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Mathematical modeling of drying characteristics of Jew’s mallow (Corchorus olitorius) leaves
Accepted Manuscript Mathematical modeling of drying characteristics of Jew’s mallow (Corchorus olitorius) leaves Adewale Olusegun Omolola, Patrick Francis Kapila, Henry Mbitha Silungwe PII: DOI: Reference:
S2214-3173(18)30105-7 https://doi.org/10.1016/j.inpa.2018.08.003 INPA 153
To appear in:
Information Processing in Agriculture
Received Date: Revised Date: Accepted Date:
21 March 2018 5 August 2018 13 August 2018
Please cite this article as: A. Olusegun Omolola, P. Francis Kapila, H. Mbitha Silungwe, Mathematical modeling of drying characteristics of Jew’s mallow (Corchorus olitorius) leaves, Information Processing in Agriculture (2018), doi: https://doi.org/10.1016/j.inpa.2018.08.003
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Mathematical modeling of drying characteristics of Jew’s mallow (Corchorus olitorius) leaves Adewale Olusegun Omolola*1 Patrick Francis Kapila1 Henry Mbitha Silungwe2 1
Department of Agricultural & Rural Engineering, 2Department of Food Science & Technology, School of Agriculture, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa *Corresponding author: [email protected]
ABSTRACT Drying behaviour of Jew’s mallow leaves using an oven dryer was studied. The influence of drying temperatures (50, 60 and 70 ⁰ C) on moisture content of the leaves at stable air velocity was considered. Five drying models, including, simple exponential, Page, Two-term exponential, Logarithmic, and Wang and Singh were fitted to drying data. Two-term exponential model adequately express the drying behaviour of Jew’s mallow leaves. Eff ective moisture diff usivity of Jew’s mallow leaves ranged from 8.18×10 -8 to 1.13×10-7 m2/s. Dependence of the computed eff ective diff usivity on oven temperature was obvious. The energy required for oven drying of Jew’s mallow leaves was found to be 14.84 kJ/mol. The L*, a*, b*, ΔE, a*/b* colour characteristics of the dried leaves range from 31.8 to 32.87, -3.73 to -4.37, 13.6 to 16.47, 69.00 to 69.73, and -0.26 to -0.34 respectively. Oven drying conditions of 50 ⁰ C 150 min and 70 ⁰ C 90 min resulted to dried leaves with desirable colour characteristics.
Keywords: Jew’s mallow; Oven drying; Mathematical modeling; Colour; Eff ective diff usivity; Activation energy
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1.
Introduction
Jew’s mallow (Corchorus olitorius), a member of Tiliaceae family is a yearly aromatic plant. The plant is about 1.5 m tall with angular stems. The leaves have jagged borders and dissimilar hairy teeth at the bottom. Its dazzling yellow flowers are more often than not very tiny and the fruit is a straight, pointed capsule [1]. Jew’s mallow seed shows elevated levels of drowsiness which can be busted or revived by using hot water treatment [2]. Jew’s mallow plant thrives best in locations with high precipitation of about 2000 mm and high temperature ranging from 25 to 30°C. Cooked Jew’s mallow has a sliming feel, similar to okra. The inclusion of Jew’s mallow to the preparation of coarse-textured leaves like cowpeas makes it convenient for elderly folks to ingest the vegetables. Dehydration is considered as an ancient method of food conservation. It represents a significant phase of food processing which can naturally be carried out through the use of direct sunlight. However, drying operation using direct sunlight is impossible to achieve everywhere and at every time. Moreover spreading out food products thinly on the floor exposes them to damaging climatic condition. Furthermore, conducting drying operation in an open air can expose food products to diverse forms of contamination [3,4]. In reference to the mentioned
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reasons, the use of mechanical drying equipment’s which includes hot air dryers for drying operation seems unavoidable [5]. Previous studies carried out on mathematical modeling of drying behaviour of different vegetables include garlic, eggplant, red pepper, dill and parsley leaves, onion, and broccoli [6,7,8,9,4,5]. Drying of Jew’s mallow leaves can help extend it shelf life during storage and diversify its utilization as foodstuff and ingredients. There is no study pertinent to modeling drying characteristics of Jew’s mallow found in the literature. Hence the aim of this study is to investigate the drying characteristics of Jew’s mallow leaves, determine the effective moisture diffusivity, activation energy of drying process and the impact of drying conditions on the colour quality of the dried leaves.
2. Materials and methods 2.1. Preparation of material Fresh Jew’s mallow leaves purchased from a vegetable farmer in Thohoyandou, Limpopo province, South Africa were used in this study. The leaves were rinsed with water to remove soil particles. Drying experiments were conducted using a cabinet dryer (Labotec instrument-model 278) installed at University of Venda, Thohoyandou, South Africa.
2.2. Drying experiment Prior to drying experiments, the original moisture content of Jew’s mallow leaves was determined using oven drying method. The leaves sample was weighed into a pre-dried moisture pan covered and placed in an oven drier at 105 ⁰ C for 24 h. The initial and final weights of the leaves sample were obtained thereafter and the moisture content was calculated using Equation 1 [10].
