Water distribution in wood after short term wetting
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ORIGINAL PAPER
Water distribution in wood after short term wetting
Mojca Zlahtic Zupanc . Ursa Mikac . Igor Sersa . Maks Merela .
Miha Humar
Received: 10 April 2018 / Accepted: 2 November 2018
� Springer Nature B.V. 2018
Abstract Water has a major influence on wood
properties, especially dynamic moisture cycles, which
affect the wood in outdoor applications. It is thus
important to understand the penetration and distribu-
tion of water in wood. In this study, rainfall events
were simulated to correspond to water immersion
periods of 1 h. Specimens were imaged by magnetic
resonance imaging (MRI) after 1 h of immersion.
These measurements were used to determine the water
distribution in the wood and to elucidate changes
during the drying of specimens of five wood species:
sweet chestnut heartwood (Castanea sativa), Euro-
pean larch heartwood (Larix decidua), Scots pine
heartwood and sapwood (Pinus sylvestris) and Nor-
way spruce (Picea abies). Both gravimetric and MRI
analysis showed that after 1 h of immersion, pine
sapwood took up the highest amount of water,
followed by spruce wood. Considerably lower mois-
ture contents were determined in pine heartwood,
chestnut and larch, which correlated with a lower
signal intensity. The outer parts of the specimens
exhibited similar patterns with all of the specimens.
The most variable results were the moisture content
time profiles in the middle part of the specimens.
Comparison of the MRI measurements and gravimet-
rically determined moisture contents during drying
validated the MRI measurements and confirmed the
method to be suitable for giving comprehensive
information about the water drying kinetic.
M. Zlahtic Zupanc � M. Merela � M. Humar (&)
Department of Wood Science and Technology,
Biotechnical Faculty, University of Ljubljana,
Jamnikarjeva 101, 1000 Ljubljana, Slovenia
e-mail: [email protected]
U. Mikac � I. SersaJozef Stefan Institute, Jamova 39, 1000 Ljubljana,
Slovenia
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https://doi.org/10.1007/s10570-018-2102-y(0123456789().,-volV)(0123456789().,-volV)
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Graphical abstract
Keywords Magnetic resonance imaging � MRI �Wood � Water � Moisture content � Drying
Introduction
Wood is one of the most important building materials.
Due to its positive environmental impact, good
properties and availability, the use of wood, specifi-
cally in use class 2 (outside, not in ground contact,
covered) and use class 3.1 (outside, not in ground
contact, not covered) applications, as defined by EN
335 (2013), has increased considerably in central
Europe in recent decades (Rametsteiner et al. 2007).
However, sufficient durability of wood is required to
meet users’ criteria for specific applications (Kutnik
et al. 2014). Since the majority of biocides are banned
because of environmental and health concerns, and
due to the negative public opinion on existing biocides
and the use of tropical timber, research philosophies
for improving the durability and prolongation of
service life of wood have focused on alternative
directions (Militz 2015; Humar et al. 2017). Recent
models clearly indicate that the service life of wood in
above ground applications is a function of inherent
durability (due to the presence of biocides and/or
biologically active extractives) and water exclusion
efficacy (Meyer et al. 2017). Increased moisture
content (MC) above a certain threshold increases the
possibility of fungal infestation (Schmidt 2006). It is
thus important to limit water uptake (Brischke and
Thelandersson 2014). In the work of Isaksson et al.
(2013), it was shown that the first signs of fungal decay
on spruce wood appeared after 325 days under
favorable conditions (with MC above 25% and
temperature suitable for fungal decay). In general, it
is accepted that wood destroying fungi need a moist
environment to grow, so the wood MC should be kept
below 25% for non-modified wood. However, some
recent findings indicate that fungi can degrade wood
even at a lower MC, as low as 16% (Meyer and
Brischke 2015). Regardless of the moisture limit for
fungal decay, it is of considerable importance to
control the wood MC. Water uptake can be controlled
with suitable design, proper detailing, modification
and an understanding of the material (Dietsch et al.
2014; Yao et al. 2018). It is therefore very important to
understand the moisture dynamics of wood, which is a
comprehensive parameter that reflects the drying and
wetting of wood.
Wood is a hygroscopic material, with the ability to
interact with water (adsorb or desorb) from humid air,
in common with other porous materials (Thybring
et al. 2017). Wood exchanges moisture with the
surrounding air, thus achieving a state of hygrothermal
equilibrium (Weise et al. 1996). The rate of this
exchange depends on the relative humidity and
temperature of the air and the current wood MC
(Chen and Wangaard 1968; Skaar 1972; Hartley et al.
1992; Vidal and Cloutier 2005; Tannert et al. 2011).
This affinity of wood for water is caused by accessible
hydroxyl groups within the wood cell walls. Cellulose
and hemicelluloses, being more hygroscopic than
lignin, are mainly responsible for moisture uptake
(Rowell and Banks 1985). The affinity between dry
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wood and water is so strong that it is impossible to
prevent moisture gain (Reeb 2009). Moisture changes
are, for example, responsible for shrinkage and
swelling, for moisture-induced stresses and for
mechanosorptive effects, which may ultimately lead
to cracking or loss of loadbearing capacity (Skaar
1988; Thelandersson and Larsen 2003; Hameury and
Sterley 2006). Just as wood is made of cells occurring
in two systems, any individual cell itself has twomajor
domains; the cell wall and the lumen. In the context of
moisture relations, the lumen is the space in which
liquid water accumulates when moisture is added after
the fiber saturation point (FSP) has been reached. At
higher moisture levels, wood moisture movement is
predominately characterized by capillary movement
of water through the wood cell lumina. Capillary water
uptake is the predominant mechanism for water
penetration during short rainfall events. At lower
MC, diffusion plays the key role. Diffusion of water
through wood depends on the wood density and
anatomical pattern (Fotsing and Tchagang 2005),
grain orientation (Mouchot et al. 2006), sap-
wood/heartwood (Rosenkilde and Glover 2002), wood
moisture and wood temperature, as well as environ-
mental parameters (Simpson 1993), growth conditions
(Cai 2005) or the presence of reaction wood (Tarmian
et al. 2012).
MC is defined as the ratio between the mass of
water (mw) in a moist wood sample and the mass of an
absolutely dry sample of wood (Merela.et al. 2009b).
