Bound Water Diffusion Research Articles

Unveiling moisture transport mechanisms in cellulosic materials: Vapor vs. bound water.

Natural textiles, hair, paper, wool, or bio-based walls possess the remarkable ability to store humidity from sweat or the environment through "bound water" absorption within nanopores, constituting up to 30% of their dry mass. The knowledge of the induced water transfers is pivotal for advancing industrial processes and sustainable practices in various fields such as wood drying, paper production and use, moisture transfers in clothes or hair, humidity regulation of bio-based construction materials, etc. However, the transport and storage mechanisms of this moisture remain poorly understood, with modeling often relying on an assumption of dominant vapor transport with an unknown diffusion coefficient. Our research addresses this knowledge gap, demonstrating the pivotal role of bound water transport within interconnected fiber networks. Notably, at low porosity, bound water diffusion dominates over vapor diffusion. By isolating diffusion processes and deriving diffusion coefficients through rigorous experimentation, we establish a comprehensive model for moisture transfer. Strikingly, our model accurately predicts the evolution of bound water's spatial distribution for a wide range of sample porosities, as verified through magnetic resonance imaging. Showing that bound water transport can be dominant over vapor transport, this work offers a change of paradigm and unprecedented control over humidity-related processes.

Effect of Samples Length on the Characteristics of Moisture Transfer and Shrinkage of Eucalyptus urophylla Wood during Conventional Drying

Moisture transfer influences wood deformation and moisture content (MC) distribution during conventional drying of Eucalyptus urophylla wood. This study aims to investigate the effect of sample length (30, 100, and 200 mm) on moisture distribution and transfer in different directions and locations and on deformation of wood. The results showed that when the MC was above the fiber saturated point (FSP), the drying rate decreases exponentially with an increase of sample length; however, below the FSP, there was no obvious relationship between the drying rate and sample length and above the FSP, the moisture distribution was non-uniform along tangential, radial, and longitudinal directions and became even below the FSP, which was more significant in the middle location of wood. The greatest MC differences occurred between the surface and sub-central layers along the tangential and radial direction, which were between the end and sub-middle locations along the longitudinal direction. The effect of sample length on the MC distribution and MC differences along wood in the three directions depended on locations and the MC stage of wood; most of the free water and bound water transferred from the wood central to the ends along the longitudinal direction for three sets of samples. Bound water diffusion significantly slowed as the sample length exceeded 200 mm; sample length affects wood collapse and its recovery, but the drying rate has a lesser effect on collapse for samples with a length below 200 mm.

The Characteristics of Moisture and Shrinkage of Eucalyptus urophylla × E. Grandis Wood during Conventional Drying.

High quality lumbers produced from Eucalyptus plantations can be used to make higher value-added solid wood products. Moisture flow affects shrinkage, deformation, and quality of Eucalyptus wood during conventional drying. In this study, 50 and 100 mm long samples were dried using a conventional drying method. The drying curves, drying rate, moisture content (MC) gradient and distribution, moisture flow, and shrinkage during the drying process were investigated. The results show: Drying was much faster in the first 15 h for all samples and became slow as MC decreased. The drying rate above fiber saturated point (FSP) was about 3.5 times of that below FSP for all samples. The drying rate of 50 mm samples above and below FSP is 1.40 and 1.33 times of 100 mm samples; MC gradients are greater in tangential, radial directions, and cross-sections for both samples when the MC is above FSP, especially at an average MC of 50%. MC gradient along the tangential and radial direction depends on the samples size and MC stages. The short samples have much greater MC gradients than the longer samples above FSP. Moisture distributions on the cross-sections of wood coincide with the moisture gradient in the cross-sections. At an average MC of 50%, the moisture distributions of 50 mm are highly uneven, while they are relatively even in the middle of 100 mm samples, and become much more even at the end of the sample. Moisture distributions become even as MC decreases in all of the samples. Water migration directions vary by state of water. In the short samples, most free water migrates more in the fiber direction from the wood center toward the end surfaces, but bound water diffusion becomes weak. The collapse in the 50 mm samples is significantly larger than that in the 100 mm samples, indicating that the collapse is affected by the dimension of the sample.

