Effects of material parameters on the diffusion and sorption properties of wood‐flour/polypropylene composites

Composites of wood in a thermoplastic matrix (wood–plastic composites) are considered a low maintenance solution to using wood in outdoor applications. Knowledge of moisture uptake and transport properties would be useful in estimating moisture‐related effects such as fungal attack and loss of mechanical strength. Our objectives were to determine how material parameters and their interactions affect the moisture uptake and transport properties of injection‐molded composites of wood‐flour and polypropylene and to compare two different methods of measuring moisture uptake and transport. A two‐level, full‐factorial design was used to investigate the effects and interactions of wood‐flour content, wood‐flour particle size, coupling agent, and surface removal on moisture uptake and transport of the composites. Sorption and diffusion experiments were performed at 20°C and 65 or 85% relative humidity as well as in water, and diffusion coefficients were determined. The wood‐flour content had the largest influence of all parameters on moisture uptake and transport properties. Many significant interactions between the variables were also found. The interaction between wood‐flour content and surface treatment was often the largest. The diffusion coefficients derived from the diffusion experiments were different from those derived from the sorption experiments, suggesting that different mechanisms occur. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 752–763, 2007     

A Simulation of Wet Pocket Lumber Drying

In general, wood containing wet pockets is difficult to dry and to ensure uniformity of moisture content at the end of the drying process. Large variations of final moisture content and severe case hardening are common problems associated with the drying of wet wood. In order to devise optimal strategies for drying wood containing wet pockets, it is necessary to understand its complex moisture movement mechanisms and therefore predict drying times and final moisture content. Sub-alpine fir dimension lumber was used in this research because of its inherent issues related to wet pockets.

A two-dimensional mathematical drying model for wood containing wet pockets was developed. An effective diffusion coefficient (D_eff) was utilized in the model and heat and mass transfer equations were solved using a control volume approach. The difficulties involved in the simulation of the drying process of wet pocket lumber are due to the differences in moisture content and physical properties between wet and normal wood. Thus, an adjustable D_eff based on the moisture content (for both below and above fiber saturation point) was used during the simulation.

Four drying runs involving green unsorted sub-alpine fir lumber were carried out in a 3-ft laboratory kiln and in an 8-ft pilot kiln. The results of the simulations were in agreement with the results obtained through the drying experiments.     

TWO-STAGE MOISTURE DIFFUSION IN WOOD WITH CONSTANT TRANSPORT COEFFICIENTS

ABSTRACT

To determine whether transport coefficients in desorption curves for northern red oak are constant, four sets of desorption data were compared against previously established mathematical conditions for infinite-series solution of the non-steady-state diffusion equation. For each data set, when moisture fraction in wood is above a certain value, designated as the first stage, these conditions are satisfied, with the diffusion and surface emission coefficients being positive and finite; below that value, designated as the second stage, these conditions are still satisfied, with the diffusion coefficient taking a smaller positive value but the surface emission coefficient becoming negative and finite. Mathematically, these two pairs of transport coefficients can be used to predict the whole diffusion curve that describes the variation of moisture fraction with time. However, the negative surface emission coefficient in the second stage of the desorption process implies that the moisture gradient has cut the surface at a point below the equilibrium moisture content, which is physically impossible. Alternatively, the second stage can be considered as a new stage with moisture fraction values normalized with respect to the lowest value in the first stage, which is also the starting point of the second stage. The transport coefficents are obtained in the same manner as in the first stage and are found to be positive and finite. The two pairs of transport coefficients can describe the diffusion curve with high accuracy. However, the assumption used in the second stage is that the initial moisture content in wood is uniform, which again is physically impossible. We therefore conclude that the transport coefficients for northern red oak are not constant. Although the two-stage approaches presented in this study can predict the diffusion curves accurately, their physical interaction is difficult to justify.     

TWO-STAGE MOISTURE DIFFUSION IN WOOD WITH CONSTANT TRANSPORT COEFFICIENTS

To determine whether transport coefficients in desorption curves for northern red oak are constant, four sets of desorption data were compared against previously established mathematical conditions for infinite-series solution of the non-steady-state diffusion equation. For each data set, when moisture fraction in wood is above a certain value, designated as the first stage, these conditions are satisfied, with the diffusion and surface emission coefficients being positive and finite; below that value, designated as the second stage, these conditions are still satisfied, with the diffusion coefficient taking a smaller positive value but the surface emission coefficient becoming negative and finite. Mathematically, these two pairs of transport coefficients can be used to predict the whole diffusion curve that describes the variation of moisture fraction with time. However, the negative surface emission coefficient in the second stage of the desorption process implies that the moisture gradient has cut the surface at a point below the equilibrium moisture content, which is physically impossible. Alternatively, the second stage can be considered as a new stage with moisture fraction values normalized with respect to the lowest value in the first stage, which is also the starting point of the second stage. The transport coefficents are obtained in the same manner as in the first stage and are found to be positive and finite. The two pairs of transport coefficients can describe the diffusion curve with high accuracy. However, the assumption used in the second stage is that the initial moisture content in wood is uniform, which again is physically impossible. We therefore conclude that the transport coefficients for northern red oak are not constant. Although the two-stage approaches presented in this study can predict the diffusion curves accurately, their physical interaction is difficult to justify.     

