advanced (Figure 1). This reduction could be attributed to the difficulty in removing water from the grains as the end of the process is approached, because at this time, the water is more strongly bound to the product, which increases the energy demand for water diffusion from the innermost part to the surface (Resende et al., 2009RESENDE, O. et al. Mathematical modeling for drying coffee (Coffea canephora Pierre) berry clones in concrete yard. Acta Scientiarum. Agronomy, 31(2):189-196, 2009.).

Figure 1:
Moisture reduction rates for buckwheat grains at different drying air temperatures.

At higher temperatures, there is a higher partial pressure of water vapor in the product, which raises the drying rate, particularly at the beginning of the process, thereby reducing the drying time. This implies that the higher the drying air temperature, the higher is the rate at which water is removed from the product. This behavior was consistent with those of several other studies previously conducted on grain drying (Costa et al., 2011COSTA, L. M. et al. Effective diffusion coefficient and mathematical modeling for drying of crambe seeds. Revista Brasileira de Engenharia Ambiental , 15(10):1089-1096, 2011.; Keneni; Hvoslef-Eide; Marchetti, 2019KENENI, Y. G.; HVOSLEF-EIDE, A. K.; MARCHETTI, J. M. Mathematical modelling of the drying kinetics of Jatropha curcas L. seeds. Industrial Crops and Products, 132:12-20, 2019.; Rosa et al., 2015ROSA, D. P. et al. Mathematical modeling of orange seed drying kinetics. Ciência e Agrotecnologia, 39(3):291-300, 2015.; Siqueira; Resende; Chaves, 2012SIQUEIRA, V. C.; RESENDE, O.; CHAVES, T. H. Determination of the volumetric shrinkage in jatropha seeds during drying. Acta Scientiarum. Agronomy , 34(3):231-238, 2012.).

The relative mean error (P) indicates the level of deviation of the observed values from the estimated values. Therefore, the models with P-values lower than 10% are recommended (Table 2), while the models with P-values above 10% are excluded from the fitting (Kashaninejad et al., 2007KASHANINEJAD, M. et al. Thin-layer drying characteristics and modeling of pistachio nuts. Journal of Food Engineering, 78(1):98-108, 2007.).

Table 2:
Coefficients of determination (R2), relative mean errors (P), and the standard deviations of the estimate (SE) for the eleven models analyzed for representing the thin-layer drying of buckwheat (Fagopyrum esculentum Moench) grains under different conditions of drying air temperature.

Finally, the following models were considered satisfactory: Page (3), Midilli (4), Thompson (6), Logarithmic (9), Two terms (12), and Approximation of diffusion (13). The other models were considered unsatisfactory because they presented P values above 10% in at least one of the conditions of drying air temperature used in the present study.

According to Kashaninejad et al. (2007KASHANINEJAD, M. et al. Thin-layer drying characteristics and modeling of pistachio nuts. Journal of Food Engineering, 78(1):98-108, 2007.), R2 values greater than 0.95 represent a good fit for model selection. In this context, the models selected according to the P-value criterion demonstrated satisfactory performance, exhibiting R2 values above 0.99. According to Botelho et al. (2018BOTELHO, F. M. et al. Soybean grain drying kinects: Varietal influence. Revista Engenharia na Agricultura, 26(1):13-25, 2018.) and Siqueira, Resende and Chaves (2012SIQUEIRA, V. C.; RESENDE, O.; CHAVES, T. H. Determination of the volumetric shrinkage in jatropha seeds during drying. Acta Scientiarum. Agronomy , 34(3):231-238, 2012.), lower SE values indicate a better fit of mathematical models. According to this criterion, Page model (3) was suitable for the temperatures of 40 and 50 °C, while Two terms (12) and the Approximation of diffusion (13) models were suitable for the temperature of 50 °C. Midilli model (4) exhibited a satisfactory fitting for all temperatures other than 80 °C. At 80 °C, the approximation of the diffusion model demonstrated satisfactory fitting by presenting lower values of P and SE. Midilli (4) and the Approximation of diffusion (13) models have been used previously to represent the drying kinetics of grains (Khanali et al., 2012KHANALI, M. et al. Mathematical modeling of fluidized bed drying of rough rice (Oryza sativa L.) grain. Journal of Agricultural Technology, 8(3):795-810, 2012.; Maia et al., 2019MAIA, R. B. et al. Drying kinetics and thermodynamic properties of pigeon pea beans. Científica, 47(2):164-174, 2019.; Perea-Flores et al., 2012PEREA-FLORES, M. J. et al. Mathematical modelling of castor oil seeds (Ricinus communis) drying kinetics in fluidized bed at high temperatures. Industrial Crops and Products , 38:64-71, 2012.).

