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. 2025 Jun 5;15(1):19781.
doi: 10.1038/s41598-025-01935-x.

Mathematical modeling of sorption isotherms and the thermodynamic properties of vacuum-dried and freeze-dried Barhi dates

Mohamed Fikry  1   2 , Saleh Al-Ghamdi  3 , Bandar Alfaifi  3 , Mansour N Ibrahim  3 , Nashi Alqahtani  4   5 , Muhammad Umar  1 , Kitipong Assatarakul  6
Affiliations

Mathematical modeling of sorption isotherms and the thermodynamic properties of vacuum-dried and freeze-dried Barhi dates

Mohamed Fikry et al. Sci Rep. .

Abstract

Studying the moisture sorption behavior of Barhi dates is key to enhancing their drying efficiency, packaging strategies, and storage conditions to ensure long-term stability and shelf-life. This research analyzed the sorption isotherms of vacuum-dried (VDBD) and freeze-dried Barhi dates (FDBD) via a dynamic vapor sorption apparatus across different temperatures and a wide range of water activity levels. Various mathematical models were evaluated to determine their accuracy in predicting sorption behavior, and the thermodynamic properties of sorption were examined in relation to the equilibrium moisture content (Xe). The results demonstrated that VDBD and FDBD followed Type III adsorption and Type V desorption isotherms. Adsorption increased with increasing water activity, whereas desorption displayed the opposite trend, with significant hysteresis between the two processes. The Peleg model provided a precise fit for both the adsorption and desorption isotherms across all the tested conditions. To maintain safe storage at the studied temperatures and 50% relative humidity, the recommended moisture content was 5% for VDBD and 9%. for FDBD. Additionally, the net isosteric heat of sorption (Qst), differential entropy (ΔS), and Gibbs free energy (ΔG) exhibited inverse correlations with Xe, increasing as the moisture content decreased during sorption. These thermodynamic parameters were effectively modeled as functions of Xe, indicating that both adsorption and desorption were nonspontaneous processes. This study provides critical insights for food processors to refine drying protocols and establish optimal storage conditions for VDBD and FDBD, ultimately preserving quality and preventing microbial contamination.

Keywords: Barhi date; Drying; Dynamic vapor sorption isotherms; Mathematical modeling; Thermodynamic properties.

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Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests.

Figures

Fig. 1
Fig. 1
Schematic view of the experimental setup.
Fig. 2
Fig. 2
Systematic diagram of the AQUADYNE DVS.
Fig. 3
Fig. 3
Time-based representation of moisture sorption for dried Barhi date subjected to gradual shifts in equilibrium relative humidity (ERH) and sample weight at 25 °C.
Fig. 4
Fig. 4
Experimental and predicted equilibrium moisture content (Xe) during adsorption and (a) desorption (b) using Peleg model.
Fig. 5
Fig. 5
Curves of the adsorption isotherms (a) and desorption isotherms (b) acquired for VDBD and FDBD at different temperatures (25, 35, and 45 °C).
Fig. 6
Fig. 6
Standard classifications of adsorption and desorption phases in food systems.
Fig. 7
Fig. 7
Sorption hysteresis loops obtained for VDBD and FDBD at different temperatures: 25 °C (a), 35 °C (b), and 45 °C (c).
Fig. 8
Fig. 8
Plots of the isosteric heat of sorption (a), differential entropy (b) and Gibbs free energy (c) against the equilibrium moisture content (Xe) of VDBD and FDBD.
See this image and copyright information in PMC

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