Wood Science and Technology

, Volume 51, Issue 4, pp 795–809 | Cite as

Effect of temperature on electrical conductivity of green sapwood of Pinus radiata (radiata pine)

Original

Abstract

Joule heating of green Pinus radiata, if controlled in a range 60–90 °C, has the potential to be used for veneer cutting, improving the peeling process and the quality of veneer. This research attempts to study the wood’s electrical conductivity, one of the key variables in controlling the Joule heating effect. Electrical conductivity of green New Zealand grown radiata pine sapwood was studied over a 20–90 °C temperature range. The sapwood studied had moisture content in the range of 100–200%. The effects of wood parameters such as grain orientation, moisture content, and basic density were evaluated. The effects of temperature and grain orientation on the conductivity were found to be much greater than those of moisture content and basic density. At 23 °C, conductivity in the longitudinal direction was around 20 times higher than in the tangential and 10 times higher than in the radial direction. Between 23 and 90 °C the longitudinal conductivity increased threefold, near linearly with temperature, whereas the tangential and radial conductivities increased nonlinearly by factors of 6 and 4, respectively. A statistical model based on the experimental results has been developed using the linear mixed effect model.

Introduction

Veneer cutting is an essential part of the wood processing industry. One necessity for high-quality veneer cutting is to soften the lignin, achieved by elevating the temperature of wood (Salmén 1984; Dupleix et al. 2013). The optimal temperature for the cutting process is 60–90 °C (Perré 2004). Conventional heating methods such as soaking wood in hot water are inefficient due to the slow heat penetration rate and associated heat losses. An alternative approach is to generate heat inside the wood’s volume, so-called volumetric heating, that can be done using either microwave heating or the Joule heating effect (Fleischer and Downs 1953; Perré 2004). Joule heating, in which an electrical current is made to flow through the log by imposing a voltage across electrodes at each end (Ansari and Cho 2010), is the preferred method due to the energy efficiency—nearly 100% of electrical energy is converted into thermal energy (Sakr and Liu 2014)—and the relatively lower cost of equipment (Perré 2004). The method has the potential to be commercially developed, but there is a lack of information about the key parameters such as electrical conductivity of green wood and its dependence on temperature and wood properties (Fleischer and Downs 1953). Conductivity is important as, for a given voltage, it determines the amplitude of the current flow, and hence the heating power and therefore the rate of temperature rise, in the timber.

Dry wood is an electrical insulator, while water with dissolved minerals is an electrical conductor. The carriers of the electrical charge in aqueous solutions are ions. Generally, if the concentration of the dissolved salt such as potassium chloride is constant, then the dependence of the electrical conductivity on the temperature, below water’s boiling point at atmospheric pressure, is near linear (McCleskey 2011; Haynes 2014). However, wood parameters such as moisture content (MC), chemical composition, moisture distribution, grain orientation, and permeability make the temperature dependence of the electrical conductivity nonlinear.

Many researchers have studied effects of temperature and wood properties on the electrical conductivity (Stamm 1927, 1929, 1960; Brown et al. 1963; Lin 1967; Skaar 1988; Forsén and Tarvainen 2000), but most of the research was done below fibre saturation point—the moisture content at which wood fibres are fully saturated with bound water and no free water in the wood cavities, commonly 20–40% of the dry mass (Skaar 1988). The average fibre saturation point of Pinus radiata is around 30% of the dry mass (Pang and Herritsch 2005). The effect of moisture content on the electrical resistance is significant below the saturation point, where a 1% decrease in MC, in the range from the saturation point down to 7% MC, increases the electrical resistance about two to four times (Skaar 1988). The effect of the moisture content is significantly smaller above the fibre saturation, when the conduction of electrical current depends predominantly on the ionic composition of samples and the distribution of free water in the wood cavities (Skaar 1988). Some studies, done above the fibre saturation point, have investigated moisture contents using electrical moisture meters but without publishing electrical conductivity (Chen et al. 1994; Brischke et al. 2008). Fredriksson et al. (2013) measured electrical conductance using pin electrodes, making the determination of electrical conductivity difficult due to the unknown surface area and length of conductor and therefore hard to compare with the current work. A few researchers have studied green wood’s electrical conductivity (Stamm 1929, 1964; Lin 1967; Sharma et al. 1997), but they predominantly investigated wood parameters at around room temperature. According to Stamm (1929, 1964) electrical conductivity of slash pine (Pinus elliottii) and redwood is close to \(0.01\, {\hbox {S}}\,{\hbox{m}}^{-1}\) at 70% moisture content; Lin showed similar results for 10 species of wood. Sharma et al. (1997) measured the conductivity in different directions of hardwood species: Eucalyptus tereticornis, Grevillea robusta, and Hevea brasiliensis grown in India. He found that the conductivity varied around \(10^{-3}\,{\hbox {S}}\,{\hbox{m}}^{-1}\) in the longitudinal direction and in the range of \(10^{-3}\)\(10^{-4}\, {\hbox {S}}\,{\hbox{m}}^{-1}\) in the transverse direction. However, the effects of temperature and other wood parameters above room temperature, especially in the range 60–90 °C associated with Joule heating, have not been well studied.