The values of Akaike Information Criterion (AIC) and Schwarz’s Bayesian Information Criterion (BIC) were used as auxiliary to further refine the selection of the best model for representing the drying kinetics of buckwheat grains, considering the parameters of the models pre-selected according to Gauss-Newton criterion (Table 3). This criterion has been used previously for selecting models to represent the drying kinetics of various vegetable products, such as Piper aduncum L. leaves (Quequeto et al., 2019aQUEQUETO, W. D. et al. Mathematical modeling of thin-layer drying kinetics of Piper aduncum L. leaves. Journal of Agricultural Science , 11(8):225-235, 2019a.), Morinda citrifolia L. grains (Quequeto et al., 2019bQUEQUETO, W. D. et al. Drying kinetics of noni seeds. Journal of Agricultural Science, 11(8):250-258, 2019b.), and Ipomoea batatas L. pulp (Souza et al., 2019SOUZA, D. G. et al. Drying kinetics of the sliced pulp of biofortified sweet potato (Ipomoea batatas L.). Engenharia Agrícola, 39(2):176-181, 2019.).

Table 3:
Akaike Information Criterion (AIC) and Schwarz’s Bayesian Information Criterion (BIC) values for the models that fitted best to the data of the drying of buckwheat (Fagopyrum esculentum Moench) grains at different temperatures.

According to Wolfinger (1993WOLFINGER, R. D. Covariance structure selection in general mixed models. Communications in Statistics, 22(4):1079-1106, 1993. ), AIC and BIC criteria could assist the selection process of the models pre-selected according to the Gauss-Newton criterion. Wolfinger (1993) stated that the lower the values of AIC and BIC, the better is the fit of the model. Therefore, Midilli model (4) presented a better fit for the temperatures of 40, 60, and 70 °C, while the Approximation of diffusion (13) presented a satisfactory fitting for the temperatures of 50 and 80 °C. The drying curves (Figure 2) for buckwheat grains reflect the selected models according to the criteria adopted.

Figure 2:
Moisture ratios estimated using Midilli and the Approximation of diffusion models for the drying of buckwheat (Fagopyrum esculentum Moench) grains at different drying air temperatures.

The selected models presented a good fit, describing the drying behavior of buckwheat accurately, and establishing a good correspondence between the observed and estimated values. Sousa et al. (2011SOUSA, K. A. et al. The drying kinetics of forage turnips (Raphanus sativus L.). Revista Ciência Agronômica , 42(4):883-892, 2011.) obtained a good fit with the Midilli model for forage turnip grains (Raphanus sativus L.) at temperatures ranging from 30 to 70 °C, while Camicia et al. (2015CAMICIA, R. G. D. M. et al. Modeling of the drying process the seeds of cowpea. Revista Caatinga, 28(3):206-214, 2015.) obtained a good fit with the Midilli model for Vigna unguiculata L. Walp grains at temperatures ranging from 30 to 50 °C. Botelho et al. (2015BOTELHO, F. M. et al. Drying kinetics and determination of effective diffusion coefficient of sorghum grains. Revista Brasileira de Milho e Sorgo, 14(2):260-272, 2015.) also obtained a good fit with the Midilli model for the drying of sorghum grains at the temperatures of 40, 50, and 60 °C, while Faria et al. (2012FARIA, R. Q. et al. Cinética de secagem de sementes de crambe. Revista Brasileira de Engenharia Agrícola e Ambiental, 16(5):573-583, 2012.) obtained a better fit with the Approximation of diffusion model at temperatures ranging from 30 to 70 °C for different moisture content conditions in the drying kinetics of crambe seeds (Crambe abyssinica Hort).

The behavior of the fitting curves in the present study was consistent with the conditions of drying air temperature, and it was observed that longer drying times were required for lower temperatures, a situation also observed in several other studies conducted previously on the drying kinetics of various agricultural products (Keneni; Hvoslef-Eide; Marchetti, 2019KENENI, Y. G.; HVOSLEF-EIDE, A. K.; MARCHETTI, J. M. Mathematical modelling of the drying kinetics of Jatropha curcas L. seeds. Industrial Crops and Products, 132:12-20, 2019.; Quequeto et al., 2019aQUEQUETO, W. D. et al. Mathematical modeling of thin-layer drying kinetics of Piper aduncum L. leaves. Journal of Agricultural Science , 11(8):225-235, 2019a.; Siqueira; Resende; Chaves, 2012SIQUEIRA, V. C.; RESENDE, O.; CHAVES, T. H. Determination of the volumetric shrinkage in jatropha seeds during drying. Acta Scientiarum. Agronomy , 34(3):231-238, 2012.; Sousa et al., 2011SOUSA, K. A. et al. The drying kinetics of forage turnips (Raphanus sativus L.). Revista Ciência Agronômica , 42(4):883-892, 2011.).

