Mathematical Modelling, Drying Kinetics, and Moisture Diffusion Behaviour of Leek Leaves (Allium ampeloprasum var. porrum) during Hot-Air Oven Drying

Authors

  • Satria Bhirawa Anoraga Department of Bioresources Technology and Veterinary, Vocational College, Universitas Gadjah Mada, Yogyakarta, Indonesia
  • Nadia Awalina Bunga Massita Department of Bioresources Technology and Veterinary, Vocational College, Universitas Gadjah Mada, Yogyakarta, Indonesia
  • Chyntia Diva Omega Department of Bioresources Technology and Veterinary, Vocational College, Universitas Gadjah Mada, Yogyakarta, Indonesia
  • Octhateani Adiibah Wigati Department of Bioresources Technology and Veterinary, Vocational College, Universitas Gadjah Mada, Yogyakarta, Indonesia
  • Sang Norma Lintang Asmara Department of Bioresources Technology and Veterinary, Vocational College, Universitas Gadjah Mada, Yogyakarta, Indonesia
  • Jhauharotul Muchlisyiyah Department of Food Science and Biotechnology, Faculty of Agricultural Technology, Universitas Brawijaya, Malang, Indonesia
  • Jamilu Suleiman Department of Agricultural and Bio-Environmental Engineering, Faculty of Engineering, Federal University Dutsin-Ma, Katsina, Nigeria

DOI:

https://doi.org/10.12928/jafost.v7i3.16023

Keywords:

Activation energy, Drying kinetics, Effective moisture diffusivity, Mathematical modelling, Water removal

Abstract

This study investigated the drying kinetics, mathematical modelling, and moisture diffusion behaviour of leek leaves (Allium ampeloprasum var. porrum) during hot-air oven drying at 45, 55, and 65 °C. The study aimed to identify the most suitable thin-layer drying model and determine the effective moisture diffusivity and activation energy of leek leaves. Drying occurred entirely in the falling-rate period, which indicates that internal diffusion controlled moisture removal. Among the evaluated models, the cubic model gave the best fit at 45 °C, with an R² of 98.96%, root mean square error (RMSE) of 0.053, and sum of squared errors (SSE) of 0.0593. The Wang and Singh model gave the best fit at 55 °C and 65 °C, with R² values of 92.26% and 93.17%, RMSE values of 0.078 and 0.102, and SSE values of 0.0874 and 0.1140, respectively. Effective moisture diffusivity increased from 9.13 × 10⁻⁹ m²/s at 45 °C to 31.69 × 10⁻⁹ m²/s at 55 °C and 43.36 × 10⁻⁹ m²/s at 65 °C. The activation energy reached 70.08 kJ/mol, showing the temperature sensitivity of moisture migration in leek tissue. These findings provide useful kinetic parameters for selecting drying conditions and improving predictive modelling in small-scale and industrial leek drying processes. This study contributes part-specific drying data for the green leaf portion of leek, which remains less represented than whole-slice and pseudo-stem drying data.

References

Direktorat Jenderal Hortikultura, “Angka Tetap Hortikultura Tahun 2023,” Direktorat Jenderal Hortik. Kementeri. Pertan., p. xxiv + 261, 2024. https://hortikultura.pertanian.go.id/wp-content/uploads/2024/04/buku_atap_2023.pdf

H. S. Al-khalaifah, M. E. Badawi, R. M. Abd El-Aziz, M. A. Ali, and A. E. Omar, “Effect of Egyptian leek leaf extract supplementation on productive and economic performance of broilers,” Front. Vet. Sci., vol. 7, p. 584921, 2020, https://doi.org/10.3389/fvets.2020.584921.

T. Xie, Q. Wu, H. Lu, Z. Hu, Y. Luo, Z. Chu, and F. Luo, “Functional perspective of leeks: Active components, health benefits and action mechanisms,” Foods, vol. 12, no. 17, p. 3225, 2023, https://doi.org/10.3390/foods12173225.

J. Zhang and J. Yang, “Allium vegetables intake and risk of breast cancer: A meta-analysis,” Iran. J. Public Health, vol. 51, no. 4, pp. 746–757, 2022, https://doi.org/10.18502/ijph.v51i4.9235.

