Moisture Transport in Wood: A Study of Physical-Mathematical Models and their Numerical Implementation

The ability to predict the moisture variations in wood is important in a number of cases. The applications are extremely wide, ranging from the conditions in the living tree to moisture induced deformations in timber structures. In between, in the course of transformation from living tree to structural timber, a number of processes such as drying and preservative treatment involve the transport and heat and mass.

In this report three particular scenarios are dealt with, and in addition, some general numerical procedures for the solution of the transport models have been developed. The main contributions of the thesis are summarized in Chapters 4 to 7. In Chapter 2 the structure and basic features of wood as related to moisture transport are briefly discussed.

Both hardwoods and softwoods are treated with particular emphasis on the different liquid and gas pathways resulting from the microscopic structure of the woods. In Chapter 3 the general theory of moisture transport in porous media is reviewed. The relevant conservation equations are stated and the constitutive relations governing the transport of the different water phases are discussed.

The application of this theory to wood is then considered and a number of apparent discrepancies pointed out. These relate particularly to the common assumption of thermodynamic equilibrium as well as to the transport of vapour and air within the wooden cellular structure. Further, the mechanisms governing the transport of free water at moisture contents slightly above the fiber saturation point are discussed, and it is demonstrated that some care must be taken when applying the conventional generalized Darcy’s law.

In Chapter 4 the problem of moisture transport below the fiber saturation point is treated. Here the conventional models often fail to describe the transport of moisture, both qualitatively as well as quantitatively, and one often speaks of the behaviour being ‘non–Fickian’. A new model capable of describing this behaviour is presented.

As in previous attempts of modeling the transfer of water below the fiber saturation point, the transport of bound water and water vapour are described separately from one another such that a state of non–equilibrium exists. The gradual approach to equilibrium is accounted for by linking the water phases via a mass transfer term whose principal functional variation is discussed in some detail.

It is found that in order to accommodate the experimental facts a measure of the proximity to equilibrium has to be introduced such that the rate of conversion of water vapour to bound water and vice versa depends on two parameters: the absolute bound water moisture content and the proximity to equilibrium.

With the model a set of sorption experiments is fitted and on the basis of this, the principle variation of the material parameters discussed. Furthermore, some of the consequences of the assumed state of non–equilibrium are illustrated by computing apparent diffusivities from a number of simulated experiments.

As has also been reported in the literature this results in sample length dependent diffusion coefficients. In Chapter 5 some of the problems associated with free water flow above the fiber saturation point are described. Here it is important to distinguish between the removal of free water and the infiltration of free water into wood.

Especially for the problem of infiltration have a number of discrepancies been reported. Indeed, it seems that whereas the conventional models predict time scales in the order of seconds or minutes, the time scales observed in experiments are in the order of days or weeks. Moreover, in a number of recent experimental studies have the moisture distributions proven to be very far from what would be expected in the basis of the conventional models.

In Chapter 6 the problem of wood preservation is treated. The type of preservative treatment dealt with consists of placing the preservative in solid form in the wood, after which it is then carried throughout the wood by a combination of convection and diffusion. In a concrete application the treatment of wooden poles with a boron compound was considered.

In Chapter 7 the numerical methods for the solution of the models developed are dealt with. The similarity between the equation governing the flow of water in partially saturated porous media and the conduction of heat in solids with simultaneous change of phase is pointed out. Using this similarity, a iterative method recently proposed for the latter problem is applied to the former problem.

The method proves to be most efficient and is shown to in fact be a reformulation of the so–called variable switching technique. Further topics dealt with are spatial weighting procedures and analytical derivation of some of the tangent matrices commonly encountered in coupled heat and mass transfer computations.

Finally, some of the features of drying are discussed and a three dimensional wood drying example presented.