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Open Access 30-03-2022 | Original Research

Water vapour sorption and moisture transport in and across fibre direction of wood

Author: Alexander Murr

Published in: Cellulose | Issue 7/2022

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Abstract

Water vapour sorption experiments are frequently used to characterise the absorption and desorption of water in wood. To evaluate whether water vapour transport—compared to sorption and sorption related processes—can be neglected in small wood samples, this study investigates the sorption kinetics of Norway spruce (Picea abies) samples with different lengths of transport pathways in and across fibre direction. Water vapour sorption experiments were performed under identical climatic conditions at ambient air pressure and ambient standard temperature. Along the whole tested range of relative humidity sample thickness was shown to have an impact on the sorption kinetics. At low relative humidity, the initial uptake and release of water was considerably influenced by the diffusion of water vapour through the lumen-pit-ray system. Differences between the sorption kinetics for samples in and across fibre direction were thus considerable. With increasing moisture content, the initial uptake and release of water increased for samples across fibre direction, while it decreased for samples in fibre direction. Moisture transport across fibre direction thus seems to be increasing and cell wall processes seem to be more relevant. At high relative humidity, differences between the sorption kinetics for samples in and across fibre direction started to disappear while the impact of sample thickness was still considerable. Therefore, an additional or modified process, which depends on the number of sorption sites but not on the anatomical orientation must be considered at an increased moisture content of wood.

Supplementary file 1 (pdf 1055 KB)

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1007/s10570-022-04520-x.

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Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Introduction

Wood is a hygroscopic material and capable to absorb large amounts of moisture from the surrounding air. Since many physical properties depend on the moisture content of wood (MC), a change of relative humidity (RH) in the surrounding air causes a corresponding change in the physical properties of wood (Niemz 1993). To characterise the behaviour of wood and to identify the relevant processes during such non-stationary (i.e. transient) conditions, experimental investigations are often realised under transient conditions in RH (Christensen and Kelsey 1959; Christensen and Hergt 1969; Rosen 1978; Avramidis and Siau 1987; Wadsö 1994b; Hill et al. 2010; Eitelberger and Svensson 2012;Thybring et al. 2018). According to the wide spread of dynamic vapour sorption devices, water vapour sorption experiments are frequently used for this purpose (Xie et al. 2011; Himmel and Mai 2015; Glass et al. 2017; Murr and Lackner 2018; Chen et al. 2021). Sample material is exposed to a well-defined change in RH and the resulting time-dependent change of sample mass (i.e. sorption kinetics¹) is measured by weighting the sample. Consequently, this method provides direct information on the uptake and release of $\hbox {H}_{2}$O-molecules (hereinafter referred to as water). The interpretation of water vapour sorption experiments is though not trivial since moisture transport, sorption and sorption related processes are strongly coupled and might affect the measured sorption kinetics (Thybring et al. 2019b). This raises the question of what kind of information can be extracted from the sorption kinetics of water vapour sorption experiments. Therefore, the processes that restrict the uptake and release of water in wood during a transient change of RH need to be identified. As water vapour has to be transported to and through the lumen-pit-ray system prior to getting bound on/in the cell wall and prior to any sorption related processes are initiated (e.g. release of binding energy, swelling, reorganisation of wood polymers), water vapour transport should be of particular importance for the initial sorption kinetics (see Fig. 1).

To avoid an overemphasis of water vapour diffusion through the lumen-pit-ray system, small or thin samples are often preferred in experimental investigations. Several studies have investigated the water vapour sorption behaviour of small wood samples but only a few analysed the impact of sample thickness or anatomical orientation on the measured sorption kinetics. Christensen and Kelsey (1959) compared the absorption kinetics between two 1 mm thick samples in longitudinal and tangential direction (i.e. in and across fibre direction) and a $40\,\upmu \hbox {m}$ thick microtomed sample in tangential direction of Klinki pine (Araucaria hunsteinii) and found slightly faster sorption kinetics for the microtomed sample but no significant differences between the 1 mm samples. In contrast, Thybring et al. (2019b) mentioned about a study on Mountain ash (Eucalyptus regnans) done by Christensen (1960), where the absorption kinetics between samples with a thickness between $20\,\upmu \text {m}$ and 3 mm in tangential direction were considerably different at low RH, while differences at high RH were not appreciable. However, Wadsö (1994b) compared the absorption kinetics of various soft- and hardwoods with a thickness between 3.8 mm and 22.8 mm (in longitudinal, tangential and radial direction) and found differences in the initial sorption kinetics at mid to high RH. Similarly, Nopens et al. (2019) have found differences in the absorption and desorption kinetics for samples with a thickness between 1 mm and 20 mm (in longitudinal direction) of Scots pine (Pinus sylvestris) and European beech (Fagus sylvatica). Further, a comparison of microtomed and cut Norway spruce wood (Picea abies) with a thickness of $25\,\mu \hbox {m}$ and 0.5 mm in longitudinal direction showed significant differences in the absorption kinetics at low RH (Murr and Lackner 2018). Similar to the different experimental observations, a variety of different approaches to model the uptake and release of water in wood can be found in the literature. Some authors have used a coupled transport model, where water vapour and bound water (i.e. water within the cell wall) were described by a separate diffusion equation that are coupled by a sorption term (Krabbenhoft and Damkilde 2004; Frandsen et al. 2007; Eitelberger et al. 2011; Konopka and Kaliske 2018). Diffusion coefficients for water vapour were given to be (almost) constant while the diffusion coefficients for bound water were described by exponentially increasing functions with MC. A simplification of the coupled approach was given by Hozjan and Svensson (2011), where the bound water diffusion was shown by a theoretical analysis to be negligible, particularly at low RH (see also Eitelberger and Svensson 2012). On the contrary, other authors have neglected the transport of water vapour and instead used a diffusion equation for the transport of bound water combined with a certain boundary condition for the flux to take account for the reorganisation of the wood polymers (Olek et al. 2011). Using an inverse analysis, a non-monotonic behaviour for the diffusion coefficients as well as differences in the diffusion coefficients between absorption and desorption were found with this model. Further, a combined transport approach has been used, where water vapour and bound water were treated together with a single diffusion equation (Time 1998; Florisson et al. 2020). With this approach, an increase of diffusion coefficients with MC across fibre direction was frequently reported, while diffusion coefficients in fibre direction were given to decrease with MC (Droin-Josserand et al. 1989; Jakieła et al. 2008; Kang et al. 2008). Additionally, heuristic models such as the PEK model (Hill et al. 2010) are also used, but they have various problems in interpreting the sorption kinetic data (see e.g. Thybring et al. 2019a). Consequently, there seems to be no consensus on whether moisture transport - compared to sorption and sorption related processes - can be neglected in water vapour sorption experiments on small wood samples under ambient conditions.

