Mathematical Modeling to Describe Drying Behavior of Kyoho (Vitis labruscana) Skin Waste: Drying Kinetics and Quality Attributes
Abstract
:1. Introduction
2. Materials and Methods
2.1. Chemicals and Instruments
2.2. Sample Preparation
2.3. Drying Process and Experimental Drying Kinetics
2.4. Modeling of Experimental Drying Kinetics
2.5. Effective Moisture Diffusivity (Deff) and Activation Energy (Ea)
2.6. Color Characterization
2.7. Rehydration
2.8. Total Phenolic and Flavonoid Contents
2.9. Antioxidant Activity
2.10. Correlation Analysis
2.11. Statistical Analysis
3. Results and Discussion
3.1. General
3.2. Drying Behavior of Kyoho Skin
3.3. Mathematical Modeling and Goodness of Fit
3.4. Effective Moisture Diffusivity (Deff) and Activation Energy (Ea)
3.5. Color
3.6. Rehydration
3.7. Total Phenolic and Flavonoid Contents
3.8. Antioxidant Activity (DPPH• and ABTS• Scavenging)
3.9. Correlation Analysis
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Model | Equation |
---|---|
Lewis | MR = = (exp – kt) |
Page | MR = = exp(–ktN) |
Henderson–Pabis | MR = = a exp(–kt) |
Logarithmic | MR = = a exp(–kt) + c |
Two-term | MR = = a1 exp (–k1t) + a2 exp (–k2t) |
Temperature (K) | Lewis | Page | Henderson–Pabis | Logarithmic | Two-Term | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
k | R2 | k | N | R2 | k | a | R2 | k | a | c | R2 | k1 | k2 | a1 | a2 | R2 | |
303.15 | 0.2311 ± 0.01 | 0.9236 | 0.1171 ± 0.05 | 1.4720 ± 0.17 | 0.9815 | 0.2827 ± 0.10 | 1.2060 ± 0.71 | 0.9640 | 0.2441 ± 0.08 | 1.2470 ± 1.05 | −0.0715 ± 0.03 | 0.9659 | −2.2010 ± 0.71 | 0.2896 ± 0.05 | 2.414 ± 0.21 × 10−10 | 1.2310 ± 0.31 | 0.9643 |
313.15 | 0.3685 ± 0.10 | 0.9395 | 0.2815 ± 0.08 | 1.2520 ± 0.13 | 0.9577 | 0.4270 ± 0.19 | 1.1560 ± 0.22 | 0.9582 | 0.4686 ± 0.16 | 1.1520 ± 0.08 | 0.0320 ± 0.004 | 0.9595 | −1.0570 ± 0.04 | 1.1820 ± 0.54 | 4.1050 ± 1.48 × 10−5 | 1.1820 ± 0.076 | 0.9639 |
323.15 | 0.5615 ± 0.18 | 0.9158 | 0.4438 ± 0.10 | 1.3800 ± 0.51 | 0.9479 | 0.7283 ± 0.31 | 1.306 ± 1.05 | 0.9606 | 0.8887 ± 0.28 | 1.3500 ± 0.34 | 0.0601 ± 0.04 | 0.9692 | 0.7949 ± 0.33 | −0.8514 ± 0.08 | 1.372 ± 0.22 | 0.0011 ± 0.001 | 0.9737 |
333.15 | 0.7772 ± 0.05 | 0.8741 | 0.6230 ± 0.20 | 1.7810 ± 0.66 | 0.9685 | 1.1430 ± 0.90 | 1.5290 ± 0.07 | 0.9667 | −0.0014 ± 0.01 | −293.50 ± 147.08 | 294.30 ± 125.70 | 0.8040 | 0.3829 ± 0.17 | 0.4025 ± 0.16 | −19.28 ± 2.57 | 20.45 ± 4.08 | 0.9378 |
Temperature (K) | Lewis | Page | Henderson–Pabis | Logarithmic | Two-Term | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
χ2 | RMSE | SSE | χ2 | RMSE | SSE | χ2 | RMSE | SSE | χ2 | RMSE | SSE | χ2 | RMSE | SSE | |
303.15 | 0.0827 | 0.0827 | 0.1096 | 0.0239 | 0.0504 | 0.0381 | 0.0586 | 0.0586 | 0.0519 | 0.0590 | 0.0591 | 0.0488 | 0.0627 | 0.0627 | 0.0512 |