There are two general approaches to determining
wood moisture content. In direct measurements, the
moisture content is determined by oven-drying or
water extraction, but both are destructive methods
with respect to timber members in situ. Indirect
measurement methods use the physical properties of
wood, which are correlated to the wood moisture
content (Dietsch et al. 2014). The most widely used
method for MC determination is the oven-drying
method (EN 13183-1 2002). It has the highest
accuracy or degree of precision for research purposes.
The method consists of cutting test pieces, measuring
their mass, and then oven-drying them. Several other
techniques have been developed from oven-based
methods (Thybring et al. 2018), such as Dynamic
Vapor Sorption (Engelund et al. 2010, 2011; Glass
et al. 2018; Thybring et al. 2018) or continuous
moisture monitoring (Van den Bulcke and Van Acker
2008; Humar et al. 2014). Unfortunately, this method
is destructive and relatively slow, and errors can occur
if the wood contains volatile material, other than
water, that evaporates during drying [e.g., resins
(Hartley and Marchant 1995)]. These issues can be
overcome if distillation or extraction methods are
applied instead of classical oven-drying methods
(Kollmann and Cote 1968; Niemz 2003). One of the
key drawbacks of direct methods forMC assessment is
their destructive nature. If MC is to be measured
during monitoring of an object, indirect methods have
to be applied (Brischke et al. 2008; Franke et al. 2013;
Krzisnik et al. 2018), process control (Simpson 1989;
Mitsui et al. 2008). In these applications, capacitive,
electrical resistance, microwave, radiometric, spectio-
metric, spectrometric or color reaction measurements
can be applied (Skaar 1988). Among the various
technologies, spectroscopy based methods have been
found to be particularly promising: near infra-red
spectroscopy (NIR) (Thygesen and Lundqvist 2000;
Tsuchikawa 2007) and nuclear magnetic resonance
(NMR) (Bucur 2003a, b; Morales et al. 2004; Merela
et al. 2009a, b). One of the key benefits of spectro-
scopic techniques is that they provide insights into
chemical wood–water interactions, as well as yielding
information on water distribution in the macro-void
wood structure (Thybring et al. 2018).
Nuclear magnetic resonance (NMR) enables
instantaneous determination of the proton density in
liquids and is thus convenient for determining the MC
of wood. It is a non-destructive, non-invasive and non-
contact technique already being successfully applied
in wood science (Callaghan 1991; Contreras et al.
2002; Bucur 2003a, b; Morales et al. 2004; Labbe et al.
2006; Oven et al. 2008, 2011; Thygesen and Elder
2008; Dvinskikh et al. 2011; Merela et al. 2009a, b;
Cox et al. 2010; Hernandez and Caceres 2010;
Kekkonen et al. 2014; Javed et al. 2015; Passarini
et al. 2015; Zlahtic et al. 2017; Mikac et al. 2018;
Gezici-Koc et al. 2017). In addition, an NMR modal-
ity, magnetic resonance imaging (MRI), is a versatile
tool widely used for investigating the spatial distribu-
tion of moisture in various specimens, including
modified wood and other porous materials (Kanazawa
et al. 2017; Thybring et al. 2018). Several studies have
used MRI to investigate wood–water interactions and
it has been shown that MRI is one of the most
appropriate methods for this purpose, given that it can
provide valuable information on the distribution and
concentration of water in wood (Brownstein 1980;
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Menon et al. 1987; Araujo et al. 1992, 1993; Hartley
et al. 1994; Robertson and Packer 1999, Rosenkilde
and Glover 2002; Casieri et al. 2004; Merela et al.
2005; Almeida et al. 2007; Kanazawa et al. 2017). It
has also been proven that MRI is effective in providing
information about the distribution and concentration
of water in wood during drying and absorption
processes (Hartley et al. 1994; Menon et al. 1987).
The majority of NMR/MRI studies on wood apply
methodologies normally associated with porous
media.Water can play various roles in the microscopic
structure of wood (Casieri et al. 2004).Wood therefore
has different 1HNMR signal sources: cell-wall water,
lumen water, and some hydrogen pertaining to wood
macromolecules. Predominately low field NMR can
distinguish between water-bound hydrogen located in
different physical and chemical environments (Araujo
et al. 1992). It is thus a good technique for determining
the distribution of water within different parts of the
wood structure. The spin–lattice (or longitudinal
relaxation, T1) and spin–spin relaxation (or transverse
relaxation, T2) times of water molecules are qualita-
tively different for compartmented water than for bulk
water (Almeida et al. 2007). In spite of these benefits,
MRI is not often used in the field of wood science,
mainly due to the expensive and relatively rare
equipment. In addition to cost related issues, the size
of the specimens is one of the limiting factors (since
better spatial resolution of MRI can be obtained with
smaller specimens). In addition, it is challenging,
although possible, to detect MC below the FSP in
wood with conventional imaging techniques because
of the short T2 times of bound water (Rosenkilde and
Glover 2002). The difficulty can be overcome by the
use the use of special MRI methods, such as the
SPRITE (Single-Point Ramped Imaging with T1
enhancement) method or by signal averaging (Wang
and Chang 1986).
Since water has a major influence on wood
properties, understanding the penetration and distri-
bution of water in wood is of great importance. The
majority of available techniques provide information
about the average MC of wood, not considering that
there might be pockets of water inside the wood, with
optimal conditions for fungal decay. In the present
study, we tried to elucidate changes in water distribu-
tion after dynamic moisture cycles simulating rain
events and to determine the time needed to dry the
central part of the specimens. For this purpose, the
MRI technique was employed to visualize the water
distribution in various wood species and to elucidate
the changes during drying. To the best of our
knowledge there are not many available methods
suitable for monitoring water distribution in porous
materials through time. Specimens in the research
were imaged after 1 h of soaking in distilled water in a
controlled climate. Understanding water distribution
is of great importance for the interpretation ofMC data
of wood exposed in outdoor conditions and to model
the effect of rain events on the wood moisture content.
Materials and methods
Wood material
The studywas performed on sweet chestnut heartwood
(Castanea sativa), European larch heartwood (Larix
decidua), Scots pine heartwood and sapwood (Pinus
sylvestris) and Norway spruce (Picea abies) wood.
Specimens were defect-free, without visible signs of
decay or blue staining, as prescribed by EN 113
(2006). The specimens were also xylotomically
oriented and had similar densities and ring widths.
The wood species were selected because they exhibit
varied water exclusion efficacies, as determined with
other tests (Zlahtic et al. 2017). In addition, these
wood species are of considerable commercial impor-
tance in Europe and are frequently used for a variety of
applications, including outdoor uses.