A. Ali, M. Kouvari, S. Riaz, N. Naumovski, L. Liao, A. Khan, W. Khalid, X. Zeng, and M. F. Manzoor, “Potential of Allium sativum in blood pressure control involves signaling pathways: A narrative review,” Food Front., vol. 4, no. 4, pp. 1666–1680, 2023, https://doi.org/10.1002/fft2.289.

N. Bernaert, E. Debonne, I. De Leyn, B. Van Droogenbroeck, and F. Van Bockstaele, “Incorporation of leek powder (Allium ampeloprasum var. porrum) in wheat bread: Technological implications, shelf life and sensory evaluation,” LWT, vol. 153, p. 112517, 2022, https://doi.org/10.1016/j.lwt.2021.112517.

J. An, H. Xie, J. Yan, H. Wei, Y. Wu, and X. Liao, “A review of applications of energy analysis: Grain, fruit and vegetable drying technology,” Energy Reports, vol. 12, pp. 5482–5506, 2024, https://doi.org/10.1016/j.egyr.2024.11.037.

B. A. Kesuma, I. Y. Pratiwi, and Y. Somawiharja, “The effect of drying methods on the physicochemical characteristics of curly red chili (Capsicum annuum L.),” J. Agri-food Sci. Technol., vol. 6, no. 4, pp. 209–218, 2025, https://doi.org/10.12928/jafost.v6i4.12906.

J. O. Ojediran, C. E. Okonkwo, A. F. Olaniran, Y. M. Iranloye, A. D. Adewumi, O. Erinle, Y. Tokunbo, O. Adeyi, and A. Adeyi, “Hot air convective drying of hog plum fruit (Spondias mombin): Effects of physical and edible-oil-aided chemical pretreatments on drying and quality characteristics,” HLY, vol. 7, no. 11, p. e08312, 2021, https://doi.org/10.1016/j.heliyon.2021.e08312.

L. Wei, P. Li, Y. Liu, and Y. Xie, “Effects of drying methods, temperature, and initial moisture content on drying characteristics, nutritional quality, texture, and oxidative stability of peanuts,” Foods, vol. 15, no. 7, pp. 1–28, 2026, https://doi.org/10.3390/foods15071248.

L. Vargas, R. Kapoor, B. Nemzer, and H. Feng, “Application of different drying methods for evaluation of phytochemical content and physical properties of broccoli, kale, and spinach,” LWT, vol. 155, p. 112892, 2022, https://doi.org/10.1016/j.lwt.2021.112892.

H. Xu, M. Wu, Y. Wang, W. Wei, D. Sun, D. Li, Z. Zheng, and F. Gao, “Effect of combined infrared and hot air drying strategies on the quality of chrysanthemum (Chrysanthemum morifolium Ramat.) cakes: Drying behavior, aroma profiles and phenolic compounds,” Foods, vol. 11, no. 15, p. 2240, 2022, https://doi.org/10.3390/foods11152240.

E. Golisz, I. Wielewska, K. Roman, and M. Kacprzak, “Probabilistic model of drying process of leek,” Appl. Sci., vol. 12, no. 22, pp. 1–12, 2022, https://doi.org/10.3390/app122211761.

I. Doymaz, “Influence of blanching and slice thickness on drying characteristics of leek slices,” Chem. Eng. Process. Process Intensif., vol. 47, no. 1, pp. 41–47, 2008, https://doi.org/10.1016/j.cep.2007.09.002.

G. Dadali and B. Özbek, “Microwave heat treatment of leek: Drying kinetic and effective moisture diffusivity,” Int. J. Food Sci. Technol., vol. 43, no. 8, pp. 1443–1451, 2008, https://doi.org/10.1111/j.1365-2621.2007.01688.x.

N. Yin, J. Luo, C. Wang, Y. Xiong, Y. Sun, E. Yuan, and H. Zhang, “Comprehensive evaluation of the effects of hot air drying temperature on the chemical composition, flavor characteristics and biological activity of Houttuynia cordata Thunb.,” Foods, vol. 14, no. 11, p. 1962, 2025, https://doi.org/10.3390/foods14111962.