The objective of this work is thus to examine the impact of water vapour diffusion through the lumen-pit-ray system on the uptake and release of water during a transient change of RH. Therefore, water vapour sorption experiments are performed on thin Norway spruce plates with a different thickness along the three main anatomical orientations (i.e. longitudinal, tangential, and radial). Experiments are carried out at ambient pressure and standard ambient temperature along a wide range of RH. The sorption kinetics between samples in fibre direction (longitudinal) and across fibre direction (tangential and radial) are compared during absorption and desorption to identify the impact of water vapour diffusion through the lumen-pit-ray system and to estimate moisture dependent changes on the transport properties. With this information the relevance of cell wall processes on the measured sorption kinetics should be estimated. However, for quantitative statements on the impact of cell wall processes on the uptake and release of water, different measurements would be necessary. The presented experimental results can be used as a state-of-the-art data for future modelling approaches and for a validation of existing transport concepts.

Materials and methods

Dynamic vapour sorption

All water vapour sorption experiments were carried out with the dynamic vapour sorption device SPSx-1$\mu$ (ProUmid GmbH, Germany). The device consists of a climatic chamber, where up to 11 samples can be tested under identical pressure, temperature and RH conditions. Sample material is placed in aluminium bowls on a rotating plate and the mass of the samples is measured automatically by placing each sample bowl successively on a micro scale with a reproducibility of $\pm 10\,\mu \hbox {g}$. Sample weighting is repeated at an 8 min interval to ensure stabilised conditions inside the climatic chamber. At the beginning and at the end of a weighting cycle (i.e. prior to the first and after the last sample was weighted), an empty reference bowl is weighted to correct the adsorption and desorption of water on the sample bowls and to correct a possible scale drift (assuming a linear drift). Relative humidity is regulated by a moistening unit using dry air ($0.2\,\%\,\hbox {RH}$; hereinafter referred to as $0\,\%\,\hbox {RH}$) or water vapour-saturated air and the two fans create a circulating flow of the water vapour-air mixture inside the climatic chamber. RH can be changed stepwise by choosing the required step-sizes for absorption or desorption. Deviations to the pre-set RH can be ensured to be below $\pm 0.5\,\%\,\hbox {RH}$, except for RH $\ge \,80\,\%$ ($\pm 1\,\%\,\hbox {RH}$). The integrated Peltier element ensures a constant temperature of $25\,^{\circ }\mathrm {C}$ with a deviation below $\pm 0.1\,^{\circ }\mathrm {C}$. More details on the dynamic sorption device can be found in Murr (2019).

Sample preparation

Samples were taken from the lower stem of a Norway spruce (Picea abies) grown in the West of Austria. A plank with a length of 1.5 m in longitudinal direction was cut through the centre of the stem and 136 annual rings were counted. After an initial drying phase of 7 days at ambient air, the plank was stored for 12 months in an air-conditioned room at a temperature of $21\,^{\circ }\mathrm {C}\,(\pm 3\,^{\circ }\mathrm {C}$) and a relative humidity of $30\,\%\,(\pm 10\,\%$). Prior to manipulation, the plank was cut to remove the inner and outer part (approximately 15 annual rings in each case). Thin samples were cut with a circular saw using a sharp blade with alternative top bevel teeth and a positive rake angle to minimise heat production. To compare the influence of sample thickness on the sorption kinetics, several samples with a thickness between 0.5 mm and 3 mm along the three anatomical orientations were cut (see Fig. 2).

Cross section was chosen to be large enough to minimise the impact of water vapour diffusion through the side surfaces (i.e. orthogonal to the sample thickness), but not too large to unnecessary slow down the time span for changing RH in the climatic chamber (Murr 2019). All samples were without any visible defects or growth irregularities and the density was determined to be $370 \pm 40\,\hbox {kg m}^{-3}$. The mean annual ring width of the wood samples used was $1.4 \pm 0.4\,\hbox {mm}$ with a proportion of early wood of approximately 85 %. To measure the uptake and release of water for the various samples under identical climatic conditions, one representative slice for each thickness and anatomical orientation was chosen (see Table 1). The restriction of the investigation to one sample each was possible as pre-testings have shown identical sorption kinetics between a number of samples for each thickness and orientation, including the samples which were investigated in this study. Further, it has to be mentioned that the entire measurement as described in Sect. 2.3 took more than 6 weeks. A successive measurement of, for example, 5 samples for each thickness and orientation would therefore extend the measurement to over half a year. The sample with a thickness of 3 mm in the radial direction was omitted in this work, as the maximum number of samples to be tested at once (i.e. under identical climatic conditions) was limited to 11 samples.