The values of the parameters of Midilli model (4) for the temperatures of 40, 60, and 70 °C revealed that the parameter “k” of the Approximation of diffusion (13) model for the temperatures of 50 and 80 °C tended to increase with the increase in the drying air temperature, while the other parameters demonstrated a random behavior (Table 4) and did not exhibit a clear tendency with the increase in temperature.

Table 4:
Parameters and coefficients of Midilli and the Approximation of diffusion models obtained for the buckwheat (Fagopyrum esculentum Moench) grains at different drying air temperatures.

Similar behavior of parameter “k” was observed by Sousa et al. (2011SOUSA, K. A. et al. The drying kinetics of forage turnips (Raphanus sativus L.). Revista Ciência Agronômica , 42(4):883-892, 2011.) in the study of the drying of forage turnip (Raphanus sativus L.) grains, where this parameter was observed to be related to the effective diffusivity of drying in the falling-rate period and could be used to partially explain the behavior of the drying air temperature.

The effective diffusion coefficients for the buckwheat grains during drying, at temperatures ranging from 40 to 80 °C (Figure 3A), were obtained by fitting the mathematical model of liquid diffusion having eight terms for the spherical form, considering an equivalent radius of 1.97 mm, to the experimental values. The influence of this model could be described by means of the Arrhenius representation of the effective diffusion coefficient (Figure 3B).

Figure 3:
Average values of the effective diffusion coefficient (A) and the Arrhenius representation of the effective diffusion coefficient (B) at different drying air temperatures for buckwheat (Fagopyrum esculentum Moench) grains (**significant at 1%, using the t-test).

The effective diffusion coefficient values varied from 1.8990 × 10-11 m2 s-1 to 17.8831 × 10-11 m2 s-1 within the temperature range of 40-80 °C (Figure 3A). As the drying air temperature increased, the diffusion coefficient also increased. According to Soares, Jorge and Montanuci (2016SOARES, M. A. B.; JORGE, L. M. D. M.; MONTANUCI, F. D. Drying kinetics of barley grains and effects on the germination index. Food Science and Technology, 36(4):638-645, 2016.), lower drying air temperatures promote greater internal resistance to water transport during drying, resulting in lower values of the effective diffusion coefficient. This is contrary to what happens at higher temperatures when the water diffusion from the center to the periphery is higher.

The activation energy, considering the mechanisms of diffusion, for the studied temperature range was obtained from the slope of the Arrhenius representation of the effective diffusion coefficient plot, and was determined to be 49.75 kJ mol-1 (Figure 3B). This value was consistent with the corresponding values reported for various agricultural products by Zogzas, Maroulis and Marinos-Kouris (1996ZOGZAS, N. P.; MAROULIS, Z. B.; MARINOS-KOURIS, D. Moisture diffusivity data compilation in foodstuffs. Drying Technology, 14(10):2225-2253, 1996.), i.e., 12.7-110 kJ mol-1.

Activation energy is the minimum energy required by the water molecules to break the barrier as they migrate to the product surface during the drying process (Sharma; Prasad, 2004SHARMA, G. P.; PRASAD, S. Effective moisture diffusivity of garlic cloves undergoing microwave-convective drying. Journal of Food Engineering , 65(4):609-617, 2004.). According to Sousa et al. (2011SOUSA, K. A. et al. The drying kinetics of forage turnips (Raphanus sativus L.). Revista Ciência Agronômica , 42(4):883-892, 2011.), the higher the activation energy value, the lower is the diffusivity of water inside the product. Therefore, the activation energy obtained under the adopted drying conditions indicated a certain resistance to water diffusivity, in contrast to the findings of other studies on drying kinetics: 24.78 kJ mol-1 for Raphanus sativus L. (Sousa et al., 2011), and 33.82 kJ mol-1 and 35.71 kJ mol-1 for two sorghum cultivars (Botelho et al., 2015BOTELHO, F. M. et al. Drying kinetics and determination of effective diffusion coefficient of sorghum grains. Revista Brasileira de Milho e Sorgo, 14(2):260-272, 2015.). However, the obtained value of activation energy was not higher than that obtained (51.03 kJ mol-1) in the drying kinetics of rice grains (Corrêa et al., 2017CORRÊA, P. C. et al. Thermodynamic properties of drying process and water absorption of rice grains. CyTA-Journal of Food, 1(2):204-210, 2017.).