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MC %
Wo Wd 100 Wo
(1)
where MC , Wo and Wd is the moisture content (%), weight (g) of sample and dried sample respectively. The original moisture present in the leaves was found to be 76.66% (w.b.) while the final moisture content of the dried samples was in the range of 5.1–5.2% (w/w). The oven temperatures used to determine the drying characteristics of Jew’s mallow leaves were 50, 60 and 70 ⁰ C. Fresh leaves of Jew’s mallow (30 g) was used for each experimental run. The velocity of air in the dryer was maintained at 1.1 m/s. Jew’s mallow leaves with width: 1.75 ± 0.1 cm were spread evenly in a drying pan and placed in the oven after it had achieved the stable conditions for the set temperatures. The reduction in moisture content of the leaves was constantly monitored at fixed intervals (10 min) during the drying process. Drying was persistent till a constant moisture drop in samples was noticed. Following every drying operation, the obtained dried leaves were cooled and preserved in a sealable polyethylene bags. The packaged samples were stored at -20 ⁰ C prior to further analysis. All the drying experiments were carried out twice.
2.3. Modeling of drying curves The experimental moisture content data were computed as moisture ratio (MR) using Eq. 2 [11].
MR
M Mo
(2)
where M is the moisture content at different time and Mo is the initial moisture content. In order to efficiently ascertain the drying kinetics of Jew’s mallow leaves, there is need to fit the drying behavior with different mathematical models. Five mathematical equations listed 4
in Table 1 were used for this purpose. The curve fitting of the hot air drying data was achieved with aid of a MATLAB software version 7.11.0.584.
Model
Table 1 - Models applied to the oven drying curves of Jew’ mallow leaves Equation References
Simple exponential
MR a exp kt
Doymaz [12]
Two-term exponential
MR a exp kt b exp gt
Omolola et al. [13]
Logarithmic
MR a exp kt c
Astiani et al. [14]
Wang & Singh
MR 1 at bt 2
Miranda et al. [11]
Page
MR exp kt n
Ganesapillai et al. [15]
2.3.1 Statistical analysis The sum of square error (SSE), root mean square error (RMSE) and coefficient of determination (R2), and were used to verify the reliability of the fits. The criteria used for picking the most excellent and reliable model was based on the highest value of R2 and the lowest values RMSE and SSE [16,17]. The statistical parameters were computed using Equations 3-5 respectively. N is the number of observations, MR cal,i is the predicted moisture ratio, MRexp,i is the experimental moisture ratio, and n is the number of constants.
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N N . MR MR MR MR i cal , i i exp, i i 1 i 1 R2 2 2 N N MR MR MR MR . i cal , i i exp, i i 1 i 1
(3)
1 2 2 1 N RMSE MR MR cal , i exp, i N i 1
(4)
SSE MRcal ,i MRexp,i
(5)
N
i 1
2.4. Determination of effective moisture diffusivity and activation energy Effective moisture diffusivity was determined using Equations 6-8 respectively as described by Doymaz [12].
2 2n 12 8 1 MR exp D t eff 2 2 2 n 0 2n 1 4L
(6)
where Equation (6) relies on the postulation that the moisture distribution in the samples is uniform and has a stable diff usivity with negligible shrinkage: The slope (φ) obtained from plotting ln (MR) against time is used in Equation 8 to compute the moisture diffusivity of the samples
2 8 Deff In MR In 2 4 L2
t
(7)
2D
eff 4 L2
(8)
where MR is moisture ratio, Deff is the effective moisture diffusivity (m²/s) and L is the halfthickness (m) of the samples. 6
2.5. Determination of activation energy The activation energy of the drying process was obtained using Equations 9-11 [4].
E a D Do exp eff R T 273.15
(9)
Equation 9 could be expressed or re-written as Equation 10 by taking the logarithm of both sides E a In D In Do (10) RT eff abs lnDeff were plotted against the absolute values of the given temperatures (50, 60 and 70 ⁰ C). The slope (k) of the plot is equal to (-Ea/R).
k
Ea R
(11)
where Do is the Arrhenius factor (m2/s), Ea is the activation energy (kJ/mol), R is the universal gas constant (8.314 × 10-3 kJ/mol K), k is slope and T is the oven temperature (⁰ C).
3. Results and discussion 3.1. Drying characteristics of Jew’s mallow leaves The drying curve of Jew’s mallow leaves at dissimilar oven temperatures is presented in figure 1. Moisture content of the samples reduced from initial 76.66% (w.b.) to 18.33%, 7.10%, and 6.50% (w.b.) at a drying temperature of 50, 60 and 70 ⁰ C, respectively. The experimental data obtained from drying Jew’s mallow leaves at oven temperatures 50, 60, and 70 ⁰ C were analysed with regards to drop in moisture ratio with drying time. According to Ashtiani et al. [14], moisture ratio curves rather than moisture content curves are more appropriate in unfolding the drying characteristics of foodstuffs. The time needed to decrease the moisture present in the
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samples to a definite point was reliant on drying temperature, being the maximum at 50 ⁰ C (150 min) and lowest at 70 ⁰ C (90 min). A short constant rate drying period at 0 to 10 min (Figure 1) was observed for all the drying temperatures used. This is could be attributed to the short initial settling down period of the samples in the oven as the surface of the samples heats up to wet bulb temperature. Furthermore, it can be deduced from the drying curves presented in figure 1 that drying of Jew’s mallow leaves occurred largely in the falling rate drying period. Generally, during the falling rate period, the rate of water movement from the interior to the surface falls below the rate which water evaporates to the surrounding air, therefore sample surface dries out. This suggests that moisture diffusivity in the samples was predominantly through diffusion mechanism. Similar remarks were reported for spinach leaves, peppermint leaves, persimmon slices, avishan leaves, and rosy garlic leaves [16, 14, 18, 19, 20].
