Original Paper
Drying kinetics and determination of effective moisture diffusivity and activation energy in cucumber pericarp tissues using thin-layer drying models
2021 Volume 27 Issue 2 Pages 181-192
Details
2021 Volume 27 Issue 2 Pages 181-192
The cucumber pericarp can be processed separately into diverse products due to the nutritional and mineral composition differing between layers. In this study, the drying characteristics of cumber endocarp and mesocarp tissues were investigated using various thin-layer drying models. Cubes of pericarp tissue were prepared from whole cucumber fruits. The results showed that drying rate increased with temperature and that a two-term model provided the best fit for the experimental drying data. The effective moisture diffusivity was estimated using a diffusion model and found to range from 5.0921 × 10−10 to 1.1426 × 10−9 m2·s−1 and from 3.9123 × 10−10 to 8.9376 × 10−10 m2·s−1 for cubes of endocarp and mesocarp tissue, respectively, at a drying temperatures ranging from 40 to 60 °C. Moreover, the variation observed in effective diffusivity was corrected by applying a shrinkage factor. The activation energy for endocarp and mesocarp tissues was 35.03 kJ·mol−1 and 35.82 kJ·mol−1, respectively.
Drying is widely recognized as being the oldest postharvesting process for extending the shelf life and reducing the volume and weight of agricultural commodities (Onwude et al., 2016). Drying of fruit and vegetables is of particular interest because dried fruit is widely used as an additive for improving the nutritional value of foodstuffs (Kunzek and Vetter, 1999). From an industrial perspective, drying is an energy-intensive process, accounting for approximately 10 to 15% of the total energy consumption in the industrial sectors of developed countries (Mujumdar, 1997; Marcotte and Grabowski, 2008). Although there are 200 different types of dryers, which are classified depending on their purpose, understanding the underlying physics of drying operations is of great practical and economic importance, and effective models are required to optimize process design, energy savings and product quality (Mrkić et al., 2007).
Due to their simplicity, thin-layer drying models have been widely used as an important tool to describe the drying characteristics of agricultural commodities (Erbay and Icier, 2010). Some mathematical models are derived from Fick's second law of diffusion. Numerous studies have used thin-layer drying models to better understand the drying characteristics of fruits, such as apples (Akpinar et al., 2003; Zlatanović et al., 2013), peaches (Zhu and Shen, 2014), apricots (Mirzaee et al., 2009), and oranges (Rafiee et al., 2010). The approach of using thin-layer models has also been used for grains, such as rice (Steffe and Singh, 1982; Tanaka et al., 2015), green bean (Doymaz, 2005), soybean (Overhults et al., 1973; White et al., 1980), corn (Page, 1949), and vegetables, such as carrots (Doymaz, 2004), Asian white radish (Lee and Kim, 2009), garlic (Madamba et al., 1996; Piñaga et al., 1984), onion (Mazza and LeMaguer, 1980), and even mushroom (Tulek, 2011). According to a survey conducted by Erbay and Icier (2010), fruit drying has been studied most frequently (36.8%), followed by vegetables (21.8%). Unfortunately, however, these studies provide insufficient information for the drying of cucumber fruits.
Cucumber (Cucumis sativus L.), a member of the gourd family Cucurbitaceae, is a popular horticultural product due to its unique flavor, crunchy texture, and health benefits (Mohammadi and Omid, 2010). In particular, consumption of fresh cucumber not only provides vitamins, minerals, and organic acids, but it also has antioxidant, anti-inflammatory, and anti-cancer properties, which makes the fruit a nutritious product (Mukherjee et al., 2013). Cucumber fruits are typically consumed after being pickled or raw in salads, on sandwiches, and in cold soups, but they are often dried and processed into a variety of products. Dried cucumber is served as a healthy snack and cucumber powder is used as a seasoning to improve the flavor of food (Esmaeelina et al., 2016). Dried cucumber is also used as an ingredient of vegetable juice (Jayaraman and Das Gupta, 2014). Moreover, the therapeutic benefits of cucumber fruit have promoted its use in the manufacture of various cosmetic products, such as soap, lotions, and facial masks. For example, the flesh and seeds are widely used to treat various skin problems, such as wrinkles and sunburn, due to the refreshing, cooling, healing, soothing, emollient, and anti-itching effect on the skin (Mukherjee et al., 2013).
