Water vapor diffusivity of engineered wood: Effect of temperature and moisture content

Construction and Building Materials 224 (2019) 1040–1055

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Water vapor diffusivity of engineered wood: Effect of temperature and moisture content A.A. Chiniforush a, H. Valipour b,⇑, A. Akbarnezhad a a b

School of Civil and Environmental Engineering, The University of Sydney, NSW 2006, Australia Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, UNSW Sydney, NSW 2052, Australia

h i g h l i g h t s
Diffusion coefficient for different engineered wood products are determined.
Dependency of diffusion coefficient on moisture content and temperature is studied.
Diffusion coefficients in the main three directions are compared.
Sorption isotherms for different engineered wood products are provided.

a r t i c l e

i n f o

Article history: Received 4 March 2019 Received in revised form 30 July 2019 Accepted 1 August 2019

Keywords: Cross-laminated timber (CLT) Diffusion coefficient Engineered wood Laminated veneer lumber (LVL) Moisture transport

a b s t r a c t This paper investigates the effects of the glue line, moisture content, and temperature on diffusion coefficients of engineered wood products. The diffusion coefficient were measured in three orthogonal directions for glued laminated timber (Glulam) made of Blackbutt (Eucalyptus pilularis), Pacific Teak (Tectona grandis), Tasmanian Oak (Eucalyptus regnans/obliqua/delegatensis), Radiata Pine (Pinus radiata), Slash Pine (Pinus elliottii), Laminated Veneer Lumber (LVL) made of Radiata Pine, and Cross Laminated Timber (CLT) made of Norwegian Spruce (Picea abies). Experiments were conducted on specimens with and without glue line at four different temperatures, i.e. 15, 25, 35, and 45 °C and three different relative humidity gradients. Adsorption isotherms were obtained, and analytical equations were fitted to the experimental data to determine the diffusion coefficient of wood as a function of temperature and moisture content. The diffusion coefficient showed a strong dependency on the temperature and moisture content, highlighting the importance of accounting for these factors in modelling of moisture transport and analysis of drying stresses, distortion and warping, as well as long-term serviceability analysis of the timber elements. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Advancements in wood and adhesive technologies have led to the manufacturing of Engineered Wood Products (EWPs) with enhanced dimensional stability and physical and mechanical properties comparable to that of modern construction materials such as concrete. In recent years, the emphasis on sustainability of the construction and building industry has promoted the use of EWPs as the main construction material in low- to mid-rise buildings [1,2]. However, widespread use of EWPs as a sustainable construction material has been hampered by the moisture dependent physical and mechanical properties of the wood [3–5]. Accordingly, a better understanding of variability in moisture transport proper⇑ Corresponding author. E-mail address: [email protected] (H. Valipour). https://doi.org/10.1016/j.conbuildmat.2019.08.013 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

ties of wood under a varying ambient condition is vital to ensure the reliability of structural timber elements over the service life of buildings [6]. During service life of timber structures, the temperature and Relative Humidity (RH) of the environment are rarely constant, resulting in variations of the Equilibrium Moisture Content (EMC) of wood. The physical and mechanical properties of wood, on the other hand, are a function of EMC [4,6,7]. Non-uniform variation of EMC can lead to moisture-induced swelling/shrinkage stresses and subsequent distortion and warping of the timber lamellas/ lumber which has been extensively addressed in the literature [8–11]. In addition to the moisture-induced distortion/warping, modelling of moisture transport and heat transfer in timber is required to accurately predict the drying stresses [12–15] and effect of different treatment on the physical and mechanical properties of the wood [16]. The manufacturing process (e.g. dry or wet

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process, type of additives, board thickness, composition, etc.) of EWP can also alter thermal and moisture diffusivity significantly [17–20]. Sonderegger et al. [17] used the cup method to determine the coefficient of diffusion (under unsteady and steady states) for European Beech and Norway Spruce wood. It was found the coefficient of diffusion under unsteady states is nearly half that of steady states. Also, the coefficient of diffusion in the longitudinal direction was found to be an order of magnitude bigger than that of the transverse direction. The results of tests conducted on fibreboards have shown that the sorption isotherm of fibreboards are similar to solid wood for relative humidity (RH) below 80% and for higher RH values the sorption isotherms are affected by the chemicals used in the fibreboards [18]. In an extensive experimental study, the coefficient of thermal conductive and water vapour resistance of different EWPs were measured and it was established that the coefficient of thermal conductivity and the water vapour resistance depends on the density, moisture content, temperature and EWPs thickness and particle size [19]. In particular, the diffusion coefficient was found to decrease with increasing density and moisture content of the considered EWPs [19]. From the structural point of view, the variation of EMC affects elastic modulus and ultimate strength of wood under short-term loading conditions [21–26] as well as viscoelastic and mechanosorptive creep under long-term service condition [27–33]. Therefore, an accurate estimation of EMC through a reliable coupled heat and mass transfer (moisture transport) analysis is required for predicting short- and long-term behaviour of the structural timber (EWP) members. Extensive research has been conducted to experimentally measure diffusion coefficient of different wood species [34–38] and robust coupled heat and mass transfer models have been developed to estimate the distribution of EMC [12,13,39]. However, a majority of previous experimental and numerical studies have been conducted on long wood lumbers by only considering diffusion in radial and tangential directions, while overlooking the longitudinal diffusion [14,31,32,40]. Furthermore, the potential effect of glue layers on the diffusion coefficient and moisture transport has been overlooked in the literature [31,40]. Moreover, constant mass transport properties, independent of either temperature or EMC, have been typically adopted in previous coupled heat and mass transfer [31,39,40]. A brief introduction to moisture transport mechanism and available experimental methods for measuring water vapor diffusivity is provided and different empirical equations for considering the effect of moisture content and temperature on the water transport properties are discussed in Section 2. Details of the test setup according to steady-state cup method and unsteady-state sorption method as well as size and type of EWP/timber specimens used for measuring the diffusion coefficient in three orthogonal directions are provided in Section 3. The procedure of measuring sorptionisotherms, important parameters in calculating the diffusion coefficients by moisture concentration potential are also illustrated and discussed in Section 3. The results of experiments are employed to express the diffusion coefficient of the EWPs as a function of temperature and Volumetric Moisture Content (VMC) in Section 4 and the complementary material properties (i.e. density, shrinkage, and swelling) for the EWPs tested are also reported.