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1.2
1
50°C 60°C 70°C
Moisture ratio
0.8
0.6
0.4
0.2
0 0
20
40
60
80 Time (min)
100
120
140
Fig. 1- Oven drying curves of Jew’s mallow leaves at different temperatures
3.2. Modeling of the drying curves The experimental moisture contents were converted to more functional moisture ratio [14]. Thereafter the curves obtained from plotting the moisture ratios against drying time were fitted with mathematical models listed in Table 1. The outcome of the statistical analyses applied to the curve fits to determine the adequacy, reliability and consistency of the models are outlined in Table 2. The model having the highest R2 value and the lowest RMSE and SSE values was chosen as the most excellent model. The mean values of R2, SSE and RMSE of the tested mathematical models were in the range of 0.9239-0.9836, 0.0124-0.0574, and 0.0392-0.0750 respectively. Amongst the tested models, the Two-term exponential model satisfied the criterion 9
160
for choosing the superlative model as its coefficient of determination (R2) {0.9836} was the highest while its SSE {0.0124} and RMSE {0.0392} values were the lowest. The Two-term exponential curve fit for Jew’s mallow drying characteristics 50, 60, and 70 ⁰ C is as shown in figure 2. The adequacy, reliability and consistency of Two-term exponential model was substantiated by plotting the calculated moisture ratios obtained from the model against the experimental moisture ratio data at 50, 60, and 70 ⁰ C as shown in Figs. 3a, 3b, and 3c respectively. The coefficients of correlation of the straight lines obtained were 0.9890, 0.9680, and 0.9670. This implies good correlation between the predicted moisture ratios obtained from Two-term exponential model and experimental moisture ratios. Hence the model is adequate, reliable and suitable for predicting the drying kinetics of Jew’s mallow leaves using oven drying method.
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Table 2 - Modeling of drying curves of Jew’s mallow leaves Model
Wang & Singh
R2
SSE
RMSE
b = 4.32E-05
0.9859
0.0149
0.0326
a = -0.0161
b = 9.12E-05
0.9641
0.0277
0.0526
a = -0.0232
b = 0.0001
0.9616
0.0258
0.0568
0.9705
0.0228
0.0473
Temperature (⁰ C)
Constants
50
a = -0.0114
60 70
Average
Simple exponential
50
a = 1.024
k = -0.0123
0.9732
0.0285
0.0451
60
a = 1.009
k = -0.0151
0.9144
0.0659
0.0812
70
a = 0.973
k = -0.0213
0.8843
0.0779
0.0987
0.9239
0.0574
0.0750
Average
Two-term exponential
50
a = 1.106
k = 0.0196
b =0.0771
g = 0.0056
0.9940
0.0063
0.0229
60
a = 1.206
k = 0.0349
b =0.1251
g = 0.0077
0.9791
0.0161
0.0449
70
a = 1.333
k = 0.0649
b =0.1806
g = 0.0051
0.9777
0.0150
0.0500
0.9836
0.0124
0.0392
Average
Page
50
k = 0.0138
n = 0.9663
0.9724
0.0293
0.0457
60
k = 0.0245
n = 0.8792
0.9208
0.0610
0.0781
70
k = 0.0546
n = 0.7603
0.9097
0.0608
0.0872
0.9343
0.0504
0.0703
Average
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Logarithmic
50
a = 0.9168
b = 0.0181
c = 0.0152
0.9859
0.0149
0.0339
60
a = 0.8437
b = 0.0291
c = 0.2367
0.9560
0.0339
0.0614
70
a = 0.8271
b = 0.0447
c = 0.2303
0.9545
0.0306
0.0661
0.9655
0.0265
0.0538
Average
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a
1
Moisture ratio
M oisture ratio vs. Time Two term exponential
0.8 0.6 0.4
0
50
100
150
Time (min)
b
1
M oisture ratio vs. Time
Moisture ratio
Two term exponential
0.8
0.6
0.4 0
20
40
60
80
100
Time (min)
c
1 M oisture ratio vs. Time
Moisture ratio
Two term exponential
0.8
0.6
0.4
0
10
20
30
40
50
60
70
80
90
Time (min)
Fig. 2- Two-term exponential curve fit for Jew’s mallow drying curves at 50 (a), 60 (b) and 70 ⁰ C (c).
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a
1.2 y = 0.988x + 0.005 R² = 0.9890
MRpredicted
1 0.8 0.6 0.4 0.2 0 0
0.2
0.4 0.6 0.8 MRexperimental
1
1.2
b 1.2 y = 0.965x + 0.017 R² = 0.9680
MRpredicted
1 0.8 0.6 0.4 0.2 0 0
c
0.2
0.4 0.6 0.8 MRexperimental
1
1.2
1.2 y = 0.964x + 0.016 R² = 0.9670
MRpredicted
1 0.8 0.6 0.4 0.2 0 0
0.2
0.4 0.6 0.8 MRexperimental
1
1.2
Fig. 3 - Validation of Two-term exponential model for predicting the oven drying characteristics of Jew’s mallow leaves at 50 (a), 60 (b) and 70 ⁰ C (c).