Table 1

Sample dimensions at MC $\approx 6\,\%$ and minimum sample mass after precondition phase ($m_{0}$) of used samples in the longitudinal (L), tangential (T) and radial (R) direction

Dimensions (mm x mm x mm)	Mass (mg)	Label
0.5 (L) $\times$ 21.4 (R) $\times$ 40.0 (T)	157	L_0.5mm
1.0 (L) $\times$ 20.2 (R) $\times$ 41.6 (T)	299	L_1mm
2.0 (L) $\times$ 21.0 (R) $\times$ 43.0 (T)	607	L_2mm
3.0 (L) $\times$ 20.7 (R) $\times$ 43.0 (T)	888	L_3mm
0.5 (T) $\times$ 21.2 (R) $\times$ 43.6 (L)	175	T_0.5mm
1.0 (T) $\times$ 21.2 (R) $\times$ 43.6 (L)	312	T_1mm
2.0 (T) $\times$ 22.2 (R) $\times$ 43.6 (L)	613	T_2mm
3.0 (T) $\times$ 21.6 (R) $\times$ 43.6 (L)	928	T_3mm
0.5 (R) $\times$ 21.5 (T) $\times$ 43.6 (L)	173	R_0.5mm
1.0 (R) $\times$ 21.6 (T) $\times$ 43.6 (L)	361	R_1mm
2.0 (R) $\times$ 22.1 (T) $\times$ 43.6 (L)	605	R_2mm

Experimental set-up

Samples according to Table 1 were distributed with decreasing thickness across the 11 sample bowls, starting with the thickest (3 mm) and ending with the thinnest samples (0.5 mm). The order of anatomical orientation (i.e. the direction of the thinnest sample dimension) was chosen for each thickness to be longitudinal, tangential and radial. Particular attention was given to maximise the accessibility of water vapour to the sample surface and to emphasise possible differences in the initial sorption kinetics of the various samples. This was done by mounting the thin wooden sample plates on a wire frame outside the sample bowl and parallel to the water vapour-air stream. Hence, samples were exposed directly in the circulating water vapour-air stream which avoids the paths of stagnant air when samples are placed inside a sample bowl (Murr 2019). An additional wire frame was placed on the reference bowl to correct for the adsorption and desorption of water on the wire frame of the samples. Samples were conditioned inside the climatic chamber at $\hbox {T}\,=\,25\,^{\circ }\mathrm {C}$ and $0\,\%\,\hbox {RH}$ until the equilibrium condition (EC)

$$\begin{aligned} \frac{\hbox {d}}{\hbox {d}t}\left( \frac{m(t)}{m_{0}}\right) < 0.00017\,\% \;\text {min}^{-1} \end{aligned}$$

(1)

was reached. Here, m(t) denotes the total sample mass and $m_0$ is the minimum sample mass which was determined after an additional drying phase of 24 h at $0\,\%\,\hbox {RH}$ (see Table 1). The EC (Eq. 1) was evaluated in a period of 120 min using a linear regression. This mass stability criterion is more than one order of magnitude lower than the most common used criterion given in Glass et al. (2017). To measure the sorption kinetics of the various samples, RH was changed stepwise and kept constant until all samples fulfilled the EC (Eq. 1). It should be noted that the sample with the slowest sorption kinetic was also the last to meet the EC and hence determined the time, when the next step change in RH was initiated. Samples with a faster sorption kinetic had thus an even lower EC than mentioned in Eq. 1, which might had an impact on the sorption kinetics in the following step change of RH (Christensen and Hergt 1969). Step-size in RH was chosen to ${\varDelta }\hbox {RH}\,=\,10$ percentage points between 0$\%$ and $90\,\%\,\hbox {RH}$ at a constant temperature of $25\,^{\circ }\mathrm {C}$ (i.e. at standard ambient temperature). An additional step to reach $94\,\%\,\hbox {RH}$ was used to provide a different starting MC for desorption at $90\,\%\,\hbox {RH}$. After absorption was completed, a reverse order sequence of the same step-sizes in RH was used for desorption. A change of relative humidity inside the climatic chamber took between 1 and 2 min for the given experimental set-up. Only for absorption above $70\,\%\,\hbox {RH}$ and desorption below $20\,\%\,\hbox {RH}$, step changes in relative humidity needed more time until the pre-set RH value was attained (see Fig. S5 in the Supplementary Information). Weighting of the samples started approximately 5 min after a step change in RH was initiated and was then repeated in an 8 min cycle until EC was reached. As mentioned by Popescu and Hill (2013), a complete measurement for each absorption and desorption step was performed in advance to reduce a possible impact of previous sorption history on the sorption kinetics.

Simulations

To simulate the diffusion of water vapour through the lumen-pit-ray structure of wood, some simplified assumptions were made. The wood samples were treated as a homogeneous sheet with a thickness corresponding to Table 1. Uptake and release of water on/in the cell wall as well as the transport of moisture through the cell wall were assumed to be very fast (i.e. instantaneous). Further, processes within the cell wall and their impact on the diffusion of water vapour were not considered (e.g. a possible reduction of water vapour diffusion due to a local drop of RH caused by the release of binding energy during absorption of water on/in the cell wall). Using these simplifications and assuming a one-dimensional moisture transport through the sample, the diffusion of water vapour in wood can be written approximately as (see e.g. Murr 2019)

$$\begin{aligned} \frac{\partial \rho _{wv}}{\partial t} = D_{\text {eff}} \cdot \frac{\partial ^{2} \rho _{wv}}{\partial x^{2}} \end{aligned}$$

(2)

Here, $\rho _{wv} = \rho _{wv} (x,t)$ is the concentration of water vapour in $\text {kg} \, \text {m}^{-3}$ and the effective diffusion coefficient for water vapour through wood includes the absorption and desorption of water, $D_{\text {eff}} = \frac{\xi \cdot D_{a}}{1+{\varDelta } R}$ in $\text {m}^{2} \, \text {s}^{-1}$. $D_{a}$ is the water vapour diffusion coefficient in air and $\xi$ is a constant reduction factor for the hindered transport through the lumen-pit-ray structure. The uptake and release of water on/in the cell wall considerably reduces the diffusion of water vapour through the samples and is given by the sink factor

$$\begin{aligned} {\varDelta } R = \frac{1}{V_{s}} \cdot \frac{{\varDelta } m_{max}}{{\varDelta } \rho _{wv}} \end{aligned}$$

(3)

Here, $V_{s}$ is the sample volume, ${\varDelta } m_{max}$ the total mass change of the sample during a given step change in RH, and ${\varDelta } \rho _{wv}$ the corresponding change in water vapour concentration. It should be mentioned that with these simplifications (Eqs. 2 and 3), the sink factor ${\varDelta } R$ is assumed to be constant within the samples instead of treating it as a time and space dependent function. Using Eq. 2 and an instantaneous change of water vapour on the surface of the sample, the normalised change of sample mass during a step change in RH can be evaluated as (Crank 1975)

$$\begin{aligned} \frac{{\varDelta } m(t)}{{\varDelta } m_{max}} = 1-\sum _{n=0}^{\infty } \frac{8}{\pi ^{2} (2n+1)^{2}} \cdot \exp \Bigl(-\frac{D_{\text {eff}} \cdot t \cdot \pi ^{2} (2n+1)^{2}}{d^{2}}\Bigr) \end{aligned}$$