A Simulation of Wet Pocket Lumber Drying

In general, wood containing wet pockets is difficult to dry and to ensure uniformity of moisture content at the end of the drying process. Large variations of final moisture content and severe case hardening are common problems associated with the drying of wet wood. In order to devise optimal strategies for drying wood containing wet pockets, it is necessary to understand its complex moisture movement mechanisms and therefore predict drying times and final moisture content. Sub-alpine fir dimension lumber was used in this research because of its inherent issues related to wet pockets.

A two-dimensional mathematical drying model for wood containing wet pockets was developed. An effective diffusion coefficient (D _eff ) was utilized in the model and heat and mass transfer equations were solved using a control volume approach. The difficulties involved in the simulation of the drying process of wet pocket lumber are due to the differences in moisture content and physical properties between wet and normal wood. Thus, an adjustable D _eff based on the moisture content (for both below and above fiber saturation point) was used during the simulation.

Four drying runs involving green unsorted sub-alpine fir lumber were carried out in a 3-ft laboratory kiln and in an 8-ft pilot kiln. The results of the simulations were in agreement with the results obtained through the drying experiments.     

Inverse Finite Element Analysis of Technological Processes of Heat and Mass Transport in Agricultural and Forest Products

Due to complexity of agricultural and forest products, the mathematical model coefficients are often dubious, as experimental determination of their values leads to erroneous results. To solve this problem an inverse finite element analysis software was developed to identify coefficient values of the heat and mass transport model and to predict and visualize the processes. The model reflected 3D structure of investigated systems comprising the heat conduction and moisture diffusion in heterogeneous, anisotropic, and irregularly shaped products represented by wood and cereal grain kernels. Test cases used to validate the software covered identification of the thermal conductivity, convective heat transfer coefficient, diffusion coefficient, equilibrium moisture content, and convective mass transfer coefficient in pine and beech wood, and also in corn. Implementation of the proposed optimization algorithm and improvement of the software functionality resulted in more effective and accurate identification of the coefficient values, demonstrated by increased accuracy and reliability of predicting the heat conduction and water diffusion processes.     

A Method for Studying Dynamic Sorption Behavior of Small Wood Samples

A method for determining mass changes (～ 0.0001 g) in small (～ 4-mm cubes) wood samples using the resonance of small mechanical springs mounted on piezoelectric sensors is presented. The size of the sample allows individual heartwood or sapwood, earlywood, latewood, and compression wood samples to be measured in an oscillating relative humidity environment and compared in terms of time constant and moisture gain. Since the apparatus is cost effective, many replicates can be achieved in one experiment. The use of small wood samples such that all tracheids are exposed removes the effect of structure on bound water transport. This, in combination with the ability to measure the response to small perturbations in relative humidity, presents the possibility to determine gaseous diffusion coefficients as a function of moisture content for individual wood types.

Preliminary, representative results of a study comparing the effect of drying temperature on sorption behavior of wood dried at 20, 90, and 150°C are presented.     

Moisture Diffusion Coefficients for Modeling the First and Second Drying Sections of Green Bricks

A model has been developed that describes the dependence of the moisture diffusion coefficient on the water fraction. Until the end of shrinkage has been achieved, the moisture diffusion coefficient is proportional to the second power of the water fraction. Due to shrinkage, the relevant capillary spaces available for water transport become smaller. Consequently, the moisture diffusion coefficient decreases continually. After the end of shrinkage, the flow resistance to the water moving toward the surface increases sharply due to penetrating air. This leads to a steep drop of the moisture diffusion coefficient by several powers of ten. Measurements were carried out with specimens of defined geometry to determine the moisture diffusion coefficient. On the basis of a specified limiting value, the model is capable of calculating the moisture diffusion for all initially specified raw materials moistures. The moisture can also be determined if the degree of drying shrinkage is known. Using the determined moisture diffusion coefficient, the first and the second drying section can be located. Drying tests were carried out in a laboratory dryer and the experimental results obtained were compared to the simulation results. The simulation results are in good agreement with the experimental results.     

