Modeling of the sorption hysteresis for wood

This paper deals with an adsorption/desorption model in order to predict evolutions of boundary conditions during the mass transfer process versus time in timber elements. This model is derived from a thermodynamic balance between the free water and its saturated vapor pressure, and is generalized for the bound water phase. It allows describing a realistic adsorption and desorption phenomena characterized by a moisture content hysteresis induced by cyclic variations of the relative humidity and the temperature. The sorption isotherm explains the equilibrium between the bound water phase in wood and the vapor pressure in the environment. The model includes different latent heats for the adsorption and desorption process. An analytic explanation allows to model partial variations in terms of relative humidity domain.     

Some considerations in heterogeneous nonisothermal transport models for wood: a numerical study

This study compares a number of coupled heat and mass transfer models and presents numerical comparisons of phenomenological coefficients between the four models (Stanish, Perre, Pang, and Avramidis) that are most frequently used in the literature to describe wood-drying processes. The USDA sorption isotherm, the Hailwood-Horrobin model, was adopted to calculate the relations between moisture content in wood and water vapor pressure at any temperature. Due to different assumptions about the driving forces of heat and mass transfer, coefficients in each model represent different values for moisture content and temperature and are closely related to each other. In the case of isothermal mass transfer, the moisture diffusion coefficient in the transverse directions from the Stanish and Pang models increased with decreasing moisture content. This contradicts the Avramidis and Perre models and numerous experimental results. Thermal diffusion effects on the drying process may not be predominant because the nonisothermal state is relatively short. Therefore, the Perre model, which does not consider the thermal diffusion effect, has been used successfully in the drying simulation. However, it may be erroneous in certain cases when the nonisothermal state prevails over the system, such as building physics. The Pang model cannot explain the phenomena of thermal diffusion and moisture thermodiffusion. It might be reasonable to modify the thermal diffusion of the Avramidis model, which is lower than that of the Stanish model. The apparent heat diffusivity was higher than the true heat diffusivity.     

Fundamentals of flakeboard manufacture: wood-moisture relationships

Summary A procedure is presented to estimate the relative vapor pressure, equilibrium moisture content, average flake temperature, and average flake moisture content in a flakeboard mat during hot-pressing. This method is based on measurements of temperature and total gas pressure in the mat during hot-pressing. A heat and mass transfer model was adapted from the literature to predict the temperature and moisture content inside an individual flake. Significant moisture gradients are predicted to develop within flakes. Convective heat transfer appears to control the change of moisture content within a flake. Thermodynamic equilibrium between the gas phase and the wood component is not achieved during hot-pressing.This work was funded by the USDA Competitive Grant Program for Forest and Rangeland Renewable Resources, Project No. 85-FSTY-9-0106 and 87-FSTY-9-0253     

An irreversible thermodynamics model for unsteady-state nonisothermal moisture diffusion in wood

Summary A model that predicts heat and moisture transfer through wood in the hygroscopic range and which is based on the principles of irreversible thermodynamics, was evaluated with unsteady-state nonisothermal moisture desorption experimental data. The model predicted the phenomenon of thermal diffusion during the initial stages of desorption and results in a very good simulation of the desorption curve and the center's temperature change with time.Symbols C_p specific heat of air (= 0.24 cal/g K @ 70 °C) - C_T specific heat of wood, cal/g K - D transverse diffusion coefficient, cm²/s - E_b activation energy, cal/mol - E_o heat of vaporization, cal/mol - E_L differential heat of sorption, cal/mol - G specific gravity of wood - H relative humidity, % - h_T convective heat transfer coefficient, cal/cm² s K - h_c convective mass transfer coefficient based on the concentration of moisture in wood, cm/s - h_v convective mass transfer coefficient based on the concentration of moisture in the air in equilibrium with the wood surface, cm/s - K_M coefficient for diffusion due to moisture gradient, g/cm s % - K_T transverse thermal conductivity coefficient, cal/cm K s - M moisture content, % - P_o saturated vapor pressure, atm - R universal gas constant, cal/mol K (= 82.056 cm³ atm/mol K) - t time, s - T temperature, K - x distance, cm Greek Letters evaporation or condensation criterion - wood density, g/cm³ - _W water density (=1), g/cm³ - _a air density, g/cm³ Department of Wood Science and Forest Products Virginia Polytechnic Institute and State University Blackburg, Virginia 24061-0503     

The thermoosmotic effect in wood

Summary Water vapor pressures computed from stationary state data for moist wood (Choong 1963) are used to infer changes in the logarithm of vapor pressure per unit change in Kelvin temperature, d ln p/dT, for comparison with corresponding values from a thermodynamic model. The model evaluates the overall heat of transfer associated with passage of vapor through wood, and hence quantifies the thermoosmotic effect. Results of the comparison verify the existence of a constant vapor entropy for wood in the stationary state.     