Table 1 Summary of diffusion coefficient with different driving potential. Driving Potential

Da

Unit

Relationship

Water vapor pressure (Pa)

DP DC

kg=ðm:s:PaÞ m2 =s

reference

Moisture Concentration (kg=m3 ) Moisture Content (kg=kg)

Du

kg=ðm:sÞ

1 Du ¼ DP P s qd @C=@H

Water content of air (kg=m3 ) Relative humidity (unitless)

Dv DH

m2 =s kg=ðm:sÞ

Dv ¼ 461:4TDP DH ¼ DP P s

T: is absolute temperature (°K), P s : saturation vapor pressure qd : dry density of @C wood, @H : slope of sorption isotherm.

which is not practically important in the investigation of the variation of mechanical properties due to moisture content (u) change [6,41]. It has been demonstrated that the moisture transport in the wood below saturation point is not only governed by diffusion process due to the vapor pressure gradient; and other parameters (temperature, moisture content, etc.) are superimposed to classical Fickian behaviour [42,43]. However, the moisture transport below the saturation point is traditionally evaluated using Fick’s first and second law of diffusion which for the one-dimensional steadystate diffusion, can be expressed as,

FirstLawðsteady  stateÞ J ¼ Da @@xa
@ a @ SecondLawðtransientÞ @@ta ¼ @x Da @x

ð1Þ

where Da is the diffusion coefficient with the driving potential a [41]. The common driving potential for diffusion in wood is moisture concentration (C; kg=m3 ) which should not be confused by moisture content (u; kg=kg) [43]. Other utilised driving potential are water activity or relative humidity (RH, unitless), chemical potential, and osmotic pressure (P; Pa) [3,44]. The diffusion coefficient for different potentials and their relationship with the diffusion coefficient for water vapor pressure potential as a reference have been summarised in Table 1. In construction materials such as EWPs, the diffusion equation should be solved across a combination of different layers. Therefore, it is important to use a driving potential, such as water vapor pressure or water content of the air (kg=m3 ), which represent continuity across different material layers [41]. Furthermore, to solve Fick’s law of diffusion (Eq. (1)) over a given domain, a boundary condition, presented in Eq. (2), should be considered to take into account the effect of external resistance to the moisture transportation.

Da :ra ¼ SðaRH  aSurface Þ

ð2Þ

In Eq. (2), S, aRH and aSurface are mass transfer coefficient, driving potential at the equilibrium condition, and driving potential on the surface, respectively. To numerically solve the governing differential equations of diffusion over any given domain, the diffusion coefficient in different directions within that domain should be available. Accordingly, in the following sections, the steady-state

2. Theoretical background The rate of moisture movement in wood is quantitatively described by molecular diffusion which is generally governed by two mechanisms, i.e. the vapor diffusion through lumens and bond water diffusion through the cell walls [3,41]. The moisture movement above the saturation point is mainly controlled by free water

1 DC ¼ DP P s @C=@H

Fig. 1. Cup test set up.

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cup method and the transient sorption method which are typically used for evaluating the diffusion coefficient are described and briefly discussed. 2.1. Cup method In the cup method, a thin layer of wood is attached to a cup containing a saturated salt solution to create constant relative humidity (RH1 ) on one side of the specimen. The whole assembly is conditioned inside an environmental chamber to generate a constant relative humidity (RH2 ) outside the cup. The seams between the cup and sample are sealed to enforce vertical transportation of the water vapor through the thin layer (see Fig. 1). Both relative humidity are kept constant to create a constant relative humidity gradient that simulates a steady-state diffusion required for calculation of diffusion coefficients according to Fick’s first law. Depending on RH1 and RH2 values, the water vapor can diffuse in/outside the cup and change the whole assembly’s weight. The water vapor permeance (dp ) and diffusion coefficient with vapor pressure as a driving potential (DP ) is deemed to be the slope of weight change vs. time (G=t) plots as per ASTM E96/E96M [45],

dp ¼

t AP s ðRH1 G

1 DP ¼ dpcor d  RH2 Þ  da =da  Rs

ð3Þ

where t, G, A, Ps ; RH; d; andda are time (in s), weight change (in kg), the surface area of the specimen (in m2 ), saturation vapor pressure (in Pa), relative humidity (unitless), the average thickness of specimen (in m), and the thickness of the air layer inside the cup (in m), respectively. Rs is the surface resistance of specimen which was suggested as 4  107 Pa:s:m2 =kg [45,46]. da is permeability of still air (in kg/(Pa.m.s)) which can be obtained from [45], Table 2 Empirical formulas for diffusion coefficient as a function of temperature and moisture content. No.

