Abstract
This study was investigated the effects of hotair temperature and slice thickness on drying characteristics of Crabapple slices. Drying experiments were carried out in the ranges of 6090 °C. The thickness conditions of Crabapple slices for thin layer drying were 3mm and 5mm. The increase in the temperature of the hotair and the decrease in the thickness of the slicing causes the drying time to be significantly shortened. Fick’s diffusion model was applied to describe the water transfer of the Crabapple slices, and the effective diffusion coefficients varied from 0.6142 × 10^{8}m^{2}/s to 1.9867 × 10^{8}m^{2}/s in a given range of drying temperature. The effective diffusivity increases with increasing temperature. The activation energy values of Crabapple were 17.46 and 23.82 kJ/mol for the thickness of 3 and 5 mm, respectively. The Page model was revealed to be a better fit to describe the drying curve of Crabapple compared to other models.
Keywords:
crabapple slices; hotair drying; drying kinetics; effective diffusion coefficients; activation energy
1 Introduction
Crabapple belong to the genus Malus (Rosaceae family). Crabapple are widely distributed in colder regions such as North America, Europe, and East Asia. In China, it is mainly distributed in Heilongjiang Province, Liaoning Province, Jilin Province and Inner Mongolia area (Dadwal et al., 2018Dadwal, V., Agrawal, H., Sonkhla, K., Joshi, R., Gupta, M. (2018). Characterization of phenolics, amino acids, fatty acids and antioxidant activity in pulp and seeds of highaltitude Himalayan Crabapple fruits (Malus baccata). Journal of Food Science and Technology, 55(6), 21602169. http://dx.doi.org/10.1007/s131970183133y. PMid:29892117.
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). Crabapple are rich sources of nutritional value, such as minerals, vitamins, and fiber, which provide essential nutrients for human health (Li et al., 2014Li, N., Shi, J., Wang, K. (2014). Profile and antioxidant activity of phenolic extracts from 10 Crabapples (Malus wild species). Journal of Agricultural and Food Chemistry, 62(3), 574581. http://dx.doi.org/10.1021/jf404542d. PMid:24392851.
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). In addition, the medicinal value of Crabapple has been extensively studied because they contain various phenolic compounds and antioxidant flavonoids (Sharma & Nath, 2016Sharma, R., Nath, A. K. (2016). Antioxidant levels and activities of reactive oxygenscavenging enzymes in Crabapple fruits (Malus baccata). Proceedings of the National Academy of Sciences. India. Section B, Biological Sciences, 86(4), 877885. http://dx.doi.org/10.1007/s4001101505296.
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; Li et al., 2014Li, N., Shi, J., Wang, K. (2014). Profile and antioxidant activity of phenolic extracts from 10 Crabapples (Malus wild species). Journal of Agricultural and Food Chemistry, 62(3), 574581. http://dx.doi.org/10.1021/jf404542d. PMid:24392851.
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). Li et al. (2016)Li, M., Xue, S., Tan, S., Qin, X., Gu, M., Wang, D., Zhang, Y., Guo, L., Huang, F., Yao, Y., Zhou, Z., Fan, S., Huang, C. (2016). Crabapple fruit extracts lower hypercholesterolaemia in highfat dietinduced obese mice. Journal of Functional Foods, 27, 416428. http://dx.doi.org/10.1016/j.jff.2016.09.017.
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suggested that Crabapple may reduce cholesterol by enhancing the CYP7A1 function in the liver. Qin et al. (2015)Qin, X., Xing, Y. F., Zhou, Z., Yao, Y. (2015). Dihydrochalcone compounds isolated from Crabapple leaves showed anticancer effects on human cancer cell lines. Molecules (Basel, Switzerland), 20(12), 2119321203. http://dx.doi.org/10.3390/molecules201219754. PMid:26633321.
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concluded that the dihydrogen detection compounds in begonia leaves have anticancer effects.
Compared with apples, the diameter of Crabapple is relatively small, about 3 cm, intensely sour and hard, which is not suitable for ingesting as food directly (Li et al., 2016Li, M., Xue, S., Tan, S., Qin, X., Gu, M., Wang, D., Zhang, Y., Guo, L., Huang, F., Yao, Y., Zhou, Z., Fan, S., Huang, C. (2016). Crabapple fruit extracts lower hypercholesterolaemia in highfat dietinduced obese mice. Journal of Functional Foods, 27, 416428. http://dx.doi.org/10.1016/j.jff.2016.09.017.