In general, the values obtained were within the range reported by Zogzas, Maroulis and Marinos-Kouris (1996ZOGZAS, N. P.; MAROULIS, Z. B.; MARINOS-KOURIS, D. Moisture diffusivity data compilation in foodstuffs. Drying Technology, 14(10):2225-2253, 1996.) for various agricultural products. The differences were closely linked to the initial moisture contents, the drying conditions adopted, and the physical and chemical characteristics of the product, with direct effects on the drying time (Diógenes et al., 2013DIÓGENES, A. M. G. et al. Cinética de secagem de grãos de abóbora. Revista Caatinga , 26(1):71-80, 2013.).

CONCLUSIONS

Midilli model presented a better fit in regard to explaining the drying kinetics of buckwheat at the temperatures of 40, 60, and 70 °C, while the Approximation of diffusion model was the most adequate for the temperatures of 50 and 80 °C. The effective diffusion coefficient tended to increase with an increase in the drying air temperature, with its values ranging from 1.8990 × 10-11 m2 s-1 for the temperature of 40 °C to 17.8831 × 10-11 m2 s-1 for 80 °C. The activation energy required to initiate the drying process was determined to be 49.75 kJ mol-1.

ACKNOWLEDGMENTS

We would like to thank the Federal University of Grande Dourados, Federation of Agriculture and Livestock of the State of Mato Grosso do Sul, and CNPq for supporting this study, from its inception to the translation of the article.