How Bound Water Regulates Wood Drying

For most wood-based product uses it is essential to remove a large part of the water content from wet or green (fresh-cut) wood, to reduce further dimensional variations under varying humidity conditions, improve its mechanical characteristics, and protect it from biological attacks. However, the internal mechanisms of drying are not fully described. Here we observe drying at different scales using macroscopic measurements (weighing), nuclear magnetic resonance measurements allowing to distinguish bound- and free-water contents, and x-ray computed tomography images of air-liquid interfaces at the smallest pore scale (wood lumens). We show that during wood drying, even well above the fiber saturation point, bound-water diffusion in cell walls (instead of capillary effects) ensures the extraction of liquid water from pores and its transport towards the surface of evaporation, and thus controls the drying rate. The distribution of bound-water content (uniform or heterogeneous) along the main sample axis and the drying-rate evolution depend on the competition between the external conditions and a characteristic rate of transport due to bound-water diffusion. For sufficiently slow drying this distribution remains homogenous until free water is fully extracted. An original physical phenomenon is thus at work, which plays a major role in regulating water extraction, in that it maintains a constant drying rate and a homogeneous distribution of the (mean) water content throughout the material. These results provide sound concepts for modeling and controlling drying properties of wood materials. They open the way to the understanding or control of the properties of many other materials containing two water types in food or civil-engineering applications. Our results complete recent observations that bound-water diffusion also controls imbibition in hardwood and finally show that transfers between bound and free water play a major role in the interaction of plantlike systems with water.

Simple geometrical model of thermal conductivity and bound-water diffusion coefficient in resin-rich regions of softwood plywood

In this study, a geometrical model for wood cells and penetrated adhesive resin at the veneer–veneer interface of plywood was developed. On the basis of this model, equations of thermal conductivity and a bound-water diffusion coefficient for resin-rich regions of softwood plywood were theoretically determined. These equations are suitable for use in numerical simulations of unsteady-state nonisothermal moisture diffusion. By introducing them into an existing coupled heat and moisture transfer model, a simple and physically reasonable simulation of moisture transfer through softwood plywood can be achieved.

Sorption and Drying Characteristics of Xylite

The wood from which xylite is formed in a long-term process undergoes numous changes while still retaining the character of a hygroscopic porous material. To plan the optimal drying schedule of xylite, the permeability coefficient, diffusion coefficient, and surface emission coefficient were determined. The porosity of xylite is low due to the demolished capillary structure; concurrently with the blocked pits, the permeability of xylite is very low, with a permeability coefficient not higher than 2.12 × 10−10 m2/Pa s. The capillary flow of free water is insignificant, allowing the diffusion transport of water to prevail. The diffusion coefficient is considerably influenced by the xylite's density. We confirm a significant increase in the bound water diffusion coefficient as the temperature increased (from 5.5 × 10−12 m2/s at 20°C to 46.3 × 10−12 m2/s at 40°C), and we predict that the activation energy will increase as the moisture content of xylite decreases (approx. 0.63 to 1.05%/% MC changes). As a consequence of the low surface resistance, the surface emission coefficient barely influences the moisture transport below the fiber saturation point.With an appropriate drying schedule, quality dried xylite can be used for various products as an equivalent substitute for dark-colored, high-density woods like ebony.

NMR imaging study and multi-Fickian numerical simulation of moisture transfer in Norway spruce samples

Wood has potential as a renewable material for a large variety of applications that often call for improved properties such as dimensional stability, moisture insensitivity, and durability. Moisture migration in wood is a particularly important factor in determining the cost-effective service life of wooden construction. Within the present research, proton NMR imaging was applied for recording the moisture spatial distribution of various samples of Norway Spruce. Moisture distribution along the radial, tangential and longitudinal directions in wood was monitored at different times upon three consecutive changes of relative humidity: (1) from 65% to 94%; (2) from 94% to 33%; (3) from 33% to 65%. Uncoated samples and specimens treated with different types of surface coatings were studied. The experiments were numerically simulated by using the multi-Fickian model. The model describes the moisture transport process in wood which is characterized by three phenomena: (a) bound water diffusion, (b) water vapor diffusion and (c) coupling between the two phases through sorption. The model is implemented into the Abaqus FEM code. The numerical results are found to be in agreement with the experimental data.

