Phenolic antioxidants were extracted from Moringa oleifera leaves by applying ultrasound-assisted extraction (UAE). The feasibility of UAE was studied by analyzing the kinetics, thermodynamics, mass transfer, and effective diffusivity mechanisms to improve the process under several temperature values (298, 300, 306 K). Extraction rate increased with temperature (0.0028, 0.0028, and 0.0029 L mg⁻¹ min⁻¹). Activation energy for the process of UAE was calculated to be 3.5225 kj mol⁻¹. Based on the results of thermodynamics parameters, UAE process of phenolic extraction from Moringa oleifera leaves was endothermic, random, and spontaneous, where the change in enthalpy, entropy, and Gibbs free energy were 1.6156 kj mol⁻¹, 0.02977 kj mol⁻¹ K⁻¹, and − 7.2356, − 7.3247, − 7.4732 kj.mol⁻¹, respectively. Furthermore, the diffusion and mass transfer model were used in order to evaluate the diffusion coefficients, mass transfer coefficients, and Biot numbers of the process. Diffusion coefficients (1.9800 × 10⁻¹⁰, 2.3070 × 10⁻¹⁰, and 2.3905 × 10⁻¹⁰ m² s⁻¹) and mass transfer coefficients (0.1320, 0.1447, and 0.1460 m s⁻¹) increased with increasing temperature, while Biot numbers (285.00 × 10³, 268.05 × 10³, and 261.22 × 10³) decreased slightly with increasing temperature. In addition, Biot number indicated that the external resistance is negligible.

Graphical abstract

中文翻译：

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超声辅助从辣木叶中提取生物活性分子的动力学、热力学和传质机制

通过应用超声辅助提取 (UAE)从辣木叶中提取酚类抗氧化剂。通过分析动力学、热力学、传质和有效扩散机制来研究阿联酋的可行性，以在几个温度值（298、300、306 K）下改进过程。提取速率随温度增加（0.0028、0.0028 和 0.0029 L mg ^-1  min ^-1）。经计算，UAE 过程的活化能为 3.5225 kj mol ^-1。基于热力学参数结果，阿联酋从辣木中提取酚类物质的工艺叶子是吸热的、随机的和自发的，其中焓、熵和吉布斯自由能的变化分别为 1.6156 kj mol ^-1、0.02977 kj mol ^-1  K ^-1和 - 7.2356、 - 7.3247、 - 7.4732 kj.mol ^{- 1}、分别。此外，使用扩散和传质模型来评估过程的扩散系数、传质系数和 Biot 数。扩散系数（1.9800 × 10 ^-10、2.3070 × 10 ^-10和2.3905 × 10 ^-10 m ²  s ^-1）和传质系数（0.1320、0.1447 和0.1460 m s ^{-1 ）}) 随温度升高而增加，而 Biot 数 (285.00 × 10 ³、268.05 × 10 ³和 261.22 × 10 ³ ) 随温度升高略有下降。此外，比奥数表明外阻可以忽略不计。

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