A STUDY ON THE SEPARATION OF DIFFUSION AND SURFACE EMISSION COEFFICIENTS IN WOOD

ABSTRACT

For a more accurate simulation of the moisture sorption process in wood, the precise separation of surface emission and diffusion coefficients is essential. In this paper, a non-linear simplex technique that was developed to obtain the optimum pair of the surface emission coefficient he, and the diffusion coefficient D from a single sorption curve is presented and tested with experimental data. An easy to use computer program was employed to carry out the evaluation. Data analysis showed that the new method resulted in a more statistically accurate calculation of b_c and D than currently existing methods.     

Modeling conventional drying of wood: Inclusion of a moving evaporation interface

A one-dimensional mathematical model is presented that accounts for a moving evaporation interface in simulating the coupled heat and mass transfer during convective drying of wood. In the model proposed, the only mechanism considered in water transport within wood is diffusion. Additionally, the transport of moisture is dominated by the gradient of the moisture content. The controlling equations were established from Whitaker’s volume averaging laws and solved numerically with the finite volume method. The simulation results for the density of vapor and the volume rate of evaporation indicate that the migrating moisture was mainly in the form of gas under conditions of lower moisture content. The evaporation interface moved at approximately constant speed and the evaporation rate of the interface decreased with time. Finally, the core temperature and average moisture content in wood were successfully simulated.     

A Diffusional Model with a Moisture-Dependent Diffusion Coefficient

Many investigators point out that a more realistic diffusion model is obtained when the effective diffusivity is considered with both temperature and moisture content dependent. Two mathematical models to predict the drying curves of pineapple at different temperatures have been compared. The simulation provided by model I, where the effective diffusion coefficient was considered as a function of the temperature, was unsatisfactory as indicated by the mean relative error (%E) of 19.8 ± 2.4%. The diffusion equation was modified by including both the effect of the temperature and the local moisture content on the effective diffusion coefficient in model II, being the %E of the simulation of 4.5 ± 2.0%.     

A Diffusional Model with a Moisture-Dependent Diffusion Coefficient

Many investigators point out that a more realistic diffusion model is obtained when the effective diffusivity is considered with both temperature and moisture content dependent. Two mathematical models to predict the drying curves of pineapple at different temperatures have been compared. The simulation provided by model I, where the effective diffusion coefficient was considered as a function of the temperature, was unsatisfactory as indicated by the mean relative error (%E) of 19.8 ± 2.4%. The diffusion equation was modified by including both the effect of the temperature and the local moisture content on the effective diffusion coefficient in model II, being the %E of the simulation of 4.5 ± 2.0%.     

WATER FLOW AND BINDER MIGRATION DURING DRYING OF COATED PAPER

The aim of this study has been to develop a mathematical model for water flow and binder migration in coated paper. The model can be used for simulation of the stages starting after the coating applicator including infrared and air drying sections. On the basis of the model the moisture, temperature and binder distribution can be determined across the paper thickness. Approximating equations concerning the paper properties are used in the model. We have measured the diffusion coefficient between the water and binder substances. Representative numerical examples are presented for separate and combined infrared and air drying processes.     

SOLUTIONS OF DIFFUSION EQUATION WITH CONSTANT DIFFUSION AND SURFACE EMISSION COEFFICIENTS

Closed-form solutions of the non-steady state diffusion equation with constant transport coefficients are presented. The diffusion coefficient is assumed to be finite, but the surface emission coefficient can be either finite or infinite. Mathematical conditions are established for the transport coefficients to be constant. When these conditions are met, the transport coefficients can then be easily evaluated. Diffusion test data can be compared against these conditions to determine whether or not the transport coefficients are constant. Desorption test data of northern red oak indicate that initial moisture content in wood and equilibrium moisture content in the environment are closely related to the constancy of the transport coefficients.     

THE INFLUENCE OF COMPRESSION WOOD ON THE DRYING CURVES OF PINUS RADIATA DRIED IN DEHUMIDIFIER CONDITIONS

Measurements of drying rate of Pinus radiata at 55°C and 30% RH are presented. The data, which has been used to establish empirical models for P. radiata under dehumidifier drying conditions, was obtained in four drying runs in a drying tunnel, each yielding detailed drying curves for twelve sample sapwood boards of size 350 × 100 × 50 mm. Compression wood was found to have a significant effect on the drying rate curve, giving lower drying rates at 40-100% MC. This effect is interpreted through the use of a numerical multiple-mechanism two-zone model and quantified by using best-fit diffusion parameters from an isothermal diffusion model. A positive correlation was discovered between the moisture diffusion coefficient and initial moisture content, a strong indicator for the presence of compression wood. In the two-zone model, the compression wood effect was replicated by using a tenfold decrease in permeability to liquid flow. Attributes of compression wood that could cause reduced permeability include an increased proportion of latewood, narrower lumen, and a scarcity of bordered pits on the radial walls of longitudinal tracheids.     