Interestingly, the endocarp and mesocarp of cucumber have considerable potential to be processed separately into dried products. The endocarp of a cucumber is the inner layer of the pericarp, which includes the ovary cavities that surround the seeds, while the mesocarp is the fleshy middle layer that is found between the endocarp and exocarp (Che and Zhang, 2019). Abulude et al. (2007) reported a significant difference in the nutritional composition of the endocarp and mesocarp in cucumber; specifically, in the protein content of the endocarp (0.22%) and the mesocarp (1.68%), the fat content of the endocarp (0.02%) and the mesocarp (0.10%), and the energy content of the endocarp (1.06%) and the mesocarp (12.42%). Also, the same study reported that the mineral composition of the endocarp and the mesocarp also differ. Therefore, it is expected that drying the pericarp layer has considerable potential for application in the food and cosmetic industries to develop a variety of products that suit the tastes of customers.
Very few studies have been undertaken to understand drying characteristics and diffusional properties using thin-layer drying models as they relate to the drying of cucumber fruit. For example, Akinola (2018) studied the drying properties of 3 mm-thick cucumber slices at different temperatures using a refractance window dryer and reported that the effective moisture diffusivity was approximately 1.94 × 10−9 to 2.54 × 10−9 m2·s−1 at drying temperatures ranging from 65 to 85 °C and an activation energy of 13.55 kJ·mol−1. Iqbal and Islam (2005) investigated the effect of temperature on the diffusivity of blanched cucumber slices in a cabinet dryer and concluded that the diffusivity varied from 1.57 × 10−10 to 1.14 × 10−9 m2·s−1, and that the activation energy was 35.6 kJ·mol−1 using Fick's second law of diffusion. However, no studies on the drying characteristics of cucumber pericarp layers has been reported in the scientific literature to date.
Knowledge of differences in the drying characteristics of cucumber endocarp and mesocarp may facilitate the manufacture of various dried cucumber products. Therefore, the objective of this study was to investigate the drying kinetics of the mesocarp and endocarp tissues in cucumber fruit at different temperatures, and to estimate the effective moisture diffusivity and activation energy in each layer using thin-layer drying models.
Sample preparation Freshly harvested cucumbers (C. sativus L.) were used for the drying experiments. The fruits were obtained from a local agricultural market (Japan Agriculture, Itoshima) in Fukuoka, Japan. After transporting promptly the cucumbers to the laboratory, the intact cucumbers were sorted according to weight and size and cleaned by wiping gently with a paper towel taking care not to physically damage the fruit. Then, the sorted cucumbers were cut into cubes for the experiment after equalizing the sample temperature to room temperature. Each experiment was replicated three times using 25 endocarp and 20 mesocarp cubes. The mean and standard deviation of the fresh weight of the cubes were 0.8856 ± 0.0808 g for the endocarp and 0.2252 ± 0.0621 g for the mesocarp.
Experimental procedure Figure 1 shows a schematic diagram of the experimental apparatus used for cucumber drying. The drying system consisted of an environmental chamber (TPAV-120-20, Isuzu Seisakusho, Japan) to keep the temperature and relative humidity (RH) of the drying-air constant. The cucumber samples were dried using a simple cylindrical convective dryer; the drying air is drawn into the dryer by a fan on the bottom and then pushed upward. The cylinder is composed of a 3 mm-thick polyvinyl chloride pipe with an internal diameter of 83 mm. A metal screen with a mesh size of 1.50 mm was fixed inside the cylinder to support the samples. The same apparatus has been used previously for thin-layer drying of rice grains by Tanaka et al. (2015).
Schematic diagram of the experimental apparatus for cucumber drying (unit: mm).
The thin-layer drying experiments were conducted at different temperatures (40, 50, and 60 °C) and a constant RH of 40%. The velocity of the air passing through the cylinder was approximately 1.4 m·s−1. Cube-shaped endocarp and mesocarp samples were prepared from the intact fruits immediately before starting the experiment; cubes were prepared using a sharp scalpel along the longitudinal direction. Figure 2 illustrates the sample shape and the sampling location along the length of the cucumber. Different dimensions of endocarp and mesocarp cubes were used in this study. Endocarp cubes measured 10 mm on each side and mesocarp cubes measured 6 mm on each side; these sizes were selected in order to obtain cubes with the largest possible volume from each pericarp layer. During the drying experiments, the variation in sample weight was recorded at 10-minute intervals using a digital balance (FX-300i, A&D Co. LTD., Tokyo, Japan; accuracy: 0.001 g) until the weight became constant. The average weight change was calculated by measuring the bulk weight of the cubes. To measure the dry mass, the cubes were transferred into a vacuum dry oven (ADP 300, Yamato Scientific Co., Tokyo, Japan) fitted with a vacuum pump (Minivac PD-52, Yamato Scientific Co., Tokyo, Japan) and dried for at least 3 days at 80 °C with a gauge pressure of −0.08 MPa. All measurements were performed in triplicate and the average values were used for calculations.
