The effect of vacuum on the drying kinetics and mathematical modelling of blueberries

Abstract

Keywords: Activation Energy; Blueberry; Drying; Effective Moisture Diffusivity; Oven; Vacuum

Introduction

Drying process occupies a substantial place in food industry. The main objective of drying process in food industry is to preserve foods and to increase their shelf lives, by decreasing their moisture contents in order to inhibit the activities of microorganisms. The demand for dried foods is particularly increasing due to their practical

use, especially considering the prominently reduced weight and volume through the drying process. Moreover, it is not necessary to use refrigeration systems for transport and store dried foods. Consequently, it also reduces the transport and storage costs. Among the traditional methods employed for drying, oven drying method offers the most simple and easy application, being even suitable for

*Corresponding author. *E-mail address: eyildir@yildiz.edu.tr This paper was recommended for publication in revised form by Regional Editor Mesut Akgün Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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domestic implementations. Oven drying provides a faster, more hygienic and homogeneous drying than sun or solar drying, methods of which can also be stated among the traditional drying methods. Furthermore, the costs of installation, maintenance and repair are lower for oven drying [1-5]. Sometimes, traditional drying methods are assisted with vacuum addition. Introducing such a vacuum assistance protects the food against oxidation, hence the nutritional values, taste, texture and color of the product are preserved [6]. Blueberries (Vaccanium corymbosum) are small, perishable fruits with blue color. Blueberries are cultivated mostly in North and South America. They have highly economic value, including many healthy nutrients and polyphenols. But they are seasonal fruits, having a very short shelf life. In nutritional values point of view, blueberries have abundant amount of water, glucose and fructose sugars. Blueberries also contain high amount of organic acids of citric and ascorbic acid, phosphorus, potassium and magnesium minerals and fibers. They are known as very good antioxidant sources and thus have the potential to reduce the adverse impacts of some diseases like memory loss, heart disease and cancer [7,8]. Research has shown that there are fifteen different anthocyanins in blueberries such as monoarabinosides, monoglucosides and monogalactosides of cyanidin, peonidin, delphinidin, petunidin and malvidin [9]. The polyphenol content of blueberries is one of the highest amount among fruits and vegetables [10]. By 2020, the top five blueberry producers were USA (294000 tons) followed by Peru (180300 tons), Canada (146370 tons), Poland (55300 tons) and Mexico (50293 tons) [11]. In the literature, although there are numerous articles focusing on the antioxidant capacities and nutritional contents of blueberries, studies investigating their drying process is still scarce. Among these studies present, Shi et al. worked on the infrared drying kinetics of blueberries [8]; Vega-Gálvez et al. worked on the drying characteristics of blueberries by using hot-air method [12]; Zielinska et al. investigated the drying of blueberries in hot-air and microwave combined system [13] and MacGregor studied wild blueberry drying in a packed bed dryer, in which the effects of air velocity, air temperature and berry diameter on drying were investigated [14]. As it is seen from the literature, a detailed research on the drying kinetics of blueberries and the conductance of its mathematical modeling is worth investigation, since the majority of the published articles involve examining their antioxidant contents. In addition, the effect of vacuum assistance for oven drying is another subject that has not been sufficiently investigated up to date. Furthermore, the application of the drying curve data to a wide range of mathematical models has not been fully carried out in the literature. From this aspect, in this study, the investigation of the drying kinetic parameters of effective moisture diffusivities (Deff) and activation energy values (Ea) for oven drying of blueberries, with and without the assistance of vacuum was studied. It was also aimed

to determine the effect of vacuum on the aforementioned kinetic parameters and drying times. Moreover, the drying curve data was applied to twelve most known mathematical models.