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). Therefore, Crabapple are generally used for jams and jellies and beverages. Drying is a common method used to extend shelf life and ease the storage of Crabapple. Sundrying is not only limited by weather conditions but also requires a long time. Besides, the sundrying method is inconvenient in controlling the contamination from microorganisms and dust during exposure (Shree, 2022Shree, S. G. (2022). Comparative study of characteristics of amla fruit using open sun drying and solar drying method. International Journal of Research Publication and Reviews, 3(7), 38053810. www. ijrpr. com). The advantage of freezedrying is that it yields highquality products, but it requires an expensive process and has a limited range of applications. Hotair drying is a popular alternative technology because it is simple, quick, and economical (Jha & Sit, 2020Jha, A. K., Sit, N. (2020). Drying characteristics and kinetics of colour change and degradation of phytocomponents and antioxidant activity during convective drying of deseeded terminalia chebula fruit. Journal of Food Measurement and Characterization, 14(4), 20672077. http://dx.doi.org/10.1007/s11694020004549.
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).
Drying kinetics describe a complex system between moisture removal and drying process variables, which is influenced by drying conditions, types of dryers and properties of the material to be dried (Deng et al., 2019Deng, L. Z., Mujumdar, A. S., Zhang, Q., Yang, X. H., Wang, J., Zheng, Z. A., Gao, Z. J., Xiao, H. W. (2019). Chemical and physical pretreatments of fruits and vegetables: Effects on drying characteristics and quality attributes – A comprehensive review. Critical Reviews in Food Science and Nutrition, 59(9), 14081432. http://dx.doi.org/10.1080/10408398.2017.1409192. PMid:29261333.
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). Therefore, predicting drying characteristics and optimizing dry parameters facilitate the improvement of the quality of dried Crabapple (Biswas et al., 2022Biswas, R., Hossain, M. A., Zzaman, W. (2022). Thin layer modeling of drying kinetics, rehydration kinetics and color changes of osmotic pretreated pineapple (Ananas comosus) slices during drying: Development of a mechanistic model for mass transfer. Innovative Food Science Emerging Technologies, 80, 103094. http://dx.doi.org/10.1016/j.ifset.2022.103094.
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). Finding a suitable kinetic model to evaluate the practicality of drying is necessary to improve the quality of Crabapple and optimize drying parameters. In previous studies, researchers have explored the drying behavior of a variety of fruit slices and developed mathematical models to describe the drying behavior. Kırbaş et al. (2019)Kırbaş, İ., Tuncer, A. D., Şirin, C., Usta, H. (2019). Modeling and developing a smart interface for various drying methods of pomelo fruit (Citrus maxima) peel using machine learning approaches. Computers and Electronics in Agriculture, 165, 104928. http://dx.doi.org/10.1016/j.compag.2019.104928.
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studied the effects of freeze drying and microwave drying on the drying characteristics of pomelo fruit treated with different models. Pinar et al. (2021) foundPinar, H., Çetin, N., Ciftci, B., Karaman, K., Kaplan, M. (2021). Biochemical composition, drying kinetics and chromatic parameters of red pepper as affected by cultivars and drying methods. Journal of Food Composition and Analysis, 102, 103976. http://dx.doi.org/10.1016/j.jfca.2021.103976.
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the effects of different drying methods on the drying kinetics of different pepper varieties. Hossain et al. (2021)Hossain, M. A., Dey, P., Joy, R. I. (2021). Effect of osmotic pretreatment and drying temperature on drying kinetics, antioxidant activity, and overall quality of taikor (Garcinia pedunculata Roxb.) slices. Saudi Journal of Biological Sciences, 28(12), 72697280. http://dx.doi.org/10.1016/j.sjbs.2021.08.038. PMid:34867031.
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use multiple models, such as Newton, to reveal the thin dewatering characteristics of Tailor. This was also observed by Ataides et al. (2022)Ataides, I. M. R., Oliveira, D. E. C., Ferreira, W. N. Jr, Resende, O., Quequeto, W. D. (2022). Drying kinetics of araticum (Annona crassiflora) epicarp. Food Science and Technology (Campinas), 42, e09521. http://dx.doi.org/10.1590/fst.09521.
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for Araticum fruits used multiple models to predict drying properties.
Therefore, the aim of this paper was to investigate the effect of drying temperature and slice thickness on the drying characteristics of Crabapple slices. Furthermore, the impact of different dry variables (thickness and temperature) on the effective diffusion coefficient and activation energy of the Crabapple during the drying process were also calculated. This study could help select the best drying model for Crabapple, a better understanding of the drying characteristics of Crabapple and the effect of drying on the quality of Crabapple slices.