Formula

Reference

F1 F2

D ¼ a0 expðb0 u þ a2 TÞ h  i pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0u D ¼ a0 exp  b0 c =ð1  ðd0  e0 uÞÞð1  d0  e0 uÞ T

[52,53] [54]

F3 F4 F5

c0

D ¼ a0 exp ðb0 =T Þ½u D ¼ a0 expðb0 u  c0 =TÞ D ¼ a0 expðb0 =T þ c0 u=TÞ

[55] [55–58] [59]

da ¼

 1:81 2:306  105 P0 T 273:15 Rv TP

ð4Þ

where T is the temperature (in °K), P is the ambient pressure (in Pa), P0 is the standard atmospheric pressure (101325 Pa), and Rv is ideal gas constant for water vapor, that is 4615 J/(°Kkg). The saturation vapor pressure (Ps, Pa) can be estimated as a function of temperature (T, °C) by Tetens equation [47,48], Eq. (5), which is accurate in the range of 0–50 °C.

  17:27T Ps ¼ 610:78exp T þ 237:3

ð5Þ

Since the mass changes in this study are greater than 100 mg, the buoyancy correction is negligible based on ASTM-E96 [45] recommendations. However, the correction for edge mask effect to eliminate two-dimensional flow in the cup edge region is necessary based on Joy and Wilson [46,49] work,

dpcor ¼

dp   2 1 þ p4dS1 ln 1þe2 pb=d

ð6Þ

in which b and S1 are the width (in m) of the masked edge and four times the specimens surface area divided by the perimeter (in m), respectively. 2.2. Sorption method In the sorption method, a specimen is conditioned at a constant relative humidity (RH1 ) until equilibrium moisture content is stabilised and no change occurs in the weight of the specimen. Then the relative humidity rapidly increased to RH2 and the weight changes are measured in regular intervals and accordingly the diffusion coefficient is calculated using the Fick’s second law (Eq. (1)). For an infinite plane sheet with a thickness of 2l and a step change in the concentration at t ¼ 0, a simplified solution for unsteady state diffusion equation (Eq. (1)) can be obtained and utilised to calculate apparent diffusion coefficient by moisture concentration driving potential as follows [41],

Dc ¼

pl2 4



dE pffiffi d t

2 ð7Þ

where Eðt Þ ¼ DMt =DM 1 is the fractional weight change as a function of time, DMt and DM1 are the weight change at time instant

Fig. 2. Comparison of empirical formulas in the literature for effect of the moisture content and temperature.

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t and at the final equilibrium stage. To evaluate Dc  from this pffiffi method, the E  t curve should be established and the slope of the curve for E < 0:5 must be calculated. 2.3. Mass transfer coefficient The apparent diffusion coefficient (Dc , from the sorption method) evaluated from Eq. (7) does not contain any correction for the external resistance to the moisture transport, however, it can be modified according to the relationship recommended in the literature [50,51] by means of true diffusivity Dc , obtained from the cup method,

1 1 3:5 ¼ þ Dc Dc lS

ð8Þ

in which l and S are half of the specimen thickness in the sorption method and mass transfer coefficient in Eq. (2). In the current study, cup tests have been conducted and accordingly diffusion coefficient

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for water concentration driving potential (DC ) were calculated at different temperature and moisture contents. Furthermore, the supplementary sorption isotherms were established and utilised to evaluate the mass transfer coefficient S by means of apparent diffusivity (Dc ) measured during the sorption test. 2.4. Empirical equation for effect of moisture content and temperature The effect of moisture content and temperature on the diffusion coefficient of wood have been studied in the literature and different empirical formulas have been proposed [52–59]. Some of the most general empirical formulas and their corresponding curves are given in Table 2 and illustrated in Fig. 2 which shows an increasing trend for the diffusion coefficient by an increase in the temperature. The proposed empirical models are typically based on estimating the theoretical formula D = aexp(E/RT), in which D, a, E, R, and T are diffusion coefficient, a constant, activation energy of bound water, gas constant, and temperature, respec-

Fig. 3. Illustration of the principal directions for different EWPs.

