A model for multiphase moisture and heat transport below and above the saturation point of deformable and swelling wood fibers – I: Mass transport

Abstract

A thermodynamically consistent model for heat and mass transfer in deformable wood fibers is developed. The hybrid mixture theory is used to model the material as a mixture of three phases, consisting of a solid, a liquid and a gas phase. The solid phase consists of dry fibers and bound water constituents, whereas the gas phase has dry air and water vapor constituents. Emphasis is put on the mass flow and mass exchange of moisture in the material both below and above the saturation point of the solid wood fibers. Generalized forms of Fick’s, Darcy’s and Fourier’s laws are derived, and the chemical potential is used as a driving force for mass flow. Mass exchange due to sorption and evaporation/condensation processes is implemented in the model, where hysteretic properties both within and above the hygroscopic moisture range are described using Frandsen’s hysteresis model. Moisture induced swelling/shrinkage is included where the porosity of the material can vary. A large strain setting formulated for general orthotropy is adopted for the mechanical deformations. To show the performance of the resulting model, it is implemented in a finite element method framework and used to simulate the processes of heat and moisture transport dynamics of a wood sample subjected to drying from an over-hygroscopic moisture state.

Keywords

• Moisture transport
• Hybrid mixture theory
• Sorption hysteresis
• Over-hygroscopic
• Swelling wood