The geomety and the sampling locations of the endocarp and mesocarp cubes.
Modeling of drying kinetics Moisture content (MC) of the drying sample was measured by using Eq. (1) and was used to calculate the moisture ratio (MR) by Eq. (2):
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where, Mt is the MC at any time t (kg·kg−1, dry basis), Wt is the total weight (kg), Wd is the dry mass (kg), MR is the moisture ratio (decimal), M0 is the initial MC (kg·kg−1, dry basis), and Me is the equilibrium MC (kg·kg−1, dry basis). Me, referred to as the equilibrium moisture content in this study, was obtained when the change in wet weight was less than 0.001 g during drying. The variation in the initial MC between the two layers was statistically analyzed by using a two-sample t-test implemented in R (version 3.2.2).
The drying rate of the endocarp and mesocarp cubes was calculated by using Eq. (3):
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where, DR is the drying rate (kg·kg−1·s−1), Mt+dt is the moisture content at time t+dt (kg·kg−1, dry basis), and dt is the time increment (s).
The semi-theoretical thin-layer drying models, derived from Newton's law of cooling or Fick' law of diffusion, were employed to describe the drying kinetics of the pericarp layers. Table 1 shows the drying models used in this study and their mathematical equations. Mathematical optimization was performed to find the best model parameters by fitting the curves to the experimental data using nonlinear least square regression analysis.
| No. | Model name | Model expression | Reference |
|---|---|---|---|
| 1 | Newton model | MR = exp(−kt) | Lowis, (1921) |
| 2 | Page Model | MR = exp(−ktα) | Page, (1949) |
| 3 | Modified Page-II model | MR = exp[−(kt)α] | White et al., (1980) |
| 4 | Henderson & Pabis model | MR = α exp(−kt) | Henderson and Pabis (1961) |
| 5 | Logarithmic model | MR = α exp(−kt) + b | Prabir et al., (1995) |
| 6 | Two-term model | MR = α exp(−k1t) + b exp(−k2t) | Henderson (1974) |
| 7 | Two-term exponential model | MR = α exp(−kt) + (1 − α) exp(−kat) | Sharaf-Eldeen et al., (1980) |
| 8 | Diffusion Approximation model | MR = α exp(−kt) + (1 − α) exp(−kbt) | Yaldýz and Ertekýn (2001) |
| 9 | da Silva model |  |
da Silva et al., (2013) |
Selection of appropriate model The variation of the model was checked with several statistical methods. The coefficient of determination (R2) was used as a major criterion for evaluating the variation between experimental data and data estimated from the model. Reduced chi-square (χ2), root mean square error (RMSE), and root mean square log error (RMSLE) were also used to evaluate the goodness of fit. The highest R2 and the lowest χ2, RMSE and RMSLE are used for the best model (Erbay and Icier, 2010). The calculation of each parameter was performed using the following equations:
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where, MRexp,i is i th experimental moisture ratio, MRpre,i is ith predicted moisture ratio, MR͞exp is the average of the experimental moisture ratio, n is the number of observations, and N is the number of constants.
Shrinkage in thickness Shrinkage of porous materials is unavoidable during the drying process. This shrinkage results in significant volume reduction and modifies the thermal-physical properties, particularly the diffusion coefficient. To determine the moisture diffusivity of material in practice, correction using a shrinkage factor is required. The average thickness was defined as the mean of the longest and shortest thicknesses of the cube. Ten cubes were used in each experiment and each experiment was replicated three times. The variation in the average thickness of the mesocarp and endocarp cubes was measured using digital calipers (CD-15AX, Mitutoyo Co., Kawasaki, Japan) while the samples were drying at temperatures of 40, 50 and 60 °C. A simple linear regression analysis was utilized to estimate the shrinkage factor.