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tively. However, some of the models (e.g. F2) have exhibited better correlation with the trend of diffusion coefficient in the longitudinal direction, and other models (e.g. F4 and F5) have had closer correlation with the trend of diffusion coefficient in the transverse directions. It should be noted that the trend captured by F4 and F5 models have more deviation for the lowest temperature (15 °C) considered in the current study. Accordingly, the relationship,

eL (Logitudional) and eV (Vertical) are taken as 1.0 and only eVG and eH are provided (see Table 5).

    b0 d0 Dc ¼ ea0 exp þ c0 þ VMC T T

The cup tests conducted according to ASTM E96 [45] provisions in four different temperatures; and at each temperature level, the relative humidity inside the chamber was set to create three constant relative humidity gradients (resulting in 12 measurement points that represent different environmental conditions). The considered temperatures and relative humidity are listed in Table 3. The error margin of the environmental chamber (LABEC LHC-80) for temperature and relative humidity were ±0.1 °C and 3%, respectively. The utilised aqueous salt solution was sodium chloride creating constant humidity of 75.6, 75.3, 74.9, and 74.5 0.2% for 15; 25; 35; and 45 °C [60,61]. The small glass cups with 60  120 and 75  150mm cross-section and 40mm depth were used to avoid possible cracking of the specimens due to shrinkage and swelling. Furthermore, the glass containers were vapor and chemical reaction proof to minimise the error in the measurement. The thin wood/EWP samples (see Fig. 5) were placed as a lid on the cup (see Fig. 1). The air gap between the sample and the surface of the aqueous salt solution was 30–35 mm depending on the amount of salt solution. The sealant was Byute FlashÒFlashing Tape containing aluminium foil with thick butyl adhesive to seal the cup test assembly. Adhesive ingredient includes Butyl Rubber, Polyisobutene, Calcium Carbonate, Titanium Dioxide, and Tackifying Resin complying with ASTM C731 [62] requirement with 0g=m2 humidity clarity. The weight measurement conducted

ð9Þ

is utilised to minimise the error estimation for lower temperatures and model the effect of Volumetric Moisture Content (VMC, %) and temperature (°K) change on the diffusion coefficient of the EWP/timber (Dc ; m2 =s). To calculate parameters a0 , b0 , c0 , d0 , and e in Eq. (9), Sum of Square Errors (SSE) between the experimental results and the proposed empirical equation is minimised by means of Genetic Algorithm. A Cartesian coordinate system L-V-H (see Fig. 3) corresponding to longitudinal (L), vertical (V) and horizontal (H) directions with respect to timber grain/lamellas orientations was adopted for defining the coefficient of diffusions in three principal directions (see Fig. 3). The principal directions in CLT panels were denoted by Par (the outermost layer has grain direction parallel to diffusion direction), Per (the outermost layer has grain direction perpendicular to diffusion direction), and O (out of plane) as shown in Figs. 3c and 4. The experimental results revealed that the diffusion coefficients in vertical and horizontal directions (namely transverse directions) have the same trend with respect to temperature and moisture content variations. Accordingly, the minimisation of error was conducted in two stages separately for longitudinal and transverse direction. The minimisation of SSE for the transverse diffusion coefficients are conducted simultaneously by means of a scaling parameter ‘‘e”. The parameters a0 , b0 , c0 and, d0 tune the trend in the transverse direction whereas parameters eV , eVG , and, eH scale the formula for different cases including Vertical (V) direction, Vertical direction with one layer of Glue (VG), and Horizontal (H) direction, respectively. For the sake of simplicity, scaling factors

3. Experimental study 3.1. Diffusivity (Cup method)

Table 3 Environmental condition inside chamber. Cup Method T (°C), RH (%) 15, 25, 35, 45,

40 30 30 30

Sorption Method T (°C), RH (%) 10, 25, 35, 45,

Fig. 4. Illustration of principal directions in CLT panels.

60 30 60 60

15, 27, 35, 45,

90 30 90 90

20, 0 ? 30 20, 30 ? 60 20, 60 ? 90

A.A. Chiniforush et al. / Construction and Building Materials 224 (2019) 1040–1055

Fig. 5. Typical samples used in the experiment.

by a scale with 10mg accuracy and 48hr frequency until the rate of weight loss/gain became constant. The samples of cup method were conditioned in 50% relative humidity and 22 °C temperature before the commencement of tests for two weeks as recommended by Time [41]. The main factors causing uncertainty/inaccuracy in the cup measurements have been also reported by Time [41]. The sources of inaccuracy in cup test are, inconsistency of target relative humidity inside and outside the cup, the inconsistency of air gap in all the test specimens due to assembling error or possible warping of the specimens during the test, and the possibility of not having perfect seal before and during the experiment. Accordingly, care was taken to address and minimise the abovementioned sources of inaccuracy in the cup test measurements.

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were monitored with the successive weighting method [63] to ensure that specimens have reached the stabilised VMC. The VMC stabilisation time for each VMC step was 1 week and 2 weeks for 50 °C and 15 °C, respectively. The stabilisation time varied for each wood type and was lesser than the specified times. However, all samples were subjected to the maximum required time (for Pacific Teak) to ensure consistency of measurements. As shown in Fig. 6, the samples were conditioned inside desiccators containing saturated salt solutions at the bottom and equipped with a fan to circulate air to achieve constant relative humidity and temperature. The fabricated desiccators were located inside an environmental chamber (LABEC LHC-80) to keep the temperature constant during conditioning procedure. Furthermore, a Sensirion EK-H4 evaluation kit and SHT7x sensors were mounted in the desiccators to monitor the experimental conditions continuously. The recommended aqueous salt solutions by ASTM E104 [60] were utilised to generate 6 incremental relative humidity in addition to the oven-dried and fully saturated condition (see Fig. 7). At the end of the sorption cycle, the samples were saturated in distilled water and the successive weighting method [63] was applied to ensure all samples have achieved fully-saturated condition. In each step, the weight was recorded using a balance with 10mg precision leading to an equivalent accuracy of 1=500 of weight change over VMC corresponding to 0  95% relative humidity. VMC in each step was calculated from [63],