G. Kumar, J. Joshi T, P. S. Rao, and P. Manchikanti, “Effect of thin layer drying conditions on the retention of bioactive components in Malabar spinach (Basella alba) leaves,” Food Chem. Adv., vol. 3, 2023, https://doi.org/10.1016/j.focha.2023.100419.

R. Shamsudin, S. H. Ariffin, W. N. Z. Zainol Abdullah, N. S. Azmi, and A. A. A. Halim, “Modelling the kinetics of color and texture changes of dabai (Canarium odontophyllum miq.) during blanching,” Agronomy, vol. 11, no. 11, 2021, https://doi.org/10.3390/agronomy11112185.

P. N. M. A. Azman, R. Shamsudin, H. C. Man, and M. E. Ya’acob, “Kinetics of quality changes in soaking water during the retting process of pepper berries (Piper nigrum L.),” Processes, vol. 8, no. 10, pp. 1–11, 2020, https://doi.org/10.3390/pr8101255.

L. Wu, S. Chen, Y. Li, W. Xie, and B. Tang, “Effect of heat pump drying temperature on moisture migration characteristics and quality of instant Tremella fuciformis,” Curr. Res. Food Sci., vol. 9, 2024, https://doi.org/10.1016/j.crfs.2024.100825.

N. Sianoun, P. Pongyeela, N. Chairerk, and J. Chungsiriporn, “Thin layer drying kinetics and mathematical modeling of moisture diffusivity in cocoa pod husk (CPH),” Eng. J., vol. 27, no. 8, pp. 1–12, 2023, https://doi.org/10.4186/ej.2023.27.8.1.

J. Muchlisyiyah, R. Shamsudin, R. K. Basha, R. Shukri, S. How, and M. Rambli, "Kinetic modelling during soaking of dried long grain paddy MR297," ASEAN Journal on Science and Technology for Development, vol. 40, no. 2, 2024, https://doi.org/10.61931/2224-9028.1537.

B. Dey, S. Jayaraman, and P. Balasubramanian, “Investigating the effects of drying on the physical properties of kombucha bacterial cellulose: Kinetic study and modeling approach,” J. Clean. Prod., vol. 452, p. 142204, 2024, https://doi.org/10.1016/j.jclepro.2024.142204.

R. Biswas, M. A. Hossain, and W. Zzaman, “Thin layer modeling of drying kinetics, rehydration kinetics and color changes of osmotic pre-treated pineapple (Ananas comosus) slices during drying: Development of a mechanistic model for mass transfer,” Innov. Food Sci. Emerg. Technol., vol. 80, p. 103094, 2022, https://doi.org/10.1016/j.ifset.2022.103094.

M. Kumar, A. Mahore, M. Kumar Choudhary, . L., R. Nalawade, A. Patel, and S. R. Kalbande, “Development of mini solar tunnel dryer and validation of thin layer drying models for pomegranate seeds,” Int. J. Environ. Clim. Chang., vol. 13, no. 2, pp. 42–49, 2023, https://doi.org/10.9734/ijecc/2023/v13i21651.

L. A. Duc, N. Hay, P. Van Kien, N. T. Tan, and D. Q. Cuong, “Mathematical model of thin layer drying of purple yam by infrared assisted heat pump drying,” Agric. Eng., vol. 29, no. 1, pp. 63–78, 2025, https://doi.org/10.2478/agriceng-2025-0005.

M. Popescu, P. Iancu, V. Plesu, C. S. Bildea, and F. A. Manolache, “Mathematical modeling of thin-layer drying kinetics of tomato peels: Influence of drying temperature on the energy requirements and extracts quality,” Foods, vol. 12, no. 20, 2023, https://doi.org/10.3390/foods12203883.

N. N. Mbegbu, J. O. Ojediran, C. O. Nwajinka, E. C. Chukwuma, and M. Aniobi, “Thin layer drying and effect of temperature on the drying characteristics of bushbuck (Gongronema latifolium) leaves,” J. Agric. Food Res., vol. 18, p. 101379, 2024, https://doi.org/10.1016/j.jafr.2024.101379.

K. A. Jimoh, N. Hashim, R. Shamsudin, H. C. Man, and M. Jahari, “Time-temperature dependent modelling of the thin-layer drying kinetics of glutinous rice,” Food Res., vol. 9, no. 1, pp. 20–27, 2025, https://doi.org/10.26656/fr.2017.9(S1).016.