REFERENCES

  • AGRAWAL, S. G.; METHEKAR, R. N. Mathematical model for heat and mass transfer during convective drying of pumpkin. Food and Bioproducts Processing, 101(1):68-73, 2017.
  • ALVES, J. D. C. et al. Potential of sunflower, castor bean, common buckwheat and vetiver as lead phytoaccumulators. Revista Brasileira de Engenharia Ambiental, 20(3):243-249, 2016.
  • BOTELHO, F. M. et al. Drying kinetics and determination of effective diffusion coefficient of sorghum grains. Revista Brasileira de Milho e Sorgo, 14(2):260-272, 2015.
  • BOTELHO, F. M. et al. Soybean grain drying kinects: Varietal influence. Revista Engenharia na Agricultura, 26(1):13-25, 2018.
  • BRASIL. Ministério da Agricultura e Reforma Agrária. Secretaria Nacional de defesa Agropecuária. Regras para análise de sementes. Brasília, 2009. 399p.
  • CAMICIA, R. G. D. M. et al. Modeling of the drying process the seeds of cowpea. Revista Caatinga, 28(3):206-214, 2015.
  • CORRÊA, P. C. et al. Thermodynamic properties of drying process and water absorption of rice grains. CyTA-Journal of Food, 1(2):204-210, 2017.
  • COSTA, L. M. et al. Effective diffusion coefficient and mathematical modeling for drying of crambe seeds. Revista Brasileira de Engenharia Ambiental , 15(10):1089-1096, 2011.
  • DIÓGENES, A. M. G. et al. Cinética de secagem de grãos de abóbora. Revista Caatinga , 26(1):71-80, 2013.
  • FARIA, R. Q. et al. Cinética de secagem de sementes de crambe. Revista Brasileira de Engenharia Agrícola e Ambiental, 16(5):573-583, 2012.
  • GOMES, F. P. et al. Drying kinetics of crushed mass of ‘jambu’: Effective diffusivity and activation energy. Revista Brasileira de Engenharia Agrícola e Ambiental , 22(7):499-505, 2018.
  • GÖRGEN, A. V. et al. Produtividade e qualidade da forragem de trigo-mourisco (Fagopyrum esculentum Moench) e de milheto (Pennisetum glaucum (L.) R. BR). Revista Brasileira de Saúde e Produção Animal, 17(4):599-607, 2016.
  • JAIN, R. K.; BAL, S. Properties of pearl millet. Journal of Agricultural Engineering Research, 66(2):85-91, 1997.
  • KASHANINEJAD, M. et al. Thin-layer drying characteristics and modeling of pistachio nuts. Journal of Food Engineering, 78(1):98-108, 2007.
  • KENENI, Y. G.; HVOSLEF-EIDE, A. K.; MARCHETTI, J. M. Mathematical modelling of the drying kinetics of Jatropha curcas L. seeds. Industrial Crops and Products, 132:12-20, 2019.
  • KHANALI, M. et al. Mathematical modeling of fluidized bed drying of rough rice (Oryza sativa L.) grain. Journal of Agricultural Technology, 8(3):795-810, 2012.
  • KOÇ, B.; EREN, I.; ERTEKIN, F. K. Modelling bulk density, porosity and shrinkage of quince during drying: The effect of drying method. Journal of Food Engineering , 85(3):340-349, 2008.
  • KOUA, B. K.; KOFFI, P. M. E.; GBAHA, P. Evolution of shrinkage, real density, porosity, heat and mass transfer coefficients during indirect solar drying of cocoa beans. Journal of the Saudi Society of Agricultural Sciences, 18(1):72-82, 2019.
  • LIMA, A. G. B. et al. Drying of bioproducts: Quality and energy aspects. In: DELGADO, J. M. P. Q.; LIMA, A. G. B. Drying and energy technologies. Springer International Publishing Switzerland, 2016, p.1-17.
  • MAIA, R. B. et al. Drying kinetics and thermodynamic properties of pigeon pea beans. Científica, 47(2):164-174, 2019.
  • PEREA-FLORES, M. J. et al. Mathematical modelling of castor oil seeds (Ricinus communis) drying kinetics in fluidized bed at high temperatures. Industrial Crops and Products , 38:64-71, 2012.
  • QUEQUETO, W. D. et al. Drying kinetics of noni seeds. Journal of Agricultural Science, 11(8):250-258, 2019b.
  • QUEQUETO, W. D. et al. Mathematical modeling of thin-layer drying kinetics of Piper aduncum L. leaves. Journal of Agricultural Science , 11(8):225-235, 2019a.
  • RESENDE, O. et al. Mathematical modeling for drying coffee (Coffea canephora Pierre) berry clones in concrete yard. Acta Scientiarum. Agronomy, 31(2):189-196, 2009.
  • ROSA, D. P. et al. Mathematical modeling of orange seed drying kinetics. Ciência e Agrotecnologia, 39(3):291-300, 2015.
  • SHARMA, G. P.; PRASAD, S. Effective moisture diffusivity of garlic cloves undergoing microwave-convective drying. Journal of Food Engineering , 65(4):609-617, 2004.
  • SIQUEIRA, V. C.; RESENDE, O.; CHAVES, T. H. Determination of the volumetric shrinkage in jatropha seeds during drying. Acta Scientiarum. Agronomy , 34(3):231-238, 2012.
  • SIQUEIRA, V. C.; RESENDE, O.; CHAVES, T. H. Mathematical modelling of the drying of jatropha fruit: An empirical comparison. Revista Ciência Agronômica, 44(2):278-285, 2013.
  • SOARES, M. A. B.; JORGE, L. M. D. M.; MONTANUCI, F. D. Drying kinetics of barley grains and effects on the germination index. Food Science and Technology, 36(4):638-645, 2016.
  • SOUSA, K. A. et al. The drying kinetics of forage turnips (Raphanus sativus L.). Revista Ciência Agronômica , 42(4):883-892, 2011.
  • SOUZA, D. G. et al. Drying kinetics of the sliced pulp of biofortified sweet potato (Ipomoea batatas L.). Engenharia Agrícola, 39(2):176-181, 2019.
  • VAZHOV, V. M.; KOZIL, V. N.; ODINTSEV, A. V. General methods of buckwheat cultivation in Altai region. World Applied Sciences Journal, 23(9):1157-1162, 2013.
  • WOLFINGER, R. D. Covariance structure selection in general mixed models. Communications in Statistics, 22(4):1079-1106, 1993.
  • ZHU, F. Chemical composition and health effects of Tartary buckwheat. Food Chemistry, 203:231-245, 2016.
  • ZOGZAS, N. P.; MAROULIS, Z. B.; MARINOS-KOURIS, D. Moisture diffusivity data compilation in foodstuffs. Drying Technology, 14(10):2225-2253, 1996.

Publication Dates

  • Publication in this collection
    11 Nov 2020
  • Date of issue
    2020

History

  • Received
    30 Apr 2020
  • Accepted
    21 Sept 2020
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