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3.3. Effective moisture diffusivity and activation energy According to Nachaisin et al. [21], the effective moisture diffusivity of food stuffs depicts their intrinsic moisture migration characteristics which include diverse parameters like liquid, molecular, vapour and hydrodynamic diffusion. The Deff values of Jew’s mallow leaves obtained from Equation 6 under different temperatures is presented in figure 3. The Deff of Jew’s mallow ranged from 8.18×10-8 and 1.13× 10-7 m2/s. These values are consistent with the range reported by Zogzas et al. [22] for agricultural foodstuffs. It could also be observed from figure 4 that Deff of Jew’s mallow leaves augmented as the drying temperature rises. This is can be credited to the rise in vapour pressure of the leaves which in turn enhanced moisture migration at elevated temperatures [23]. The activation energy for oven drying Jew’s mallow leaves as computed from the slope obtained from the plot of InD eff against absolute temperature (Fig. 5) was found to be 14.84 kJ/mol. According Xiao et al. [24], the activation energy, for a typical drying operation range from 12.7 to 110 kJ/mol. The activation energy obtained in this study is lesser than the activation energies reported by Khazael et al. [19], Ben Haj Said et al. [20], Kaya & Aydin [25], and
Doymaz [26] for avishan leaves (38.6–51.1 kJ/mol), rosy garlic leaves (46.80–52.68
kJ/mol), nettle leaves (79.873– 109.003 kJ/mol) and banana slices (32.65 kJ/mol) respectively. However, the value of activation energy obtained for drying Jew’s mallow leaves in the present study was observed to be greater than the value reported by Premi et al. [27] for drum-stick leaves (12.50 kJ/mol).
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1.20E-07
y = 2E-09x + 2E-09 R² = 0.950
1.00E-07 Deff (m2/s)
8.00E-08 6.00E-08
4.00E-08 2.00E-08 0.00E+00 0
20
40 Temperature (oC)
60
80
Fig. 4 - Influence of oven temperature on the effective moisture diffusivity of Jew’s mallow leaves 1/T (1/K) 0.0029 -15.95
0.00295
0.003
0.00305
0.0031
0.00315
-16 -16.05
lnDeff
-16.1
y = -1785.3x - 10.813 R² = 0.959
-16.15
-16.2 -16.25 -16.3 -16.35 -16.4
Fig. 5 - Arrhenius-type relationship between logarithm of eff ective moisture diff usivity and absolute temperature.
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3.4. Colour of dried leaves Colour is avital quality characteristic in foodstuff to nearly every consumer. It serves as an indicator of the intrinsic good qualities [4]. The relationship of colour with consumer acceptability of foodstuffs is common and inevitable [4]. Generally drying operation changes the surface characteristics of foods and hence alters their reflectivity and colour [28].The colour of dried Jew’s mallow leaves was determined using a Hunterlab colorimeter (ColorFlex, Hunter Lab, USA). Calibration of the colorimeter was ensured previous to colour determination experiments. The colours were depicted as L* a* and b*representing lightness, redness, and yellowness respectively. The colour data of dried Jew’s mallow leaves is shown in Table 3. The mean colour varied across the applied drying temperatures and time range. This variation was expected as dissimilar drying conditions were used in this study. L*, a*, b* ΔE, and a*/b* ranged from 31.8 to 32.87, -3.73 to -4.37, 13.6 to 16.47, 69.00 to 69.73, and -0.26 to -0.34 respectively. According to Doymaz et al. [4], higher L* and lower a*/b* are required in dried foodstuff. For this study, samples dried at 50 ⁰ C 150 min and 70 ⁰ C 90 min had higher L* and lower a*/b* values. This suggests that 50 ⁰ C 150 min and 70 ⁰ C 90 min can be taken as the optimum oven temperatures for drying Jew’s mallow leaves. Furthermore, colour change (ΔE) was prominent in samples dried at 60 ⁰ C compared to samples dried at 50 and 70 ⁰ C. According to Fellows [28], colour change in fruit and vegetables is caused by heat and oxidation during drying and residual polyphenol oxidase enzyme activity which results to browning during storage. Table 3 - Colour quality of dried Jew’s mallow leaves Temperature (0C) Time (min) L* a* 50 150 32.63±2.67 -3.73±1.19 60 110 31.8±1.50 -4.7±0.17 70 90 32.87±1.40 -4.37±0.51
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b* 14.03±1.62 13.6±1.14 16.47±0.60
ΔE 69.00±2.29 69.73±1.35 69.27±1.43
a*/b* -0.26±0.06 -0.34±0.02 -0.26±0.03
4. Conclusions Oven drying characteristics of Jew’s mallow leaves was investigated. The study revealed that drying duration decreased conspicuously as oven temperature increased. Drying of Jew’s mallow leaves occurred primarily in the falling rate period. This suggests that diffusion mechanism was principally responsible for moisture migration from the leaves. The curve fitting revealed that the Two-term exponential model adequately predicted the drying behaviour of oven drying of Jew’s mallow leaves as it had the highest R2 value and lowest SSE and RMSE values. The Deff values ranged from 8.18× 10 -8 to 1.13× 10-7 m2/s within the applied oven temperatures (50, 60 and 70 ⁰ C ). Activation energy required to get rid of moisture within the leaves throughout the oven drying process was found to be 14.84 kJ/mol. Colour analysis carried out on the dried leaves suggest that drying conditions of 50 ⁰ C 150 min and 70 ⁰ C 90 min can be taken as the optimum oven temperatures for drying Jew’s mallow leaves. This study presents functional insights on drying of Jew’s mallow leaves, thereby contributing to knowledge and literature.