Specimens for MRI scanning were sawn from one
bigger specimen, as indicated in Fig. 1. The dimen-
sions of the specimens used for MRI scan were defined
by the size of the RF (radiofrequency) coil used, i.e.,
1.2 cm 9 1.2 cm 9 1.2 cm (longitudinal 9 radial 9
tangential direction). Specimens were not treated and
were kept under room conditions (T = 23 �C; RH =
65%) before the experiment.
High-resolution magnetic resonance imaging
Prior to the measurements, the specimens were
immersed in distilled water for 1 h, with sample
masses determined pre- and post-immersion. One-
hour immersion was used to simulate a rain event.
Although water penetration into wood during immer-
sion is not fully comparable to the mechanism of water
penetration during a rain event, this approach was used
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because it enables a standardized procedure that
reflects the properties of wood species and has been
found to be the closest method to rain events (Zlahtic
et al. 2015).
For the MRI scan, the immersed specimen was
placed at the top of a glass tube filled with freshly
activated silica gel (4.5460 g), inserted in a larger
glass tube and fixed with Teflon (polytetrafluo-
roethylene—PTFE) tape to prevent rotation during
the MRI scan. Silica gel enabled drying of wood that
had been immersed in water prior to the measure-
ments. If no silica gel was applied, the relative air
humidity (RH) in the chamber reached 100%, which
prevents drying almost completely.
After the MRI measurements, the specimens were
oven-dried at 103 ± 2 �C until their mass became
stable and they were then weighed. A gravimetrical
method according to EN 13183-1 (2002) was used to
determine MC before and after MRI scanning.
MRI measurements were performed on a TecMag
Redstone (Houston TX, USA) MRI spectrometer with
a superconducting 9.4 T Jastec magnet (Kobe, Hyogo,
Japan). The specimen in the glass tube was inserted in
a 20-mm diameter RF coil. A 1D MRI pulse sequence
was used to obtain the water distribution along the
longitudinal, tangential and radial directions. To
visualize the 3D distribution of water in the specimen
3D, MRI was performed using the gradient-echo (GE)
technique. The specimen was reoriented in the magnet
in such a way that it allowed 1D profiles to be taken
along tangential, radial and longitudinal directions.
Before the first 1D experiment, the orientation inside
the magnet was additionally checked by acquiring a
low-resolution 3D GE image.
Changes in moisture were monitored for 24 h in
four specimens and for 64 h in one specimen. In order
to determine the water distribution after soaking, 1D
MR signal intensity profiles were acquired in three
perpendicular orientations, with the following
parameters: field of view (FOV) of 20 mm, echo time
(TE) of 1.56 ms, and repetition time (TR) of 1 s were
each measured for the first 20 min. In the 24-h
experiments, the acquisition of 1D profiles was
followed by 3D GE imaging to visualize the 3D
distribution of the water in the specimen. The scan
parameters were: FOV 20 mm, imaging matrix
128 9 128 9 128 (isotropic resolution was
156 lm), excitation flip angle 30�, TE 1 ms, and total
imaging time 17 min. After that, 1D MR signal
intensity profiles were scanned for 22 h at identical
parameters to those of the first scan but with a lower
temporal resolution (TR of 120 s). The last measure-
ment was again 3D GE imaging. For one specimen of
each wood species, 3D GE images were acquired
every 4 h (after acquisition of the 1D profiles was
finished) to detect water migrations inside the
specimen.
Since the 64-h drying process was very long, it was
monitored in one specimen only. The monitoring
included 3D GE imaging using the same parameters as
described previously but with a higher spatial resolu-
tion-imaging matrix of 256 9 256 9 256 with iso-
tropic resolution of 78 lm, yielding a total imaging
time of 7 h. The drying process was monitored
initially by 20-min scanning with a sequence of 1D
profiles, which was followed by acquisition of the 3D
GE image. After 48 h of drying, another 3D GE image
was acquired and between acquisitions of the two 3D
images, the drying process was monitored by measur-
ing 1D profiles at 2-min intervals.
Data analysis
MRI datasets were analyzed by ImageJ (Schneider
et al. 2012) digital image processing software.
Because the settings for the MRI measurements were
not the same in all experiments (probe and coil tuning,
receiver gain etc.) normalization of the 1D MRI
Fig. 1 Specimens prepared
for magnetic resonance
imaging
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signals was performed. For each specimen, the time-
dependence of the integrated signal and the signal
values at both edges (lower and upper) and from the
middle of the specimen were obtained from 1D
profiles along the z direction (profiles in the longitu-
dinal direction). The integrated intensities were nor-
malized at 48 min after soaking in distilled water. For
signal normalization at the specified three points (both
edges and in the middle), the signal values were
divided by the signal value at the lower edge of the
specimen of the profile at 48 min after soaking.
Calibration of the MRI method for wood moisture
measurements
Wood specimen preparation
Additional experiments on parallel specimens were
performed to link the measured MR signal with the
corresponding MC. In total, 14 specimens were
prepared (two per each wood category) with the same
dimensions as for the previous experiment. One
specimen per species was used for the MRI scan and
one further specimen for equilibrium moisture content
(EMC) determination. The specimens were condi-
tioned in 7 different condition chambers equipped
with a fan and saturated salt solutions to regulate the
relative air humidity (RH = ± 1%), as can be seen in
Table 1. In order to prevent wetting of the samples in
the condensing environment, they were protected with
a shelter. Specimens were weighed (Sartorius, Ger-
many) after the equilibrium state was reached and
before each of the MRI experiments. The EMC was
then calculated according to the gravimetric method
from the difference between the equilibrium (me) and
the oven-dry mass (m0) of each specimen [Eq. (1)],
with an accuracy of the balance of 0.0001 g.
MC ð%Þ ¼ me � m0
m0
� 100 ð1Þ
1D profiles with the same parameters as were used in
for moisture distribution measurements were acquired
from specimens of knownMC to obtain the correlation
between the 1D profile signal intensity and MC for
each wood category. The specimens (within the glass
tube) were positioned and imaged in a 20-mm
diameter RF coil together with a phantom sample,
which was placed on top of the specimens and was
used for normalization among different experiments.
The glass tube was then closed, so as to prevent
changes in MC. Different signals were obtained
according to the different MCs in the different
materials.