Generally, veneer logs of P. radiata have two regions: sapwood, with free water in the wood’s cavities, and heartwood, a much drier central portion, with virtually all tracheids filled with air (Harris 1991a), making this part less conductive. Thus, on a macroscale, electrically the log structure can be simplified to an arrangement of two parallel resistors, where electric current will predominantly flow through the less resistive sapwood part. This paper aims to identify key variables that have significant effects on the electrical conductivity of green P. radiata's sapwood well above the fibre saturation point. Based on the obtained results, an equation of electrical conductivity as a function of the selected variables will be developed.

Materials and methods

Sample preparation

The logs, from which samples were taken, had a small end diameter (SED) and a large end diameter (LED) between 350 to 450 mm and the heartwood LED and SED between 100 to 200 mm. The sapwood of freshly sawn, green P. radiata is readily distinguishable from the heartwood, by visual means. Two 3-m-long, freshly flat-sawn beams of outerwood/sapwood of green P. radiata, grown in the Canterbury region of New Zealand, were used in this study. The beams were cut into parts of 500 mm length and had been stored inside sealed plastic bags in a freezer at −20 °C for less than 3 months, to avoid significant drying of the wood. A day prior to each experiment, one of the frozen parts was cut, using a bench saw, into blocks with a thickness and width of 30 mm; the lengths of the blocks were kept at 500 mm. Then, using a drop saw, the blocks were chopped along their length making cubes with sides of 30 mm. Only the cubes with straight grain were selected. The chosen cubes, sealed in a plastic bag, were left inside a fridge overnight at 2 °C, to defrost. Each cube was tested once in a single selected direction. In total, 44, 24, and 24 cubes were used in the longitudinal, tangential, and radial directions, respectively; the cubes were cut out of four 500-mm-long parts from different places within the 3-m freshly sawn beams. The mean basic density and moisture content of the tested cubes were \(416\,{\hbox {kg}}\,{\hbox{m}}^{-3}\) (\({\hbox {SD}} = 14\,{\hbox {kg}}\,{\hbox{m}}^{-3}\)) and 173% (\({\hbox {SD}} = 10\%\)), respectively.

Experimental set-up

To control the moisture content within the cubes during heating of samples, sealed boxes were custom built (Fig. 1). The main part of each box consisted of a sealed plastic enclosure with threaded cable glands; all the parts were designed to operate reliably up to 100 °C. Two brass plate electrodes were mounted inside the boxes. Brass tubes were welded to the plates and put through the cable glands. Using crocodile clips, the brass tubes were attached to an AC electric source. To improve the contact between the timber samples and the brass electrodes, a self-adhesive electrically conductive silver foam (SOFT-SHIELD 4850 from Parker Chomerics) was stuck to the brass plates. To measure the temperature of the sample, each box was equipped with a temperature sensor (PT-100) and connected to a data logger (Pico Technology PT-104) that recorded the temperature every second.
Fig. 1

