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Fractal modeling of moisture diffusion in wood Tibebu, Dessie


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. In order to investigate this mechanism in this hierarchical structure, fractal geometry analysis was used as proper tool. This study has three major objectives: first, to investigate and understand water sorption, pore structure, and fractal property of two softwood and two hardwood species; second, to develop a theoretical fractal moisture diffusion model for wood cell wall by taking into consideration its structural geometry using the tortuous capillary bundle model and fractal theory; and third, to upscale that model to gross wood by employing electrical resistance modeling and validation. The proposed fractal diffusion model is a function of both pore and tortuosity fractal dimensions, porosity, and pore size distribution of the wood cell wall. The water vapor sorption behaviors of various wood types were studied using the dynamic sorption method. Their pore structure and fractal characteristics were investigated using nitrogen and mercury intrusion porosimetry. The pore size distribution ranged from 1.4 nm to 350 um, and porosity ranged between 58 and 76 %. The pore and tortuous fractal dimension values ranged from 2.5 to 2.98, and from 1.034 to 1.076, respectively, with a higher degree of pore complexity for larger pores. 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. When the pore and tortuosity fractal dimensions were close to 2 and 1, respectively, the diffusion coefficient values approached to the minimum. 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.

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