Fractal Modeling of Moisture Diffusion in Wood Cell Wall

Abstract The mechanisms of moisture diffusion in wood are not yet fully understood, due to the complex and hierarchical structure of the wood cell wall constituents. To investigate this mechanism in this hierarchical structure, fractal geometry analysis was used as proper tool. The objective of this study is to develop a theoretical fractal moisture diffusion model for wood cell wall by taking into consideration its structural geometry and to upscale that model to gross wood by employing electrical resistance modeling and validation. The proposed fractal diffusion model is a function of fractal dimensions, porosity, and pore size distribution of the wood cell wall as well as ambient conditions such as moisture content, temperature, and inverse slope of the sorption isotherm. The water vapor sorption data that was used to drive the experimental diffusion coefficient of various wood types were studied using the dynamic sorption method. Mercury intrusion porosimetry was used to explore the detailed structural parameters of wood cell wall pore size distributions and calculate the pore fractal dimension. The derived fractal diffusion model was validated using experimental and data calculated by a past published model. The trends for diffusion coefficients predicted by the fractal model were similar to the experimental and calculated data and successfully predicted the diffusion coefficients at low moisture contents. Pore size ratio, pore, and tortuous fractal dimensions were negatively correlated to fractal diffusivity, while the porosity was positively correlated. The findings of this study contribute to the creation of a decision support system that would allow predicting wood geometric properties and moisture diffusivity properties based on wood structural and ultrastructural attributes.