VMC ¼ GMC  GMC ¼

qwood dry qwater

W Step W Ov en W Ov en

ð10Þ

3.2. Diffusivity and surface emissivity (Sorption Method) The sorption method tests were conducted at 20 °C for three relative humidity gradients listed in Table 3. The edges of samples were sealed by means of Silicone Sealant to ensure moisture transports only in the considered direction normal to the plane of samples. The samples were oven dried first to measure the oven-dried weight of specimens. Silicone Sealant was then applied to the edges and samples were maintained in the sealed bags containing silica gel (as a desiccant) for conditioning the specimens at 0% relative humidity in 20 °C. After a week, samples were measured again to calculate weight change due to the sealant and immediately placed in the environmental chamber with 20 °C, and 30% relative humidity (the first step) and weight changes were monitored at 1-hour intervals. When the weight of samples stabilised, samples were kept inside sealed bags and environmental chamber set to the next relative humidity step. When the condition inside the chamber stabilised again the samples were returned back to the chamber and weight monitoring at 1-hour intervals carried out. For each step, apparent diffusivity and surface emissivity were calculated from Eq. (7) and Eq. (8). The speed of air circulation in the chamber was in the range of 5–7 m/s.

Fig. 6. Fabricated desiccator with continuous air circulation and humidity and temperature sensor.

3.3. Sorption isotherm The samples for each type of wood/EWP (see Fig. 5) were oven dried at 104 °C to measure oven-dried weight and then incrementally conditioned to different relative humidity levels. The weights

Fig. 7. Equilibrium Relative Humidity for Saturated Aqueous Salt Solutions.

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where GMC is Gravimetric Moisture Content (u), W Step is the stabilised weight of specimen in each step of conditioning and W Ov en is the oven-dried weight of the specimen. The density and maximum volumetric shrinkage of wood samples were also measured according to ISO 13061-2 [64] and ISO 13061-14 [65], respectively. 3.4. Material The hardwood species considered were glulams made of Pacific Teak (PT, Tectona grandis), Tasmanian Oak (TO, Eucalyptus regnans/ obliqua/delegatensis), and Blackbutt (BB, Eucalyptus pilularis). The softwood species include Radiata Pine (RP, Pinus radiata), Slash Pine (SP, Pinus elliottii), Laminated Veneer Lumber (LVL) of Radiata Pine and Cross Laminated Timber (CLT) of Norway Spruce (Picea abies) [66]. For each created environmental condition (DRH and T), 12 specimens of each wood species were monitored in three principle directions, i.e. L, V and H. The specimens were cut into thin chips as shown in Fig. 5 with a nominal dimension of 6  60  120mm in planes with normal in longitudinal (L) direction and 6  75  150mm in planes with normal in horizontal (H) and vertical direction (V) (while the radial and tangential direction is not clearly distinguishable in EWPs, horizontal and vertical terms were used instead, see Fig. 3), to approximately have the same rate of weight change in all directions. The thin specimens reduce the error due to masked edge effect that occurs in the thick specimens in which the water vapor could travel through other paths in addition to the intended direct [45]. 3.5. Modification for CLT specimens The CLT specimens had a cross section comprising of 3 layers of 20 mm thick Spruce wood with parallel and perpendicular to grain orientations (see Figs. 3c and 4). In practice, however, CLT panels can have any thickness and arrangement of layers. Therefore, the diffusion measurement is presented for each layer separately in longitudinal (L) and transverse (T) directions, in addition to out of plane direction. Furthermore, the diffusion coefficients measured from cup method should be accordingly modified. For each cross-section arrangement, the weight change includes a summation of longitudinal (L) layer/s and transverse (T) layer/s as follows,

Parallel direction : GLPar þ GT Par ¼ GTot Par Perpendicular direction : GLPer þ GT Per ¼ GTot Per

ð11Þ

in which weight change (G) can be obtained from Fick’s first law,

G ¼ Da

At d

ð12Þ

If b is defined as a ratio of middle layer cross section area to total cross section (b ¼ ALPar =A ¼ AT Per =A ¼ 0:600), Eq. (11) can be manipulated and re-written as,

Perpendicular direction : Da L ð1  bÞ dAt þ Da T b dAt Per Per ¼ Da TotPar

At dPer

ð13Þ

¼> Da L ð1  bÞ þ Da T b ¼ Da TotPer

by solving system of equation Eq. (13), the diffusion coefficient in longitudinal Da L and transverse Da T directions can be calculated by,