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).

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.

Application of percolation modelling on end-grain water absorption in aspen (Populus tremula L.)

The aim of this study was to improve our understanding of the capillary uptake of water in aspen sapwood and heartwood, which may help to explain the variable performance of aspen used outdoors. The study uses a percolation model developed for softwoods to examine capillary liquid absorption in aspen and compares predicted results with ones obtained experimentally using computed tomographic scanning. The study shows that there is an equilibrium saturation level where new flow paths are being found at the same rate as old ones are being blocked. This is seen as a plateau where the water content maintains a relatively constant height within the material. This makes it possible to model the capillary behaviour of aspen sapwood. In heartwood, however, the uptake of moisture seems to be mainly restricted to bound water, except for a short region in the sample wet end. This absorption is thus governed mainly by bound water diffusion. This improved understanding of the capillary behaviour of aspen may contribute to a future market expansion where aspen may be utilized to a greater extent outdoors and above ground.

Theoretical analysis of moisture transport in wood as an open porous hygroscopic material

Abstract Moisture transport in an open porous hygroscopic material such as wood is a complex system of coupled processes. For seasoned wood in natural climate three fully coupled processes active in the moisture transport are readily identified: (1) diffusion of vapor in pores; (2) phase change from one state to another, also called moisture sorption; and (3) diffusion of bound water in wood tissue (in the cell wall). A mathematical model for predicting moisture transport in wood for a given condition must at least consider the dominating active processes simultaneously to be considered accurate. In this study, a theoretical investigation is conducted on the influence of the model parameters on the model response to a known step change of ambient vapor pressure. The objective is twofold. First, to investigate if model simplification can be conducted in a transparent and stringent manner, not compromising required model accuracy and precision. Second, to show model characteristics that could enable tailored experimental studies to verify or discard variations of this type of transport model. The model sensitivity analyses clearly showed that there are large differences on the degree of influence of the three processes on the outcome of the coupled model. Least significant is the bound water diffusion. Based on the results from the sensitivity analyses, a simplified model for moisture transport in wood is proposed.

The contradictory effect of drying internal checks and moisture changes on the ultrasonic propagation in poplar wood (Populous nigra)

This study was conducted to examine the effect of drying internal checks on the accuracy of poplar wood (Populous nigra) moisture monitoring using nondestructive ultrasonic inspection. A hand-held ultrasonic tester (Sylvatest duo, 9906-015) operating at a frequency of 16 kHz was used to measure the ultrasonic propagation velocity. The measurement was carried out based on the longitudinal wave transmitting pulse method. In contrast to the weak relationship between the wood moisture content (MC) and ultrasonic velocity at MC above fiber saturation point (FSP), a reduction in MC at the domain of bound water diffusion resulted in increase of ultrasonic velocity. The ultrasonic propagation rate was more sensitive to the drying checks than the MC changes. Due to the contradictory effect of drying internal checks and MC loss on the ultrasonic propagation, it can be concluded that the drying check occurrence can impact the accuracy of moisture monitoring by the ultrasonic technique.

Erratum to: Quantitative determination of bound water diffusion in multilayer boards by means of neutron imaging

Erratum to: Quantitative determination of bound water diffusion in multilayer boards by means of neutron imaging

Quantitative determination of bound water diffusion in multilayer boards by means of neutron imaging

Diffusion processes into multilayered samples of Norway spruce (Picea abies [L.] Karst.) exposed to a differentiating climate (dry side/wet side) were determined and quantified by means of neutron imaging (NI). The experiments were carried out at the neutron imaging facility NEUTRA at the Paul Scherrer Institute (PSI) in Villigen (Switzerland).