Calculation of effective moisture diffusivity Treybal (1980) introduced that a theoretical thin-layer drying model for cubic geometry can be expressed as a cubic form of the diffusion equation for a slab which was proposed by Crank (1975). Thus, the effective moisture diffusivity was calculated using Eq. (8):
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where, MR is the moisture ratio (dimensionless), Deff is the effective moisture diffusivity (m2·s−1), t is the drying time (s), L is the cube length (m), and n is a series of positive integer numbers. The same equation was employed for drying apple cubes by Zlatanović et al. (2013). Eq. (9), involving Eq. (8) as the first term of the infinite series solution to the diffusion equation, agreed well with Eq. (8) in the range of MR inferior to 0.6 when drying time is sufficiently long. Therefore, Eq. (9) can be employed to determine the effective moisture diffusivity from the slope of ln(MR) versus drying time (Lopez et al., 2000). Accordingly, the effective moisture diffusivity was determined using Eq. (10) by estimating k0 of ln(MR) from Eq. (9) versus drying time:
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Activation energy calculation The effective diffusivity of a solid at different temperatures is generally described by the Arrhenius equation (Mazza and Le Maguer, 1980; Steffe and Singh, 1982; Piñaga et al., 1984; Madamba et al., 1996):
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where, Do is the maximal diffusion coefficient (m2·s−1), R is the universal gas constant (kJ·mol−1·K−1), T is the temperature (K), and Ea is the activation energy (kJ·mol−1). Using Eq. (12), derived from Eq. (11), the activation energy was calculated by plotting ln(Deff) versus 1/T (Mirzaee et al., 2009; Rafiee et al., 2010; Zhu and Shen, 2014):
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Drying kinetics of endocarp and mesocarp The changes in the moisture ratio of the endocarp and mesocarp cubes at air temperatures of 40, 50, and 60 °C, an RH of 40%, and an airflow velocity of 1.40 m·s−1 were investigated. The average initial MC (dry basis) of each layer was approximately 24.90 kg·kg−1 (d.b.) in the endocarp and 23.58 kg·kg−1 (d.b.) in the mesocarp. The result of two-sample t-test (α = 0.05, onetailed) showed that the difference between the pericarp layers was statistically significant (p = 0.0226*) and the MC of the endocarp was slightly higher than that of the mesocarp (Table 2). A higher MC in the endocarp tissue was also reported by Abulude et al. (2007). Table 3 shows the initial and equilibrium MC values at different temperatures.
| Group | n | Mean | STD | SEM | df | t | P |
|---|---|---|---|---|---|---|---|
| Endocarp | 9 | 24.90 | 1.2300 | 0.4100 | 16 | 2.188 | 0.0226* |
| Mesocarp | 9 | 23.58 | 1.3303 | 0.4434 |
(n: number of samples; Mean: average initial moisture content; STD: standard deviation; SEM: Standard error of mean; df: degree of freedom; t: t-value; P: p-value)
| Group | Drying temperature (°C) | Endocarp (kg·kg−1, d.b.) | Mesocarp (kg·kg−1, d.b.) |
|---|---|---|---|
| Initial MC | - | 24.90 ± 1.230 | 23.58 ± 1.330 |
| Equilibrium MC | 40 | 0.321 ± 0.029 | 0.127 ± 0.013 |
| 50 | 0.093 ± 0.011 | 0.049 ± 0.005 | |
| 60 | 0.016 ± 0.002 | 0.005 ± 0.001 |
Figure 3 shows the variation in the MR of the 10 mm endocarp cubes at different temperatures. The MR of the endocarp cubes decreased exponentially over the time before becoming constant in 420, 320, and 230 min at 40, 50, and 60 °C, respectively. In the endocarp, an increase in temperature decreased drying time. Figure 4 shows the DR versus the MR of the endocarp tissue at different temperatures. The falling drying rate period was observed at all temperatures, and higher temperatures increased the DR of endocarp tissue. The maximal drying rate was observed at around 0.7 kg·kg−1 (d.b.) of MR regardless of temperature, and higher temperatures resulted in a higher drying rate.
Variations of moisutre ratio in endocarp tissue at different temperatures.
Drying rate of endocarp cubes at different temperatures.
The drying curves obtained for the 6 mm mesocarp cubes are shown in Figure 5. The MR in the mesocarp cube decreased over the drying time and remained stable at 290, 170, and 110 min at 40, 50, and 60 °C, respectively. In the mesocarp, higher temperatures also decreased drying time. Figure 6 shows the DR versus the MR of the mesocarp cubes in which the falling drying rate period was observed during drying and the DR was highest at around 0.5 kg·kg−1 (d.b.) of MR at all temperatures. In addition, the highest drying rate was observed at the highest drying temperature.
Variations of moisutre ratio in mesocarp tissue at different temperatures.
Drying rate of mesocarp cubes at different temperatures.
It is a general observation that, for any foodstuff, including cucumber fruit, higher temperatures are associated with shorter drying times and higher drying rates. This is because the higher air temperature increases the heat transfer potential between the cucumber and the dry air, which increases dehydration from the cucumber tissues. Similar findings have been reported by Lee and Kim (2009), Rafiee et al. (2010), Tulek (2011), and Zhu and Shen (2014).
