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.     

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.     

Nonisothermal moisture diffusion experiments analyzed by four alternative equations

Summary Five steady-state nonisothermal diffusion experiments were performed with one surface maintained at approximately 70°C and the other at 35°C, with the latter at a relative humidity of 65%. Relative humidities on the warm side varied from 11% to 65% resulting in equilibrium moisture contents from 2.1% to 8.9%. A reversal of flux direction was observed as the relative humidity of the warm side was decreased below that on the cool side indicating a strong influence of the temperature gradient. This reversal was predicted by two nonisothermal equations: one based on a gradient of activated moisture content and the other on a gradient of chemical potential. The flux reversal was not accounted for by the isothermal forms of Fick's law based on gradients of moisture content and partial water-vapor pressure.The author is grateful to Dr. R. V. Jelinek of S. U. N. Y. College of Environmental Science and Forestry for his programming of the computer to solve the differential equations for calculation of the fluxes and moisture-content profiles     

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.     

Thermal diffusion of bound water in wood

Summary There are few references in the wood science literature to nonisothermal moisture movement. Some experiments by Voight, Babbitt, and Choong indicate that thermal diffusion in wood may be very significant.Three equations are presented to represent nonisothermal moisture movement through wood in the transverse direction. The first, described in detail in a previous paper, is based upon two driving forces: Soret potential which results in thermal diffusion and chemical potential which results from a gradient of equilibrium relative humidity. All three equations include the same term for Soret potential and, in the second two equations, the thermal-diffusion term was derived by the application of activation theory. The isothermal term in these two equations utilizes moisture content gradient as the driving force and therefore a knowledge of the sorption isotherm is not necessary. The third equation contains an additional term for moisture-content activation to account for the increase in flux with an increased moisture content. All three equations give approximately the same result with the same input data at low moisture contents. The results diverge at high moisture contents and experimental data are required to determine which equation is most representative of the physical phenomenon of nonisothermal moisture movement.     

An investigation of the external and internal resistance to moisture diffusion in wood

Summary An attempt was made to resolve the resistance to moisture diffusion in wood into its components, namely, the external and internal resistances by using Newmann's solution of Fick's second law. The effect of specimen thickness, moisture content, and temperature on the coefficients were also investigated.This research was supported by the National Science Foundation     

Wood drying and Fick's second law

Summary The diffusion equation (sometimes referred to as Fick's second law) is derived in terms of water movement under the action of capillary forces. The mass diffusivity is thereby expressed in terms of the capillary diffusion coefficient. A numerical calculation is given for yellow poplar.Notations C diffusion coefficient for water in wood with capillary pressure as the driving force, kg/msPa - D diffusion coefficient for water in wood with moisture content as the driving force, kg/ms - F mass flux, kg/m²s - p_c capillary pressure, Pa - p_cf capillary pressure extrapolated linearly to fibre saturation, Pa - T absolute temperature, K - t time, s - x distance ordinale in the direction of flow, m - mass diffusivity, m²/s - density of liquid water, kg/m³ - _g basic density (dry mass/green volume), kg/m³ - _w density of wood substance, kg/m³ - moisture content of wood - _cls moisture content at continuous liquid saturation - _cs moisture content at complete saturation - _f moisture content at fibre saturation     

Equilibrium moisture content and the movement of water through wood above fibre saturation

The present work brings together the results of two previous studies on the diffusion coefficient and on capillary pressure, both above fibre saturation. The hypothesis making the data mutually consistent, is the constancy of the diffusion coefficient where capillary pressure is the driving force. Also given is an isotherm for wood which extends over the full range of moisture content, from dry to complete saturation. A further consequence of the work is the probability density function for capillary pressure with respect to water adsorbed and the corresponding distribution of capillary sizes.     