The integrated signal intensities of 1D profiles were
used to determine the correlation between MC and
signal intensity. A linear relationship betweenMC and
integrated signal intensity was found in each material
(wood species):
S ¼ aMCþ b; ð2Þ
where S is the integrated signal intensity, MC is the
specimen‘s moisture content and a and b are constants
determined from the measured data for each wood
species and are listed in Table 2 together with the
coefficient of determination R2.
Normalization procedure
The obtained calibration curves (Table 2) were used to
determine MCs from the 1D profiles measured during
drying. Specimen MCs after 1 h soaking in distilled
water and at the end of the MRI experiments were
determined by the gravimetric method. The relation in
Eq. 2 was used to calculate the MC during MRI
measurements, from the measured 1D-signal intensity
profiles. After the first 1D profile was obtained
approximately 30 min after soaking (the time needed
to set the MRI experiment and determine the proper
specimen orientation in the magnet), the signal
intensity at time zero (t0) was determined by extrap-
olating the integrated signal intensity slope to zero
time (time when the specimen was taken out of the
water and the MC was determined gravimetrically) to
determine the obtained signal (Sobt) at t0. The
Table 1 Established atmosphere for the conditioning of
specimens prior to MRM calibration at 20 �C
Climate Relative air humidity (%) Saturated salt solution
1 20 CH3COOK
2 33 MgCl2
3 44 K2CO3
4 65 NaNO2
5 75 NaCl
6 87 ZnSO4
7 97–100 Distilled water
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theoretical signal (Stheo) was calculated from the
known relation between the signal intensity and the
MC (parameters a and b from Table 2) and knownMC
at t0:
Stheoðt0Þ ¼ a�MCðt0Þ þ b ð3Þ
MCs at different times after soaking were determined
from the integrated signal intensity of the longitudinal
1D profile as:
MCðtnÞ ¼StheoðtnÞ � b
að4Þ
where Stheo (tn) is determined from the measured
signal at tn as:
Stheo tnð Þ ¼ SobtðtnÞ �Stheo t0ð ÞSobt t0ð Þ ¼ SobtðtnÞ � rðt0Þ ð5Þ
The same procedure was performed for the upper,
middle and lower parts, as well by using the ratio r(t0)
from integrals.
Gravimetric method for moisture content
determination
Parallel to the MRI experiment, specimens made from
the same material were continuously weighed to an
accuracy of 0.0001 g (Sartorius, Germany). Speci-
mens were soaked in distilled water for 1 h and then
weighed every 120 s for 60 h, under constant labora-
tory conditions (20 �C/65% RH). After exposure,
specimens were oven-dried at 103 ± 2 �C to a
constant mass and weighed to determine the oven-
dry mass. The mass change was then calculated
(Eq. 1). These data were used for verification of the
MRI results.
Analysis of wood drying dynamics
The moisture content MC is proportional to the water
concentration C in wood (MC½%� ¼ 100m1w
q0C, where
m1w is the mass of a single water molecule and q0 is thedensity of the oven-dry wood). The diffusion equation
that describes the transport of water in the wood, and is
usually written as a function ofC, can therefore also be
written as a function of MC. In the case of one-
dimensional diffusion along the x direction, the
equation is:
oMC
ot¼ o
oxDoMC
ox
� �: ð6Þ
Here we consider a case in which the diffusion
coefficient D is constant and the sample along the
diffusion direction extends from - l to l (�l\x\l).
Wood dries due to surface water evaporation, which is
proportional to the difference between the MC at the
surface and the equilibrium moisture content MCeq.
The process can be described by the following
boundary condition at x ¼ � l and x ¼ l:
� DoMC
ox¼ aðMC �MCeqÞ; ð7Þ
where a is the surface evaporation rate. The wood
drying problem given by Eqs. 6, 7 can be solved
analytically for a case in which the sample has an
initially uniform moisture content MCiu greater than
MCeq (Crank 1975):
Table 2 Calibration curves of the equilibrium moisture content of wood as a function of the normalized nuclear magnetic resonance
signal intensity
Wood species
(Abbreviations)
Scots pine sapwood
(PsS)
Scots pine heartwood
(PsH)
Norway spruce
(Pa)
European larch
(Ld)
Sweet chestnut
(Cs)
y = ax ? b
a 0.7209 0.3471 0.4397 0.1614 0.6875
b - 5.3222 - 1.5604 - 2.8246 - 1.0387 - 5.1855
R2 0.9787 0.865 0.9633 0.8898 0.9738
The abbreviations of materials are used later in plots
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MC x; tð Þ ¼ MCiu �MCeq
� �X1n¼1
2L cosðbnx=lÞe�b2nDt=l2
ðb2n þ L2 þ LÞ cosðbnÞþMCeq
ð8Þ
Here bn s is the positive root of the equation
b tanðbÞ ¼ L and L is a dimensionless variable defined
as L ¼ al=D. When considering the average moisture
content in the sample, Eq. 8 is integrated over the
sample dimension, i.e., from – l to l, and divided by 2l,
thus obtaining:
MC tð Þ ¼ MCiu �MCeq
� �X1n¼1
2L2e�b2nDt=l2
b2nðb2n þ L2 þ LÞ
þMCeq ð9Þ
As proposed in Yuniarti et al. (2018), Eq. 9 can be
simplified by reducing the summation only to the first
term, for which decay with time is the slowest. This
approximation yields a simple model function for the
wood drying process:
MC tð Þ ¼ MCi �MCeq
� �e�t=s þMCeq: ð10Þ
whereMCi corresponds to the average initial moisture
content of the drying wood sample and s is the wooddrying characteristic time constant equal to:
s ¼ l2
b21D: ð11Þ
In the case of a small L, b tanðbÞ can be approximated
by b2 so that the characteristic time constant becomes:
s � l
a; L ! 0; ð12Þ
while in the case of a large L, b1 converges to p=2 so
that
s � 4l2
p2D; L ! 1; ð13Þ
Results and discussion
Since MRI measurements are challenging to interpret,
it is more convenient to present the results graphically,
with separate graphs for each species prepared.