Fitting and validation of drying model The established semi-theoretical drying models shown in Table 1 were fitted to the drying curves obtained for the endocarp and mesocarp cubes at different temperatures. The parameters in each model were estimated by using non-linear regression analysis. Table 4 summarizes the fitted parameters of the nine thin-layer drying models used to analyze endocarp tissues at different drying temperatures. The results show the ranges obtained for the statistical parameters used to assess model accuracy: R2 from 0.9592 to 0.9992; χ2 from 3.2653 × 10−3 to 3.8960 × 10−5 kg·kg−1 (d.b.); RMSE from 5.6424 × 10−2 to 5.9382 × 10−3 kg·kg−1 (d.b.); and RMSLE from 1.7563 × 10−2 to 2.3689 × 10−3. The best model for describing the drying characteristics was selected as the one with the highest R2 values and the lowest χ2, RMSE, and RMSLE. The two-term model and the approximation-of-diffusion model met these criteria. In the two-term model at different temperatures, the statistical parameters (R2, χ2, RMSE, and RMSLE) varied from 0.9992 to 0.99976, 3.9180 × 10−5 to 1.2703 × 10−4 kg·kg−1 (d.b.), 5.9382 × 10−3 to 1.0693 × 10−2 kg·kg−1 (d.b.), and 2.3689 × 10−3 to 4.0824 × 10−3, respectively. The parameters of the approximation-of-diffusion model ranged from 0.9992 to 0.9979, 3.8960 × 10−5 to 1.1369 × 10−3 kg·kg−1 (d.b.), 6.0030 × 10−3 to 1.0255 × 10−2 kg·kg−1 (d.b.), and 2.4001 × 10−3 to 4.0072 × 10−3, respectively, at different temperatures.
| No. | Temp. | Constants | R2 | χ2 | RMSE | RMSLE |
|---|---|---|---|---|---|---|
| 1 | 40 | k = 0.00028713 | 0.9633 | 0.00326527 | 0.05642370 | 0.01756329 |
| 50 | k = 0.00038475 | 0.9592 | 0.00268399 | 0.05115555 | 0.01557648 | |
| 60 | k = 0.00059195 | 0.9738 | 0.00117942 | 0.03519078 | 0.01094556 | |
| 2 | 40 | k = 0.00486771; a = 0.66635387 | 0.9903 | 0.00050448 | 0.02189185 | 0.00801130 |
| 50 | k = 0.00589529; a = 0.66784387 | 0.9882 | 0.00057830 | 0.02343897 | 0.00835858 | |
| 60 | k = 0.00610757; a = 0.69974061 | 0.9940 | 0.00025739 | 0.01563723 | 0.00559906 | |
| 3 | 40 | k = 0.00033833; a = 0.66640503 | 0.9903 | 0.00050448 | 0.02189185 | 0.00801048 |
| 50 | k = 0.00045884; a = 0.66788200 | 0.9882 | 0.00057830 | 0.02343896 | 0.00835792 | |
| 60 | k = 0.00068515; a = 0.69978779 | 0.9940 | 0.00025739 | 0.01563723 | 0.00559849 | |
| 4 | 40 | k = 0.00022752; a = 0.81860146 | 0.9663 | 0.00161754 | 0.03920028 | 0.01080691 |
| 50 | k = 0.00031215; a = 0.83451799 | 0.9882 | 0.00157778 | 0.03871549 | 0.01048524 | |
| 60 | k = 0.00052441; a = 0.89867051 | 0.9940 | 0.00096473 | 0.03027371 | 0.00866230 | |
| 5 | 40 | k = 0.00024474; a = 0.81774342; b = 0.01433167 | 0.9671 | 0.00159883 | 0.03845664 | 0.01100717 |
| 50 | k = 0.00032192; a = 0.83408036; b = 0.00602742 | 0.9644 | 0.00160328 | 0.03851014 | 0.01061219 | |
| 60 | k = 0.00053689; a = 0.89767962; b = 0.00494498 | 0.9754 | 0.00097360 | 0.03000960 | 0.00870054 | |
| 6 | 40 | k1 = 0.00019158; k2 = 0.11140608; a = 0.69369342; b = 0.30630460 | 0.9976 | 0.00012703 | 0.01069255 | 0.00408254 |
| 50 | k1 = 0.00024963; k2 = 0.11224304; a = 0.67017674; b = 0.32982235 | 0.9986 | 0.00008615 | 0.00880532 | 0.00355133 | |
| 60 | k1 = 0.00039488; k2 = 0.11101061; a = 0.68073546; b = 0.31926409 | 0.9992 | 0.00003918 | 0.00593821 | 0.00236893 | |
