A model for bound-water transport in wood

Summary A model for the isothermal transport of bound water through the cell wall of wood is developed, based on the assumption that the driving force for moisture movement is the gradient of spreading pressure , as first proposed by Babbitt (1950). This pressure is a surface phenomenon, derivable from the surface sorption theory of Dent (1977), a modification of the BET sorption theory. The force resisting moisture transport is assumed to be inversely proportional to moisture content and directly proportional to the equivalent viscosity of the sorbed water, calculated to be orders of magnitude larger than that of free water. The coefficients normally used to describe isothermal moisture transport in wood are derived from the model, and their predicted behavior as functions of the relative vapor pressure h of the cell wall are described graphically. An attempt is made to calculate a quantitative magnitude for the diffusion coefficient D, based on an assumed relationship between viscosity and the activation energy for water diffusion.     

Diffusion and the drying of wood

Summary Fick's laws, stating that diffusion rate is proportional to the concentration gradient, have traditionally been used to describe the drying of wood. The author contends that they have been used inappropriately, since according to Fick's laws the rate varies as the concentration gradient of diffusing molecules, whereas many wood scientists use the concentration gradient of non-diffusing molecules —the bound water. When the temperature-dependent component of the diffusion coefficient is combined with the concentration gradient of diffusing molecules, the resulting driving force is proportional to the vapour pressure, and the diffusion coefficient is independent of temperature.     

Diffusion of bound water in wood

Summary Choong's (1963) data for isothermal sorption of water vapor by wood are used to compute pressures, chemical potentials, and entropies of water in the wood specimens of his nonisothermal mass equilibrium experiments. Entropies of both the bound water and water vapor were reasonably constant. A balance existed between thermal diffusion and mass diffusion, as indicated by gradients in temperature and chemical potential. This balance also is suggested by opposing gradients in spreading pressure and vapor pressure. Equal chemical potentials showed that the vapor and bound water were in equilibrium. The model proposed by Siau (1980) for nonisothermal diffusion is consistent with these results. Expressions are given for the two unknown parameters in this model: moisture conductivity and heat of transfer. The constant entropy of water vapor is used to show that the heat of transfer exceeds the activation energy for bound water diffusion by about 25 percent.The author wishes to thank Dr. Christen Skaar for his helpful comments during preparation of this paper for publication     

木材导热系数的研究

本文运用非平衡态热力学线性理论分析了含水率在纤维饱和点以下木材的传热,结果表明木材中的水蒸汽和束缚水参与了传热,木材导热系数由传导导热系数与因水蒸汽和束缚水扩散产生的两个等效导热系数组成。推广Siau关于木材细胞的导热理论,依据水分吸附和扩散的原理,导出了木材弦向和径向导热系数计算公式,与已发表的36种气干材弦向实验值和23种气干材径向实验值符合较好。分析木材径向传热的方法也适用于木材纵向传热。     

A THEORY OF DETERMINING MASS TRANSFERPARAMETERS FOR WOOD PARTICLE MATERIALS

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The effect of openings on combined bound water and water vapor diffusion in wood

This study was undertaken to estimate the effect of openings between cell walls on combined bound water and water vapor diffusion in wood. Using a newly developed model, the radial and tangential moisture diffusion coefficients can be predicted depending on the opening area. The new model explicitly involves a term for water vapor diffusion through the openings, as well as a term for the combined diffusion of bound water and water vapor. A classical model developed by Stamm and Choong had higher longitudinal moisture diffusion coefficients than that in the parallel model at higher moisture content, which is inconsistent with the Wiener bound rule. The new model suggested in this article is useful for analyzing the experimental results and understanding the variability of the diffusion coefficients.     

Moisture diffusion coefficient of reaction woods: compression wood of Picea abies L. and tension wood of Fagus sylvatica L.

The moisture diffusion coefficient of compression wood in spruce (P. abies) and tension wood in beech (F. sylvatica) was examined. The results indicated that the diffusion coefficient measured under steady-state condition (cup method) could well characterize the drying kinetics of the reaction woods. The compression wood offered more resistance to the moisture diffusivity when compared with the corresponding normal wood. The thick cell wall rich in lignin explains the small mass diffusivity in compression wood. In contrast, the mass diffusivity in beech is almost always higher in tension wood than in normal wood, in spite of similar density values. The high moisture diffusion in tension wood can be explained by the ease of bound water diffusion in the gelatinous layers (G-layers).     