Furthermore, MC data in different parts of specimens
and different times of drying are presented (Table 3):
MC0 corresponds to MC at the start of measurement;
MC10 corresponds to MC after 10 h of measurement
and the last point (MC20) corresponds toMC after 20 h
of measurement. MC after 60 h (MC60) can be
resolved from graphs only. In order to make these
complex plots easier to understand, details of the
graphs have been briefly described at the beginning of
the results. The relationship between MC and time of
drying for all five specimens can be seen in Fig. 2,
which comprises five curves per graph, numbered 0 to
4. Three measurements took 24 h, while one of them
was prolonged to between 58 and 60 h. The average
MC of the wood specimen is plotted on the vertical
axis, while the horizontal axis represents the drying
time. It can be seen from the graphs how the average
MC of wood changes during the drying of wet wood
above freshly activated silica gel inside the 20-mm
diameter RF coil, while MRI scanning was in
progress. In order to enable easier comparison of
typical curves recorded for each of the specimens, the
most representative curve for each material is plotted
in Fig. 2. Since the pattern of drying depends consid-
erably on the position on the specimen, the moisture
distribution in relation to drying time with individual
wood species is presented in Fig. 3, in which MC
changes in the upper (U), middle (M) and lower
(L) parts of the specimens are presented. The lower
part of the specimens is the part that was closest to the
freshly activated silica gel. The last graph in Fig. 4
shows the results of MC monitoring during laboratory
tests, in order to verify the relevant approach. The
curves in the graph are thus a result of continuous
weighing using a laboratory scale.
The shapes of the curves representing the drying of
PsH, Pa, Ld, Cs samples exhibited low variation
between each measurement, with the exception of PsS,
in which specimens 3 and 4 exhibited significant
deviation from the other three specimens. However,
the shape of the curves of all specimens was similar for
all the wood species monitored. Differences between
the specimens in the PsS specimen group can be linked
to anatomical differences and variability of the
specimens (Lesar et al. 2009; Zlahtic et al. 2017). In
addition, it should be noted that PsS had the highest
uptake of water; the variability was thus the most
noticeable. During 1 h of immersion, PsS took up
approximately 66% (MC0) water. This water was
released fairly fast, which was observed as a sharp
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decline in the linear part of the curve (Fig. 2, PsS).
High initial MC resulted in the most prominent
difference between the initial (MC0 = 66%) and final
(MC60 = 16%) MC. However, the MC determined
after 60 h of drying was still the highest compared to
other species: MC of Scots pine sapwood was 16%,
which was approximately twice the value determined
for other materials.
The second highest MC0 (46%) after 1 h of soaking
in distilled water was measured in spruce wood (Pa)
(Fig. 2, Table 3), with the shape and decline of the
curve similar to that of PsS. In the first 20 h of drying,
Table 3 Moisture content in different wood species [Scots
pine sapwood (PsS), Scots pine heartwood (PsH), Norway
spruce (Pa), European larch (Ld) and sweet chestnut (Cs)],
parts (T–total specimen, U–upper part, M—middle part and
L—lower part) and time [0—the start of measuring (MC0),
10 h (MC10) and 20 h (MC20)] of measurement
Wood species/specimens (Fig. 1) Time (h)
T Ua Ma La
MC0 MC10 MC20 MC0 MC10 MC20 MC0 MC10 MC20 MC0 MC10 MC20
PsS
0 66.0 52.1 40.8 66.0 46.0 36.4 40.1 46.9 37.6 87.4 54.6 40.9
1 65.6 52.3 41.0 66.4 44.1 34.6 35.8 37.6 30.3 74.4 42.4 32.4
2 66.7 52.3 40.9 67.8 42.9 33.6 34.1 35.8 28.8 71.3 41.1 32.2
3 64.8 56.3 48.7 64.2 54.6 44.9 37.5 41.3 37.9 77.6 50.4 40.6
4 62.2 44.3 33.8 64.8 35.3 24.8 27.7 26.8 21.6 48.1 25.0 20.2
PsH
0 21.3 10.8 8.9 22.5 7.5 6.6 8.1 8.6 7.6 28.1 8.7 6.8
1 20.1 10.1 8.3 21.9 6.9 6.1 7.5 7.4 6.5 20.8 7.3 6.1
2 18.3 9.9 8.5 19.9 7.5 6.7 8.6 8.4 7.6 22.0 8.2 6.8
3 19.2 10.2 9.0 21.0 8.6 7.7 11.5 10.4 9.4 32.0 9.9 8.3
4 19.2 10.3 8.6 20.9 6.8 6.0 6.7 7.6 6.8 18.7 7.4 6.3
Pa
0 46.0 28.6 20.5 58.2 16.1 13.9 14.0 17.1 14.1 46.0 18.1 13.6
1 42.4 24.4 18.8 52.6 13.6 12.2 13.2 15.7 13.2 42.4 15.7 12.4
2 44.9 28.1 20.3 52.8 15.6 13.4 14.6 18.0 15.5 55.0 22.0 15.1
3 43.5 24.3 18.5 50.5 14.2 12.9 15.9 16.7 14.3 62.4 19.2 14.1
4 51.6 28.1 18.1 60.1 14.9 11.9 14.1 14.9 12.3 51.6 14.4 10.1
Ld
0 19.5 11.5 9.4 21.8 7.8 7.4 10.0 7.4 7.2 22.3 7.7 7.3
1 16.5 10.1 8.4 21.5 9.2 8.0 10.2 8.6 7.8 19.4 10.5 8.5
2 15.8 10.0 8.6 18.4 9.4 8.3 10.4 9.0 8.1 19.7 10.8 8.7
3 17.2 10.0 8.6 21.3 8.9 8.1 9.9 8.8 7.9 24.4 10.8 8.7
4 18.9 11.0 8.9 25.4 9.5 8.1 9.7 8.9 8.0 20.9 10.1 8.4
Cs
0 21.3 12.0 11.5 25.5 8.8 8.6 8.1 8.8 8.7 31.7 8.9 8.8
1 21.0 12.9 11.7 25.2 10.0 9.1 8.6 9.1 8.7 31.2 9.4 9.1
2 20.0 12.2 11.0 21.8 9.3 8.6 8.4 8.7 8.4 23.2 8.9 8.7
3 21.1 12.0 11.0 23.1 8.4 8.1 8.0 8.4 8.2 21.6 8.7 8.5
4 25.1 11.6 11.2 27.4 8.6 8.4 8.2 8.4 8.4 25.5 9.1 8.4
aThe lower surface (L) was closer to the activated silica gel. The silica gel was beneath the sample. The upper surface was at the top
of the test tube, so the microclimates surrounding the samples were different. The middle part is midway between the upper and lower
surfaces
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MC20 was reduced to 18–20% and, after 60 h, the MC
of spruce wood was further reduced by half (MC60-
= 9%), with the value being half that determined for
Scots pine sapwood. There are several reasons for this.