The plastic box used to control the moisture content of the samples

Experimental procedure

Minimising the resistance of contacts

Prior to inserting the cubes into the boxes, their dimensions in all three directions were measured using a vernier calliper, with a resolution of 0.05 mm. The cubes were weighed with a resolution of 0.01 g. To pass an electrical current, wood, with its anisotropic electrical conductivity and rough surface, requires each point on the contact surface being attached to the electrodes; unlike metal materials that can rely on a single contact point on each electrode. A localised contact increases the magnitude of electrical resistance at the contact, overestimating the real electrical resistance of the wood; in an ideal scenario, the contact resistance shall be reduced to zero, mathematically described as:
$$\begin{aligned} R_\mathrm{exp} \mathrel {\mathop {=}\limits _{ R_\mathrm{c} \rightarrow 0}} 2 \cdot R_\mathrm{c} + R_\mathrm{w}, \end{aligned}$$
(1)
where R is the electrical resistance \((\Omega )\), exp denotes the resistance measured in the experiment, c refers to the electrical resistance of a single contact, arising due to air gaps between the electrodes and sample surfaces, and w stands for the real electrical resistance of the wood sample. Although the silver foam can conform to the samples’ contact surfaces, increasing the surface area of the contacts, the foam’s porous structure leaves small air pockets on the contact surface. Therefore, to further improve the contacts, they were coated either by a silver epoxy (MG Chemicals 8330S-21G), a silver leaf or a 22-carat orange gold leaf, the latter two produced by Noris Blattgold GmbH. The applied material had to be a metal, because electrolytes, such as gels with dissolved sodium chloride, penetrate into wood, significantly enhancing the wood’s electrical conductivity. The leaves were extremely thin; thus, when applied over the contact surface, they replicated the irregularities of the contact surfaces. The gold and silver leaves, applied without an adhesive material to the wood, were considered weightless, while the mass of applied silver epoxy was measured. The number of cubes covered by each coating type for each direction is shown in Table 1.
Table 1

Number of samples used per each direction and type of coating

Type of coating

Directions

L

R

T

Silver epoxy

16

12

12

Gold leaf

20

12

12

Silver leaf\(^\mathrm{a}\)

8

\(^\mathrm{a}\) The silver leaf was not used in the radial and tangential directions due to the superior performance of the gold leaf

Recording data

The sealed boxes, with the cubes inside, were weighed and put into an oven that was at room temperature, around 23 °C. A sinusoidal voltage of 50 V at 400 HZ was supplied to each box by a programmable AC source (Chroma 61504). This frequency was selected to coincide with concurrent work on an experimental log-scale Joule heating apparatus. However, to avoid significant Joule heating, the duration of the excitation was 3 s, after which the electrical parameters such as voltage across the sample, measured by KEYSIGHT U3402A, electrical current through the sample, measured by KEYSIGHT U34461A, and the temperature inside the boxes were recorded. Thereafter, the temperature in the oven was set to 30 °C. After 35 min of heating at the set temperature, another excitation was performed. The procedure was repeated every 10 °C up to 90 °C. The 35-minute temperature equilibration period was determined by computer modelling as described in the following section.