Da L ¼

bDa Tot

Da T ¼

bDa Tot

Par

ð1bÞDa Tot

Per

2b1 Per

ð1bÞDa Tot 2b1

ð14Þ Par

4.1. Shrinkage, swelling, and density Density (q) (kg=m3 ), average volumetric shrinkage (b) (%), maximum Volumetric Moisture Content (VMC max ) and maximum Gravimetric Moisture Content (GMC max ) of all specimens are given in Table 4. It is seen that the hardwood species had the greatest dry density and volumetric shrinkage, however, LVL and CLT had the maximum porosity (or maximum VMC) and maximum GMC. The VMC as an indicator of the percentage of voids filled by water has a better physical meaning than GMC. For instance, in wood species with a lower density, the value of GMC, which may even exceed 100%, does not clearly reflect the total sorption capacity of the specimen. Accordingly, all the results in the present study are presented as a function of VMC; however, the VMC can be easily converted to GMC using the densities in Table 4. 4.2. Sorption isotherms A formula previously proposed by Chiniforush et al [67],

VMC ðHR Þ ¼ uS HR nS þ uM HR nM þ uL HR nL

ð15Þ

is fitted to the experimental results and the sorption isotherms are depicted in Fig. 8. It is seen that for the sorption isotherms, the VMC in 15 and 50 °C for a specific relative humidity (HR ) are very similar. However, to calculate the diffusion coefficient by moisture concentration as the driving potential, the moisture concentration had to be linearly interpolated between two isotherms. For a specific relative humidity, hardwood species (specially BB) had a greater VMC for HR < 0:95; whereas, the VMC max (HR ¼ 1:0) is greater for softwood species specially Spruce CLT and Radiata Pine LVL specimens (see Table 4). This can be attributed to the lesser proportion of large pores in hardwood species compared to the softwood species (for HR > 0:95) [67]. 4.3. Diffusion coefficients The variations in the measured diffusion coefficients of wood species by moisture concentration potential versus variation of moisture content at different temperatures are shown in Figs. 9– 15. The variation of diffusion coefficient by VMC/GMC at 15, 25, 35, and 45 °C are shown by blue, green, orange, and red curves, respectively. The diffusion coefficient as a function of temperature and moisture content exhibits a different trend in longitudinal and transverse (across the grain) direction. Therefore, for each type of specimen/wood species, Eq. (9) was separately fitted to the longitudinal diffusion coefficient and the results are summarised in Table 5. The multipliers eV , eVG , and eH in conjunction with Eq. (9) were also fitted to the experimental results of vertical (with and without glue) and horizontal direction, respectively. The diffusion coefficients in the transverse directions were in the range of 109 to 1010 m2 =s which is consistent with the range of diffusion

Parallel direction : Da L b dAt þ Da T ð1  bÞ dAt Par Par ¼ Da TotPar dAt ¼> Da L b þ Da T ð1  bÞ ¼ Da TotPar Par

4. Results and discussion

Table 4 Density (q) (kg=m3 ), average volumetric shrinkage (b) (%), maximum Volumetric Moisture Content (VMC max ) and maximum Gravimetric Moisture Content (GMC max ). Species

qdry

bV

VMC max

GMC max

CLT LVL RP SP BB PT TO

444.62 539.52 531.95 607.77 801.34 688.49 582.38

10.84 11.87 10.41 11.11 13.63 9.58 14.76

0.610 0.615 0.525 0.547 0.494 0.455 0.492

1.234 1.022 0.903 0.761 0.543 0.584 0.756

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Fig. 8. Sorption Isotherms for studied species at 15 and 50 °C.

coefficient reported in the literature [6,68–70]. The vertical direction (eV = 1.0) had the maximum transverse (across fibre) diffusion coefficient for all the species. In average, a layer of glue reduced the diffusion coefficient in the vertical direction by 28% (i.e. eVG ¼ 0:72). In contrast to a small clear wood sample (typically used in the literature [50,70–72]) with a distinguished orientation of radial and tangential direction, the horizontal diffusion coefficient (other principal transverse direction) is slightly less than the vertical one (around 0.84 times). In all cases (i.e. longitudinal and transverse), the diffusion coefficients increased exponentially by an increase in the temperature. This exponentially increasing trend of the diffusion coefficient with respect to temperature is

consistent with the results reported in the literature [52–59]. The diffusion coefficient in the longitudinal direction at 25, 35 and 45 °C was significantly (in average 109, 317 and 682%) higher than that at 15 °C. The CLT, LVL, and TO exhibited the greatest increase of diffusion coefficient with respect to temperature whereas RP had the smallest increase. In the transverse direction, the increase in coefficient of diffusion with respect to temperature rise was less than the longitudinal direction. The average increase of transverse diffusion coefficient at 25, 35 and 45 °C were 69, 176 and 336% of that at 15 °C. Among the specimens tested, CLT and LVL had the smallest change (around exp(4220/T)) of the transverse diffusion coefficient with respect to temperature.

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Fig. 9. Effect of moisture content and temperature on diffusion coefficient of CLT.

Fig. 10. Effect of moisture content and temperature on diffusion coefficient of LVL.