2 Materials and methods
2.1 Materials
Crabapple are purchased from local orchards in China. The experiment used fresh, bright colors, uniform size, free from pests and diseases, and sample selection and mechanical damage. The Crabapple are washed with distilled water and peeled manually. In this experiment, the Crabapple were cut into 3mm and 5mm thick with the core removed and measured with a vernier caliper. The average diameter of the Crabapple is 3.39 ± 0.2 cm. The initial moisture content of Crabapple was determined according to standard methods. The sample sections were weighed on an electronic balance. Finally, put it into an electric heating constant temperature blast drying oven (DHG9053A).
2.2 Experimental procedure
Drying experiments using laboratoryscale electric electrothermal constant temperature blast drying oven (DHG9053A, Shanghai Jinghong Experimental Facilities Corporation Ltd, Shanghai, China). The dryer mainly consists of a heat control unit, which can fix temperatures ranging from 10 to 250 °C, a heating chamber, a temperature probe, a fan, and a temperature fluctuation of ±1 °C. The experimental drying procedures in the heating air blast were carried out at 60 °C, 70 °C, 80 °C, and 90 °C, respectively. The constant wind speed of the dryer is 1.0 m/s. Before the drying experiment, the dryer was set to the desired temperature for approximately one hour to ensure that each group of experiments was carried out at the predetermined temperature.
Then, Crabapple samples were spread in a thin layer on the wire mesh, ensuring each slice was a single layer without any overlapping parts. Crabapple samples were placed in a thin layer on the stainless net in the middle of the heating chamber. The weight of the sample was kept at 150 ± 0.1 g and recorded at 10 min intervals.
The sample was weighed with an electron analytical balance (±0.01 g accuracy, JA5003, Shanghai Balance Instrument Plant, Shanghai, China). Sample quality was measured every 10 minutes. When the mass of the sample remains constant after three times, it is considered to have reached equilibrium. Each sample was measured at each drying temperature three times to obtain the average value. Samples are randomly taken for analysis based on preset drying times.
2.3 Mathematical model
In those models, MR represents the ratio of the free water content of a sample to the initial water content. The moisture ratio(MR) of Crabapple slices under various drying conditions was calculated using the following Equation 1 (Aydar, 2021Aydar, A. Y. (2021). Investigation of ultrasound pretreatment time and microwave power level on drying and rehydration kinetics of green olives. Food Science and Technology (Campinas), 41(1), 238244. http://dx.doi.org/10.1590/fst.15720.
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):
where M and M_{0} are the moisture content of the product at any drying time and at the initial time, respectively. Me is the equilibrium moisture content. The value of Me is relatively small compared to M or M_{0} and can be ignored. Thus, the equations can be simplified to MR =M/M_{0}.
Then, the drying rate (DR) of Crabapple was calculated as Equation 2 (TamaritPino et al., 2020TamaritPino, Y., BatíasMontes, J. M., SeguraPonce, L. A., DíazÁlvarez, R. E., GuzmánMeza, M. F., QuevedoLeón, R. A. (2020). Effect of electrohydrodynamic pretreatment on drying rate and rehydration properties of Chilean sea cucumber (Athyonidium chilensis). Food and Bioproducts Processing, 123, 284295. http://dx.doi.org/10.1016/j.fbp.2020.07.012.
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)
where Mt and Mt+Δt are moisture content at time t (kg water/kg dry matter) and moisture content at time t+Δt, respectively, t is time (min), and dt is the time difference (min).
2.4 Correlation coefficient and error analysis
In order to select an appropriate mathematical model to describe the drying process of sliced Crabapple, this study uses the theoretical modeldiffusion model and five ordinary classical thinlayer drying model equations to represent the drying curve of sliced Crabapple. Table 1 shows the model equations for empirical thinlayer drying.
This experiment uses OriginPro8.5(OriginPro 8.5; OriginLab Corp., Northampton, MA, USA) mathematical and statistical software to analyze linear and nonlinear regression equations and then gives various statistical parameters such as the measurement coefficient (R^{2}) and the reduced chisquare (χ^{2}).
R^{2} is the primary criteria of the statistical analysis parameters of the drying curve of the material, and the χ^{2} is the reduced chisquare. χ^{2} is according to the following Equation 3 (Engin, 2020Engin, D. (2020). Effect of drying temperature on color and desorption characteristics of oyster mushroom. Food Science and Technology (Campinas), 40(1), 187193. http://dx.doi.org/10.1590/fst.37118.