L. Li, H. Pan, J. Chen, W. Cao, W. Liu, X. Duan, and G. Ren, “Infrared‐assisted spouted bed drying of Chinese yam cubes: Effect of constant and variable temperature drying processes on drying behavior, uniformity, and quality attributes,” J. Sci. Food Agric., vol. 103, no. 6, pp. 2815–2823, 2023, https://doi.org/10.1002/jsfa.12416.

D. H. Braga, A. A. de Lima Santos, I. C. Bicalho, and I. H. Rodriguez, “Drying acerola residue in a spouted bed: Fluid dynamic study and functional quality analysis,” J. Food Process Eng., vol. 47, no. 6, 2024, https://doi.org/10.1111/jfpe.14656.

C. Shen, W. Chen, T. Aziz, E. Khojah, F. Al-Asmari, A. S. Alamri, M. Alhomrani, H. Cui, and L. Lin, “Drying kinetics and moisture migration mechanism of yam slices by cold plasma pretreatment combined with far-infrared drying,” Innov. Food Sci. Emerg. Technol., vol. 95, p. 103730, 2024, https://doi.org/10.1016/j.ifset.2024.103730.

S. Tripathy and P. P. Srivastav, “Effect of dielectric barrier discharge (DBD) cold plasma-activated water pre-treatment on the drying properties, kinetic parameters, and physicochemical and functional properties of Centella asiatica leaves,” Chemosphere, vol. 332, p. 138901, 2023, https://doi.org/10.1016/j.chemosphere.2023.138901.

İ. Doymaz and Ö. Özdemir, “Effect of air temperature, slice thickness and pretreatment on drying and rehydration of tomato,” Int. J. Food Sci. Technol., vol. 49, no. 2, pp. 558–564, 2014, https://doi.org/10.1111/ijfs.12337.

M. B. Zacharias, S. J. Granella, and T. B. Moraes, “TD-NMR monitoring of water dynamics in ethanol- and ultrasound-assisted drying of beetroot cubes,” Food Phys., vol. 3, p. 100091, 2026, https://doi.org/10.1016/j.foodp.2026.100091.

Z. Ning, R. Khir, F. Niederholzer, and Z. Pan, “Characteristics of moisture diffusivity and shrinkage evolution of in-hull almonds under hot air drying,” LWT, vol. 232, p. 118455, 2025, https://doi.org/10.1016/j.lwt.2025.118455.

I. Satar, A. Yuniarti, N. Yusof, and W. Abdo, “The impact of drying temperature and duration on the physicochemical and sensory properties of cascara powder enriched with emprit ginger (Zingiber officinale var. amarum),” J. Agri-food Sci. Technol., vol. 6, no. 4, pp. 228–241, 2025, https://doi.org/10.12928/jafost.v6i4.12287.

C. Wang, Y. Lu, X. An, and S. Tian, “Thin-layer drying characteristics of Easter lily (LiliumlongiflorumThunb.) scales and mathematical modeling,” Food Sci. Technol., vol. 42, 2022, https://doi.org/10.1590/fst.23222.

J. Zhang, X. Feng, S. Xie, Y. Zhong, Y. Sun, and W. Wang, “Research on drying kinetics, microstructure, and flavor changes of areca nut drying process based on water molecule migration,” Food Chem. X, vol. 31, p. 103047, 2025, https://doi.org/10.1016/j.fochx.2025.103047.

N. Alqahtani and M. Fikry, “Impact of microwave pretreatment on drying kinetics, mass transfer and thermodynamic characteristics of Barhi dates during drying process,” Sci. Rep., vol. 16, no. 1, p. 9022, 2026, https://doi.org/10.1038/s41598-026-39727-6.

E. Ndlovu, J. van Staden, and M. Maphosa, “Morpho-physiological effects of moisture, heat and combined stresses on Sorghum bicolor [Moench (L.)] and its acclimation mechanisms,” Plant Stress, vol. 2, p. 100018, 2021, https://doi.org/10.1016/j.stress.2021.100018.

Graphical abstract 16023

Downloads

Published

2026-06-26

Issue

Section

Articles