Materials And Methods

Samples Chile origin blueberries were retrieved from a local market in Istanbul, Turkey on November 2021. Similar sized blueberries were selected (~ 1 cm radius) and cut into two parts horizontally before the experiments, to investigate the thin-layer diffusion. In each experiment set, 4.40 ± 0.30 g of blueberries were dried. Prior to drying, by using AOAC method, the initial moisture content (M0) of the blueberries was determined [15]. For the M0 determination, conventional hot air-drying oven (KH-45, Kenton, Guangzhou, China) was used at 105°C for 2 hours. Accordingly, the initial moisture content of the blueberries was determined on a wet basis as 84.33%, which was 5.38 kg water/kg dry matter. Experimental Method In the first stage of the dying experiments, oven (EV018, Nüve, Ankara, Turkey) drying, at drying temperatures of 60, 70, and 80°C were tested. At every 15 minutes, samples were weighed to determine their moisture contents. Sample weights were measured by using a digital balance (AS 220.R2, Radwag, Radom, Poland), which had a weighting accuracy of 0.001 g. In the second stage of the experiments, vacuum assistance was supplied on the same oven of Nüve EV-018, by using a vacuum pump KNF N022AN.18 (KNF, Freiburg, Germany) which operated at 100 W and 40 kHz frequency. The pressure inside the oven was measured as 0.3 atm during drying. In 15 minute intervals, the samples were weighed after the pressure valve connected to the oven was opened and the pressure inside the oven came into equilibrium with room pressure. Three parallel drying experiments were conducted in each drying method. Drying Curves In order to construct the drying curves of the blueberries, the moisture contents (M), drying rates (DR) and moisture ratios (MR) must be determined. These parameters were calculated by using Eq. (1), (2) and (3) [16-18] given below: (1) In Eq. (1) M represents the content of moisture in kg water/kg dry matter, mw represents the water content of the blueberries in kg, and md is the dry matter content in kg. (2)

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In Eq. (2) DR represents the drying rate in kg water/kg dry matter × min, t is the drying time in minutes and Mt+dt is the amount of moisture during the time t+dt in kg water/ kg dry matter.

for the nonlinear Levenberg-Marquardt procedure regressions. The coefficient of determination (R2), reduced chisquare (χ2) and root mean square error (RMSE) values were obtained from Eq. (7) through Eq. (9) [23-28]:

In the above equation MR represents the moisture content (dimensionless), Mt, Mi, and Me represent the amount of moisture at any time, at initial conditions and at balance, respectively. Since the moisture levels in the balance are very low compared to the initial and at any moment humidity values, Me is neglected in the calculations [19]. Effective Moisture Diffusivity and Activation Energy Calculations Drying of food materials is a function of internal diffusion and usually occurs in the falling rate period. To describe moisture diffusion, generally Fick’s 2nd law of diffusion is used. While solving this equation, several assumptions were made. The shrinkage was neglected, the diffusion coefficient was accepted as constant, and it was assumed that the mass transfer occurred symmetrically with respect to the center only by diffusion. The applicable equation of Fick’s 2nd law for the unsteady state condition in a 2L thick thin layer is given in Eq. (4) [20,21]: (4) In Eq. (4) n is the positive integer, t is the time in seconds, Deff in m2/s, and L is the half-thickness of the sample in meters. For long drying times, n is assumed as 1 [20,21]. Thus Eq. (4) can be simplified to Eq. (5): (5) By using the equation given above, Deff can be calculated from the slope of the ln(MR) versus t plot. On the other hand, the relation between the Deff and temperature variation can be expressed by the Arrhenius equation, which is shown in Eq. (6) [22]: (6) In the aforementioned equation D0 is the pre-exponential factor in m2/s, Ea in kJ/mol, R is the universal gas constant in kJ/mol × K, and T is the drying temperature in °C. Ea can be calculated from the slope of the plot of ln(Deff) versus 1/T. Mathematical Modelling The mathematical model equations that were used in this study are presented in Table 1. In the modelling process, Statistica software (Statsoft Inc., Tulsa, OK) was used

(9) The best model was selected as the one giving the highest 𝑅2, along with the lowest 𝜒2 and RMSE values [19,29]. Table 1. Mathematical models and equations Model Equation

𝑀𝑅= 𝑎×exp(-𝑘𝑡)+(1-a)×exp(-𝑘×𝑎×𝑡) Two-Term Exponential 𝑀𝑅= 𝑎×exp(-𝑘𝑡)+(1-𝑎)×exp(-𝑔×𝑡)

*a, b, c, g are coefficients and n is the drying exponent specific to each equation; k, k1, k2 are the drying coefficients specific to each equation; t is the time.