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):
where MR_{exp}, i is the experimentally observed moisture ratio, MR_{pre}, i is the predicted moisture ratio, N is the number of observations, and z is the number of constants in the model. The model was best when χ^{2} was at a minimum value and R^{2} at a maximum value.
2.5 Calculation of effective diffusivities
The drying characteristics of raw food products in the falling rate period are generally calculated by the Fick diffusion Equation 4. In 1975, Crank developed this equation into Equation 5 (Crank, 1975Crank, J. (1975). The mathematics of diffusion. Oxford, England: Claren don Press.).
where Deff is the effective moisture diffusion, m2/ s; L0  is the half thickness of the Crabapple slices; n is required to be a positive integer.
In the actual calculation, for a longer drying process, Equation 6 can be directly simplified to the following equation (Vijayan et al., 2020Vijayan, S., Arjunan, T. V., Kumar, A. (2020). Exergoenvironmental analysis of an indirect forced convection solar dryer for drying bitter gourd slices. Renewable Energy, 146, 22102223. http://dx.doi.org/10.1016/j.renene.2019.08.066.
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).
Take the calculated MR to the correct number, then use the drying time T as the horizontal coordinate and Ln (MR) as the vertical coordinate system to make a straightline equation (Equation 7).
Equation 8 is as follows:
2.6 The calculation of activation energy
The simplified Arrhenius equation represents the water diffusion coefficient and temperature relationship. Activation energy can be confirmed from the slope of the linear of Equation 9 (Demiray Tulek, 2014Demiray, E., Tulek, Y. (2014). Drying characteristics of garlic (Allium sativum L) slices in a convective hotair dryer. Heat and Mass Transfer, 50(6), 779786. http://dx.doi.org/10.1007/s0023101312869.
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):
where D_{0} represents the experimental factor in the Arrhenius equation (m^{2}/s); Ea stands for activation energy (KJ/mol); R is the gas constant (8.314 KJ/mol K); T stands for absolute temperature (K).
According to the experimental drying data, a line with Xaxis as drying time and the yaxis as ln(MR) is drawn. The value of the effective water diffusivity can be obtained from the slope of the line (Equation11). The calculation formula is as follows (Omolola et al., 2019Omolola, A. O., Kapila, P. F., Silungwe, H. M. (2019). Mathematical modeling of drying characteristics of Jew’s mallow (Corchorus olitorius) leaves.Information Processing in Agriculture, 6(1), 109115. https://doi.org/10.1016/j.inpa.2018.08.003.
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) ( Equation 10):
3 Results and discussion
3.1 Drying characteristic
The Crabapple slices were dried in an electric electrothermal constant temperature blast drying oven and dried with thicknesses of 3 and 5mm at selected temperature levels (60,70,80, and 90°C). Figure 1 shows the variations in the moisture ratio of the Crabapple at different thicknesses and temperatures, depicting the relationship between the water ratio (MR) and the drying time. As seen from the Figure 1, the moisture content continued to decrease with the extension of drying time. Demiray Tulek (2014)Demiray, E., Tulek, Y. (2014). Drying characteristics of garlic (Allium sativum L) slices in a convective hotair dryer. Heat and Mass Transfer, 50(6), 779786. http://dx.doi.org/10.1007/s0023101312869.
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investigated the same results that the MR of the garlic samples considerably decreased with increasing drying time.
Drying curves of Crabapple slices undergoing hotair at different temperatures for sample thickness of (a) 3 mm and (b) 5 mm.
Interestingly, the decrease in slice thickness and an increase in operative temperature resulted in a reduction of the drying time. The equilibrium moisture time of the Crabapple with the slice thickness of 3 mm was 160, 130, 110 and 100 min at 60, 70, 80 and 90 °C, respectively. Moreover, the Crabapple slices of 5mm consume significantly longer time which was 260, 200, 150, 140 min at the corresponding temperature, respectively. Regardless of other conditions, the thickness of the red fruit increases, and the drying time is prolonged. One explanation of this phenomenon could be indicated by the reduced water travel distance and increased sample surface area. Doymaz İsmail (2011) foundDoymaz, İ., İsmail, O. (2011). Drying characteristics of sweet cherry. Food and Bioproducts Processing, 89(1), 3138. http://dx.doi.org/10.1016/j.fbp.2010.03.006.
