Mathematical modelling of thin-layer drying kinetics of Matricaria pubescens leaves

Technical Summary: Mathematical Modelling of Thin-Layer Drying Kinetics of Matricaria pubescens Leaves

Problem Statement
Matricaria pubescens (Desf.) Sch.Bip., a medicinal plant native to arid and semi-arid regions of Algeria, possesses significant phytochemical value, including polyphenols, flavonoids, and condensed tannins, which exhibit antioxidant, antidiabetic, and antihypertensive properties. However, the plant is typically harvested with high moisture content, making rapid drying essential to prevent microbial contamination and enzymatic degradation of bioactive compounds. While the phytochemistry of M. pubescens is well-documented, a critical gap exists in the literature regarding its drying kinetics. Without optimized drying protocols, the quality and therapeutic efficacy of the plant material are at risk. This study addresses the lack of data on the drying behavior of M. pubescens leaves, specifically investigating the influence of air temperature and velocity on drying kinetics and identifying the most suitable mathematical models for process prediction.

Methodology
The research was conducted using a laboratory wind tunnel (Gunt-Hambuer-type device, CE130) under controlled conditions. Fresh M. pubescens leaves were harvested from the Bechar region of Algeria in early 2024. The initial moisture content was approximately 4% (dry basis).

The experimental design involved a thin-layer drying approach with the following variables:

• Temperatures: 30°C, 40°C, and 50°C.
• Air Velocities: 0.5 m/s, 1.0 m/s, and 1.5 m/s.

Moisture content was monitored continuously using a digital balance, with measurements taken at 10-second intervals until equilibrium was reached. The drying process was analyzed by plotting moisture ratio (MR) against time, drying rate against time, and drying rate against moisture content.

To model the drying kinetics, seven thin-layer drying models (Newton, Page, Henderson and Pabis, Logarithmic, Two-term, Wang and Singh, and Midilli and Kucuk) were evaluated using non-linear regression (Curve Expert 1.6). Model selection was based on statistical parameters: the coefficient of determination ($R^2$), reduced chi-square ($\chi^2$), and root mean square error (RMSE).

Furthermore, the study calculated the effective moisture diffusivity ($D_{eff}$) using Fick's second law of diffusion and determined the activation energy ($E_a$) via the Arrhenius equation. A characteristic drying curve (CDC) approach was also employed to derive a polynomial equation for the drying rate.

Key Results

1. Drying Behavior: The drying process occurred entirely in the falling rate period, indicating that internal moisture diffusion is the rate-limiting step. Increasing the air temperature significantly reduced the total drying time; for instance, at a constant velocity of 1 m/s, raising the temperature from 30°C to 50°C reduced drying time by approximately two-thirds. Conversely, variations in air velocity (0.5 to 1.5 m/s) had no statistically significant effect on the drying kinetics or moisture evolution, suggesting that external mass transfer resistance is negligible compared to internal resistance.
2. Model Selection: All seven tested models provided a satisfactory fit to the experimental data, with $R^2$ values ranging from 0.970 to 0.999. However, the Midilli and Kucuk model was identified as the most appropriate for predicting the drying characteristics of M. pubescens, demonstrating the highest $R^2$ (up to 0.9999) and the lowest $\chi^2$ and RMSE values across all conditions.
3. Diffusivity and Activation Energy: The effective moisture diffusivity ($D_{eff}$) values ranged from $2.29 \times 10^{-11}$ to $30.60 \times 10^{-11}$ m²/s. $D_{eff}$ increased with temperature but showed a complex relationship with air velocity; specifically, $D_{eff}$ decreased at higher air velocities (1.0 and 1.5 m/s) compared to lower velocities at elevated temperatures. The activation energy ($E_a$) was calculated to be 64.98 kJ/mol, 80.18 kJ/mol, and 62.57 kJ/mol for air velocities of 0.5, 1.0, and 1.5 m/s, respectively. The relatively high activation energy of 80.18 kJ/mol observed at an air velocity of 1.0 m/s indicates that the drying kinetics are strongly temperature-dependent and controlled by internal diffusion.
4. Characteristic Drying Curve: The CDC approach successfully correlated the normalized drying rate with normalized moisture content using a second-degree polynomial, independent of specific drying conditions.

Significance and Claims
The paper claims to provide the first systematic evaluation of the drying kinetics of Matricaria pubescens leaves. By establishing that the Midilli and Kucuk model accurately describes the drying process and that internal diffusion is the dominant mechanism, the study offers a foundational framework for optimizing drying conditions. The authors assert that these findings are crucial for standardizing the preservation of this medicinal plant, ensuring the retention of its bioactive compounds, and preventing quality degradation during the drying process. The identification of temperature as the primary driver of drying efficiency, rather than air velocity, provides practical guidance for industrial and laboratory-scale drying operations of this species.