(4)

where d is the thickness of the sample and ${\varDelta } m(t)$ is the time-dependent mass change of the sample during a given step change in RH. To evaluate Eq. 2 under more realistic boundary conditions (i.e. the measured RH inside the measuring chamber given in Fig. S5), a simulation based on the interpolated RH values was carried out (Figs. 6b and 8). For the simulations the software Wolfram Mathematica 12.1 was used. The reduction factor in longitudinal direction was chosen as $\xi = 0.9$ (Frandsen et al. 2007) and the water vapour diffusion coefficient in air was used as mentioned in Schirmer (1938). This results in an effective water vapour diffusion coefficient of $D_{\text {eff}} \approx 5 \cdot 10^{-9} \, \text {m}^{2} \, \text {s}^{-1}$ for the step change $0\,\%$ $\rightarrow$ $10\,\%\,\hbox {RH}$ (see Fig. 6).

Error estimation

Regarding the measurement error, the humidification process inside the climatic chamber (Murr 2019) and the variation in sample material (i.e. sample geometry and density) were identified as the main sources of error in the given experimental set-up. On the basis of pre-testings with cut samples of the same wooden plank, these errors were estimated to be below $3\,\%$ of the total mass change per step.

Results and discussion

To compare the sorption kinetics between samples with a different sample thickness or among different step changes in RH, the time-dependent change of sample mass was either divided by the minimum sample mass ($m_{0}$) or normalised to the total mass change of the investigated step change in RH,

$$\begin{aligned} \frac{{\varDelta } m(t)}{{\varDelta } m_{max}} = \frac{m(t)-m(0)}{m(t_{max})-m(0)} \end{aligned}$$

(5)

which is sometimes termed as fractional mass change E(t). For each step change the time was set to start at $t\,=\,0$ and $t_{max}$ refers to the time, when EC (Eq. 1) was fulfilled by the sample with the slowest sorption kinetics ($t_{max} > 1000\,\hbox {min}$). To evaluate the sample mass at a specific time, a linear interpolation of the measured data was used. Moisture content of wood is generally a time-dependent function and was calculated on the basis of minimum sample mass, $MC(t)\,=\,(m(t)-m_{0})/m_{0}$. In the following, desorption data were given in terms of absolute values, except for Figs. 3b, 4b and S1b in the Supplementary Information. The time axis was chosen to emphasise the initial sorption kinetics in the Figures and is always considerably smaller than the time when EC was reached. Experimental results of the step change $90\,\%$ $\rightarrow$ $94\,\%\,\hbox {RH}$ and $94\,\%$ $\rightarrow$ $90\,\%\,\hbox {RH}$ were only shown in Figs. 9 and S4 in the Supplementary Information. This was done so that the differences in RH step size do not have to be additionally considered in the interpretation of the results.

Samples with different thickness

In fibre direction

The absorption and desorption kinetics for samples with a thickness between 0.5 mm and 3 mm in longitudinal direction (i.e. in fibre direction) is shown for an exemplary step change in Fig. 3a, b. In both cases, differences in the sorption kinetics among the various samples can be seen particularly at the initial phase ($\hbox {t}\,\lesssim \,30\,\hbox {min}$) of the mass change. With increasing time, these differences in the sorption kinetics decrease leading to a similar increase or decrease of relative sample mass until EC was reached (indicated by the straight dotted line).

To investigate if the impact of sample thickness on the initial sorption kinetics is also present for other step changes in RH, a representation of the uptake and release of water after an arbitrary chosen evaluation time of $t_{ev}=10\,\hbox {min}$ was used. For each step change in RH, differences in the amount of absorbed (Fig. 3c) and desorbed water (Fig. 3d) can be seen among the four tested samples. A minimum in the differences was observed in the mid range of RH, which corresponds to the smallest total mass change per step (see bars in the background of Fig. 3c, d). As the relative mass change of the thinner samples is always faster than for the thicker ones, these results show that sample thickness has a significant impact on the initial sorption kinetics even for samples with a thickness of 1 mm and below. To investigate the impact of sample thickness on the sorption kinetics at a later phase, uptake and release of water was evaluated at $t_{ev}=100\,\hbox {min}$. In contrast to the initial phase, differences among the samples almost disappeared in the low and mid range of RH for both absorption (Fig. 3e) and desorption (Fig. 3f). Since equilibrium mass was not reached at this time (see differences between markers and bars in the background of Fig. 3e, f), the remaining mass change must be almost independent of water vapour diffusion through the lumen-pit-ray system. Hence, it seems as if processes within the cell wall are dominating the sorption kinetics of longitudinal samples in this phase. An exception is though the high range of RH, where significant differences in the uptake and release of water among the samples can be seen even after 100 min. The impact of sample thickness for samples in fibre direction lasts thus much longer in the high range of RH compared to the mid and low range of RH. For the step change $10\% \rightarrow 0\%$ RH, differences among the samples were also detected after 100 min (Fig. 3f). These differences seem though to be an effect of the slow change of RH inside the measuring chamber of the used sorption device (see Sect. 2.3 and Fig. S5), which slows down the release of water at low RH as well as the uptake of water at high RH (see grey area in Fig. 3c–f).

Across fibre direction

An evaluation of the absorption and desorption kinetics for samples with a thickness between 0.5 mm and 3 mm in tangential direction (i.e. across fibre direction) during an exemplary step change in RH is given in Fig. 4a, b. Differences in the sorption kinetics among the various samples can be clearly seen and the uptake and release of water is noticeable slower than for the longitudinal samples.