First, pine wood specimens take up considerably more
water and so a longer time is needed for drying.
Furthermore, the water holding capacity of the silica
gel is limited, so the relative humidity in the cell with
Scots pine specimens is likely to be higher than with
spruce wood specimens. During drying, the free water
from the cell cavities is first removed and, since this
water depends on weak capillary bonds for binding, it
can evaporate faster than bound water. Bound water
uses strong hydrogen bonds and cannot be removed
without modification of the chemical structure of the
wood. The wood MC changes are therefore faster in
the upper part of the hygroscopic region but, on
approaching a dry state, they slow down. This can be
seen in the curves representing the drying of PsS and
Pa, in which the first hours of drying show the highest
changes and the largest drop in MC occurs, whilst
smaller changes in MC are later observed.
In the remaining materials (PsH, Ld and Cs), the
lower MC after soaking corresponded to lower signal
intensities (Fig. 2 and 3). The lower water uptake was
a result of the refractory nature of these wood
specimens in comparison to Scots pine sapwood
specimens. The uptake of water by PsH, Ld and Cs
was approximately 20% during 1 h of immersion.
These values were less than half of those determined
with Pa and three times lower than with PsS. In the
later stages, the drying kinetics stabilized, and the MC
did not change considerably in the next 20–60 h. The
MC in PsH, Ld and Cs after 20 h of drying was similar
to that reported for spruce (8–11%).
In Fig. 2, typical drying curves for each wood
species are plotted, in order to enable easier compar-
ison between the most representative curves for each
of the materials used in this study. The graph clearly
shows the relationships between the wood species.
The highest MC0 (66%) was found with PsS, so it was
to be expected that the biggest difference between
initial and final MC during drying was found with PsS.
This material also had the highest MC60 (16%) at the
end of MRI scanning, indicating that the equilibrium
state was not reached. The highestMCwas determined
with Scots pine sapwood (PsS), while the MC of larch
(Ld), Scots pine heartwood (PsH) and sweet chestnut
(Cs) were found to be comparable. If all of the data of
the wood MC are normalized between 1 (highest MC)
and 0 (final MC), two types of curve appear (data not
shown), depending predominantly on the initial MC.
The drying curves of larch (Ld), Scots pine heartwood
(PsH) and sweet chestnut (Cs) are much steeper than
the drying curves of spruce (Pa) and Scots pine
sapwood (SpS), mainly because drying samples (SpS,
Pa) containing higher amounts of water (in relative
and absolute terms) takes longer. It was therefore to be
expected that larch (Ld), Scots pine heartwood (PsH)
and sweet chestnut (Cs) would reach the equilibrium
state faster, which is reflected in a steeper curve
(Fig. 2).
In each plot in Fig. 3, the three different curves
illustrate MC changes during drying in the upper (U),
0
10
20
30
40
50
60
70
80
0 5 10 15 20 25 30 35 40 45 50 55 60
MC
(%)
Time (h)
PsS PsH Pa Ld Cs
Fig. 2 Moisture content
changes during drying
above freshly activated
silica gel. Typical curves
represent drying of Scots
pine sapwood (PsS), Scots
pine heartwood (PsH),
Norway spruce (Pa),
European larch (Ld) and
sweet chestnut (Cs)
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0
20
40
60
80
MC
(%)
PsS U M L
0
20
40
60
80 PsH
U M L
0
20
40
60
80
MC
(%)
Pa
U M L
0
20
40
60
80 Ld
U M L
0
20
40
60
80
0 5 10 15 20 25 0 5 10 15 20 25
0 5 10 15 20 25 0 5 10 15 20 25
0 5 10 15 20 25
MC
(%)
Cs
U M L
Time (h)
Time (h)
Fig. 3 Moisture content
changes during drying
above freshly activated
silica gel. MC was
monitored in different parts
(U-upper part, M-middle
part and L-lower part) of the
specimens. Typical curves
represent the drying of Scots
pine sapwood (PsS), Scots
pine heartwood (PsH),
Norway spruce (Pa),
European larch (Ld) and
sweet chestnut (Cs)
Fig. 4 Moisture content changes of specimens during drying
determined by continuous weighing (a) and moisture content
changes during drying inside a magnet above freshly activated
silica gel (total MC) (b). Typical curves represent the drying of
Scots pine sapwood (PsS), Scots pine heartwood (PsH), Norway
spruce (Pa), European larch (Ld) and sweet chestnut (Cs)
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lower (L) and middle parts of the relevant specimen. It
can be seen that drying of the upper and lower parts of
the specimens is similar, in spite of the fact that the
silica gel was positioned below the specimens only.
Because the specimens were not placed directly on the
silica gel, the humidity inside the glass tube did not
vary much and the impact of the silica gel on specimen
drying can be ignored. It can also be assumed that the
influence of gravity on drying can be ignored, due to
the small dimensions of the specimens.
The upper and lower curves showed a similar trend
to that seen in Fig. 2. The highest MC was thus
determined at the beginning, followed by a consider-
able MC decrease in the first hours of drying, and
stabilization thereafter. The MC of the outer and
middle parts of the specimen was very different with
short drying times, showing that water slowly pene-
trated into the specimen during soaking. With increas-
ing drying time, the differences became smaller and,
after 24 h of drying, the MC was uniform inside the
whole specimen. It should be noted that the MC of
Scots pine sapwood was considerably higher than with
the other wood species; water had thus also penetrated
into the middle part. It took a longer time to reduce the
MC of the middle parts.
Figure 3 provides an overview of the curves
representing the middle part of the specimens of the
various wood species. At the beginning of drying,
MC0 was lower than the MC determined after several
hours of drying, and the outer parts of the specimens
began to lose MC during drying. Water from the outer
parts evaporated, as well as migrating into the middle
part of specimens, which resulted in an increased MC
of the middle part of the specimens after a certain time.
However, with prolonged drying times, the MC of the
middle part also started to decrease and reached the
same MC as the upper and lower parts (Fig. 3).
As can be seen from Fig. 3, the curves correspond-
ing to the middle parts differ among the wood species.