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that the drying time of pumpkin slices is longest at 60 °C and shortest at 75 °C. The effect of temperature and slice thickness on drying time was following earlier study on Madeira banana and Esmolfe apple (Pinheiro et al., 2022Pinheiro, M. N. C., Madaleno, R. O., Castro, L. M. M. N. (2022). Drying kinetics of two fruits Portuguese cultivars (Bravo de Esmolfe apple and Madeira banana): An experimental study. Heliyon, 8(4), e09341. http://dx.doi.org/10.1016/j.heliyon.2022.e09341. PMid:35520611.
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).
3.2 Drying rate curve
Figure 2 shows the drying rate curves of the Crabapple slices of 3mm and 5mm at different drying temperatures (60, 70, 80 and 90 °C). The moisture content gradually decreased with the increase in drying time. As expected, the drying temperature of the slices increased, and the drying time was significantly shortened. This is due to the significant difference in steam pressure between the fruit slices and the surrounding environment at a higher temperature. As a result, the rate of water migration gradually decreased from the inside to the outside of the sample (Wang et al., 2022aWang, C., Lu, Y., An, X., Tian, S. (2022a). Thinlayer drying characteristics of Easter lily (LiliumlongiflorumThunb.) scales and mathematical modeling. Food Science and Technology, 42, e23222. https://doi.org/10.1590/fst.23222.
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). The study by Jiang et al. (2021)Jiang, M., Wu, P., Xing, H., Li, L., Jia, C., Chen, S., Zhang, S., Wang, L. (2021). Water migration and diffusion mechanism in the wheat drying. Drying Technology, 39(6), 738751. http://dx.doi.org/10.1080/07373937.2020.1716001.
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found that the average migration rate of moisture inside wheat grains was smaller than the average evaporation rate outside wheat grains. He et al. (2021)He, X., Lin, R., Cheng, S., Wang, S., Yuan, L., Wang, H., Wang, H., Tan, M. (2021). Effects of microwave vacuum drying on the moisture migration, microstructure, and rehydration of sea cucumber. Journal of Food Science, 86(6), 24992512. http://dx.doi.org/10.1111/17503841.15716. PMid:34056720.
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also concluded that promoting sea cucumber moisture transfer movement during the drying process could shorten the drying time. These results agree with (Bhattacharya et al., 2015Bhattacharya, M., Srivastav, P. P., Mishra, H. N. (2015). Thinlayer modeling of convective and microwaveconvective drying of oyster mushroom (Pleurotus ostreatus). Journal of Food Science Technology, 52(4), 20132022. http://dx.doi.org/10.1007/s1319701312092.
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; Miraei Ashtiani et al., 2018Miraei Ashtiani, S. H., Sturm, B., Nasirahmadi, A. (2018). Effects of hotair and hybrid hotairmicrowave drying kinetics and textural quality of nectarine slices. Heat and Mass Transfer, 54, 915927. https://doi.org/10.1007/s0023101721870.
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).
Drying rate versus moisture content of Crabapple slice undergoing hotair at different temperatures for sample thickness of (a) 3 mm and (b) 5 mm.
The thickness of the Crabapple slices also affects the drying time (Figure 2). With the same moisture content, the thinner the thickness of the piece, the greater the drying rate, and the shorter the drying time of the red sliced slices. The slice thickness is 3mm and 5mm, and the moisture content is more than 2.5 kg water/kg DW and 2 kg water/kg DW, respectively. However, when the moisture content of Crabapple slices was less than 2.5 kg water/kg DW and 2 kg water/kg DW, respectively, the drying rate decreased with the increase in drying temperature. The above phenomenon shows that at the same slice thickness when the drying process is about to end, the lower the water content inside the slice, the smaller the drying rate. It is more difficult to exclude the moisture in the slice. Jongyingcharoen et al. (2019)Jongyingcharoen, J. S., Wuttigarn, P., Assawarachan, R. (2019). Hotair drying of coconut residue: shelf life, drying characteristics, and product quality. IOP Conference Series. Earth and Environmental Science, 301(1), 012033. http://dx.doi.org/10.1088/17551315/301/1/012033.
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found that the smaller the thickness of coconut dregs, resulting in a shorter drying time during the drying process (70 minutes). Ndisya et al. (2020)Ndisya, J., Mbuge, D., Kulig, B., Gitau, A., Hensel, O., Sturm, B. (2020). Hotair drying of purplespeckled Cocoyam (Colocasia esculenta (L.) Schott) slices: optimisation of drying conditions for improved product quality and energy savings. Thermal Science and Engineering Progress, 18, 100557. http://dx.doi.org/10.1016/j.tsep.2020.100557.
