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<p>Four diffusion models were constructed based on integer-order and fractional-order diffusion equations coupled with first-type and third-type boundary conditions, respectively. Drying experiments of radiata pine sapwood below the fiber saturation point (FSP) were carried out under different temperatures, relative humidities and specimen lengths. Based on the experimental data, the mass transfer parameters and fractional-order operator <i>α</i> corresponding to the four models were obtained, and their variation trends with temperature, humidity and specimen length were analyzed. Finally, the application scenarios of the four models were summarized in combination with the drying parameters obtained from each model and the physical patterns revealed. It is found that the diffusion coefficient <i>D</i> and convective mass transfer coefficient <i>h</i> have highly consistent variation trends with temperature and humidity, and there is a universal linear correlation between them, which has been verified in a variety of materials. Additionally, the diffusion coefficients obtained from the integer-order models (Models 1 and 3) satisfy the Arrhenius equation, whereas those from the fractional-order models (Models 2 and 4) do not; nevertheless, the fractional-order models achieve the highest accuracy in simulating the drying curves. Furthermore, the fractional-order operator <i>α</i> shows no obvious dependence on temperature or relative humidity, but decreases with increasing specimen length, causing the diffusion behavior to approach Fickian diffusion. Moisture content is also a critical factor: <i>α</i> decreases substantially when the moisture content falls below 12%.</p>

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Non-Fickian behavior and moisture transfer parameters in wood below FSP: Temperature, humidity, and length effects via four diffusion models

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Xingchen Ding,
  • Jiuqing Liu,
  • Qi Ou,
  • Jie Yan,
  • Chengwen Sun,
  • Chunmei Yang

摘要

Four diffusion models were constructed based on integer-order and fractional-order diffusion equations coupled with first-type and third-type boundary conditions, respectively. Drying experiments of radiata pine sapwood below the fiber saturation point (FSP) were carried out under different temperatures, relative humidities and specimen lengths. Based on the experimental data, the mass transfer parameters and fractional-order operator α corresponding to the four models were obtained, and their variation trends with temperature, humidity and specimen length were analyzed. Finally, the application scenarios of the four models were summarized in combination with the drying parameters obtained from each model and the physical patterns revealed. It is found that the diffusion coefficient D and convective mass transfer coefficient h have highly consistent variation trends with temperature and humidity, and there is a universal linear correlation between them, which has been verified in a variety of materials. Additionally, the diffusion coefficients obtained from the integer-order models (Models 1 and 3) satisfy the Arrhenius equation, whereas those from the fractional-order models (Models 2 and 4) do not; nevertheless, the fractional-order models achieve the highest accuracy in simulating the drying curves. Furthermore, the fractional-order operator α shows no obvious dependence on temperature or relative humidity, but decreases with increasing specimen length, causing the diffusion behavior to approach Fickian diffusion. Moisture content is also a critical factor: α decreases substantially when the moisture content falls below 12%.