PsS exhibited the highest MC, followed by Pa. Drying
of PsH, Ld and Cs resulted in similar curves. The
lowest MC was determined with those specimens. All
the specimens had MC0 values in the middle part
approximately half those in the outer parts of the
specimens (which was also influenced by the short
time of immersion in water; with longer times this
difference was negligible). MC0 in the middle of PsS
was around 35% (also see Table 3), which is consid-
erably less than that of the lower part (Fig. 3), in which
MC0 was around 70% (Table 3). After 20 h of drying,
the MC in the wood reached equilibrium, and was
comparable in all parts of the specimens (MC20-
= 30%), as seen from Table 3. A similar trend was
also observed with other specimens (Fig. 2, 3 and
Table 3).
Among other things, Fig. 3 shows the pattern of
MC changes during drying of the lower part of the
specimens. Those parts of the specimens take up
higher amounts of water during drying, so they
contribute most to the overall behavior of the speci-
mens. It is not surprising that the drying patterns of
MC shown in Fig. 3 were very similar to the drying
patterns of the overall specimens obtained from Fig. 2.
It should be noted that the specimens were fairly small,
so the influence of the surface was more prominent
than it would be on materials in use.
In order to verify the procedure, a similar exper-
iment was performed gravimetrically. The gravimetric
approach was used to validate the MRI method.
However, it should be noted that the gravimetric
method provides information about the overall aver-
age MC of wood, while MRI also provides informa-
tion about the water distribution in wood. The
gravimetric method is thus a considerably less com-
prehensive method than MRI measurements. MC
changes during drying that were determined with
continuous weighing using a laboratory scale can be
seen in Fig. 4a. A comparison of this graph to the
graph in Fig. 4b shows a similar shape and slope of the
curves in the two graphs, though some minor differ-
ences were noted. These were mainly the result of the
biological diversity of the material. This graph con-
firms that our MRI observations and the normalization
procedure in this research were correct.
One of the key benefits of the MRI method is that it
does not provide only information about average
(total) MC, but also the water distribution in each
layer. These measurements can be repeated at prede-
fined time periods (Mikac et al. 2018). The method is
based on the linear relationship between the amplitude
of the NMR signal and the mass of water in moist
wood samples. The relationship can be precisely
calibrated for a given RF probe and spectrometer setup
(Araujo et al. 1992). Once the system is calibrated, the
MC of any sample can be determined. The method is
robust, fast and non-invasive. The correlation between
the oven-dry and MRI method is 0.996 for the whole
MC range (Merela et al. 2009a, b). Furthermore, this
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method provides a 3D presentation of the water
distribution. These micrographs are very informative.
In each MRI image, each cube is represented by more
than 2 million dots. On a linear scale, a centimeter is
represented by 10.6 dots. Every dot represents a
volume of approximately 0.000824 mm3. Unfortu-
nately, 2D and #Dmeasurements cannot be done at the
same time, which results in gaps in some of the plots
(Mikac et al. 2018). Figure 5 shows 3DMRI images of
all five materials tested in this study. The figures show
overall water distribution, considering both free and
bound water. However, separation of the free and
bound water signals would require additional mea-
surements, which were not possible in this study due to
time limitations, since single measurements take at
least 1 day. The first image was obtained after 1 h of
drying inside the magnet. The next images were
obtained after 5, 10 and 20 h of drying. These images
were added for better visualization of the water drying
kinetics in different specimens. With spruce wood
after 1 h of drying, most of the water can be seen at the
edges of the specimen.With time, this water emigrates
Fig. 5 MRI of different materials (the abbreviations of the materials are the same as in Table 2) obtained after different times of
drying. FOV was 20 mm, the imaging matrix was 128 9 128 9 128 (isotropic resolution 156 lm, with total imaging time 34 min)
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to the central part of the sample, where it is only
distributed along the less dense early-wood. The wood
tissue in early-wood has bigger cell lumina, so it is
more permeable. There was also water accumulation
in the second and third growth rings, although the
reason for this was uncertain and more research with
microscopy should be undertaken to investigate this
phenomenon. The same pattern of water distribution in
early-wood can be seen in the drying images of pine
and larch. In sweet chestnut, the highest amounts of
water were in the upper and lower parts of the
specimen, while the middle part of specimen retained
less water. It seems that the vessels in chestnut are not
a good path for moisture transport, which may be
explained by the tyloses that are present in vessels.
From Fig. 5, it can be seen that the upper part of
specimens dried faster than the lower part. The same
feature can also be seen in Table 3, although these
differences were relatively small. The upper and lower
parts of the specimens are reported separately, since
the microclimates in the test tubes differ. The lower
parts of the samples were closer to the freshly
activated silica gel. Since we were not able to control
these micro conditions, we decided to address it in the
manuscript.
Analysis of MCs measured at different times after
drying with the model given by Eq. 10 enabled a
quantitative analysis of the drying dynamics of
different wood species. In Fig. 6, the best fits of the
model to the averaged measured MC data are shown
for all five examined wood species, while Table 4
contains the corresponding best fit parameters MCi,
MCeq, s and D. The latter was calculated from the best
fit parameter s using Eq. 13, assuming L is large
(L � 1). The half-dimension of the sample along the
direction with the fastest diffusion was equal to
l = 6 mm.
Despite the simplicity of the model, which does not
take into account the different water compartments in
wood, the dependence of the diffusion constant onMC
and temperature, and other non-diffusion processes of
drying, the model curves fit well to the experimental
MCs with all wood species except sweet chestnut (Cs),
for which the coefficient of determination was the
lowest (R2 = 0.996). As can be seen from the 3D MR
images of moisture distribution in Fig. 5, sweet
chestnut had the least uniform initial MC. The model
in Eq. 10, which was derived for the uniform initial
MC distribution, cannot therefore fit to the Cs data
well. Another possible explanation for the fit discrep-
ancy is incomplete MC data acquisition due to the
nature of the measurements, which also included 3D
MR scanning, during which drying profiles (2D) were
not recorded. This resulted in data gaps in the graphs in
Fig. 6. With some species, such as sweet chestnut
(Cs), Scots pine heartwood (PsH) and, to some extent,
also Norway spruce (Pa), the MC curves exhibited a
kink at approximately 10 h of drying. The kink may
also originate in a transition from a faster drying
regime to a slower drying one, possibly due to faster
drying of the free water compartment (Azzouz et al.
2018).
