A multi-scale approach for simulation of transient moisture transport processes in wood below the fiber saturation point

This paper presents a new, physically-based model for transport processes in wood for conditions below the fiber saturation point. The macroscopic mathematical description of these processes involves three coupled differential equations: two mass balance laws for the bound water and the water vapor phase, and an energy balance equation. These governing equations and the corresponding boundary conditions are expressed in terms of the state variables bound water concentration, water vapor concentration, and temperature. Macroscopic material properties are estimated based on a multiscale approach in the framework of continuum micromechanics. The phase change between the two water phases and the thus resulting coupling between the differential equations cannot be suitably captured in a purely macroscopic description, therefore a microscale sub-model is presented. Numerical solutions of the model equations are derived by means of the Finite Element Method. Finally, the model is applied to prediction of moisture profiles in a wood sample under transient environmental conditions. Comparing these results with corresponding profiles obtained non-destructively by proton magnetic resonance imaging (MRI) validates the model and confirms suitability of the underlying physical assumptions.