Funding statement This work was funded by the University of Venda postdoctoral research fellowship, Thohoyandou, South Africa.
Competing interest statement The authors declare no conflict of interest.
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S2214-3173(18)30105-7 https://doi.org/10.1016/j.inpa.2018.08.003 INPA 153
To appear in:
Information Processing in Agriculture
Received Date: Revised Date: Accepted Date:
21 March 2018 5 August 2018 13 August 2018
Please cite this article as: A. Olusegun Omolola, P. Francis Kapila, H. Mbitha Silungwe, Mathematical modeling of drying characteristics of Jew’s mallow (Corchorus olitorius) leaves, Information Processing in Agriculture (2018), doi: https://doi.org/10.1016/j.inpa.2018.08.003
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Mathematical modeling of drying characteristics of Jew’s mallow (Corchorus olitorius) leaves Adewale Olusegun Omolola*1 Patrick Francis Kapila1 Henry Mbitha Silungwe2 1
Department of Agricultural & Rural Engineering, 2Department of Food Science & Technology, School of Agriculture, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa *Corresponding author: [email protected]
ABSTRACT Drying behaviour of Jew’s mallow leaves using an oven dryer was studied. The influence of drying temperatures (50, 60 and 70 ⁰ C) on moisture content of the leaves at stable air velocity was considered. Five drying models, including, simple exponential, Page, Two-term exponential, Logarithmic, and Wang and Singh were fitted to drying data. Two-term exponential model adequately express the drying behaviour of Jew’s mallow leaves. Eff ective moisture diff usivity of Jew’s mallow leaves ranged from 8.18×10 -8 to 1.13×10-7 m2/s. Dependence of the computed eff ective diff usivity on oven temperature was obvious. The energy required for oven drying of Jew’s mallow leaves was found to be 14.84 kJ/mol. The L*, a*, b*, ΔE, a*/b* colour characteristics of the dried leaves range from 31.8 to 32.87, -3.73 to -4.37, 13.6 to 16.47, 69.00 to 69.73, and -0.26 to -0.34 respectively. Oven drying conditions of 50 ⁰ C 150 min and 70 ⁰ C 90 min resulted to dried leaves with desirable colour characteristics.
Keywords: Jew’s mallow; Oven drying; Mathematical modeling; Colour; Eff ective diff usivity; Activation energy
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1.
Introduction
Jew’s mallow (Corchorus olitorius), a member of Tiliaceae family is a yearly aromatic plant. The plant is about 1.5 m tall with angular stems. The leaves have jagged borders and dissimilar hairy teeth at the bottom. Its dazzling yellow flowers are more often than not very tiny and the fruit is a straight, pointed capsule [1]. Jew’s mallow seed shows elevated levels of drowsiness which can be busted or revived by using hot water treatment [2]. Jew’s mallow plant thrives best in locations with high precipitation of about 2000 mm and high temperature ranging from 25 to 30°C. Cooked Jew’s mallow has a sliming feel, similar to okra. The inclusion of Jew’s mallow to the preparation of coarse-textured leaves like cowpeas makes it convenient for elderly folks to ingest the vegetables. Dehydration is considered as an ancient method of food conservation. It represents a significant phase of food processing which can naturally be carried out through the use of direct sunlight. However, drying operation using direct sunlight is impossible to achieve everywhere and at every time. Moreover spreading out food products thinly on the floor exposes them to damaging climatic condition. Furthermore, conducting drying operation in an open air can expose food products to diverse forms of contamination [3,4]. In reference to the mentioned
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reasons, the use of mechanical drying equipment’s which includes hot air dryers for drying operation seems unavoidable [5]. Previous studies carried out on mathematical modeling of drying behaviour of different vegetables include garlic, eggplant, red pepper, dill and parsley leaves, onion, and broccoli [6,7,8,9,4,5]. Drying of Jew’s mallow leaves can help extend it shelf life during storage and diversify its utilization as foodstuff and ingredients. There is no study pertinent to modeling drying characteristics of Jew’s mallow found in the literature. Hence the aim of this study is to investigate the drying characteristics of Jew’s mallow leaves, determine the effective moisture diffusivity, activation energy of drying process and the impact of drying conditions on the colour quality of the dried leaves.
2. Materials and methods 2.1. Preparation of material Fresh Jew’s mallow leaves purchased from a vegetable farmer in Thohoyandou, Limpopo province, South Africa were used in this study. The leaves were rinsed with water to remove soil particles. Drying experiments were conducted using a cabinet dryer (Labotec instrument-model 278) installed at University of Venda, Thohoyandou, South Africa.
2.2. Drying experiment Prior to drying experiments, the original moisture content of Jew’s mallow leaves was determined using oven drying method. The leaves sample was weighed into a pre-dried moisture pan covered and placed in an oven drier at 105 ⁰ C for 24 h. The initial and final weights of the leaves sample were obtained thereafter and the moisture content was calculated using Equation 1 [10].