Analysis of moisture diffusivity of larch timber during convective drying condition by using Crank＇s method and Dincer＇s method

Two analytical procedures （Crank＇s method and Dincer＇s method） for porous solid materials were reevaluated and used to determine moisture diffusion coefficients and moisture transfer coefficients for larch lumber subjected to drying. A diffusion-like equation was used to describe drying process data. The lumber was idealized in the modeling as infinite plates. The moisture transport process inside the board was assumed to be one-dimensional. The macroscopic drying kinetics curves of larch timber at particular conditions were determined experimentally. Based on these data, calculation for both the moisture diffusion coefficients and moisture transfer coefficients by the Dincer＇s analytical procedure were made. The dynamic moisture diffusion coefficients by the traditional Crank＇s method were calculated. In general, diffusion coefficients calculated by the Dincer＇s method were all higher than those by Crank＇s method. These results could be due to the differences between two analytical methods and also different characteristics between solid moisture diffusion process and heat transfer process. Therefore the analysis and solution procedures of moisture diffusion differential equations need to be adapted in the future. With drying temperature＇s increasing moisture diffusion coefficient （D） and moisture transfer coefficient （k） increases accordingly. Also the relationships between diffusion coefficients and temperature as well as material moisture contents were analyzed by using Arrhenius equation and bound water transport theory.     

Classification of the conductance of moisture through wood cell components

This study aimed to clarify the conductance of moisture through wood cell components. Moisture diffusion coefficients were determined from three models (Stamm, Siau, and Kang et al.) and cell wall, pit, and ray dimensions were experimentally observed in a wood specimen. Fractions of moisture diffusing along each path in each of the models were analyzed. As moisture content decreased, the fraction of water diffusing as bound water through cell walls in tangential and longitudinal directions decreased while water vapor diffusion through lumens and pits became more dominant. Diffusion coefficients predicted by each model were compared with experimental values. Although predicted values differed from experimental values, predicted trends for diffusion rate dependence on moisture content were similar to the experimental results. In particular, the models of Stamm and Kang et al., which consider moisture transport through rays and pits, show a very consistent trend for transverse diffusion, which is always faster radially than tangentially. Input of more accurate dimensions of cell walls and cavities into the models should result in more reliable values, closer to the experimentally determined diffusion coefficients.     

Water uptake by scots pine sapwood,and its restriction by the use of water repellents

Summary Water in contact with wood surfaces is able to penetrate into the cellular structure by three routes: 1. As liquid water into cell lumena, by capillarity. — 2. As water vapour, by diffusion into cell lumena. — 3. As bound water, by diffusion within the cell wall.Transport from cell lumena into adjacent cell walls occurs rapidly by diffusion. In Scots pine (Pinus sylvestris) sapwood, it is shown that transport over short distances occurs much more rapidly by capillarity than by either of the diffusion processes. Treatment of wood with resin/wax water repellent formulations greatly reduces the rate of water flow due to capillarity and hence significantly cuts down the rate of dimensional change of specimens exposed to wet conditions.Swelling rates due to vapour phase and bound water diffusion were measured experimentally, and these data were used to predict the water sorption rates for specimens treated with a theoretically perfect water repellent, viz. that which excludes all liquid water.It was found experimentally that specimens immersed in water, after treatment with resin/wax water repellents, swelled more rapidly than predicted by the above procedure. This more rapid swelling is probably due to a certain amount of liquid water flow made possible by displacement of the hydrophobic film from cell wall surfaces (preferential wetting). It is suggested that the use of hydrophobic agents bonded chemically to the cell wall may be necessary to attain optimum water repellent effectiveness.     

Dependence of the water vapor diffusion coefficient of aspen (Populus spec.) on moisture content

Summary The dependence of the diffusion coefficient of water in aspen (Populus sp.) on moisture content over the range of 0 to 18 percent moisture content at 43 °C was determined. The method requires a series of adsorption experiments and application of a numerical method for solving the diffusion equation with a moisture-content-dependent diffusion coefficient. The diffusion coefficient was found to increase exponentially with moisture content. The numerical method includes variable boundary conditions, as defined by the surface emission coefficient, so that the effect of surface equilibrium moisture content can be examined. The experimental moisture content-time curves can be predicted by the numerical method and showed an average deviation of 0.2 percent moisture content with the largest deviation being 0.7 percent moisture content. Practical implications and uses of the information derived from the numerical method are also discussed.This research was partially funded under the USDA Competitive Grant program     