In contrast to the temperature dependency of the diffusion coefficient, the dependency of the diffusion coefficient on the moisture content (VMC or GMC) is not the same for longitudinal and transverse directions. An increase in the VMC/GMC was found to result in an increase in diffusion coefficient of the transverse direction while at the same time reducing the diffu-

sion coefficient in the longitudinal direction (see Figs. 9a–15a). This is consistent with the results reported in the literature [69,73] for diffusion coefficients in both directions. The SP and PT specimens had the greatest (i.e. exp(0.630VMC)) and smallest (i.e. and exp(0.049VMC)) decreasing trends, respectively. The rate of decrease in the longitudinal diffusion coefficient with

A.A. Chiniforush et al. / Construction and Building Materials 224 (2019) 1040–1055

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Fig. 11. Effect of moisture content and temperature on diffusion coefficient of Radiata Pine (Pinus radiata).

Fig. 12. Effect of moisture content and temperature on diffusion coefficient of Slash Pine (Pinus elliottii).

respect to VMC/GMC was found to be greater at higher temperatures. The rate of change in the transverse diffusion coefficient is, however, much smaller than longitudinal direction (approximately 1/10th). The CLT and LVL specimens had the greatest rate of transverse coefficient of diffusion change with respect to GMC/VMC (i.e.

exp(0.153VMC) and exp(0.132VMC)) at 45 °C, whereas PT had almost no dependency to moisture content at 45 °C. The ratio of longitudinal to vertical diffusion coefficient (DL =DV ) for the studied species are shown in Fig. 16. It is seen that for CLT, LVL, RP and SP specimens the DL =DV ratio decreases initially with an increase in moisture content; the rate of the decrease is how-

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A.A. Chiniforush et al. / Construction and Building Materials 224 (2019) 1040–1055

Fig. 13. Effect of moisture content and temperature on diffusion coefficient of BB (Eucalyptus pilularis).

Fig. 14. Effect of moisture content and temperature on diffusion coefficient of Pacific Teak (Tectona grandis).

ever found to gradually reduce, with the DL =DV ratio converging eventually to a constant. Among the species considered, the BB and PT had the smallest rate of decrease, i.e. 1.19 and 0.38 times per 1% increase of VMC, whereas SP and TO had the greatest rate of decrease, i.e. 18.41 and 10.39 times per 1% increase of VMC.

Furthermore, except for BB and PT specimens, the DL =DV ratio is found to be greater at the higher temperatures than the lower temperatures. The DL =DV ratio however converges eventually to the same value with further increase in the moisture content, regardless of the temperature. For instance, in Fig. 16a, at VMC ¼ 3:5%,

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Fig. 15. Effect of moisture content and temperature on diffusion coefficient of Tasmanian Oak (Eucalyptus regnans/obliqua/delegatensis).

the DL =DV ratio is 21.47 and 13.32 in 45 °C and 15 °C, respectively. At VMC ¼ 8:0%, however, the value of DL =DV converges to 1.52 for all temperatures. Walker [69] reported that the DL =DV ratio for wood species varies from 100 to 2 with an increase in GMC from 5% to 25% which is equivalent to an increase in VMC from 3 to 15%, when considering an average density of 600kg=m3 . In Table 6, the measured diffusion coefficients in the present study are compared with reported values in the literature. Moreover, the existing empirical equations for diffusion coefficient [53,55,57,74] (if existed) are plotted against the experimental results in Figs. 10– 15. Apart from differences in measurement accuracy of the methods used in different studies, the difference between the experimental results and the existing literature can be attributed to the following factors. First, there are quite a few types of Pine (Radiata, Splash, Scots, etc.) available and therefore the Pine species tested in this study might not be exactly the same as those tested in previous studies [43,52,55,72,75]. Second, the climate and locations where a tree grows could affect the structure of the wood, therefore resulting in different water transport properties [43]. Third, the position of samples in the body of the tree (sapwood or heartwood), the age of timber, and state of wood (dry or green) significantly influence the diffusivity properties [6,43,76]. Furthermore, the sorption method is mainly utilised in the literature during the drying of wood species to estimate the diffusion coefficient and an average value for the transverse direction (ignoring longitudinal diffusion for long samples) and moisture content (while moisture content is changing during the test) was reported. Also, the applicable range (temperature and relative humidity) of the proposed empirical equations could have been another source of error in the extrapolation of the diffusion coefficient. The calculated diffusion coefficients from the cup method were utilized in conjunction with apparent diffusivity measure from the sorption method to calculate the surface emissivity from Eq. (8). The results for different wood species in different directions are summarised in Table 7. As can be seen, surface emissivity increases

generally by an increase in relative humidity range (e.g. 30! 60 to 60 ! 90%). In terms of species, surface emissivity for softwoods in longitudinal and transverse directions are in the same range (in average 3:57  107 m=s); however, for the hardwoods the longitudinal surface emissivity is significantly greater than transverse direction. Both these trends are consistent with findings of the previous studies [50,77]. The results from the sorption method demonstrates a higher dispersion, which can be attributed to the approximation of numerical solution for un-steady-state transport equation as well as simplifying assumption in the solution [59]. Moreover, the variable speed of air circulation inside humidity chamber and samples thickness are major factors which create inconsistency in the results [41,59]. 5. Conclusion Water vapor diffusivity of wood and engineered wood products (i.e. LVL, Glulam and CLT) in the range of 15–45 °C temperature and 30–90% relative humidity was investigated by means of the cup method. Sorption isotherms of the considered species were extracted for two temperatures, i.e. 15 and 50 °C to calculate the diffusion coefficient by water concentration potential. An empirical equation for diffusion coefficient (in three principal directions) as a function of temperature and volumetric moisture content was proposed and calibrated with correlation factors of R2 > 0:90. Supplementary sorption tests were conducted to measure surface emissivity (mass transfer coefficient) as an important boundary condition parameter required for solving diffusion equation. The following conclusions are drawn from the experimental results.
Diffusion coefficient increases exponentially by an increase in temperature and the effect of temperature on the diffusion coefficient is more pronounced in the longitudinal direction.