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found that the thickness of the sample slice increased the drying time in the hotair drying experiment of purple spotted coconut slices. Similar results on the effect of the thickness have been reported for carrot slices (Doymaz, 2017Doymaz, İ. (2017). Drying kinetics, rehydration and colour characteristics of convective hotair drying of carrot slices. Heat and Mass Transfer, 53(1), 2535. http://dx.doi.org/10.1007/s0023101617918.
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), papaya (Sairam et al.,2017Sairam, N., Kumar, M. N., Edukondalu, L., Kumar, G. Y. (2017). Effect of slice thickness on drying kinetics of papaya using food dehydrator. International Journal of Agriculture Environment and Biotechnology, 10(6), 749756. http://dx.doi.org/10.5958/2230732X.2017.00092.4.
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) and gastrodia elata (Li et al., 2021Li, K., Zhang, Y., Wang, Y. F., ElKolaly, W., Gao, M., Sun, W., Li, M. (2021). Effects of drying variables on the characteristic of the hotair drying for gastrodia elata: Experiments and multivariable model. Energy, 222, 119982. http://dx.doi.org/10.1016/j.energy.2021.119982.
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). The drying rate decreased continuously with the decrease of moisture content and increased with the increase of temperature. From the figure, the sliced Crabapple did not show a continuous drying period. The whole drying process represents a period of decreasing rate. Some previous studies have also found that the drying rate increases with temperature, such as ‘gueroba’ fruit pulp (Jorge et al., 2021Jorge, A. P. P., Ferreira, W.N. Jr., Silva, L. C. M., Oliveira, D. E. C., Resende, O. (2021). Drying kinetics of ‘gueroba’ (Syagrus oleracea) fruit pulp. Revista Brasileira de Engenharia Agrícola e Ambiental, 25(1), 2329. https://doi.org/10.1590/18071929/agriambi.v25n1p2329.
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), pear slices (Doymaz Ismail, 2012Doymaz, I., Ismail, O. (2012). Experimental characterization and modeling of drying of pear slices. Food Science and Biotechnology, 21(5), 13771381. http://dx.doi.org/10.1007/s1006801201813.
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), tomato slices (Sadin et al., 2014Sadin, R., Chegini, G. R., Sadin, H. (2014). The effect of temperature and slice thickness on drying kinetics tomato in the infrared dryer. Heat and Mass Transfer, 50(4), 501507. http://dx.doi.org/10.1007/s0023101312553.
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) and (Cuccurullo et al., 2019Cuccurullo, G., Metallo, A., Corona, O., Cinquanta, L. (2019). Comparing different processing methods in apple slice drying. Part 1. Performance of microwave, hotair and hybrid methods at constant temperatures. Biosystems Engineering, 188, 331344. http://dx.doi.org/10.1016/j.biosystemseng.2019.10.021.
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).
3.3 Drying model
Table 2 represents the statistical results and the values of coefficient and reduced chisquare obtained by different thin layer drying models. As can be seen from Table 2, the R^{2} and X^{2} values in all drying models ranged from 0.9703 to 0.9988,0.00012 to 0.00335, respectively. The values of R^{2} obtained from the Page equation are higher than those from other models. The values of R^{2} in all the models were greater than 0.96, which indicates that the fitting is good (Doymaz, 2011Doymaz, I. (2011). Thinlayer drying characteristics of sweet potato slices and mathematical modeling. Heat and Mass Transfer, 47(3), 277285. http://dx.doi.org/10.1007/s0023101007223.
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). From Table 2, the values of R^{2} and X^{2} in the Page equation model are maximum and minimum, respectively. Therefore, the Page model can be assumed to illustrate the thin layer drying behavior of Crabapple sliced. Figure 3 shows the comparison of the predicted moisture ratios obtained by Page model and the experimental moisture ratio values at various drying air temperatures 60, 70, 80 and 90 °C.
Comparison of drying curves of Crabapple slices undergoing hotair drying for sample thickness of (a) 3 mm and (b) 5 mm. Solid line (d) represents curve fitting using Page model.
3.4 Effective diffusion coefficient calculation
The effective moisture diffusivity (D_{eff}) is usually considered an index of drying hydrodynamic mass transfer. D_{eff} is affected by temperature and slice thickness (Mahapatra and Tripathy, 2018Mahapatra, A., Tripathy, P. P. (2018). Modeling and simulation of moisture transfer during solar drying of carrot slices. Journal of Food Process Engineering, 41(8), e12909. http://dx.doi.org/10.1111/jfpe.12909.
http://dx.doi.org/10.1111/jfpe.12909...