| 7 | 40 | k = 0.00111161; a = 0.20846841 | 0.9803 | 0.00152222 | 0.03802772 | 0.01150109 |
| 50 | k = 0.00155234; a = 0.20183679 | 0.9779 | 0.00131624 | 0.03536141 | 0.01050230 | |
| 60 | k = 0.00227404; a = 0.21045775 | 0.9884 | 0.00053080 | 0.02245582 | 0.00680390 | |
| 8 | 40 | k = 0.00401127; a = 0.32017656; b = 0.04687447 | 0.9979 | 0.00011369 | 0.01025476 | 0.00400716 |
| 50 | k = 0.00839994; a = 0.33133226; b = 0.02961516 | 0.9986 | 0.00008459 | 0.00884542 | 0.00357661 | |
| 60 | k = 0.00905234; a = 0.32107708; b = 0.04344209 | 0.9992 | 0.00003896 | 0.00600303 | 0.00240099 | |
| 9 | 40 | a = 0.00009797; b = 0.01274947 | 0.9940 | 0.00031199 | 0.01721606 | 0.00638709 |
| 50 | a = 0.00013099; b = 0.01495650 | 0.9921 | 0.00038487 | 0.01912132 | 0.00680722 | |
| 60 | a = 0.00023038; b = 0.01707857 | 0.9961 | 0.00016529 | 0.01253110 | 0.00449658 |
The fitted parameters of the drying models for the mesocarp cubes at 40, 50, and 60 °C are shown in Table 5. The statistical parameters were in the following ranges: 0.9678 to 0.9998 for R2; 1.6212 × 10−3 to 9.2300 × 10−6 kg·kg−1 (d.b.) for χ2; 3.9244×10−2 to 2.8820 × 10−3 kg·kg−1 (d.b.) for RMSE; and 1.2473 × 10−2 to 1.0069 × 10−3 for RMSLE. The two-term model was selected as the best model for describing the drying kinetics of cucumber mesocarp; the parameters (R2, χ2, RMSE, and RMSLE) varied from 0.9993 to 0.9998, 9.2300 × 10−6 to 2.3640 × 10−5 kg·kg−1 (d.b.), 2.8820 × 10−3 to 4.6129 × 10−3 kg·kg−1 (d.b.), and 1.0069 × 10−3 to 1.8524 × 10−3, respectively. The two-term model and the approximation-ofdiffusion model are both derived from Fick's law of diffusion (Onwude et al., 2016). Consequently, it is assumed that these models are well suited for predicting the drying characteristics that describe typical drying curves.
| No. | Temp. | Constants | R2 | χ2 | RMSE | RMSLE |
|---|---|---|---|---|---|---|
| 1 | 40 | k = 0.00060073 | 0.9678 | 0.00157960 | 0.03924420 | 0.01247340 |
| 50 | k = 0.00108645 | 0.9755 | 0.00083083 | 0.02846146 | 0.01247340 | |
| 60 | k = 0.00144407 | 0.9880 | 0.00035880 | 0.01870380 | 0.00669432 | |
| 2 | 40 | k = 0.00855990; a = 0.65737850 | 0.9948 | 0.00021679 | 0.01435092 | 0.00492290 |
| 50 | k = 0.01470979; a = 0.63748382 | 0.9967 | 0.00010768 | 0.01011419 | 0.00376352 | |
| 60 | k = 0.01249115; a = 0.68890870 | 0.9978 | 0.00006775 | 0.00802244 | 0.00311054 | |
| 3 | 40 | k = 0.00071596; a = 0.65737902 | 0.9948 | 0.00020093 | 0.01435092 | 0.00492288 |
| 50 | k = 0.00133534; a = 0.63749513 | 0.9967 | 0.00010768 | 0.01011419 | 0.00376344 | |
| 60 | k = 0.00172615; a = 0.68891635 | 0.9978 | 0.00006775 | 0.00802244 | 0.00311051 | |
| 4 | 40 | k = 0.00052051; a = 0.88577456 | 0.9690 | 0.00120226 | 0.03379569 | 0.00983752 |
| 50 | k = 0.00102465; a = 0.94972604 | 0.9755 | 0.00078603 | 0.02732624 | 0.00913244 | |
| 60 | k = 0.00141431; a = 0.97878458 | 0.9880 | 0.00035644 | 0.01840145 | 0.00649740 | |
| 5 | 40 | k = 0.00054527; a = 0.88475444; b = 0.00910186 | 0.9694 | 0.00117718 | 0.03299836 | 0.00974166 |
| 50 | k = 0.00105567; a = 0.94710396; b = 0.00633603 | 0.9757 | 0.00077338 | 0.02674654 | 0.00902774 | |
| 60 | k = 0.00143128; a = 0.97679055; b = 0.00294449 | 0.9880 | 0.00035799 | 0.01819725 | 0.00645880 | |