An evaluation of the initial sorption kinetics ($t_{ev}=10\,\hbox {min}$) over the whole tested range of RH shows a significant impact of sample thickness on the uptake (Fig. 4c) and release of water (Fig. 4d). Hence, also for tangential samples with a thickness of 3 mm and below, a considerable impact of sample thickness on the initial sorption kinetics was observed. Similar results were obtained by comparing the radial samples as shown in Fig. S1 in the Supplementary Information. This is contrary to the findings of Christensen (1960) reported in Thybring et al. (2019b), where no differences in the sorption kinetics of tangential samples (with a thickness between $20\,\mu \hbox {m}$ and 3 mm) were reported above $60\%$ RH. An investigation of the uptake (Fig. 4e) and release of water (Fig. 4f) at an evaluation time of 100 min shows further, that these differences among the tangential samples generally last longer than for the longitudinal samples. Hence, it seems that water vapour diffusion in tangential samples is still relevant for the sorption kinetics in this phase. Comparing the different paths in and across the fibre direction of wood, these results indicate that the diffusion of water vapour through the lumen-pit-ray system is one of the limiting processes in the (initial) uptake and release of water in wood. Consequently, for investigations of sorption and sorption related processes, thin longitudinal samples are more recommendable than thin tangential or radial samples as water vapour transport through the longitudinal samples is faster and thus has less impact on the uptake and release of water. A fact that remains unclear is the proximity of the uptake and release of water between the 1 mm and 2 mm tangential samples in the low range of RH (Fig. 4). An explanation based on an additional transport path for water vapour through the not sealed side surface of the tangential samples seems to be improbable, as the large differences between the sorption kinetics of the 2 mm and 3 mm samples do not support this possibility. The radial samples showed a similar effect, although the proximity of the 1 mm and 2 mm sample was less pronounced (see Fig. S1 in the Supplementary Information).

Samples with different anatomical orientation

Low range of RH

Investigating the differences between the sorption kinetics of samples in and across fibre direction at low RH, longitudinal samples show a considerable faster absorption (Fig. 5a) and desorption kinetics (Fig. 5b) than the tangential samples.

For both orientations, thicker samples show a slower normalised mass change than the thinner samples, which is indicated by the arrows for each anatomical orientation. Similar results were obtained with the radial samples as shown in Fig. S2 in the Supplementary Information. To evaluate if diffusion of water vapour through the lumen-pit-ray system has a significant contribution on the sorption kinetics, an illustration over $\sqrt{t/d^{2}}$ was used. For a sheet diffusion process with an instantaneous change of RH at the surface of the sheet (Eq. 4), this illustration leads to an identical mass change for each thickness (Fig. 6a) (see also Crank 1975). However, if the measured change of RH in the measuring chamber is used as a boundary condition at the sample surface (see Fig. S5a in the Supplementary Information), differences in the mass change become apparent (Fig. 6b). Analysing the measured sorption kinetics in the $\sqrt{t/d^{2}}$ representation, differences among the samples with different thickness can be seen for both orientations (Fig. 5c, d). The thinner samples seem to be delayed in their sorption kinetics while with increasing thickness samples tend towards identical kinetics. Comparing the measured mass change of the longitudinal samples with the simulated solution for the sheet diffusion process, a certain similarity can be seen (cf. Figs. 5c and 6b). This indicates that water vapour supply and water vapour diffusion through the lumen-pit-ray system do have a considerable impact on the uptake and release of water for thin wood samples at low RH. Differences in the lumen-pit-ray structure of wood (e.g. the proportion of early and late wood) might therefore be seen in the initial sorption kinetics. Based on these results it seems as if processes within the cell wall have a smaller impact on the kinetics in this range of RH.

High range of RH

In the high range of RH, the sorption kinetics of samples in longitudinal and tangential direction show a remarkable similarity during absorption (Fig. 7a) and particularly during desorption (Fig. 7b). For absorption, an identical uptake of water can be observed for the 0.5 mm samples while with increasing thickness the differences between the longitudinal and tangential samples increase. In contrast for desorption, the release of water is identical for the 0.5 mm samples as well as for the 1 mm samples and only slight differences were found for the thicker samples. A similar trend was observed between the longitudinal and radial samples (Fig. S3 in the Supplementary Information). Therefore, the sorption kinetics between samples in and across fibre direction seems to be more similar for desorption, but this appears to be related to the moisture content of the wood samples (see Section Transition low to high range of RH).

A fact that was not expected from the results of the study by Christensen (1960) mentioned in Thybring et al. (2019b) is the difference in the sorption kinetics among samples with a different thickness. Even though the anatomical orientation is less relevant for the uptake and release of water at high RH, sample thickness still has a considerable impact. Pre-testings on another sample set of the same wooden plank with the same step changes in RH confirmed this results. Furthermore, experiments with a step-size in relative humidity of ${\varDelta }$RH = 30 percentage points led to similar results. To evaluate if a diffusion process through the sample thickness can explain these differences, a representation of the sorption kinetics over $\sqrt{t/d^{2}}$ was used. As shown in Fig. 7c and d, both the shape of the sorption kinetics as well as the differences among the samples deviate considerably from the simulated water vapour diffusion behaviour given in Fig. 6b. This deviation also becomes evident when comparing the measured desorption kinetics (Fig. 7b) with a corresponding simulated solution for a plane sheet diffusion process using an arbitrary chosen high and a low diffusion coefficient. With a high diffusion coefficient, differences between the four samples occur mainly in the fast rising initial phase, and these differences decrease rapidly with increasing time (Fig. 8a). In contrast, with a low diffusion coefficient, differences between the four samples occur from the slow rising initial phase to long measurement times and these differences decrease slowly with increasing time (Fig. 8b). Both cases differ from the measured desorption kinetics (Fig. 7b), which is characterised by a rapid rising initial phase followed by a slowly rising later phase. Hence, it seems as if processes within the cell wall have a larger impact on the sorption kinetics in the high range of RH. These results are supported by other investigations in the literature, where the deviation of the measured sorption kinetics from a simple moisture diffusion process was frequently mentioned as a non-Fickian behaviour (Wadsö 1994a; Krabbenhoft and Damkilde 2004; Olek et al. 2005; Himmel and Mai 2016). However, as sample thickness was shown to have a considerable impact on the sorption kinetics, the uptake and release of water cannot solely depend on processes within the cell wall of wood. Hence, either a barrier for the moisture transport or a process that depends on the sample mass but not on the sample orientation (i.e. a dependence on the number of sorption sites) seems to be relevant in the high range of RH. Thermal effects, a boundary layer, or an additional or modified moisture transport might be possible candidates for this process. Future experiments should thus compare the sorption kinetics of chemically modified samples (see e.g. Thybring and Fredriksson 2021 and references therein) or of samples with different dry densities to investigate the impact of sorption sites on the absorption and desorption of water in the high range of RH. Similarly, a comparison of the sorption kinetics of spruce wood with a different proportion of early and late wood could provide further insights. It should be mentioned that with increasing sample thickness diffusion processes become more dominant as their characteristic time scales with the square of the thickness ($t\sim d^{2}$). As a result, the uptake and release of water in thicker samples should be increasingly dominated by diffusion (e.g. water vapour diffusion through the lumen-pit-ray system). This might explain the increasing differences in the sorption kinetics between samples in and across fibre direction with increasing thickness (see Figs. 7a,b and S3a,b in the Supplementary Information).