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Fig. 16. Ratio of longitudinal to vertical/transverse diffusion coefficient (effect of moisture content and temperature).


Longitudinal diffusion coefficient decreases exponentially by an increase in the moisture, whereas the transverse diffusion coefficient exhibits an opposite trend.
The ratios of longitudinal to transverse diffusion coefficient decrease exponentially by an increase in moisture content. The ratios are greater for higher temperatures and converge ultimately to the same value as the moisture content increases. At lower volumetric moisture content (VMC), the coefficient of

diffusion in the longitudinal direction is an order of magnitude bigger than that of the transverse direction. This finding is consistent with the results of tests conducted on small size clear wood specimens [17].
Surface emissivity for softwood species in longitudinal and transverse direction are in the same range; however, for the hardwood species, the longitudinal surface emissivity are significantly greater than transverse.

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A.A. Chiniforush et al. / Construction and Building Materials 224 (2019) 1040–1055 Table 5 Diffusivity (Dc ) as a function of temperature and moisture content (Eq. (9)). Parameter

CLT

LVL

RP

SP

BB

PT

TO

Longitudinal

a0 b0 c0 d0

66.06 6829.6 0.6016 71.543

67.721 6916.3 0.5208 72.419

12.965 5814.1 0.5309 5.9720

41.133 5856.7 0.6444 4.4240

0.4360 60020 0.3336 61.163

0.076 5986.3 0.3372 87.162

188.541 6904.3 0.4051 5.9280

Transverse

eVG * eH *

0.7619 0.9479 1.4000

0.8029 0.8921 1.2156

0.6179 0.8038 3.9690

0.6442 0.5269 3.3700

0.7289 0.7747 1.8493

0.9828 0.9959 1.7512

0.4809 0.9674 3.3700

4188.9 1.6999 491.92

4256.2 0.9726 267.46

4488.8 0.5912 162.71

4531.5 0.6243 181.32

4624.3 0.4452 136.50

4775.6 0.2600 84.22

4516.4 0.6116 176.60

a0  104 b0 c0 d0 *For CLT: eG ¼ eT , eVG ¼ eOG , and eH ¼ eO . *For LVL: eVG ¼ eHG .

Table 6 Comparison of measured diffusion coefficient and reported values in the literature. Species

T (°C)

GMC (%)

BlackButt (longitudinal)

35 23 40 35 23 35 30 23 32.2 32.2 43.3 43.3 35 35 35 35

7–14 –

BlackButt (transverse) Pine (longitudinal)

Pine (transverse) Oak (transverse)

Spruce (longitudinal) Spruce (transverse) Teak (longitudinal) Teak (transverse)

7–14 7–14 7–14 12.85 7–14 9.8 37.2 9.8 35.1 7–14 7–14 7–14 7–14

Table 7 Calculated surface emissivity for different relative humidity gradients. Specimens/species-direction

CLT-H CLT-V CLT-L LVL-H LVL-V LVL-L RP-H RP-V RP-L SP-H SP-V SP-L BB-H BB-V BB-L PT-H PT-V PT-L TO-H TO-V TO-L

Ref.

Dc  1010 (m2 =s) Eq. (9)

Literature

3.0–6.7 1.3–4.1 3.1–10.6 0.56–0.57 4.4–43.8 (RP) 17.7–137.1 (RP) 18.1 (RP) 1.3–1.6 (RP) 1.5 3.3 2.8 3.2 14.0–47.5 (CLT) 2.4–3.4 (CLT) 1.6–2.1 0.28–0.30

2.3 4.9 8.3 0.2–0.3 19.5 143 43 0.90 0.56–0.76 5.17–5.85 0.93–1.10 6.05–7.42 196 1.3–1.6 40 1.7–2.8

[72] [68] [68] [72] [50] [71] [78] [50] [56] [56] [56] [56] [71] [71] [71] [71]

References

S  107 ðm=sÞ 0 ? 30%

30 ? 60%

60 ? 90%

1.512 2.190 2.838 2.783 3.196 3.253 4.400 4.675 3.386 2.407 2.217 2.597 0.555 1.219 10.814 0.630 0.446 2.628 0.810 0.790 5.046

3.867 3.205 4.637 2.650 3.671 3.131 4.581 6.366 5.224 4.711 2.560 3.504 0.694 1.312 11.808 1.338 1.068 3.187 1.565 1.441 8.766

3.631 3.235 4.880 2.127 3.079 3.260 4.303 5.649 4.774 2.723 3.764 3.403 0.555 0.948 11.827 1.297 1.777 3.769 1.397 0.827 6.275

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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