). The value of the effective diffusion coefficient is calculated based on the Equation 6 of the sliced redness, and the calculation value is shown in Table 3. The effective diffusivity of water of the Crabapple was 0.6142 × 10 ^{9} ~ 1.9867 × 10 ^{8}(m^{2}/s) during the drying process at 60 °C~90 °C. From Table 3, the value of the water effective diffusion coefficient increases with the increase in drying temperature. Generally, the effective diffusion coefficient of food is 10^{12}~10^{8} (Jha Sit, 2020Jha, A. K., Sit, N. (2020). Drying characteristics and kinetics of colour change and degradation of phytocomponents and antioxidant activity during convective drying of deseeded terminalia chebula fruit. Journal of Food Measurement and Characterization, 14(4), 20672077. http://dx.doi.org/10.1007/s11694020004549.
http://dx.doi.org/10.1007/s11694020004...
). Macedo et al. (2020)Macedo, L. L., Vimercati, W. C., Araújo, C., Saraiva, S. H., Teixeira, L. J. Q. (2020). Effect of drying air temperature on drying kinetics and physicochemical characteristics of dried banana. Journal of Food Process Engineering, 43(9), e13451. http://dx.doi.org/10.1111/jfpe.13451.
http://dx.doi.org/10.1111/jfpe.13451...
reported that the effective diffusivities of sliced bananas were 3.538 × 10^{−9} m^{2} s^{−1}. Besides, at a constant drying temperature, D_{eff} values increase with slice thickness. Torubeli et al. (2021)Torubeli, S. T., Samuel, R. T., Gumus, R. H. (2021). Drying characteristics and kinetics of okra at different thickness. International Journal of Chemical and Process Engineering Research, 8(1), 110. http://dx.doi.org/10.18488/journal.65.2021.81.1.10.
http://dx.doi.org/10.18488/journal.65.20...
studies of the drying kinetics of okra at various thicknesses have shown that values at all temperatures of 5mm are higher than values at 10mm and 15mm. This is because diffusion channels are smaller in larger samples and moisture is more readily migrated, resulting in greater D_{eff} (Deng et al., 2018Deng, L.Z., Yang, X.H., Mujumdar, A. S., Zhao, J.H., Wang, D., Zhang, Q., Wang, J., Gao, Z.J., Xiao, H.W. (2018). Red pepper (Capsicum annuum L.) drying: Effects of different drying methods on drying kinetics, physicochemical properties, antioxidant capacity, and microstructure. Drying Technology, 36(8), 893907. http://dx.doi.org/10.1080/07373937.2017.1361439.
http://dx.doi.org/10.1080/07373937.2017....
).
Values of effective diffusivity attained at various air temperatures on hotair drying of Crabapple slices with different thickness.
3.5 Calculation of activation energy
Dry activation can indicate the minimum energy required by the unit Moore's moisture during the drying process. The greater the activation of the material, the more difficult it is to dry (Wang et al., 2018cWang, H., Yang, X. H., Zhang, Q. (2018c). Characteristics and drying model of spinach pulsating gas jet impingement drying. Food Science and Technology (Campinas), 43(07), 8389.). The two sides of the Equation 9 take the natural number to get the following equations:
The Equation 12 shows that Ln Deff is linear with a slope reciprocal to absolute temperature, and the activation energy (Ea) can be calculated from Figure 4. The activation energy of all samples ranged from 10–110 kJ/mol (Rafiee et al., 2010Rafiee, S., Sharifi, M., Keyhani, A., Omid, M., Jafari, A., Mohtasebi, S. S., Mobli, H. (2010). Modeling effective moisture diffusivity of orange slice (Thompson Cv.). International Journal of Food Properties, 13(1), 3240. http://dx.doi.org/10.1080/10942910802144345.
http://dx.doi.org/10.1080/10942910802144...
). The activation energy of 3mm and 5mm sliced Crabapple were 17.46 and 23.82 KJ/mol, respectively. The activation energy of the Crabapple resembles the gala apples (19.20~27.10 kJ/mol) (Kriaa Nassar, 2022Kriaa, K., Nassar, A. F. (2022). Study of gala apples (Malus pumila) thinlayer microwave drying: drying kinetics, diffusivity, structure and color. Food Science and Technology (Campinas), 41(2), 483493.), taro (18.04 ~ 28.78 KJ/mol) (Abbaspour‐Gilandeh et al., 2019Abbaspour‐Gilandeh, Y., Kaveh, M., Jahanbakhshi, A. (2019). The effect of microwave and convective dryer with ultrasound pretreatment on drying and quality properties of walnut kernel. Journal of Food Processing and Preservation, 43(11), e14178. http://dx.doi.org/10.1111/jfpp.14178.
http://dx.doi.org/10.1111/jfpp.14178...
