Keywords: moisture transfer, timber structures, natural varying humidity, sorption, finite element analysis.

This paper presents a study of sorption rate function in a so-called multi-Fickian or multi-phase model. This model describes the complex moisture transport system in wood, which consists of separate water-vapor and bound-water diffusion interacting through sorption. In the numerical example the influence of the sorption rate function on water transport is presented. It can be seen that the sorption rate function has a noticeable influence on coupled water transport in wood.

Moisture transport of a hygroscopic and open porous material such as wood is a complex system of coupled processes. A mathematical model used to predict moisture transport in wood for a given condition that must at least consider the dominating active processes to be accurate and all active processes to comply with the physics [1,2]. Since the processes constituting the moisture transport are fully coupled, experimental studies have found it difficult to investigate each process isolated from the others. The model used here for calculation is a coupled Fickian model for which vapour transport in pores and bound water transport in wood tissue are modelled by two individual transport equations following Fick's law. The transport equations are fully coupled by a process of phase change from vapour to bound water or vice versa, i.e. sorption. Changes in the humidity of the ambient air causes changes of the state moisture of the wood. There is, however, not a unique one to one relationship between air humidity and the moisture state of wood. The moisture state history of the wood influences this relationship and must therefore be taken into account.

Results from the numerical analyses where the connectivity of the two main equations of the Fickian model are presented. The main subject of investigation is the parameters that connect those two main equations. The influence on the main quantities (moisture and humidity of the timber elements) on the dependence of the parameters that connect the main equations is presented in a numerical example. Results from the numerical study show that the sorption rate function has a noticeable influence on the coupled water transport in the wood and it can be concluded that if moisture transport from cell wall to cell lumen does not exist, the diffusion process of moisture in the cell wall is relatively quick compared to one when sorption does exist.

1

H.L. Frandsen, S. Svensson, L. Damkilde, "A hysteresis model suitable for numerical simulations of moisture content in wood", Holzforschung, 61, 172-181, 2007.

2

H.L. Frandsen, S. Svensson, "Implementation of sorption hysteresis in multi-Fickian moisture transport", Holzforschung, 61(6), 693-701, 2007.

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