Results And Discussion

Drying Curves The drying curves and the drying rate curves of oven and vacuum assisted oven drying are given in Figure 1 and Figure 2, respectively. As seen in Figure 1, from M0 of 5.3800 kg water/kg dry matter, Mf of the oven drying were decreased to 0.3102, 0.2514 and 0.1328 for the drying temperatures of 60, 70 and 80°C, respectively. The drying times were obtained as 420, 390 and 210 minutes for the same temperatures. On the other hand, for the vacuum assisted oven drying, Mf were decreased to 0.1468, 0.1381 and 0.1167 for the drying temperatures of 60, 70 and 80°C,

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Figure 1. Drying curves of oven and vacuum-assisted oven drying.

Figure 2. Drying rate curves of oven and vacuum-assisted oven drying. respectively. With vacuum assistance, the drying times were seen to be decreased further to 240, 210 and 150 minutes at these temperatures. Hence, vacuum’s decreasing effect on the Mf and the drying times was clearly observed. Considering this remarkable decrease in the drying times, it can be said that vacuum assisted oven drying offers economic benefits, when compared to solely oven drying of blueberries. These reduced drying times also decrease the amount of energy used for drying, hence offering environmental benefits as well. In addition, as the drying temperatures increased, the drying times were seen to decrease. Similar results were obtained in literature studies [25,29]. From Figure 2, the rising-rate periods and falling-rate periods were observed for both of the drying methods. In the oven drying, the rising rate periods were obtained from the M0 of 5.3800 kg water/kg dry matter to 4.5965, 4.4650 and 4.4870 kg water/kg dry matter for the drying temperatures of 60, 70 and 80°C, respectively. Then the falling-rate periods were encountered until the Mf. For the vacuum-assisted oven drying, the rising rate periods were obtained from the M0 of 5.3800 kg water/kg dry matter to 4.1522, 3.9505 and 3.7537 kg water/kg dry matter for the drying temperatures of 60, 70 and 80°C, respectively.

Results

Deff values were obtained from Eq. (5) for each method and each drying temperature, from the slope of the ln(MR) versus drying time plots. Obtained equations are presented in Eq. (10) through (15): (10)

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oven drying, on the other hand, the maximum R2 value is obtained in Alibas model at 80°C (0.999784) and the minimum R2 value (0.996137) is obtained in two-term exponential model at 80°C. Though many of the used models adequately described the data obtained, for oven drying Alibas is the most suitable model with highest R2 values of 0.999968, 0.999506, 0.999901; lowest χ2 values of 0.000004, 0.000071, 0.000013; and lowest RMSE values of 0.001658, 0.006734, 0.002944 for 60, 70 and 80°C drying temperatures, respectively. This is followed by the models of Midilli et al. (R2: 0.999960-0.998238; χ2: 0.000227-0.000005; RMSE: 0.012722-0.004851), two-term exponential (R2: 0.9998660.998121; χ2: 0.000242-0.000015; RMSE: 0.0131390.003360), Aghbashlo et al. (R2: 0.999944-0.998573; χ2: 0.000144-0.000005; RMSE: 0.011172-0.00217) and logarithmic (R2: 0.999749-0.997672; χ2: 0.000272-0.000026; RMSE: 0.014622-0.004603). On the other hand, for vacuum-assisted oven drying, again Alibas is the most suitable model, which offered the highest R2 values of 0.999448, 0.999811, 0.999784; the lowest χ2 values of 0.000129, 0.000057, 0.000160 and the lowest RMSE values of 0.007568, 0.004616, 0.005166 for 60, 70 and 80°C, respectively. This is followed by the models of Aghbashlo et al. (R2: 0.999784-0.999243; χ2: 0.000101-0.000040; RMSE: 0.008861-0.005167), Midilli et al. (R2: 0.999149-0.998726; χ2: 0.000315-0.000223; RMSE: 0.012004-0.010253), logarithmic (R2: 0.998634-0.995714; χ2: 0.001058-0.000213; RMSE: 0.023003-0.011905) and two-term exponential (R2: 0.996763-0.996137; χ2: 0.001431-0.000604; RMSE: 0.021839-0.018325). Figure 3 presents the comparison of the calculated MR values and the experimental MR values obtained for the most suitable model of Alibas for both methods. As all of the data lied on the 45° line, it can be concluded that the models fitted could be excellently used to represent the experimental data.