313.15 | 0.0614 | 0.0681 | 0.0664 | 0.1009 | 0.0603 | 0.0422 | 0.0545 | 0.0607 | 0.0417 | 4.3924 | 0.0606 | 0.0403 | 0.0543 | 0.0600 | 0.0360 |
323.15 | 0.0618 | 0.0824 | 0.0611 | 0.0808 | 0.0688 | 0.0378 | 0.0436 | 0.0598 | 0.0286 | 0.0573 | 0.0565 | 0.0223 | 0.0383 | 0.0564 | 0.0191 |
333.15 | 0.0622 | 0.1113 | 0.0619 | 0.0220 | 0.0622 | 0.0154 | 0.0330 | 0.0640 | 0.0164 | 0.1889 | 0.1793 | 0.0964 | 0.0485 | 0.1236 | 0.0305 |
Temperature (K) | Deff (m2/s) × 10−8 | Ea(kJ/mol) | R2 |
---|---|---|---|
303.15 | 2.87 ± 1.37 a | 33.78 ± 1.06 | 0.9355 |
313.15 | 3.60 ± 1.08 b | 0.9852 | |
323.15 | 5.15 ± 1.00 c | 0.9733 | |
333.15 | 9.82 ± 1.74 d | 0.9804 |
Temperature (K) | L | a | b | ΔE |
---|---|---|---|---|
303.15 | 24.67 ± 0.38 a | 18.28 ± 0.11 b | 2.71 ± 0.01 b | 1.45 ±0.23 a |
313.15 | 26.28 ± 0.27 b | 16.62 ± 0.05 a | 3.49 ± 0.05 d | 3.22 ± 0.04 b |
323.15 | 28.74 ± 0.78 c | 20.20 ± 0.47 c | 3.05 ± 0.03 c | 3.83 ± 0.67 b |
333.15 | 30.41 ± 0.15 d | 21.53 ± 0.17 d | 2.06 ± 0.02 a | 5.66 ± 0.06 c |
Temperature (K) | TPC (mg GAE/g) | TFC (mg QE/g) |
---|---|---|
303.15 | 0.37 ± 0.04 b | 2.36 ± 0.78 b |
313.15 | 0.33 ± 0.03 b | 2.19 ± 0.74 ab |
323.15 | 0.30 ± 0.04 ab | 1.35 ± 0.43 ab |
333.15 | 0.23 ± 0.03 a | 1.05 ± 0.33 a |
Temperature (K) | Antioxidant Activity | |
---|---|---|
DPPH• Method | ABTS• Method | |
303.15 | 93.06 ± 0.48 c | 96.69 ± 1.17 d |
313.15 | 84.57 ± 0.19 b | 82.24 ± 0.94 c |
323.15 | 85.38 ± 0.40 b | 43.14 ± 2.02 b |
333.15 | 73.31 ± 1.13 a | 11.87 ± 1.89 a |
Parameter | 303.15 K | 313.15 K | ||||||
---|---|---|---|---|---|---|---|---|
TPC | TFC | DPPH• | ABTS• | TPC | TFC | DPPH• | ABTS• | |
TPC | 1 | 0.95 | 0.94 | −0.33 | 1 | 0.99 | 0.53 | −1 * |
TFC | 1 | 0.79 | −0.61 | 1 | 0.42 | −0.99 | ||
DPPH• | 1 | −0.01 | 1 | −0.51 | ||||
ABTS• | 1 | 1 | ||||||
Parameter | 323.15 K | 333.15 K | ||||||
TPC | TFC | DPPH• | ABTS• | TPC | TFC | DPPH• | ABTS• | |
TPC | 1 | 1 ** | 0.50 | 0.07 | 1 | 1 ** | -0.82 | −0.93 |
TFC | 1 | 0.50 | 0.08 | 1 | -0.82 | −0.93 | ||
DPPH• | 1 | −0.81 | 1 | 0.97 | ||||
ABTS• | 1 | 1 |
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Sridhar, K.; Charles, A.L. Mathematical Modeling to Describe Drying Behavior of Kyoho (Vitis labruscana) Skin Waste: Drying Kinetics and Quality Attributes. Processes 2022, 10, 2092. https://doi.org/10.3390/pr10102092
Sridhar K, Charles AL. Mathematical Modeling to Describe Drying Behavior of Kyoho (Vitis labruscana) Skin Waste: Drying Kinetics and Quality Attributes. Processes. 2022; 10(10):2092. https://doi.org/10.3390/pr10102092
Chicago/Turabian StyleSridhar, Kandi, and Albert Linton Charles. 2022. "Mathematical Modeling to Describe Drying Behavior of Kyoho (Vitis labruscana) Skin Waste: Drying Kinetics and Quality Attributes" Processes 10, no. 10: 2092. https://doi.org/10.3390/pr10102092