SOLUTIONS OF DIFFUSION EQUATION WITH CONSTANT DIFFUSION AND SURFACE EMISSION COEFFICIENTS

ABSTRACT

Closed-form solutions of the non-steady state diffusion equation with constant transport coefficients are presented. The diffusion coefficient is assumed to be finite, but the surface emission coefficient can be either finite or infinite. Mathematical conditions are established for the transport coefficients to be constant. When these conditions are met, the transport coefficients can then be easily evaluated. Diffusion test data can be compared against these conditions to determine whether or not the transport coefficients are constant. Desorption test data of northern red oak indicate that initial moisture content in wood and equilibrium moisture content in the environment are closely related to the constancy of the transport coefficients.     

A New Correlation for the Estimation of Moisture Diffusivity in Corn Kernels from Drying Kinetics

ABSTRACT

The modelisation of cereal drying kinetics is more, and more often performed by the diffusion equation (Fick's law) Eor homogeneous materials rather than lumped or semi-empirical equations. The heterogeneity of the material is accounted for by the use of an effective diffusivity the prediction of which is essential for the determination of the functional relationship between diffusion coefficient and arain moisture content and temperature. For this dependence, the method of resolution may be analytical or numerical. In this study, the estimation of diffusion coefficient is based on drying curves obtained with arains in the ranae of initial moisture content of 18-509 and a temperature of 50:120??. The important result corresponds to the finding that the moisture diffusivity is a function not only of variabies of the state i.e. moisture content and temperature, but also of the initial moisture content as in the following : 'D = P4g X, exp(8 X ). AD and B are both dependent on temperature     

A Numerical Simulation for Solving the Dippusion Equations in the Drying of Hardware Timber

A numerical simulation is described for solving the thermal conduction and mass diffusion equations in boards of hardwood timber, and the Einite-volume method used here has been applied to the drying of Eucalypt timber, an Australian hardwood. The predictions of the variation in the average moisture content with time agree well with both ex~erimental data from the literature and analvtical solutions of the-diffusion equation. The nume ical simulation treats the boundary conditions more accurately than the analytical solutions when the moisture movement is two dimensional, as it is through the cross-section of a timber board. This feature makes the simulation useful when describing the drying process under intermittent drying conditions. These conditions are encountered in the drying of timber in solar kilns, and this simulation may be used to predict the distributions of temperature andmoisture content inboards of timber which are being dried intermittently inside conventional kilns. The numerical simulation for intermittent drying has shown, inthe example studied here, chat the same overall change in average moisture concentration can be achieved with 12-hour active drying and 12-hour relaxationperiodaas forcontinuousdryingbyincreasingthedry-bulb temperature by 10°C for this timber. In spite of the higher dry-bulb temperature used in the active drying period of intermittent drying. the moisture concentration profiles within the board are predicted to be more uniform than with continuous drying, because the internal moisture diffusion process continues during the relaxation period. These mare uniform moisture concentration profiles in intermittent drying are likely to result in lower stress levels within the timber than with continuous drying.     

PARAMETERS INFLUENCING DRYING BEHAVIOR OF RUBBER WOOD (HEVEA BRAZILLIENSIS) AS DETERMINED FROM DESORPTION EXPERIMENT

In this study, the drying properties of rubber wood, which are the basic parameters for kiln scheduling design, were determined from desorption experiment. Equilibrium moisture content expression was developed. The diffusion coefficients at different drying environments were evaluated. It is more appropriate to determine the diffusion coefficients by the optimum scheme in comparison to other schemes; the logarithmic, square-root and half-fraction of evaporable moisture schemes. Finally, the diffusion coefficient of rubber wood was described by, instead of wood moisture content, the drying temperature and relative humidity, which are the parameters controlling the drying kiln operation.     

THE INFLUENCE OF COMPRESSION WOOD ON THE DRYING CURVES OF PINUS RADIATA DRIED IN DEHUMIDIFIER CONDITIONS

ABSTRACT

Measurements of drying rate of Pinus radiata at 55°C and 30% RH are presented. The data, which has been used to establish empirical models for P. radiata under dehumidifier drying conditions, was obtained in four drying runs in a drying tunnel, each yielding detailed drying curves for twelve sample sapwood boards of size 350 × 100 × 50 mm. Compression wood was found to have a significant effect on the drying rate curve, giving lower drying rates at 40–100% MC. This effect is interpreted through the use of a numerical multiple-mechanism two-zone model and quantified by using best-fit diffusion parameters from an isothermal diffusion model. A positive correlation was discovered between the moisture diffusion coefficient and initial moisture content, a strong indicator for the presence of compression wood. In the two-zone model, the compression wood effect was replicated by using a tenfold decrease in permeability to liquid flow. Attributes of compression wood that could cause reduced permeability include an increased proportion of latewood, narrower lumen, and a scarcity of bordered pits on the radial walls of longitudinal tracheids.