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     

Diffusion of bound water in wood

Summary A model for isothermal bound water diffusion in wood is derived from Babbitt's (1950) analysis of diffusion in adsorbing solids. Calculations of the energy required for water molecules to become dissociated from their sites is identified as one component of the activation energy for diffusion. Consideration of the resistance to diffusion leads to a second component of activation energy associated with overcoming the attraction of water molecules for themselves. Also, an approximate expression for the resistance coefficient is developed. These results are combined into a transport model for bound water. The model shows that equations for bound water movement based on fluid mechanics (Babbitt 1950) and thermodynamics (Katchalsky, Curran 1965) are identical when the driving force for diffusion is defined as the moisture flux per unit transport coefficient. Activation energies and diffusion coefficients derived from the model compare favorably with literature values.The author wishes to thank Dr. Christen Skaar for his interest and advice during preparation of this paper for publication     

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)     

Determination of the effective water conductivity of red pine sapwood

Summary The instantaneous profile method was used to establish the boundary desorption curve of the effective water conductivity function of red pine (Pinus resinosa Ait.) sapwood in the radial and tangential directions from nearly saturated to dry conditions at 18, 56 and 85 °C. The results obtained demonstrate that the effective water conductivity is a function of moisture content, temperature, and direction of flow. The effective water conductivity increases by several orders of magnitude (10⁴–10⁵) as moisture content increases from dry to nearly saturated conditions at a given temperature. The effective water conductivity also increases by a factor varying between 10 and 50 as temperature rises from 18 to 85 °C in the moisture content range considered. The variation of the moisture content–water potential relationship with temperature can explain part of the temperature effect. The effective water conductivity was generally higher in the radial direction than in the tangential direction in a ratio varying from about 1/1 to 3/1 depending on moisture content and temperature. Finally, the flux–gradient relationships obtained at given moisture contents were found to be linear, confirming the validity of using a moisture flux equation considering the water potential gradient as the driving force for the experimental conditions considered in the present work. The knowledge of the effective water conductivity function and of the moisture content–water potential relationship allows the utilization of a two-dimensional model of moisture movement in wood during drying using the gradient in water potential as the driving force for drying at temperatures up to 85 °C. Received 27 February 1998     

木材微波干燥内部压力对水分移动的影响

在微波干燥过程中,能量是以电磁波的形式直接渗透到木材的内部,并通过微波电磁场与水分子及木材中极化分子(羟基)的相互作用而迅速产生大量的热,导致木材内水分移动机理与常规干燥很大的不同。实验结果表明:微波干燥过程中,存在内高外低的压力场,内中蒸汽压力是水分移动的驱动力。     

Moisture content—water potential relationship of wood from saturated to dry conditions

Summary The water potential concept as applied to wood-water relations is presented. The gradient in water potential can be used as the driving force of moisture in wood in a model of drying in isothermal conditions provided the moisture content — water potential relationship is known. This relationship is established for aspen sapwood in desorption from saturated to dry conditions at 20, 35 and 50 °C for two specimen orientations. The tension plate, pressure plate and pressure membrane methods were used at high moisture contents and equilibration over saturated salt solutions was used at low moisture contents. The results obtained demonstrate that these methods can be used in combination in order to establish the relationship within the whole range of moisture contents. The equilibrium moisture contents obtained by the tension plate, the pressure plate and the pressure membrane methods for tangential desorption were slightly higher than those measured for radial desorption. The water potential increased with temperature at a given moisture content. This effect cannot be solely explained by the variation of surface tension of water with temperature.This research was supported by the Fonds pour la Formation de Chercheurs et l'Aide à la Recherche, Gouvernement du Québec, and by the Natural Sciences and Engineering Research Council of Canada     

Thermal diffusion in Masson pine wood

In order to analyze the effects of the temperature gradient on moisture movement during the highly intensive microwave-vacuum drying, thermal diffusion of Masson pine wood was studied. Internal distribution of temperature and moisture in Masson pine samples sealed by epoxy resin and aluminum foil was measured, the magnitude of thermal diffusion was calculated and the influencing factors of thermal diffusion were discussed. Results showed that with the transfer of moisture toward the low temperature in wood, opposite temperature and moisture gradient occurred. The initial moisture content （MC）, temperature and time are important factors affecting this process; the thermal diffusion is in proportion to wood temperature, its initial moisture and time. The temperature and distance from hot surface is strongly linearly correlated, and the relationship between MCs at different locations and distance from the hot end surface changes from logarithmically form to exponentially form with the increase in experimental time.     