Theoretical water sorption energies by conformational analysis

Summary Values of the sorption energies of single molecules of water on all available sorption sites of amorphous cellulose I have been obtained by conformational analysis. The sorption energies are equated to the total energy (Etot) of interaction between the water molecule and all the atomic groups of the cellulose. Van der Waal, H-bond and electrostatic energies comprised the E_tot. The interference of water molecules on two vicinal sorption sites were also obtained and sites in which such interference can occur were identified for amorphous cellulose. Curves relating E_tot to percentage equilibrium moisture content are reported as well as exact sorption isotherms constructed as E_tot as a function of humidity for the amorphous and crystalline cellulose I. These isotherms were constructed for different relative proportions of amorphous to crystalline cellulose and can be constructed for any of their relative proportions from the isotherms for amorphous-only and crystalline-only cellulose. The sorption energies of the monolayer were all calculated. Curves of energy of sorption of bound water were also obtained by introducing the calculated energy values in equations from already established sorption theories.Sorption capacities of amorphous and crystalline Cellulose I were calculated and the respective isotherms constructed and discussed from the point of view of existing sorption theories.     

木材干燥导水系数和换水系数的研究

木材(板、方材)的导水系数和换水系数是反映木材干燥或存放过程中水分迁移的重要物性参数。然而,我国对木材导水系数和换水系数的研究和测定工作十分有限。木材干燥有关的理论计算中,常用原苏联的数据。由于这些数据本身可能存在的误差及用于我国树种的可靠程度难以估计,故使理论结果的实际运用受到限制。本文采用等厚试件系数分离法研究和测定了木材干燥过程动态导水系数和换水系数。     

Modeling the process of absorption and desorption of water above and below the fiber saturation point

Summary The process of absorption of water along the tangential direction of the wood is studied by immersing the sample in water. The transport of water is then obtained below the fiber saturation point at the beginning of the absorption and above this fiber saturation point during the process. The potential which drives the transport of the bound-water and free-water through the wood has been considered by testing a diffusional transport model. The transient diffusion with a constant diffusivity has been found to describe not only the process of absorption but also the process of desorption with diffusion of water through the solid and evaporation from the surface. Analytical solutions have been successfully used to describe the stage of absorption during a time of four hours at the end of which an equilibrium of absorption is attained, as well as the following stage of desorption. A model based on a numerical method with finite differences has been found to describe the process of absorption and desorption in various cases, and especially when the equilibrium of absorption has not been attained.This work was carried out with the help and support of the M. R. T. and the French CTB (Wood Technical Center)     

An experimental assessment of driving forces for drying in hardwoods

Summary An investigation has been carried out into whether the internal moisture movement inside Australian hardwood timber is best described by a diffusion model with driving forces based on gradients in moisture content or in partial pressure of water vapour. Experimental data from two sets of drying schedules applied to timber from three species of Australian hardwoods (yellow stringybark, spotted gum and ironbark) reported in Langrish et al. (1997) have been used to assess the use of the two driving forces, and the standard error has been used as the criterion for goodness of fit. Moisture-content driving forces have fitted the data better than a model based on vapour-pressure driving forces alone. The use of moisture-content driving forces with diffusion parameters obtained from data from one drying schedule is also better in predicting the drying behaviour with another schedule than vapour-pressure driving forces for yellow stringybark and ironbark. These results may be due to the complexity of the moisture-movement process through timber, with more than one moisture-transport mechanism being active, so that the use of only one driving force for moisture movement is at best only an approximation to the true behaviour.Symbols D diffusion coefficient, m² s^–1 (moisture-content gradient), m³ s kg^–1 (vapour-pressure gradient) - D_e activation energy, K - D_r pre-exponential factor m² s^–1 (moisture-content gradient), m³ kg^–1 (vapour-pressure gradient) - J mass flux of water divided by density, m s^–1 - t time, s - x position, m - X moisture content, kg kg^–1 This work has been supported by the Australian Research Council, the Ian Potter and George Alexander Foundations, and The University of Sydney Research Grant Scheme.     