Implementation of sorption hysteresis in multi-Fickian moisture transport

Abstract In the cellular structure of wood, bound-water diffusion and water-vapor diffusion interact via sorption in a complex moisture-transportation system. At low relative humidities, moisture transport may be modeled by a Fickian diffusion equation with a good approximation. At higher relative humidities, slow sorption and faster bound-water diffusion cause effects, which have been referred to as non-Fickian or anomalous, as they cannot be modeled by one Fickian diffusion equation. Previous research has demonstrated that a set of coupled diffusion equations, namely the multi-Fickian model, can represent this behavior. The multi-Fickian model describes the combined transport of bound water and vapor and their interaction through sorption. The bound-water concentration is also influenced by sorption hysteresis. In the worst case, sorption hysteresis may result in deviations of up to 30–35% in moisture content. Hence, for a precise moisture content computation, sorption hysteresis must be taken into account. The present paper explains the relation between sorption hysteresis and multi-Fickian moisture transport, and clarifies how models for the two phenomena are coupled. To illustrate the effects, a finite element simulation, which is based on the combined model, is presented.

A revised multi-Fickian moisture transport model to describe non-Fickian effects in wood

Abstract This paper presents a study and a refinement of the sorption rate model in a so-called multi-Fickian or multi-phase model. This type of model describes the complex moisture transport system in wood, which consists of separate water vapor and bound-water diffusion interacting through sorption. At high relative humidities, the effect of this complex moisture transport system becomes apparent, and since a single Fickian diffusion equation fails to model the behavior, it has been referred to as non-Fickian or anomalous behavior. At low relative humidities, slow bound-water transport and fast sorption allow a simplification of the system to be modeled by a single Fickian diffusion equation. To determine the response of the system, the sorption rate model is essential. Here the function modeling the moisture-dependent adsorption rate is investigated based on existing experiments on thin wood specimens. In these specimens diffusion is shown to be negligible, allowing a separate study of the adsorption rate. The desorption rate has been observed to be slower at higher relative humidities as well, and an expression analogous to the adsorption rate model is proposed. Furthermore, the boundary conditions for the model are discussed, since discrepancies from corresponding models of moisture transport in paper products have been found.

Effects of the method of identification of the diffusion coefficient on accuracy of modeling bound water transfer in wood

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.

Transient multiphase model for the high‐temperature thermal treatment of wood

AbstractThe hygrothermal behavior of wood at high temperature is analyzed, taking into account all the phases present such as wood, liquid water in free and bound forms, and water vapor. The moisture transport phenomenon includes water vapor convection and diffusion along with capillary water convection in the pores of the particle as well as bound water diffusion in the solid wood. Local thermodynamic equilibrium is assumed, which is represented by a sorption isotherm that relates the moisture contents in the solid and gas phases. The equations of the model were solved numerically using the commercial software Femlab® for the temperature and the moisture content profiles. The mathematical model predictions were compared with the experimental data and a reasonably good agreement was obtained. A parametric study was also carried out to determine the effects of several parameters such as heating rate, initial moisture content, and the sample thickness on the temperature and moisture content distributions within the samples during heat treatment. © 2006 American Institute of Chemical Engineers AIChE J, 2006

Inverse analysis of the transient bound water diffusion in wood

Abstract 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.

Diffusion of bound water in starchy materials: application to drying

A model for isothermal bound water diffusion in grains and other starchy materials was derived. Assuming that spreading pressure gradient is the driving force for diffusion, an analytical expression for the variation of diffusion coefficient with moisture content was derived. When applied to predict the variation of the diffusion coefficient with moisture for some cereal grains and starches, the curves show a maximum for moisture contents about 0.10–0.15 kg water per kg dry solid. The expression for moisture variation of the diffusion coefficient was used to simulate the drying behavior of cereal grains for known values of initial and equilibrium moisture contents with satisfactory results.