Mesoscopic modeling of vapor transport in wood in tangential and radial direction

Holzforschung, 2005

The methods so far applied to determine the bound water diffusion coefficient in wood do not provide credible results on this coefficient as well as on the boundary condition. An alternative approach based on the concept of solving the inverse transfer problems was recently applied. Two European species were investigated in the present study. A series of sorption experiments was performed and followed by the numerical identification of the coefficients. Several case studies were carried out for the constant and bound water content dependent diffusion coefficients. The obtained results were validated by comparison to a set of experimental data.

Scientific Reports, 2019

Timber is the only widely used construction material we can grow. The wood from which it comes has evolved to provide structural support for the tree and to act as a conduit for fluid flow. These flow paths are crucial for engineers to exploit the full potential of timber, by allowing impregnation with liquids that modify the properties or resilience of this natural material. Accurately predicting the transport of these liquids enables more efficient industrial timber treatment processes to be developed, thereby extending the scope to use this sustainable construction material; moreover, it is of fundamental scientific value — as a fluid flow within a natural porous medium. Both structural and transport properties of wood depend on its micro-structure but, while a substantial body of research relates the structural performance of wood to its detailed architecture, no such knowledge exists for the transport properties. We present a model, based on increasingly refined geometric param...

Mediterranean Journal of Chemistry

Wood is a natural and highly anisotropic material. Therefore, mechanical characteristics of the material depend on the direction of wood. In this paper, we propose to describe the transfer of the water inside the wood in two dimensions by immersing the sample in liquid water. The potential which drives the transport of water through the wood is controlled by the diffusion transient process. A model based on a numerical finite difference method has been found to follow the absorption process of water above the fibers saturation point of two-dimensions.

This paper is concerned with pure diffusion of water vapor within the wood material. It's well known that such a phenomenon is mathematically modelled by a system of evolution equations to be solved. Our purpose is to solve with simple but efficient and powerful numerical tools the posed problem in a non-isotropic medium. To achieve this goal we' ve developed a finite volume method following a novel methodology. This methodology is based upon a semi-integral formulation of balance equation. Let's mention that finite volume methods are carried out under weaker assumptions on the exact solution than those required by the finite difference method widely used in wood industry. Boundary conditions associated to our problem are of Fourier' s type and the material possesses a finite thickness. These boundary conditions are numerically expressed by an approach consisting to consider the points of the interior frontier as being simultaneously in the material (hence satisfy the balance equation) and on the frontier (hence verify the boundary conditions). Error estimates obtained by [5] are recalled and numerical simulations are compared with experimental results.

2024

The mechanisms of moisture diffusion in wood are not yet fully understood, due to the complex and hierarchical structure of the wood cell wall constituents. To investigate the diffusion mechanism in such hierarchical structure, fractal geometry analysis was used as proper tool. The objective of this study is to develop a theoretical fractal moisture diffusion model for wood cell wall by taking into consideration its structural geometry and to upscale that model to gross wood by employing electrical resistance modeling and validation. The proposed fractal diffusion model is a function of fractal dimensions, porosity, and pore size distribution of the wood cell wall as well as ambient conditions such as moisture content, temperature, and inverse slope of the sorption isotherm. The water vapor sorption data that was used to drive the experimental diffusion coefficient of various wood types were studied using the dynamic sorption method. Mercury intrusion porosimetry was used to explore the detailed structural parameters of pore size distributions and calculate the pore fractal dimension. The derived fractal diffusion model was validated using experimental and data calculated by a past published model. The trends for diffusion coefficients predicted by the fractal model were similar to the experimental and published data. The developed model was successfully predicted the diffusion coefficients at low moisture contents. Pore fractal dimension, tortuous fractal dimension, and pore size ratio were negatively correlated to fractal diffusivity, while the porosity was positively correlated. The findings are expected to predict the moisture transport and the wood cell wall geometric properties through the fractal dimensions of the structure.

Transport in Porous Media, 2006

An alternative approach to determining the bound water diffusion coefficient is proposed. It comprises a method for solving the inverse diffusion problem, an improved algorithm for the bound-constrained optimization as well as an alternative submodel for the diffusion coefficient's dependency on the bound water content. Identification of the diffusion coefficient for Scots pine wood (Pinus sylvestris L.) using the proposed inverse approach is presented. The accuracy of predicting the diffusion process with the use of the coefficient values determined by traditional sorption methods as well as by the inverse modeling approach is quantified. The similarity approach is used and the local and global relative errors are calculated. The results show that the inverse method provides valuable data on the bound water diffusion coefficient as well as on the boundary condition. The results of the identification can significantly improve the accuracy of mass transfer modeling as studied for drying processes in wood. Inverse method • Computer-aided identification • Fick's law • Scots pine wood • Sorption experiments • Validation of identification Nomenclature a Constant in Eqs. 13 and 14 (-) b Constant in Eq. 14 (-) D Diffusion coefficient (m 2 /s) D 0 Coefficient in Eqs. 12-14 (m 2 /s)

International Journal of Thermal Sciences, 2016

Non-Fickian diffusion in native and thermally modified wood was analyzed by the inverse method. A low quality of the identified diffusivity values was found for the diffusivity which was either constant or varying with water content. This was explained by the non-Fickian behavior. It was especially distinct for thermally modified wood for which an increased delay in obtaining the hygroscopic equilibrium was clearly shown. Such a delay was explained by time required for molecular reorganization to produce new sorption sites. This phenomenon was accounted to improve the physical model by modifying the convective boundary condition. A relaxation mechanism was used for this purpose with an adequate time constant.