Transition low to high range of RH

The sorption kinetics of thin wood samples in and across fibre direction differ significantly between the low and high range of RH. Hence, there seems to be at least one transition in the processes which dominate the uptake and release of water in thin wood samples. To allow such a transition between two or more processes to happen, either the characteristic times of the involved processes or their relative amplitudes (or both) have to change with increasing RH. As the uptake and release of water depends on moisture transport, sorption and sorption related processes, the slowest of the involved processes will dominate the sorption kinetics. This fact has to be considered in all types of experiments under transient conditions in RH (e.g. measuring the heat of sorption or swelling). To investigate the transition between the low and high range of RH, the ratio between the normalised mass change of the tangential and longitudinal samples,

$$\begin{aligned} \frac{{\varDelta } M_{T}}{{\varDelta } M_{L}} :=\frac{{\varDelta } m_{T}(t)}{{\varDelta } m_{T,max}} \Bigg / \frac{{\varDelta } m_{L}(t)}{{\varDelta } m_{L,max}} \end{aligned}$$

for each sample thickness was used. Evaluation time for the ratio was chosen to $t_{ev}=10\,\hbox {min}$ to capture particularly the initial phase of the sorption kinetics. If ${\varDelta } M_{T}/{\varDelta } M_{L}<1$, the uptake and release of water for the tangential sample is slower than for the longitudinal sample. In the case of ${\varDelta } M_{T}/{\varDelta } M_{L}=1$, the uptake and release of water is identical for both samples. The fact that a similar initial mass change between the samples ensures a similar sorption kinetics until EC is reached is supported by the measurements of this study (see e.g. Fig. 7). Figure 9 shows the four mass change ratios along the moisture content of wood. For each sample thickness a continuous increase of the ratio ${\varDelta } M_{T}/{\varDelta } M_{L}$ can be seen. These results indicate a continuous transition in the processes which dominate the initial sorption kinetics between the low and high range of RH. Since for each thickness the ratio ${\varDelta } M_{T}/{\varDelta } M_{L}$ between absorption and desorption is similar, the processes involved in this transition must be independent on the uptake and release of water. Similar results were obtained for the ratio between the radial and longitudinal samples (Fig. S4 in the Supplementary Information). Consequently, processes which are different between absorption and desorption seem to have a minor impact on the initial sorption kinetics. Further, moisture content of wood seems to be an appropriate parameter for the transition as in a representation over RH differences between absorption and desorption were observed.

This appears plausible as changes in wood properties (and thus in the involved processes) should depend mainly on the state of the material instead on the surrounding conditions (see e.g. Niemz 1993). Comparing the four mass change ratios among each other, an increase of the ratio with decreasing sample thickness can be seen. This seems reasonable, as in the limiting case of a sample thickness close to the cell wall thickness water vapour diffusion through the lumen-pit-ray system can be omitted and should lead to a similar sorption kinetics between the anatomical orientations. In contrast, with increasing sample thickness water vapour diffusion through the lumen-pit-ray system will get more dominant since the characteristic time for a diffusion process increases proportionally to the square of the sample thickness. An evaluation of the mass change ratio at a later time led also to an increase of ${\varDelta } M_{T}/{\varDelta } M_{L}$. This supports the findings that water vapour diffusion across fibre direction has a considerable impact on the measured sorption kinetics even after the initial phase. It should be mentioned that along with a later evaluation time differences between the mass change ratio during absorption and desorption emerged. This indicates that processes which are different between absorption and desorption have a larger impact on the sorption kinetics at the later phase.

Moisture transport across fibre direction

To evaluate if moisture transport properties change with MC, the initial uptake and release of water between the low and high range of RH was compared. Absorption at low RH and desorption at high RH were used to avoid the ranges with a slow change of RH of the sorption device (see Sect. 2.3). As shown in Table 2, the initial mass change ($t_{ev}=10\,\hbox {min}$) for the thinnest sample in longitudinal direction is smaller at high RH compared to low RH. A similar behaviour was observed for the thicker samples (cf. Fig. 3c,d). Hence, either the moisture transport decreases noticeable with increasing MC², or sorption and sorption related processes have to increase in characteristic time and/or in relative amplitude. In contrast to the samples in fibre direction, samples across fibre direction were shown to have a larger initial mass change at high RH compared to low RH (see Table 2). Again, a similar behaviour was observed for the thicker samples (cf. Figs. 4c,d and S1c,d in the Supplementary Information). Based on the fact that at low MC water vapour diffusion across fibre direction has a larger impact on the sorption kinetics than in fibre direction, these results indicate that moisture transport across fibre direction has to increase with increasing MC. Alternatively, one of the barriers which prevents the uptake and release of water across fibre direction has to decrease considerably with increasing MC. This view is supported by other investigations in the literature, where an increase of moisture transport across fibre direction was frequently mentioned (Siau 1984; Droin-Josserand et al. 1989; Krabbenhoft and Damkilde 2004). Furthermore, steady-state diffusion measurements on pine, spruce and beech samples (see Wadsö 1994b; Sonderegger et al. 2011 and references therein) as well as gas permeability measurements on several hardwoods (Choong et al. 1974) also reported about an increase of moisture transport across fibre direction with increasing MC. Sorption and sorption related processes by contrast seem to be less responsible for this significant increase, as they should have a similar impact for the three anatomical orientations.