(15) In the oven-drying method Deff values were calculated as 1.14×10-9, 1.45×10-9 and 2.83×10-9 m2/s, for the drying temperatures of 60, 70 and 80°C, respectively. On the other hand, by the addition of vacuum, Deff values were increased to 2.54×10-9, 3.17×10-9 and 4.33×10-9 m2/s, for the drying temperatures of 60, 70 and 80°C, respectively. For the calculation of the Ea values, Eq. (6) was used. The plot of ln(Deff) versus 1/T was employed for both drying methods, and the obtained equations are given in Eq. (16) and Eq. (17): (16)

(17) By using these two equatons Ea values were calcuated as 25.93 and 43.98 kJ/mol, for the methods of oven and vacuum-assisted oven drying, respectively. Since the addition of vacuum increased the Deff values, Ea was also observed to increase, as verified by other studies in literature [25,29]. Mathematical Modelling Results The mathematical modelling results obtained for oven and vacuum assisted oven drying are presented in Table 2. Model equations that resulted with R2 values less than 0.996 were not included in this table. The maximum R2 value is obtained in Alibas model at 60°C (0.999968) and the minimum R2 value (0.997672) is obtained in logarithmic model at 70°C, for oven drying method. For vacuum-assisted

Figure 3. Experimental and calculated MR values obtained from the models of Alibas for oven drying and vacuum-assisted oven drying.

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Table 2. The obtained mathematical model coefficients and statistical data. Model

Conclusion

In this study, oven drying and vacuum-assisted oven drying of blueberries were conducted, through which the effect of vacuum on the drying characteristics were investigated. Drying temperatures were set to 60, 70 and 80°C. The drying kinetic parameters of Deff and Ea were calculated, and the drying curve data were fitted to twelve mostly used mathematical models present in the literature. The vacuum assistance was seen to decrease the drying times from 420, 390 and 210 minutes to 240, 210 and 150 minutes, for the

temperatures of 60, 70 and 80°C, respectively. Considering the prominently reduced drying times with vacuum assistance, it can be said that the foresaid method offers economic benefits. The reduced drying times also decrease the amount of energy used for drying, hence being favorable in terms of environmental contribution. The drying rate curves showed that at the beginning of the drying (first 30 minutes), a rising-rate period was seen followed by a falling-rate period for all of the experiments. As the drying temperature increased, Deff values also increased. Vacuum

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assistance was seen to increase both Deff and Ea. Deff values were calculated between 1.14×10-9-2.83×10-9 m2/s and 2.54×10-9-4.33×10-9 m2/s, for oven and vacuum-assisted oven drying, respectively. Ea for oven drying was calculated as 25.93 kJ/mol, and increased to 43.98 kJ/mol by the addition of vacuum. Yielding the highest R2 values between 0.999968-0.999506 for oven drying and 0.999784-0.999243 for vacuum assisted oven drying, Alibas model was determined as the best model for both drying methods. For the future studies, different pretreatments can be applied before the drying process.

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