This article describes the transfer of the water inside the wood in the field of the free water, which is controlled by the diffusion in transitory regime, especially when the wood is immersed in some liquid water. The method used is to couple the experimental study with a theoretical approach. Also we developed mathematical models of the transfers of water capable of identifying this phenomenon.

AIChE Journal, 1992

A model that predicts heat and moisture transfer in the hygroscopic range of a complex porous material such as wood, was evaluated with unsteady-state nonisothermal diffusion experimental data. Water chemical potential gradient was taken as the driving force for diffusion, and the derivation of the temperature-gradient phenomenological coefficient in the mass balance equation was based on the principles of nonequilibrium thermodynamics. The results reveal an excellent prediction of the specimen's average moisture content during desorption in the hygroscopic range. Moreover, a very good agreement was also shown between the specimen's center temperature and the model predictions. The model revealed the existence of a thermal-diffusion phenomenon during the initial stages of the desorption process. This phenomenon was not predicted by Fick's equation for diffusion.

Holzforschung, 2003

Summary An inverse identification method for characterization of wood sorptive properties is presented. The method relies on a computer simulation of a real experiment, in our case a desorption experiment, where spruce heartwood samples were dried from 27% to 8% moisture content. Three samples, distinguished by the respective moisture flow pattern through the specimen, were investigated. A computer aided material characterization using the so-called inverse problem identification method was performed on the measurements. The solution of the specified inverse problem enabled us to estimate the moisture diffusion coefficients of wood and to determine the moisture content field in the sample simultaneously. The method is first verified on two simple cases of uniaxial moisture flow, and then is used to characterize the diffusion coefficients on a biaxial moisture flow sample. In the latter case some salient features of the proposed method are exhibited.

Holzforschung, 2011

The combined bound water and water vapour diffusion of wood is of great interest in the field of building physics. Due to swelling stresses, the steady-state-determined diffusion coefficient clearly differs from the unsteady-state-determined diffusion coefficient. In this study, both diffusion coefficients and the water vapour resistance factor of Norway spruce (Picea abies [L.] Karst.) and European beech (Fagus sylvatica L.) were investigated for the principal anatomical directions (radial, tangential and longitudinal) and in 15° steps between these directions. The values were determined with the cup method as the basic principle. The unsteady-state-determined diffusion coefficient is, independent of the direction, about half that of the steady-state-determined diffusion coefficient. Both diffusion coefficients are about two to three times higher for spruce than for beech. They are up to 12 times higher in the longitudinal direction than perpendicular to the grain for spruce, and u...

2011

To predict the risk if mould growth, rot, deformations and cracks in wood, it is necessary to know the moisture levels in constructions and building components. This paper presents a theory and a twodimensional PC-model based on the use of Kirchhoff potentials to calculate moisture flow in wood. Anisotropy is allowed for using different flow coefficients in the different directions, in both sapwood and heartwood. The theory also deals with the internal boundary between sapwood and heartwood, and the external boundary to the outer air. The discrete form of the partial differential equation and the numerical technique to solve the problem are presented. The values of the flow coefficients used in the model are based on direct laboratory measurements. Calculation results from the model are compared with independently measured twodimensional moisture distributions. The agreement is good. The output data from this model should be used as input data in risk models for mould growth and rot.

2016

The hygroscopic behaviour of wood leads to changes in the physical and mechanical properties. The correct estimation of the moisture content is important for the design and life cycle of timber structures. Therefore experimental test series were performed to determine the moisture content distribution over the cross section as a function of loading duration, respecting the glue lines of glulam and block glued cross sections. Alongside, numerical simulations of the moisture diffusion process were set up and validated with the experimental test series. The correlation of the numerical simulation with the reality offers guidance in the design of timber structures.

Wood Science and Technology, 2013

The objective of this article is to determine an expression for the effective mass diffusivity related to the description of wood drying using a diffusion model and experimental data. With this objective, a three-dimensional numerical solution of diffusion equation for the parallelepiped, with convective boundary condition, was used to describe the drying process. For the adopted diffusion model, the convective mass transfer coefficient h was considered constant. The effective mass diffusivity D was considered as a function of the local moisture content, and several expressions were tested to describe the process. To this end, the numerical solution was coupled to an optimizer based on the inverse method, which determines the process parameters D and h using an experimental dataset. For both temperatures of the drying air studied in this article (40 and 80°C), the results obtained by considering the variable effective mass diffusivity are better than those obtained when considering such parameter with a value constant. In addition, with the results for D and h obtained by optimization, the drying kinetics was simulated with success. List of symbols A, B Coefficients of the discretized diffusion equation (dimensionless) D Effective mass diffusivity (m 2 s-1) h Convective mass transfer coefficient (m s-1) M Local moisture content at instant t (db, kg kg-1) M Average moisture content at instant t (db, kg kg-1) M 0 Initial moisture content (db, kg kg-1) M 1 Equilibrium moisture content (db, kg kg-1

Forests, 2019

Despite the importance of cell wall diffusion to nearly all aspects of wood utilization, diffusion mechanisms and the detailed effects of moisture remain poorly understood. In this perspective, we introduce and employ approaches established in polymer science to develop a phenomenological framework for understanding the effects of moisture on diffusion in unmodified wood cell walls. The premise for applying this polymer-science-based approach to wood is that wood polymers (cellulose, hemicelluloses, and lignin) behave like typical solid polymers. Therefore, the movement of chemicals through wood cell walls is a diffusion process through a solid polymer, which is in contrast to previous assertions that transport of some chemicals occurs via aqueous pathways in the cell wall layers. Diffusion in polymers depends on the interrelations between free volume in the polymer matrix, molecular motions of the polymer, diffusant dimensions, and solubility of the diffusant in the polymer matrix....