Table 2

Initial uptake (at low RH) and release of water (at high RH) related to minimum sample mass for samples with a thickness of 0.5 mm in the longitudinal (L), tangential (T) and radial (R) direction. Measurement error is below $\pm 0.06\%$

Sample	Low RH [%]	High RH [%]	Difference [%]
L	1.96	1.54	$\mathbf {-0.42}$
T	0.82	1.50	$\mathbf {+0.68}$
R	0.92	1.55	$\mathbf {+0.63}$

To analyse if such a significant increase of moisture transport across fibre direction can be explained with the existing concepts of a water vapour transport through the lumen-pit-ray system or a bound water transport through the cell wall of wood (see e.g. Engelund et al. 2013 and references therein), a short discussion on the two transport mechanism is given below. The coupled moisture transport will not be discussed, as a proper treatment with a coupled transport model needs an accurate information on both sorption and sorption related processes, which are still not available. Further, for a meaningful simulation a three dimensional modelling using the accurate three dimensional wood structure (e.g. using X-ray tomographic microscopy (Trtik et al. 2007)) is essential, as a one dimensional simulation cannot sufficiently capture the complex movement of moisture and the associated interaction between moisture transport, sorption and sorption related processes inside the wood samples.

Transport of water vapour

The moisture transport through the lumen-pit-ray system of wood is usually described by a water vapour diffusion process. For this, the water vapour diffusion coefficient in air (see e.g. Schirmer 1938) is commonly used by applying a constant reduction factor for the various pathways along the three anatomical orientations (cf. Sect. 2.4). According to the geometrical differences, the diffusion coefficient in longitudinal direction is given to be considerable larger than in tangential (or radial) direction, $D_{wv}^{L}\,\approx \,20\cdot D_{wv}^{T}$ (Krabbenhoft and Damkilde 2004; Frandsen et al. 2007; Eitelberger et al. 2011). An evaluation of the water vapour diffusion coefficient in air between $0\%\,\hbox {RH}$ and $90\%\,\hbox {RH}$ yields a decreases of less than $3\%$. This slight decrease in combination with the constant reduction coefficients can neither explain the increased moisture transport across fibre direction nor the similar sorption kinetics for samples with the same thickness in the high range of RH. Similar results can be obtained when the transport of water vapour includes an instantaneous absorption and desorption of water vapour on the surface of the cell wall (see Sect. 2.4). This is because the effective diffusion coefficients along the three anatomical orientations are similarly reduced by the uptake and release of water. Thus, to describe an increase of moisture transport across fibre direction with the diffusion of water vapour through the lumen-pit-ray system, the tangential and radial water vapour diffusion coefficients must increase with MC. A possible mechanism for this increase might be a higher permeability of the bordered pit pairs, either by an increased permeability of the pit membrane (torus or margo) or by a movement of the pit membrane to open the pit (i.e. deaspiration of pits). This seems reasonable, since the resistance of pits to the diffusion of non-swelling gases across fibre direction was mentioned e.g. to be more than $99\%$ for dry conifer wood (Petty 1973). The impact of pit aspiration on the gas permeability in wood is given in literature (Comstock 1970; Smith and Banks 1971; Meyer 1971), and moisture-dependent changes in the shape and aspiration state of bordered pits have been mentioned by Patera et al. (2021). However, further experimental studies on the moisture-dependent changes of bordered pits (i.e. deformation, aspiration, and changes in permeability) are needed to assess their impact on the water vapour diffusion through wood. Alternatively, water vapour sorption experiments on wood samples with a different pit structure might be compared to estimate the impact of pit permeability on the increased uptake and release of water across fibre direction. In comparison to Norway spruce (Picea abies), northern white cedar (Thuja occidentalis) would be of interest, as the pit membrane hardly shows a thickened torus and the pits seem to remain more permeable at low MC (Liese and Bauch 1967; Bauch et al. 1972).

Transport of bound water

Inside the cell wall of wood, moisture transport is usually described by a diffusion process, in which water is transported through the cell wall in a bound state (see e.g. Krabbenhoft and Damkilde 2004 and references therein). Bound water diffusion coefficients were given to increase exponentially with MC and the coefficient in longitudinal direction is assumed to be larger than in tangential (or radial) direction, $D_{bw}^{L}(MC)\,\approx 2.5\cdot D_{bw}^{T}(MC)$ (Siau 1984). An evaluation of this bound water diffusion coefficients at $0\%$ and $20\%$ MC (i.e. at $0\%$ and approximately $90\%$ RH) gives an increase of one order of magnitude for each direction. Similar results were also obtained using molecular dynamics simulations (Kulasinski et al. 2017; Zitting et al. 2021). With such an increase of the diffusion coefficients it is difficult to justify both the similar sorption kinetics between samples of different anatomical orientation and the differences in the sorption kinetics between samples of different thickness (see Figs. 7 and S3 in the Supplementary Information). Though, it should be mentioned that these bound water diffusion coefficients are not necessarily correct (see e.g. Wadsö 1993b and references therein) and that the difference in the bound water diffusion coefficients has never been directly determined. However, there seems to be two problems if bound water diffusion is used to explain the increasing uptake and release of water for samples across fibre direction. Firstly, water vapour has to be bound on the surface of the cell wall prior a transport of bound water through the cell wall is possible. If sorption related processes are involved, they need to be fast enough to allow an additional transport path across or an alternative transport path along the cell wall of wood. As a consequence of the fast processes within the cell wall, the sorption kinetics of thin wood samples should increasingly resemble a diffusion process in the high range of RH, which contradicts the measured results and the results in literature (Avramidis and Siau 1987; Wadsö 1993a; Frandsen et al. 2007). However, Kulasinski et al. (2017) mentioned a considerable increase in bound water diffusion due to a difference in the binding of $\hbox {H}_{2}\hbox {O}$-molecules. At low moisture content, $\hbox {H}_{2}\hbox {O}$-molecules are strongly bound to the wood polymers, causing a slow moisture transport within the cell wall. In contrast, as moisture content increases, an interconnected network of water clusters forms, causing a strong increase in moisture transport. Similarly, a decrease in the mobility of the bound $\hbox {H}_{2}\hbox {O}$-molecules with lower moisture content of wood was mentioned by Zitting et al. (2021). Accordingly, the uptake and release of water in the cell wall does not necessarily have to be accompanied by the sorption-relevant processes. Secondly, to provide a similar moisture transport in and across fibre direction, the combined water vapour and bound water transport has to be comparable for the corresponding anatomical orientations. As water vapour diffusion across fibre direction is considerably less than in fibre direction, the corresponding bound water diffusion coefficient has to be in a similar magnitude as the water vapour diffusion coefficient to resolve this issue. Such high values seem though to be unrealistic compared to bound water diffusion coefficients in other materials (Aldous et al. 1997; Aguerre and Suarez 2004; Wang et al. 2020). An alternative to this would be if either the surface evaporation limits the transport of moisture in the sample or if the transport of bound water can transport a greater amount of water than the transport of water vapour.