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MC %
Wo Wd 100 Wo
(1)
where MC , Wo and Wd is the moisture content (%), weight (g) of sample and dried sample respectively. The original moisture present in the leaves was found to be 76.66% (w.b.) while the final moisture content of the dried samples was in the range of 5.1–5.2% (w/w). The oven temperatures used to determine the drying characteristics of Jew’s mallow leaves were 50, 60 and 70 ⁰ C. Fresh leaves of Jew’s mallow (30 g) was used for each experimental run. The velocity of air in the dryer was maintained at 1.1 m/s. Jew’s mallow leaves with width: 1.75 ± 0.1 cm were spread evenly in a drying pan and placed in the oven after it had achieved the stable conditions for the set temperatures. The reduction in moisture content of the leaves was constantly monitored at fixed intervals (10 min) during the drying process. Drying was persistent till a constant moisture drop in samples was noticed. Following every drying operation, the obtained dried leaves were cooled and preserved in a sealable polyethylene bags. The packaged samples were stored at -20 ⁰ C prior to further analysis. All the drying experiments were carried out twice.
2.3. Modeling of drying curves The experimental moisture content data were computed as moisture ratio (MR) using Eq. 2 [11].
MR
M Mo
(2)
where M is the moisture content at different time and Mo is the initial moisture content. In order to efficiently ascertain the drying kinetics of Jew’s mallow leaves, there is need to fit the drying behavior with different mathematical models. Five mathematical equations listed 4
in Table 1 were used for this purpose. The curve fitting of the hot air drying data was achieved with aid of a MATLAB software version 7.11.0.584.
Model
Table 1 - Models applied to the oven drying curves of Jew’ mallow leaves Equation References
Simple exponential
MR a exp kt
Doymaz [12]
Two-term exponential
MR a exp kt b exp gt
Omolola et al. [13]
Logarithmic
MR a exp kt c
Astiani et al. [14]
Wang & Singh
MR 1 at bt 2
Miranda et al. [11]
Page
MR exp kt n
Ganesapillai et al. [15]
2.3.1 Statistical analysis The sum of square error (SSE), root mean square error (RMSE) and coefficient of determination (R2), and were used to verify the reliability of the fits. The criteria used for picking the most excellent and reliable model was based on the highest value of R2 and the lowest values RMSE and SSE [16,17]. The statistical parameters were computed using Equations 3-5 respectively. N is the number of observations, MR cal,i is the predicted moisture ratio, MRexp,i is the experimental moisture ratio, and n is the number of constants.
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N N . MR MR MR MR i cal , i i exp, i i 1 i 1 R2 2 2 N N MR MR MR MR . i cal , i i exp, i i 1 i 1
(3)
1 2 2 1 N RMSE MR MR cal , i exp, i N i 1
(4)
SSE MRcal ,i MRexp,i
(5)
N
i 1
2.4. Determination of effective moisture diffusivity and activation energy Effective moisture diffusivity was determined using Equations 6-8 respectively as described by Doymaz [12].
2 2n 12 8 1 MR exp D t eff 2 2 2 n 0 2n 1 4L
(6)
where Equation (6) relies on the postulation that the moisture distribution in the samples is uniform and has a stable diff usivity with negligible shrinkage: The slope (φ) obtained from plotting ln (MR) against time is used in Equation 8 to compute the moisture diffusivity of the samples
2 8 Deff In MR In 2 4 L2
t
(7)
2D
eff 4 L2
(8)
where MR is moisture ratio, Deff is the effective moisture diffusivity (m²/s) and L is the halfthickness (m) of the samples. 6
2.5. Determination of activation energy The activation energy of the drying process was obtained using Equations 9-11 [4].
E a D Do exp eff R T 273.15
(9)
Equation 9 could be expressed or re-written as Equation 10 by taking the logarithm of both sides E a In D In Do (10) RT eff abs lnDeff were plotted against the absolute values of the given temperatures (50, 60 and 70 ⁰ C). The slope (k) of the plot is equal to (-Ea/R).
k
Ea R
(11)
where Do is the Arrhenius factor (m2/s), Ea is the activation energy (kJ/mol), R is the universal gas constant (8.314 × 10-3 kJ/mol K), k is slope and T is the oven temperature (⁰ C).
3. Results and discussion 3.1. Drying characteristics of Jew’s mallow leaves The drying curve of Jew’s mallow leaves at dissimilar oven temperatures is presented in figure 1. Moisture content of the samples reduced from initial 76.66% (w.b.) to 18.33%, 7.10%, and 6.50% (w.b.) at a drying temperature of 50, 60 and 70 ⁰ C, respectively. The experimental data obtained from drying Jew’s mallow leaves at oven temperatures 50, 60, and 70 ⁰ C were analysed with regards to drop in moisture ratio with drying time. According to Ashtiani et al. [14], moisture ratio curves rather than moisture content curves are more appropriate in unfolding the drying characteristics of foodstuffs. The time needed to decrease the moisture present in the
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samples to a definite point was reliant on drying temperature, being the maximum at 50 ⁰ C (150 min) and lowest at 70 ⁰ C (90 min). A short constant rate drying period at 0 to 10 min (Figure 1) was observed for all the drying temperatures used. This is could be attributed to the short initial settling down period of the samples in the oven as the surface of the samples heats up to wet bulb temperature. Furthermore, it can be deduced from the drying curves presented in figure 1 that drying of Jew’s mallow leaves occurred largely in the falling rate drying period. Generally, during the falling rate period, the rate of water movement from the interior to the surface falls below the rate which water evaporates to the surrounding air, therefore sample surface dries out. This suggests that moisture diffusivity in the samples was predominantly through diffusion mechanism. Similar remarks were reported for spinach leaves, peppermint leaves, persimmon slices, avishan leaves, and rosy garlic leaves [16, 14, 18, 19, 20].