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.     

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。     

Implementation of a relaxation equilibrium term in the convective boundary condition for a better representation of the transient bound water diffusion in wood

In this work, a relaxation term was added to the convective boundary condition to increase the accuracy of the transient bound water diffusion modeling in wood. The implemented term accounts for a relaxation time constant in the equilibrium moisture content. The inverse finite element analysis approach was used to determine the values of all coefficients of the modified diffusion model. This procedure was performed for beech wood (Fagus sylvatica L.) in the radial and longitudinal directions. The experimental data obtained by Perré et al. (2007) for transient diffusion configurations were used here. The accurate control of moist air parameters and the improved procedure for mass measurements of a sample during sorption experiments were used. The influence of the modification of the boundary condition on accuracy of diffusion modeling was analyzed.     

Wood in the stationary state: Zero entropy gradients for water vapor and bound water

Summary According to nonequilibrium thermodynamics, the local rate of entropy production is minimized for moist wood in the stationary state. Furthermore, the rate of entropy production due to moisture flow must be zero in this state. Conservation of energy applied to the steady flow of water vapor through an arbitrarily selected volume element of wood shows that the vapor entropy gradient is zero. Because the entropy production due to moisture flow must be balanced by a corresponding entropy flow away from the element, entropy gradients for bound water and water vapor are equal and the bound water entropy gradient also is zero.     

Experimental determination of the convective heat and mass transfer coefficients for wood drying

The knowledge of the convective heat and mass transfer coefficients is required for the characterization of the boundary conditions of the heat and mass transfer equations of a wood drying model based on water potential. A new experimental method for the determination of the convective mass transfer coefficient is presented. This method is based on the measurement of the moisture content, and indirectly the water potential, at the surface of a wood specimen at different drying times. Drying experiments were performed on red pine (Pinus resinosa Ait.) sapwood from nearly saturated to dry conditions at 56 °C, 52% relative humidity and air velocities of 1.0, 2.5 and 5.0 m s⁻¹. The results show that the convective mass transfer coefficient is constant until the wood surface moisture content reaches about 80% and then decreases more or less gradually as the moisture content decreases further. The convective mass transfer coefficient increases with air velocity. A regression analysis shows that there is no significant improvement in considering the water potential gradient near the wood surface when the difference in water potential between the surface and the surrounding air (ψ_s − ψ_∞) is used to determine the convective mass flux at the surface. Also, ψ_s − ψ_∞ is more appropriate than the water vapour pressure difference (pv_s − pv_∞) as the responsible driving force of the moisture flux leaving the wood surface. The convective heat transfer coefficient was determined during the same experiments. A plateau is observed at high values of moisture content corresponding to the constant drying rate period. Received 27 February 1998     

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.     

Moisture content gradient in a softwood board during drying: simulation from a 2-D model and measurement

Summary A 2-D mathematical model was developed to simulate moisture movement and heat transfer in width and thickness directions within a softwood board during drying. The model is based on wood physiological features and behaviour observed during drying. In sapwood, liquid water movement is assumed to be a consequence of capillary action between liquid and gas phases inside the cell lumens. However, liquid flow does not occur in wood close to the exposed surfaces because at timber surfaces the wood cells are damaged during the sawing process and consequently the liquid column is broken. In heartwood, liquid flow is negligible since the pits are normally aspirated during the formation of heartwood in the growing tree. Water vapour moves under a partial vapour pressure gradient while bound water diffuses within the wood material due to differences in chemical potential. The model was solved numerically to predict moisture-content profiles. Experiments were undertaken to measure the moisturecontent gradient. Samples were removed from a tunnel dryer at intervals throughout drying, frozen overnight and then cut into slices for moisture-content determination. The experimental results were used to verify the model.This work is supported by the New Zealand Foundation of Research, Science and Technology under contract CO4415     

Variation in surface conductance to water vapor diffusion in peach fruit and its effects on fruit growth assessed by a simulation model

Surface conductance to water vapor diffusion was measured in individual peach fruits (Prunus persica (L.) Batsch) and plotted as a function of fresh fruit mass for four cultivars. Surface conductance increased with fresh fruit mass, but the pattern differed with cultivar, and fruit-to-fruit variation occurred. Relationships between fruit mass and surface conductance were modeled by fitting mathematical equations to the data. The simulation model of Fishman and Génard (1998) was used to study dry mass and water components of fruit growth (1) when surface conductance varied with fruit size or was constant, and (2) when surface conductance values were high, moderate or low with respect to fruit mass. Increased surface conductance with fresh fruit mass resulted in fruit growth cessation. Fruits differing in surface conductance had similar dry mass. However, under well-watered conditions (stem water potential between -1 and -0.2 MPa), the water balance components of growth (osmotic and hydrostatic pressure, water potential and water balance) differed greatly and, as a result, the lower the surface conductance the greater the fresh fruit mass. These differences were buffered under drought conditions (stem water potential between -2.4 and -0.6 MPa).     