Conclusion

Water vapour sorption experiments on thin Norway spruce samples have shown that at low moisture content of wood, the initial uptake and release of water is influenced by the diffusion of water vapour through the lumen-pit-ray system. Differences in the initial sorption kinetics can thus be observed between samples with a different thickness and between samples with a different anatomical orientation (i.e. in and across fibre direction). Therefore, even in water vapour sorption experiments with small wood samples under ambient conditions, moisture transport cannot be neglected. With increasing moisture content, the results indicated an increased moisture transport across fibre direction and an increased impact of cell wall processes on the uptake and release of water. These changes might explain the similar sorption kinetics between thin samples in and across fibre direction in the high range of relative humidity. However, sample thickness was shown to have a considerable impact on the uptake and release of water. Therefore, an additional or modified process must be considered at an increased moisture content of wood, which mainly depends on the sample thickness (or on the number of sorption sites) but not on the anatomical orientation. Water vapour sorption experiments with chemically modified wood or with wood of different dry density should provide further information on this process. Nevertheless, additional measurements on the sorption related processes (e.g. measuring the heat of sorption) might be necessary to correctly interpret the water vapour sorption behaviour at an increased moisture content of wood. Longitudinal samples with a thickness of less than 1 mm should be used for these measurements and the samples should be directly exposed to the water vapour-air flow. Regarding the interpretation and modelling of sorption data and other experimental investigations under transient conditions in relative humidity, the transport of moisture and the impact of sample thickness have to be considered particularly at an increased moisture content of wood.

Acknowledgments

Roman Lackner is acknowledged for providing the sorption device (Unit of Material Technology, Universität Innsbruck) and Thomas Bechtold is acknowledged for reading the final version of the manuscript (Research Institute of textile chemistry and textile physics, Universität Innsbruck).

Declarations

Conflict of interest

The author has no relevant financial or non-financial interests to declare.

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Supplementary Information

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Supplementary file 1 (pdf 1055 KB)

There is a variety of expressions which are used synonymously for the time-dependent change of sample mass during water vapour sorption experiments in wood science: sorption kinetics, absorption/adsorption and desorption kinetics, kinetics, temporal mass change, sorption rates, absorption/adsorption and desorption rates, or rates. In this work the term sorption kinetics as well as absorption and desorption kinetics will be used.

The small decrease of the water vapour diffusion coefficient in air (Schirmer 1938; VDI-Gesellschaft 2006) is too low to explain these differences between the low and high range of RH. Even the often mentioned increasing bound water diffusion inside the cell wall cannot resolve this issue, since it would rather force the opposite trend.

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Title: Water vapour sorption and moisture transport in and across fibre direction of wood
Author: Alexander Murr
Publication date: 30-03-2022
Publisher: Springer Netherlands
Published in: Cellulose / Issue 7/2022
Print ISSN: 0969-0239
Electronic ISSN: 1572-882X
DOI: https://doi.org/10.1007/s10570-022-04520-x

Dimensions (mm x mm x mm)	Mass (mg)	Label
0.5 (L) \(\times\) 21.4 (R) \(\times\) 40.0 (T)	157	L_0.5mm
1.0 (L) \(\times\) 20.2 (R) \(\times\) 41.6 (T)	299	L_1mm
2.0 (L) \(\times\) 21.0 (R) \(\times\) 43.0 (T)	607	L_2mm
3.0 (L) \(\times\) 20.7 (R) \(\times\) 43.0 (T)	888	L_3mm
0.5 (T) \(\times\) 21.2 (R) \(\times\) 43.6 (L)	175	T_0.5mm
1.0 (T) \(\times\) 21.2 (R) \(\times\) 43.6 (L)	312	T_1mm
2.0 (T) \(\times\) 22.2 (R) \(\times\) 43.6 (L)	613	T_2mm
3.0 (T) \(\times\) 21.6 (R) \(\times\) 43.6 (L)	928	T_3mm
0.5 (R) \(\times\) 21.5 (T) \(\times\) 43.6 (L)	173	R_0.5mm
1.0 (R) \(\times\) 21.6 (T) \(\times\) 43.6 (L)	361	R_1mm
2.0 (R) \(\times\) 22.1 (T) \(\times\) 43.6 (L)	605	R_2mm

Sample	Low RH [%]	High RH [%]	Difference [%]
L	1.96	1.54	\(\mathbf {-0.42}\)
T	0.82	1.50	\(\mathbf {+0.68}\)
R	0.92	1.55	\(\mathbf {+0.63}\)

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Abstract

Supplementary Information

Publisher's Note

Introduction

Materials and methods

Dynamic vapour sorption

Sample preparation

Experimental set-up

Simulations

Error estimation

Results and discussion

Samples with different thickness

In fibre direction

Across fibre direction

Samples with different anatomical orientation

Low range of RH

High range of RH

Transition low to high range of RH

Moisture transport across fibre direction

Transport of water vapour

Transport of bound water

Conclusion

Acknowledgments

Declarations

Conflict of interest

Publisher's Note

Supplementary Information

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