木材内部水分扩散特性研究现状及发展趋势

扩散是水分在木材内部移动的一种重要途径。文中围绕木材内部水分的扩散机理、测试方法及其影响因素3个方面阐述水分扩散的驱动力类型及其在木材内部的基本移动路径,总结稳态和非稳态水分扩散系数的测试及计算方法;综述树种、早/晚材、心/边材、幼龄/成熟材等因素对水分扩散特性的影响机制;归纳木材含水率、温度等因素对木材内部水分扩散的作用规律;结合国内外关于水分扩散的研究现状,指出一些亟待解决的问题,以期为木材干燥、木结构建筑、木质包装材料的研究与应用提供参考。     

竹材热压干燥过程中的水分扩散研究

采用非稳态法测定龙竹竹材热压干燥过程中的水分扩散系数,并探讨了温度对水分扩散系数的影响.结果表明:干燥温度越高,干燥各阶段水分扩散系数及平均水分扩散系数也越大;初始高含水率阶段,随含水率逐渐降低,水分扩散系数呈逐步增加趋势,在纤维饱和点附近时达最大值;随后,随含水率逐渐降低呈逐步减少趋势.     

Mechano-sorptive effects on timber creep

Summary Fick's law of predicting the moisture content of beams, combined with a simple mechano-sorptive model is applied to the analysis of creep resulting from moisture variations due to changing environmental conditions. The natural climatic conditions are modelled with the daily and annual cyclic variations represented by sine waves. As the moisture change responding to varying climatic conditions is always greater near the boundaries of a timber section, the creep rate close to the surface layer is higher than that in the middle of the cross-section. Therefore with time, an increased portion of the load will be carried by the inner part of the material.     

关于植物吸水动力的新见解

叶肉细胞产生的渗透吸力和根细胞产生的渗透压力是水分吸收运输的主要动力。根压是吸水结果而不是吸水动力。蒸腾只是一个失水过程而不能直接产生吸水动力,所谓蒸腾拉力是叶肉细胞通过渗透吸水在导管内产生的负压。水分的吸收运输完全是建立在渗透平衡基础上进行的。     

A model of moisture movement in wood based on water potential and the determination of the effective water conductivity

Summary A model of isothermal moisture movement in wood during drying using the gradient in water potential as the driving force is proposed. The moisture transport coefficient used in this model is the effective water conductivity. It is a function of moisture content, temperature, and direction of flow. The boundary desorption curve of the effective water conductivity function is established in the radial and tangential directions of aspen sapwood from nearly saturated to dry conditions at 20, 35, and 50 °C using the instantaneous profile method. The results show that the effective water conductivity increases exponentially with moisture content and temperature. The effect of temperature cannot be solely explained by the variation of the viscosity of water. The variation of the moisture content-water potential relationship with temperature would explain a large part of this effect. The effective water conductivity was generally higher in the radial direction than in the tangential direction in a ratio varying from 1/1 to 25/1 depending on moisture content and temperature. The flux-gradient relationship obtained at given moisture contents were found to be linear, confirming the validity of the model for the experimental conditions considered in the present work.The authors wish to thank Peter Garrahan of Forintek Canada Corp., Ottawa for his comments and suggestions. This research was undertaken while the senior author was a grant-holder from the Fonds pour la Formation de Chercheurs et l'Aide à la Recherche, Gouvernement du Québec