Johannes Eitelberger

Theory of transport processes in wood below the fiber saturation point. Physical background on the microscale and its macroscopic description

Abstract The macroscopic formulation of moisture transport in wood below the fiber saturation point has motivated many research efforts in the past two decades. Many experiments demonstrated the difference in steady state and transient moisture transport and the inadequacy of models derived for steady state transport when used to describe transient processes. A suitable modeling approach was found by distinguishing between the two phases of water in wood, namely bound water in the cell walls and water vapor in the lumens. Such models are capable of reproducing transient moisture transport processes, but the physical origin of the coupling between the two phases remains unclear. In this paper, the physical background on the microscale is clarified and transformed into a comprehensive macroscopic description, ending up with a dual-scale model comprising three coupled differential equations for bound water, water vapor, and internal energy, as well as a simplified microscale model for determination of the coupling term.

Multiscale homogenization of wood transport properties: Diffusion coefficients for steady-state moisture transport

Abstract This paper describes a multiscale homogenization model for macroscopic diffusion properties of wood. After a short introduction the physical background of steady-state diffusion processes in wood will be highlighted, resulting in a physically motivated macroscopic description of diffusion processes with only one diffusion equation and thus one diffusion tensor. This macroscopic diffusion tensor is derived by revisiting the morphological structure of wood in the framework of continuum micromechanics. The starting point is the cellular structure of wood; further homogenization steps include wood rays and the succession of annual rings. The quality of the model is assessed by a comparison of model predictions and measured values at different temperatures and moisture contents.

The Sorption Behavior of Wood Studied by Means of an Improved Cup Method

In transport models for wood, sorption is an essential parameter. Sorption is the balancing process between the two phases of water present in wood below the fiber saturation point, namely water vapor in the lumens and bound water in the cell walls. To gain better insight into the physical background of transport processes, a special experimental test setup—the improved cup method—is presented. It allows for separation of sorption from other processes. In this test, a diffusion cup contains a thin specimen of wood, with one side facing outwards to a climate chamber and the opposite side facing inwards the cup. In contrast to the common cup method, the herein presented method uses a data logger for relative humidity and temperature placed inside the cup. The use of thin cross-cut specimens allows for explicit separation of the different processes occurring during transient moisture transport. Mass changes were determined and relative humidity inside the cups was measured for eight specimens of Norway spruce with different specimen thicknesses. Relative humidity was increased in three uniform steps in the test chamber from 4.0 up to 76.5%. The results obtained with this special test setup indicate that the sorption process is different than assumed in previous publications. This emphasizes the need of improved modeling approaches.

Computational Multiscale Approach to the Mechanical Behavior and Transport Behavior of Wood

Moisture considerably affects the macroscopic material behavior of wood. Since moisture takes effect on wood at various length scales, a computational multiscale approach is presented in this paper in order to explain and mathematically describe the macroscopic mechanical and transport behavior of wood. Such an approach allows for appropriate consideration of the underlying physical phenomena and for the suitable representation of the influence of microstructural characteristics of individual wood tissues on the macroscopic behavior. Continuum (poro-)micromechanics is applied as homogenization technique in order to link properties at different length scales. Building the model on universal constituents with tissue-independent properties and on universal building patterns, the only tissue-dependent input parameters are wood species, mass density, moisture content, and temperature. All these parameters are easily accessible, what renders the models powerful and easily applicable tools for practical timber engineering.

Modeling of Transient Moisture Diffusion in Wood below the Fiber Saturation Point

During the last two decades the macroscopic formulation of moisture transport in wood below the fiber saturation point has motivated many research efforts. From experiments the difference in steady-state and transient transport processes is well known, but could not be explained in a fully physically motivated manner. In the following article, first the microstructure of wood is depicted, followed by a description of the physical background of steady-state and transient transport processes in wood, and thereon based mathematical formulations. For a correct macroscopic description of transient transport processes, three coupled differential equations have to be solved in parallel, which is done using the finite element method. The validation of the whole model by comparison of model predictions with experimentally derived values is currently in progress and will be published in near future.