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1.2
1
50°C 60°C 70°C
Moisture ratio
0.8
0.6
0.4
0.2
0 0
20
40
60
80 Time (min)
100
120
140
Fig. 1- Oven drying curves of Jew’s mallow leaves at different temperatures
3.2. Modeling of the drying curves The experimental moisture contents were converted to more functional moisture ratio [14]. Thereafter the curves obtained from plotting the moisture ratios against drying time were fitted with mathematical models listed in Table 1. The outcome of the statistical analyses applied to the curve fits to determine the adequacy, reliability and consistency of the models are outlined in Table 2. The model having the highest R2 value and the lowest RMSE and SSE values was chosen as the most excellent model. The mean values of R2, SSE and RMSE of the tested mathematical models were in the range of 0.9239-0.9836, 0.0124-0.0574, and 0.0392-0.0750 respectively. Amongst the tested models, the Two-term exponential model satisfied the criterion 9
160
for choosing the superlative model as its coefficient of determination (R2) {0.9836} was the highest while its SSE {0.0124} and RMSE {0.0392} values were the lowest. The Two-term exponential curve fit for Jew’s mallow drying characteristics 50, 60, and 70 ⁰ C is as shown in figure 2. The adequacy, reliability and consistency of Two-term exponential model was substantiated by plotting the calculated moisture ratios obtained from the model against the experimental moisture ratio data at 50, 60, and 70 ⁰ C as shown in Figs. 3a, 3b, and 3c respectively. The coefficients of correlation of the straight lines obtained were 0.9890, 0.9680, and 0.9670. This implies good correlation between the predicted moisture ratios obtained from Two-term exponential model and experimental moisture ratios. Hence the model is adequate, reliable and suitable for predicting the drying kinetics of Jew’s mallow leaves using oven drying method.
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Table 2 - Modeling of drying curves of Jew’s mallow leaves Model
Wang & Singh
R2
SSE
RMSE
b = 4.32E-05
0.9859
0.0149
0.0326
a = -0.0161
b = 9.12E-05
0.9641
0.0277
0.0526
a = -0.0232
b = 0.0001
0.9616
0.0258
0.0568
0.9705
0.0228
0.0473
Temperature (⁰ C)
Constants
50
a = -0.0114
60 70
Average
Simple exponential
50
a = 1.024
k = -0.0123
0.9732
0.0285
0.0451
60
a = 1.009
k = -0.0151
0.9144
0.0659
0.0812
70
a = 0.973
k = -0.0213
0.8843
0.0779
0.0987
0.9239
0.0574
0.0750
Average
Two-term exponential
50
a = 1.106
k = 0.0196
b =0.0771
g = 0.0056
0.9940
0.0063
0.0229
60
a = 1.206
k = 0.0349
b =0.1251
g = 0.0077
0.9791
0.0161
0.0449
70
a = 1.333
k = 0.0649
b =0.1806
g = 0.0051
0.9777
0.0150
0.0500
0.9836
0.0124
0.0392
Average
Page
50
k = 0.0138
n = 0.9663
0.9724
0.0293
0.0457
60
k = 0.0245
n = 0.8792
0.9208
0.0610
0.0781
70
k = 0.0546
n = 0.7603
0.9097
0.0608
0.0872
0.9343
0.0504
0.0703
Average
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Logarithmic
50
a = 0.9168
b = 0.0181
c = 0.0152
0.9859
0.0149
0.0339
60
a = 0.8437
b = 0.0291
c = 0.2367
0.9560
0.0339
0.0614
70
a = 0.8271
b = 0.0447
c = 0.2303
0.9545
0.0306
0.0661
0.9655
0.0265
0.0538
Average
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a
1
Moisture ratio
M oisture ratio vs. Time Two term exponential
0.8 0.6 0.4
0
50
100
150
Time (min)
b
1
M oisture ratio vs. Time
Moisture ratio
Two term exponential
0.8
0.6
0.4 0
20
40
60
80
100
Time (min)
c
1 M oisture ratio vs. Time
Moisture ratio
Two term exponential
0.8
0.6
0.4
0
10
20
30
40
50
60
70
80
90
Time (min)
Fig. 2- Two-term exponential curve fit for Jew’s mallow drying curves at 50 (a), 60 (b) and 70 ⁰ C (c).
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a
1.2 y = 0.988x + 0.005 R² = 0.9890
MRpredicted
1 0.8 0.6 0.4 0.2 0 0
0.2
0.4 0.6 0.8 MRexperimental
1
1.2
b 1.2 y = 0.965x + 0.017 R² = 0.9680
MRpredicted
1 0.8 0.6 0.4 0.2 0 0
c
0.2
0.4 0.6 0.8 MRexperimental
1
1.2
1.2 y = 0.964x + 0.016 R² = 0.9670
MRpredicted
1 0.8 0.6 0.4 0.2 0 0
0.2
0.4 0.6 0.8 MRexperimental
1
1.2
Fig. 3 - Validation of Two-term exponential model for predicting the oven drying characteristics of Jew’s mallow leaves at 50 (a), 60 (b) and 70 ⁰ C (c).