| 6 | 40 | k1 = 0.00037065; k2 = 1.06782505; a = 0.64136980; b = 0.35862918 | 0.9998 | 0.00000923 | 0.00288196 | 0.00100693 |
| 50 | k1 = 0.00060101; k2 = 1.10576816; a = 0.56691526; b = 0.43308502 | 0.9996 | 0.00001439 | 0.00359909 | 0.00140110 | |
| 60 | k1 = 0.00087071; k2 = 1.09539618; a = 0.58483614; b = 0.41516302 | 0.9993 | 0.00002364 | 0.00461287 | 0.00185243 | |
| 7 | 40 | k = 0.00060073; a = 1.00067462 | 0.9678 | 0.00162117 | 0.03924420 | 0.01247340 |
| 50 | k = 0.00329574; a = 0.25486522 | 0.9883 | 0.00039635 | 0.01940451 | 0.00654009 | |
| 60 | k = 0.00406483; a = 0.27465689 | 0.9950 | 0.00015097 | 0.01197605 | 0.00419366 | |
| 8 | 40 | k = 0.01080426; a = 0.35986082; b = 0.03426426 | 0.9998 | 0.00000930 | 0.00293232 | 0.00102581 |
| 50 | k = 0.00108645; a = 1.32973039; b = 0.99999855 | 0.9755 | 0.00087574 | 0.02846146 | 0.00983410 | |
| 60 | k = 0.00144406; a = 1.44894393; b = 0.99999525 | 0.9880 | 0.00037820 | 0.01870380 | 0.00669432 | |
| 9 | 40 | a = 0.00018246; b = 0.01966183 | 0.9967 | 0.00013495 | 0.01132252 | 0.00379217 |
| 50 | a = 0.00027133; b = 0.02912069 | 0.9977 | 0.00007607 | 0.00850098 | 0.00312757 | |
| 60 | a = 0.00049146; b = 0.03005228 | 0.9983 | 0.00005105 | 0.00696424 | 0.00269993 |
Effective moisture diffusivity of endocarp and mesocarp The effective moisture diffusivity under different drying conditions was estimated by plotting ln(MR) versus drying time and using the slope method. The slope of the regression equation was calculated by using the data within the period when the drying rate decreased. The calculated effective moisture diffusion coefficients, the MR range, and their R2 values are shown in Table 6. Figure 7 shows the semi-log plot of the MR in the 10 mm endocarp and 6 mm mesocarp tissues at different temperatures. The bold lines in Figure 7 indicate the values obtained by substituting the values of Deff, estimated using the slope method. In the endocarp tissues, the effective diffusivity ranged from 5.0921 × 10−10 m2·s−1 at 40°C to 1.1426 × 10−9 m2·s−1 at 60°C. In mesocarp tissues, the effective diffusivity ranged from 3.9123 × 10−10 to 8.9376 × 10−10 m2·s−1 as the temperature increased from 40 to 60 °C. It was observed that the diffusivities in the endocarp were larger than those in the mesocarp, and that variations increased gradually with an increase in temperature. All of the calculated diffusion coefficients ranged from 4.00 × 10−13 to 6.10 × 10−7 m2·s−1, which corresponded to the diffusivity in fruit (Panagiotou et al., 2004); similar trends were reported by Iqbal and Islam (2005) and Akinola (2018). Moreover, the diffusivity coefficients were in good agreement with previous studies, such as those on apple slices by Akpinar et al. (2003) and carrot slices by Doymaz (2004).
| Pericarp layer | Temperature (°C) | MR range (decimal) | Effective moisture diffusivity (m2·s−1) | R2 |
|---|---|---|---|---|
| Endocarp | 40 | 0.7143 – 0.0794 | 5.0921 × 10−10 | 0.9933 |
| 50 | 0.6647 – 0.0812 | 7.7907 × 10−10 | 0.9820 | |
| 60 | 0.6252 – 0.0859 | 1.1426 × 10−9 | 0.9904 | |
| Mesocarp | 40 | 0.6082 – 0.0774 | 3.9123 × 10−10 | 0.9869 |
| 50 | 0.5122 – 0.0804 | 6.1813 × 10−10 | 0.9993 | |
| 60 | 0.4585 – 0.0915 | 8.9376 × 10−10 | 0.9652 |
Semi-log plot of moisture ratio versus drying time and theoretical lines from the Fick's equation.