Moisture loss and cube temperature

After the last excitation, each sealed plastic box, with the cube inside, was weighed to determine the mass of moisture lost out of the box during the experiment, the average value of which was around \(3\times 10^{-4}\,{\hbox {kg}}\). The cubes lost some additional moisture to the unoccupied volume inside the plastic boxes, calculated as:
$$\begin{aligned} V_\mathrm{f} = V_\mathrm{box} - V_\mathrm{g}, \end{aligned}$$
(2)
where \(V_\mathrm{f}\), \(V_\mathrm{box}\), and \(V_\mathrm{g}\) are the unoccupied volume inside the box \(({\hbox {m}}^{3})\); the internal volume of the plastic box, equal to \(2.1 \times 10^{-4}\,{\hbox {m}}^{3}\); and the green volume of the sample, with the average value of \(2.8 \times 10^{-5}\,{\hbox {m}}^{3}\) , respectively. In the worst-case scenario, assuming the air in the box was dry prior to the experiment and then reached 100% of relative humidity at 90 °C, the mass of vapour in the unoccupied volume can be determined as:
$$\begin{aligned} m_\mathrm{V} = \frac{V_\mathrm{f}}{\upsilon _{\mathrm{V@}90\,{^{{}^\circ} \mathrm{C}}}}, \end{aligned}$$
(3)
where \(m_\mathrm{V}\) is the mass of the vapour \(({\hbox {kg}})\) and \(\upsilon _{\mathrm{V@}90\,{^{{}^\circ} \mathrm{C}}}\) is the specific volume of the saturated vapour at 90 °C, equal to 2.3593 \(({\hbox {m}}^{3}\,{\hbox {kg}}^{-1})\) (Cengel and Boles 2011). Thus, taking into account the mass of moisture lost out of the box during the experiment of \(3\times 10^{-4}\, {\hbox {kg}}\) and the maximum mass of evaporated water trapped inside the box, calculated using Eq. 3 to be about \(8\times 10^{-5}\, {\hbox {kg}}\), the total average loss of moisture from the cubes was around \(3.8 \times 10^{-4}\, {\hbox {kg}}\), decreasing the average moisture content of the cubes from 173 to 169%. According to Stamm (1929, 1964), the effect of moisture content on electrical conductivity is almost insignificant at such elevated moisture contents, being less than the measured effect of a 1 °C increase of temperature within green sapwood of P. radiata.
To ensure that the internal temperature of the cubes reached the target temperature at each temperature step, the heating process was modelled using computational fluid dynamics (CFD). The model was developed using a commercial software (ANSYS CFX 17.0), employing the finite volume method (FVM). As the samples were located inside the plastic boxes, preventing significant drying of the samples, the mass conservation equation and heat diffusion due to internal convection of water were not considered. Therefore, the model was described by the following single governing equation of energy conservation which was solved using the second-order backward Euler scheme:
$$\begin{aligned} \frac{\partial \rho C_p T}{\partial t} = \nabla \cdot \left( k \nabla T \right) , \end{aligned}$$
(4)
where \(\rho\) is the green density \(({\hbox {kg}}\,{\hbox {m}}^{-3})\), \(C_p\) is the heat capacity \(({\hbox {J}}\,{\hbox {kg}}^{-1}\,{^{\circ }}{\hbox {C}}^{-1})\), T is the temperature (°C), t is the time (s), and k is the thermal conductivity \(({\hbox {W}}\, \hbox {m}^{-1}\,{^{\circ }}\hbox {C}^{-1})\). The thermal properties of P. radiata used in the model are functions of moisture content and basic density (Pang et al. 1995):
$$\begin{aligned} C_p = 4184\frac{({\hbox {MC}}/100+0.324)}{1.0+{\hbox {MC}}/100}, \end{aligned}$$
(5)
where MC is the moisture content (%), and
$$\begin{aligned} k = \frac{{\hbox {BD}}}{1000}(0.4+0.5 \cdot {\hbox {MC}/100}) + 0.024, \end{aligned}$$
(6)
where BD is the basic density \((\hbox {kg}\,\hbox {m}^{-3})\). The block’s external surface temperature were assumed to be equal to the temperature inside the plastic box. Thus, the boundary conditions were expressed as:
$$\begin{aligned} T_\mathrm{s} = T_\mathrm{exp}(t), \end{aligned}$$
(7)
where \(T_\mathrm{s}\) is the temperature of the cube’s external surface and \(T_\mathrm{exp}(t)\) is the temperature inside the plastic box, recorded during the experiment as a function of time, t. The cube’s geometry was meshed using rectangular hexahedrons, created using the sweeping and edge size control methods. Mesh and time-step independence of the result was achieved using a uniform mesh 64,000 mesh elements, built as an array of \(40\times 40\times 40\) elements, and 500 time-steps. Figure 2 displays the results of the CFD model, showing that around 35 min is required to reach the target temperature inside the cube at that heating rate.
Fig. 2

The modelled heating of a single test sample during the experiment. The solid and dashed lines represent the cube’s surface and internal temperatures (in the centre of the cube) respectively, while the crosses show the time when the actual electrical conductivity measurements were taken

Post-processing of data

The volume of each block was measured using the water displacement method. The blocks were left inside the oven, at 105 °C, to reach a constant dry mass. The moisture content of the wood and its basic density were then calculated, using the following equations:
$$\begin{aligned} {\hbox {MC}}= & {} \frac{m_\mathrm{g} - (m_\mathrm{o} - m_\mathrm{c})}{(m_\mathrm{o}-m_\mathrm{c})} \times 100\%, \end{aligned}$$
(8)
$$\begin{aligned} {\hbox {BD}}= & {} \frac{m_\mathrm{o}-m_\mathrm{c}}{V_\mathrm{g}}, \end{aligned}$$
(9)
where \(m_\mathrm{g}\), \(m_\mathrm{o}\), and \(m_\mathrm{c}\) are the green mass, the oven-dry mass, and the optional mass of the silver epoxy coating, respectively \((\hbox {kg})\). Basic density, derived from the oven-dry mass, is independent of moisture content and hence can be used as a basis for comparison and to predict other properties (Harris and Cown 1991). The electrical conductivity of wood is calculated as:
$$\begin{aligned} \sigma = \frac{l}{R \cdot A}, \end{aligned}$$
(10)
where \(\sigma\) is the electrical conductivity \((\hbox {S}\, \hbox {m}^{-1})\), l is the length of the sample along which the electrical current flows \((\hbox {m})\), A is the cross-sectional area of the sample \((\hbox {m}^{2})\), and R is the measured resistance of the sample \((\Omega )\), calculated as:
$$\begin{aligned} R = \frac{U}{I}, \end{aligned}$$
(11)
where U and I are the recorded voltage \((\hbox {V})\) and electrical current \((\hbox {A})\), respectively.