) and elephant cassava (22.91 KJ/mol) (Kosasih et al., 2020Kosasih, E. A., Zikri, A., Dzaky, M. I. (2020). Effects of drying temperature, airflow, and cut segment on drying rate and activation energy of elephant cassava. Case Studies in Thermal Engineering, 19, 100633. http://dx.doi.org/10.1016/j.csite.2020.100633.
http://dx.doi.org/10.1016/j.csite.2020.1...
). It is higher than the activation energies of 14.97 kJ/mol for okra slice (Afolabi Agarry, 2014Afolabi, T. J., Agarry, S. E. (2014). Thin layer drying kinetics and modelling of okra (Abelmoschus esculentus (L.) Moench) slices under natural and forced convective air drying. Food Science and Quality Management, 28(6), 3549.) and Asian white radish (16.49~20.26KJ/mol) (Lee Kim, 2009Lee, J. H., Kim, H. J. (2009). Vacuum drying kinetics of Asian white radish (Raphanus sativus L.) slices. LebensmittelWissenschaft + Technologie, 42(1), 180186. http://dx.doi.org/10.1016/j.lwt.2008.05.017.
http://dx.doi.org/10.1016/j.lwt.2008.05....
). But these values are lower than that of the walnut kernel (26.35~36.44 kJ/mol) (Kaveh et al., 2018Kaveh, M., Jahanbakhshi, A., AbbaspourGilandeh, Y., Taghinezhad, E., Moghimi, M. B. F. (2018). The effect of ultrasound pretreatment on quality, drying, and thermodynamic attributes of almond kernel under convective dryer using ANNs and ANFIS network. Journal of Food Process Engineering, 41(7), 114. http://dx.doi.org/10.1111/jfpe.12868.
http://dx.doi.org/10.1111/jfpe.12868...
), Flos Lonicerae (28.90~36.05 kJ/mol) (Liu et al., 2015Liu, Y., Sun, Y., Miao, S., Li, F., Luo, D. (2015). Drying characteristics of ultrasound assisted hotair drying of Flos Lonicerae. Journal of Food Science and Technology, 52(8), 49554964. http://dx.doi.org/10.1007/s1319701416123. PMid:26243915.
http://dx.doi.org/10.1007/s13197014161...
) and values of (25.66~30.29) KJ /mol by Wang et al. (2022b)Wang, C., Tian, S., An, X. (2022b). The effects of drying parameters on drying characteristics, colorimetric differences, antioxidant components of sliced Chinese jujube. Heat and Mass Transfer, 58(9), 15611571. http://dx.doi.org/10.1007/s00231022032025.
http://dx.doi.org/10.1007/s00231022032...
for Chinese jujube slices.
4 Conclusion
The study showed that drying temperature and slice thickness have a certain effect on the Crabapple slices. The high drying temperature and thin slicing thickness can shorten the drying time. The drying stage of the Crabapple showed a descending rate drying duration without a constant rate interval under our drying conditions. The effective diffusion coefficient increased with the increase of drying temperature and slice thickness. The effective diffusion coefficient was determined to be between 0.6142 × 10 ^{8} m2/s and 1.9867 × 10 ^{8} m^{2}/s. The activation energy also increased with the thickness of the slice. The value of 3mm sliced red activation energy was found at 17.46 KJ/mol, and that of 5mm was 24.82KJ/mol. The Page equation model can well describe the drying process of Crabapple because it expresses the maximum of R^{2} and the minimum of X^{2}. Therefore, the Page model was the most suitable for describing the drying characteristics of the sliced Crabapple.
Acknowledgements
The authors appreciate the support from the Foundation for the Characteristic Discipline of Processing Technology of Plant Foods (No. YSTSXK201812) and Special Fund for Business of Heilongjiang Provincial Department of Education (No. 135409409; 145109319). We also would like to thank the reviewers and the editors for their comments on an earlier version of this paper.

Practical Application: Hotair drying mathematical model of Crabapple slices can be used as a guideline toward optimal design of drying methods and conditions. Dryingkinetics models are essential for equipment design, process optimization and product quality improvement.
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Publication Dates

Publication in this collection
16 Dec 2022 
Date of issue
2023
History

Received
27 Aug 2021 
Accepted
21 Oct 2022