Figures 8 and 9 show the variation in the thickness versus the MR of the endocarp and the mesocarp, respectively. The endocarp cubes shrank linearly from 6 mm to about 2 mm, whereas the mesocarp cubes shrank from 10 mm to approximately 5 mm. This trend has reported as being typical for the shrinkage of foodstuffs (Mahiuddin et al., 2018). To obtain actual effective diffusivity, the regression models for the average thickness variation were applied to modified diffusion coefficients.
Regression analysis of average thickness versus MR in endocarp.
Regression analysis of average thickness versus MR in mesocarp.
 |
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where, LE and LM are the estimated variation in thickness of the mesocarp and endocarp cubes, respectively (mm). The determination coefficients were estimated to be 0.9740 for the endocarp and 0.9795 for the mesocarp. The effective diffusion coefficients were corrected by applying these regression models to Eq. (9). Figures 10 and 11 show the corrected effective moisture diffusivity curves. The model correction resulted in larger coefficients being obtained for the mesocarp than the endocarp, which was the opposite of the results obtained without considering shrinkage. In the endocarp, the peaks in diffusivity ranged from 5.8236 × 10−8 m2·s−1 at 40 °C to 8.1218 × 10−8 m2·s−1 at 60 °C. In the mesocarp, the peaks in diffusivity ranged from 2.4316 × 10−7 m2·s−1 at 40 °C to 3.8140 × 10−7 m2·s−1 at 60 °C. The higher diffusivity in mesocarp has already been reported by Tanaka et al. (2018) using an X-ray CT machine. The modified effective diffusivities decreased exponentially as drying processed. Similar findings have been reported by Rani and Tripathy (2019) and Hassini et al. (2007).
The variation of the effective moisture diffusivity in endocarp with considering shrinkage.
The variation of the effective moisture diffusivity in endocarp with considering shrinkage.
Activation energy of endocarp and mesocarp The activation energy of moisture diffusivity was determined from the slope of the regression line of ln(Deff) against 1/T, which is shown in Figure 12. A similar slope was observed in the endocarp, which means the effective moisture diffusivities in both pericarp layers are affected equally by temperature variations. Consequently, the activation energy was calculated to be 35.03 kJ·mol−1 in the endocarp and 35.82 kJ·mol−1 in the mesocarp (Table 7). These values were in good agreement with the results obtained for cucumber slices, which was investigated by Iqbal and Islam (2005). The similar value obtained for the activation energy estimated in this study have already been reported for apple pomace by Sun et al. (2007), carrot slices by Doymaz (2004), and pistachio nuts by Kashaninejad et al. (2007).
Semi-log plot of ln(Deff) versus 1/T of endocarp and mesocarp.
| Pericarp layer | Activation energy (kJ·mol−1) | R2 |
|---|---|---|
| Endocarp | 35.03 | 0.9998 |
| Mesocarp | 35.82 | 0.9981 |
In this study, the drying characteristics of mesocarp and endocarp tissues in cucumber fruit were investigated and a mathematical equation describing cucumber drying was developed using established thin layer drying models. The 10 mm endocarp cubes and 6 mm mesocarp cubes were dried at 40, 50, and 60 °C, at an RH of 40%, and an air velocity of 1.40 m·s−1 using a cylindrical convective dryer. The initial moisture content in the endocarp was slightly higher than that in the mesocarp. Higher temperatures increased drying rates in both layers. Mathematical models describing the drying kinetics of cucumber pericarps was developed by using established semi-theoretical thin-layer drying models. The variation in the MR was successfully described by the two-term model for both pericarp layers, which is derived from Fick's law of diffusion. The effective moisture diffusivities with and without considering shrinkage were estimated from drying curves by using a thin-layer drying model for a cube. The values obtained for the endocarp cubes ranged from 5.0921 × 10−10 to 1.1426 × 10−9 m2·s−1, while those obtained for the mesocarp cubes ranged from 3.9123×10−10 to 8.9376×10−10 m2·s−1 with an increase of temperature from 40 to 60 °C. The calibrated peak effective moisture diffusivities ranged from 5.8236 × 10−8 m2·s−1 at 40 °C to 8.1218 × 10−8 m2·s−1 at 60 °C in the endocarp, and from 2.4316 × 10−7 m2·s−1 at 40°C to 3.8140×10−7 m2·s−1 at 60°C in the mesocarp. The activation energy of cucumber was calculated using the Arrhenius equation and the value was estimated to be 35.03 kJ·mol−1 in the endocarp and 35.82 kJ·mol−1 in the mesocarp.
Acknowledgements This work was supported by the Cabinet Office, Government of Japan, Cross-ministerial Strategic Innovation Promotion Program (SIP), “Technologies for Smart Bio-industry and Agriculture” (funding agency: Bio-oriented Technology Research Advancement Institution, NARO).