On the activation energy of diffusion of water in wood

Summary The diffusion equation for water in wood is expanded in terms of temperature and moisture gradient on the assumption that the driving force for the diffusion of water in wood is the partial pressure of water vapour. An analytic expression is then developed for the activation energy of diffusion in terms of enthalpy and entropy changes associated with the sorption process. The expression is compared with another published curve and some similarity was observed.Symbols C water concentration, kg/m³ - D diffusion coefficient for water vapour in wood with vapour pressure as the driving potential, kg/ms Pa - D_c diffusion coefficient for water vapour in wood with water concentration as the driving potential, m²/s - D_c a constant value of D_c, m²/s - E activation energy of diffusion, J/kg - F flow density, kg/m² s - f h/l - h specific enthalpy, J/kg - L l/R T - l latent heat of vapourization of free water, J/kg - l_s latent heat of vapourization of sorbed water, J/kg - p partial pressure of water vapour, Pa - p_s pressure of water vapour at saturation, Pa - R specifc gas constant for water, J/kg K - r relative humidity - s specific entropy, J/kg K - w dry basis moisture content - x length coordinate, m - a constant temperature equal to 6,800 K - -/ln r - _w density of wood (dry mass/moisture volume) at a given moisture content, kg/m³ - s/R - L style as 2 lines above - free water relative to sorbed water The author is grateful to the Editorial Board in relation to the use of (4)     

Internal mass transfer coefficient during drying of softwood (Pinus elliottii Engelm.) boards

A drying experiment with 36 mm thick softwood boards having an average initial moisture content of approximately 1.2 (dry basis) was performed. Drying temperatures of 40, 60 and 80°C were used. Relative humidity and superficial air velocity were maintained at 40% and 3.0 m s^?1, respectively. Internal moisture content was monitored along the process in the single direction of the internal flux of water. Loss in mass of the entire timber board was also determined. An effective coefficient of mass transfer was tuned to internal experimental profiles of moisture content by involving the Fick’s second law. An explicit finite difference method for the numerical solution of the mass balance represented by the Fick’s equation was combined with the simplex method of optimization to obtain a mass transport parameter in the magnitude of 1.5–3.5 × 10^?9 m² s^?1. A positive and significant effect of temperature on the effective diffusion coefficient, which was well described by an Arrhenius type expression, was deduced from this investigation. Although a negative effect of the average moisture content on the internal resistance to mass transfer was also observed, it was much less evident; mainly above the wood fiber saturation point. A negligible influence of the local moisture content on the investigated transport parameter was noticed when either a linear or a nonlinear model correlating these variables was adopted.     

Diffusion of non-swelling gases through dry conifer wood

Summary The conditions under which mutual, Knudsen and transition-range diffusion occur are described, and the corresponding gaseous diffusion coefficients are stated. The coefficient of hindered diffusion through pit membrane pores is shown to be about one third of the mutual diffusion coefficient and not about one thirtieth as postulated by earlier workers. A new longitudinal diffusion equation is developed, and results of a new gas permeability technique are used to derive coefficients for Picea sitchensis and Abies grandis. Only a small proportion of the tracheids is assumed to be conducting, owing to pit aspiration. About 98% of the resistance to longitudinal diffusion is in the tracheid lumina, 1% in the pit apertures and 0.2% in the pit membrane pores. From similar considerations a new tangential diffusion equation is developed, and coefficients are calculated. Roughly 90% of the resistance to tangential diffusion occurs in the pit apertures, 10% in the pit membrane pores and only 0.3% in the tracheid lumina. The agreement between the theoretical and published experimental values is satisfactory. For tangential diffusion the agreement is closer by an order of magnitude than that obtained by earlier workers. The experimentally determined temperature dependence of the diffusion coefficients is shown to be consistent with the above results. A hindered diffusion coefficient of one thirtieth of the mutual coefficient would lead to a temperature dependence not observed experimentally.     

Dissolved carbon dioxide gas diffusion in green Nothofagus fusca heartwood

Summary Non-steady state desorption of dissolved carbon dioxide gas from green Nothofagus fusca heartwoood boards saturated with carbon dioxide gas at a pressure of 1.5 MPa was used to measure transverse dissolved carbon dioxide gas diffusivities at 1, 20 and 30 °C. Mean transverse diffusion coefficients were 0.6×10^-11m²s^-1 at 1 °C, 4.2×10^-11m²s^-1 at 20 °C, and 8.4×10^-11m²s^-1 at 30 °C. These are 0.6, 2.5 and 3.8% of the dissolved carbon dioxide gas diffusivities in water at 1, 20 and 30 °C respectively. The activation energy of dissolved carbon dioxide gas diffusion in green N. fusca heartwood is 59. 4 kJ mol^-1. This is three times the activation energy of dissolved carbon dioxide gas diffusion in water. This suggests the presence of a reaction mechanism between the dissolved carbon dioxide molecules and the cell wall constituents.The Forest Research Institute, Ministry of Forestry, New Zealand, supported this work by way of a postgraduate studentship.