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     

Modelling the process of release of a chemical from wood in finite volumes of water in succession

Summary Chemicals used for protection of wood against fungi may be released in water when the sample comes into contact with water. The process of release of pentachlorophenol in water was studied in this paper, when the presaturated wood specimen is immersed in a finite volume of water up to a time at which equilibrium is not attained. The wood sample is then dried and immersed again in water. This process is continued many times. Moreover a finite coefficient of matter transfer at the wood surface is observed. A numerical model with finite differences was successfully tested by comparing the kinetics of release obtained either by experiments and calculation. The process was simplified in the sense that only the transfer of the chemical through the water located in the wood was considered. The model is thus able to provide the kinetics of release and the profiles of concentration.     

高温热处理木材吸湿特性

【目的】研究高温热处理对人工林樟子松、杉木、美洲黑杨木材平衡含水率和吸湿特性的影响,为科学评价热处理木材吸湿特性提供理论基础,为人工林木材高附加值利用和实际高温热处理木材生产提供参考。【方法】以水蒸气为保护介质,设定180、200和220 ℃3个温度进行高温热处理,采用双室温、湿度控制法,在25 ℃环境中以8种不同类型饱和盐溶液精确控制水蒸气相对湿度进行等温吸附试验,运用Hailwood-Horrobin模型拟合等温吸附曲线,分析高温热处理对木材水蒸气等温吸附曲线线形、平衡含水率、单层分子吸附水和多层分子吸附水的影响。【结果】 180、200和220 ℃处理后,试样吸湿平衡含水率均值相当于素材含水率均值的80%、70%和50%左右;3个树种素材试样和高温热处理材试样均表现为第2类等温吸附曲线形态特征,Hailwood-Horrobin模型能够较好拟合不同树种素材和高温热处理材等温吸附曲线,不同热处理条件试样等温吸附曲线的拟合度均高于0.980 0,处理温度越高,等温吸附曲线越接近直线;高温热处理后代表含有单位摩尔数吸附位的绝干木材质量参数( W )显著增加,不同相对湿度下高温热处理材的单层分子吸附水和多层分子吸附水含量也随之降低;180、200和 220 ℃处理后,木材试样单层分子吸附水含量相较于素材下降20%、30%和50%左右,高温热处理对多层分子吸附水含量影响规律与之相近;高温热处理后单层分子吸附水、多层分子吸附水和吸附水总量的最大值相较于素材明显下降,且处理温度越高,下降幅度越大。【结论】高温热处理可明显降低3个树种试样的吸湿平衡含水率,且处理温度越高,平衡含水率下降幅度越大;高温热处理会一定程度影响木材等温吸附曲线线形,Hailwood-Horrobin模型可用于描述高温热处理材等温吸附曲线,且拟合度较高;高温热处理可明显降低3个树种试样等温吸附过程单层分子吸附水和多层分子吸附水含量,且处理温度越高影响越明显,单层分子吸附水和多层分子吸附水最大含量均明显降低,进而影响吸附水总量最大值。     

刨花对流干燥过程的传热传质研究动态

详细介绍并归纳多孔介质与木材领域内的传热传质理论研究概况,从中寻找出适合研究刨花对流干燥过程传热传质的方法.经过理论分析,提出可根据非平衡热力学理论和相平衡理论,建立一个描述刨花对流干燥时刨花外部对流传热传质和内部热、湿迁移过程的非平衡热力学模型.     

A new boron impregnation technique of wood by vapor boron of boric acid to reduce leaching boron from wood

This study was designed to reveal impregnation ability and to enhance leaching resistance of boron from borate-treated wood. Vapor boron treatment was applied in compressed and uncompressed states at high temperatures such as 180 and 200°C for 6, 8 and 15 min. Following ten-cycle leaching periods, amounts of boron leached from vapor boron treated wood was measured by ion chromatography. According to the results, boric acid can be vaporized under heat and can be impregnated into wood. Success of the technique can be increased by increasing vapor pressure in a closed chamber. Leachability results proved the boron vaporization along with water vapor at various ratios depends on the process variables. These results have importance on dry wood treatment under heat by boron vapor with a little water presence which does not necessitate a further drying process.     

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.     

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.