Drying dynamics can be characterized by the
characteristic time constant s. However, as can be
seen from Eqs. 11–13, s is not dependent only on the
intrinsic properties of the sample, such as the diffusion
constant D and the surface evaporation rate a. It
depends also on the sample size, in our case on the
linear sample dimension l. To determine both D and a,one would need two independent measurements of s,e.g., with two samples of the same wood species
having different dimensions. Such experiments were
not done in this study. Only one of the intrinsic
parameters, either D or a, can therefore be determined
from one value of s, provided that L converges on one
of the extremes: on 0 to determine a using Eq. 12 or on1 to determine D using Eq. 13. In Table 4, D values
are calculated using this approach. To test what the
corresponding L values are, a typical surface evapo-
ration rate of 1.4 9 10-7 m/s was selected from the
literature (Niklewski et al. 2016). This coefficient
yields values of L for the diffusion constants in
Table 4 in the range from 1.7 to 7.5 and the
corresponding b1 in the range from 1.03 to 1.39. This
could in principle result in underestimated diffusion
coefficients by 30% with (b1 = 1.39) and up to 130%
(b1 = 1.03). Values of D for Cs, Ld and PsS are
therefore totally unreliable and are not given in the
table. As the estimated values of L cannot be
considered low, Eq. 12 for calculation of the surface
evaporation rate a also cannot be applied. The only
reliable parameter of wood drying dynamic in our
study is therefore the characteristic time constant s.Comparison of s for different wood species in Table 2
shows that that drying was slowest with Scots pine
sapwood (PsS), was also slow with Norway spruce
(Pa), while it was almost equally fast with the
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remaining three wood species (Cs, Ld and PsH). These
three species also had identical initial and equilibrium
MCs, while the initial MC of Norway spruce (Pa) was
considerably higher and was the highest with Scots
pine sapwood (PsS). Interestingly, the equilibriumMC
was lowest with PsS, which may also be a conse-
quence of too short a data acquisition window, which
mainly covered the faster drying regime and to a lesser
extent the slower drying regime.
The presented approach for analysis of the drying
dynamic is simple but efficient. It is important to note
that this is a quantitative approach. It describes the
drying dynamic with only three parameters, i.e., the
initial and equilibriumMCs and the characteristic time
constant of the drying process. In our study, MC data
were obtained by NMR/MRI. In principle, this method
can be used for any MC data, as long as the MC
measurements are not too scarce in time. For this
method, MCs corresponded to spatially averaged MC
values, meaning that the real potential of MRI, i.e., its
spatial resolution, was not exploited. For that, other
more sophisticated models that would take into
account possible different spatial MC profiles of the
drying front, need to be developed. However, NMR
provides another advantage over the standard gravi-
metric method for MC determination, namely, instan-
taneous MC measurement. This allows MC
acquisition with a high temporal resolution, which
can be important for monitoring fast drying processes.
Conclusion
MRI was demonstrated to be a suitable method for
monitoring drying kinetics in wood. The results
showed that the shape of the MC curves representing
0
10
20
30
40
50
60
70
MC
(%)
t (h)
PsS
0
10
20
30
40
50
MC
(%)
t (h)
Pa
0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 10 20 30 40 50 600
5
10
15
20
MC
(%)
t (h)
Cs
0
5
10
15
20
MC
(%)
t (h)
Ld
0 10 20 30 40 50 60 0 10 20 30 40 50 600
5
10
15
20
MC
(%)
t (h)
PsH
Fig. 6 Best fits between the
measured averagedMC time
courses (black) and their
model predictions (red/grey)
obtained as best fits of the
model in Eq. 10 to the data
Table 4 Best fit
parameters of the MC time-
dependence model (Eq. 10)
to the data in Fig. 6
Species MCi [%] MCeq [%] s [h] D [10-10 m2/s] R2
PsS 66.0 ± 0.3 4.4 ± 0.2 36.4 ± 0.2 1.11 ± 0.31 0.997
Pa 45.6 ± 0.1 9.7 ± 0.06 16.7 ± 0.1 2.43 ± 1.54 0.996
Cs 19.7 ± 0.1 9.1 ± 0.03 9.4 ± 0.1 / 0.965
Ld 18.3 ± 0.04 8.2 ± 0.03 8.8 ± 0.06 / 0.997
PsH 19.3 ± 0.02 7.6 ± 0.01 8.4 ± 0.04 / 0.997
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the drying of PsH, Pa, Ld and Cs wood exhibited low
variation, while with PsS, significantly different
drying kinetics were observed due to anatomical
differences, variability of the specimens and the
highest amount of water uptake. One hour of immer-
sion of PsS resulted in the highest water uptake, 66%
(MC0). This water was released fairly fast, which
could be seen from a sharp decline in the linear part of
the MC curve, although the MC for PsS determined
after 60 h of drying was still the highest compared to
the other species, being twice that of the other samples.
The second highest MC0 (46%) was measured with
spruce wood and the lowest MC after 1 h of soaking in
distilled water was observed with pine heartwood,
sweet chestnut and larch. The highest changes in MC
occurred in the first hours of drying, followed by
slower drying until the equilibrium MC was reached.
In the specimens with the smallest water uptake (PsH,
Ld and Cs), of approximately 20% during 1 h of
immersion, a fast MC decrease was observed for the
first 5 h, whilst in the later stages, drying stabilized
and the MC did not change considerably in the next
20–60 h. The situation was different in Pa and PsS, in
which a significantly higher water uptake was
observed and, at 60 h of drying, the MC had still not
stabilized. The lower water uptake with pine heart-
wood, chestnut and larch is a result of the refractory
nature of these wood specimens.
MRI allowed the observation of spatially resolved
MC changes in the specimens. Time dependencies of
MC during drying in the upper, lower and middle parts
of the specimens were also determined. The results
showed that drying of the upper and lower parts of the
specimens was similar to the drying of the overall
specimens. The most interesting were the MC curves
corresponding to the middle part of the specimens. At
the beginning of drying, the initial MC0 was lower
than determined after several hours. At the end of the
drying experiment, the MC of the middle part of the
specimen reached the sameMC as the upper and lower
parts.
Similar experiments were also performed gravi-
metrically. These data indicated that the high-resolu-
tion MRI observations and the normalization used in
this research were correct and provided verification of
the results. What is more, the MRI measurements gave
more comprehensive information about the water
drying kinetics than the classic gravimetric method.
Acknowledgments The authors acknowledge the support of
the Slovenian Research Agency within the framework of project
L4-5517, L4-7547, program P4-0015 and the infrastructural
centre (IC LES PST 0481-09). Part of the research was also
supported by the project Tigr4smart.
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