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3.3. Effective moisture diffusivity and activation energy According to Nachaisin et al. [21], the effective moisture diffusivity of food stuffs depicts their intrinsic moisture migration characteristics which include diverse parameters like liquid, molecular, vapour and hydrodynamic diffusion. The Deff values of Jew’s mallow leaves obtained from Equation 6 under different temperatures is presented in figure 3. The Deff of Jew’s mallow ranged from 8.18×10-8 and 1.13× 10-7 m2/s. These values are consistent with the range reported by Zogzas et al. [22] for agricultural foodstuffs. It could also be observed from figure 4 that Deff of Jew’s mallow leaves augmented as the drying temperature rises. This is can be credited to the rise in vapour pressure of the leaves which in turn enhanced moisture migration at elevated temperatures [23]. The activation energy for oven drying Jew’s mallow leaves as computed from the slope obtained from the plot of InD eff against absolute temperature (Fig. 5) was found to be 14.84 kJ/mol. According Xiao et al. [24], the activation energy, for a typical drying operation range from 12.7 to 110 kJ/mol. The activation energy obtained in this study is lesser than the activation energies reported by Khazael et al. [19], Ben Haj Said et al. [20], Kaya & Aydin [25], and
Doymaz [26] for avishan leaves (38.6–51.1 kJ/mol), rosy garlic leaves (46.80–52.68
kJ/mol), nettle leaves (79.873– 109.003 kJ/mol) and banana slices (32.65 kJ/mol) respectively. However, the value of activation energy obtained for drying Jew’s mallow leaves in the present study was observed to be greater than the value reported by Premi et al. [27] for drum-stick leaves (12.50 kJ/mol).
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1.20E-07
y = 2E-09x + 2E-09 R² = 0.950
1.00E-07 Deff (m2/s)
8.00E-08 6.00E-08
4.00E-08 2.00E-08 0.00E+00 0
20
40 Temperature (oC)
60
80
Fig. 4 - Influence of oven temperature on the effective moisture diffusivity of Jew’s mallow leaves 1/T (1/K) 0.0029 -15.95
0.00295
0.003
0.00305
0.0031
0.00315
-16 -16.05
lnDeff
-16.1
y = -1785.3x - 10.813 R² = 0.959
-16.15
-16.2 -16.25 -16.3 -16.35 -16.4
Fig. 5 - Arrhenius-type relationship between logarithm of eff ective moisture diff usivity and absolute temperature.
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3.4. Colour of dried leaves Colour is avital quality characteristic in foodstuff to nearly every consumer. It serves as an indicator of the intrinsic good qualities [4]. The relationship of colour with consumer acceptability of foodstuffs is common and inevitable [4]. Generally drying operation changes the surface characteristics of foods and hence alters their reflectivity and colour [28].The colour of dried Jew’s mallow leaves was determined using a Hunterlab colorimeter (ColorFlex, Hunter Lab, USA). Calibration of the colorimeter was ensured previous to colour determination experiments. The colours were depicted as L* a* and b*representing lightness, redness, and yellowness respectively. The colour data of dried Jew’s mallow leaves is shown in Table 3. The mean colour varied across the applied drying temperatures and time range. This variation was expected as dissimilar drying conditions were used in this study. L*, a*, b* ΔE, and a*/b* ranged from 31.8 to 32.87, -3.73 to -4.37, 13.6 to 16.47, 69.00 to 69.73, and -0.26 to -0.34 respectively. According to Doymaz et al. [4], higher L* and lower a*/b* are required in dried foodstuff. For this study, samples dried at 50 ⁰ C 150 min and 70 ⁰ C 90 min had higher L* and lower a*/b* values. This suggests that 50 ⁰ C 150 min and 70 ⁰ C 90 min can be taken as the optimum oven temperatures for drying Jew’s mallow leaves. Furthermore, colour change (ΔE) was prominent in samples dried at 60 ⁰ C compared to samples dried at 50 and 70 ⁰ C. According to Fellows [28], colour change in fruit and vegetables is caused by heat and oxidation during drying and residual polyphenol oxidase enzyme activity which results to browning during storage. Table 3 - Colour quality of dried Jew’s mallow leaves Temperature (0C) Time (min) L* a* 50 150 32.63±2.67 -3.73±1.19 60 110 31.8±1.50 -4.7±0.17 70 90 32.87±1.40 -4.37±0.51
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b* 14.03±1.62 13.6±1.14 16.47±0.60
ΔE 69.00±2.29 69.73±1.35 69.27±1.43
a*/b* -0.26±0.06 -0.34±0.02 -0.26±0.03
4. Conclusions Oven drying characteristics of Jew’s mallow leaves was investigated. The study revealed that drying duration decreased conspicuously as oven temperature increased. Drying of Jew’s mallow leaves occurred primarily in the falling rate period. This suggests that diffusion mechanism was principally responsible for moisture migration from the leaves. The curve fitting revealed that the Two-term exponential model adequately predicted the drying behaviour of oven drying of Jew’s mallow leaves as it had the highest R2 value and lowest SSE and RMSE values. The Deff values ranged from 8.18× 10 -8 to 1.13× 10-7 m2/s within the applied oven temperatures (50, 60 and 70 ⁰ C ). Activation energy required to get rid of moisture within the leaves throughout the oven drying process was found to be 14.84 kJ/mol. Colour analysis carried out on the dried leaves suggest that drying conditions of 50 ⁰ C 150 min and 70 ⁰ C 90 min can be taken as the optimum oven temperatures for drying Jew’s mallow leaves. This study presents functional insights on drying of Jew’s mallow leaves, thereby contributing to knowledge and literature.
Funding statement This work was funded by the University of Venda postdoctoral research fellowship, Thohoyandou, South Africa.
Competing interest statement The authors declare no conflict of interest.
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