Statistical modelling

Based on the experimental data, the four independent variables of temperature, moisture content, basic density, and the grain orientation were considered. Other wood parameters such as extractives of wood and electrical conductivity of the extractives’ aqueous solutions were considered in an unpublished preliminary study; however, no correlation with Joule heating was found. To avoid multicollinearity—a phenomenon in which two or more independent variables are moderately or strongly correlated, causing inaccurate estimation of the predicted coefficients (Faraway 2005)—in the model, initial data analysis using scatter plotting was performed. The variables that have a significant effect on the electrical conductivity were considered in the model. Then, using the statistical programming language, R 3.2.5 (R Core Team 2016), with a user-created package, lme4 (Bates et al. 2015), the fitted mixed effect regression model was developed. As the lme4 package does not calculate p-values, the lmerTest package (Kuznetsova et al. 2016) was used to calculate the p-values.

Results

The electrical conductivity of the cubes was measured from 23 to 90 °C, in three principal (longitudinal, radial, and tangential) directions, total of 92 samples. These data are presented in the form of natural logarithm of electrical conductivity versus temperature in Fig. 3. The wood was the most conductive in the longitudinal direction, with a mean value of electrical conductivity of \(0.037\, \hbox {S}\, \hbox {m}^{-1}\), at around 23 °C. This compares to \(0.01\,\hbox {S}\, \hbox {m}^{-1}\) at 170% moisture content, measured by Stamm (1964) for slash pine in the longitudinal direction at room temperature. The electrical conductivities in the radial and tangential directions at the same temperature were 0.0037 and \(0.0018\, \hbox {S}\, \hbox {m}^{-1}\), respectively.
Fig. 3

The natural logarithm of electrical conductivity of green P. radiata versus temperature. The circle, square, and triangle scatters denote the longitudinal, radial, tangential directions, respectively. The colours of scatters (black, grey, and white) represent the type of coating (the gold leaves, silver epoxy, and silver leaves)

The average longitudinal electrical conductivity was approximately 10 and 20 times higher than the average radial and tangential conductivities, respectively (Fig. 4). Similar ratio values between longitudinal and the transverse directions were provided by Burr and Stamm (1947), who measured electrical conductivity of softwood and hardwood, saturated with a solution of potassium chloride, at 30 °C. However, the ratios between the longitudinal and transverse directions, measured by Sharma et al. (1997) at 70% moisture content, were lower, varying from 5 to 10 times. In Fig. 4, these ratios, however, decreased with the rise of temperature, and at around 90 °C, they were about 7 for the longitudinal to radial ratio and 10 for the longitudinal to tangential ratio. The ratio of radial to tangential conductivity decreased from about 2 to 1.4. The most significant effect of the temperature rise was seen in the tangential direction, increasing the average conductivity by around 6 times; the increase in the longitudinal and radial directions were about 3 and 4 times, respectively. The mean values of electrical conductivity at 90 °C in the longitudinal, radial, and tangential directions were 0.12, 0.016, and \(0.011\,\hbox {S}\, \hbox {m}^{-1}\), respectively.
Fig. 4

The effect of temperature on the ratios of the longitudinal electrical conductivity to the radial and tangential electrical conductivities

According to Harris and Cown (1991), the denser the wood tissue, the less water it can accommodate. To assess this relationship in the experimental data, a Pearson product-moment correlation coefficient was calculated. The experimental data showed a strong negative correlation between moisture content and basic density, with \(r = -.94, \, 95\% {\hbox { CI }} [-.95, -.93]\), \(p< 0.001\), determined based on the total number of samples. To avoid multicollinearity behaviour, either the moisture content or the basic density (but not both) could be used in the statistical model. However, as stated by Skaar (1988), the effect of moisture content in green conditions was negligible in all directions (Fig. 5), making the statistical model of electrical conductivity of green P. radiata’s sapwood a function only of temperature and direction.
Fig. 5

The effect of moisture content on the electrical conductivity in the longitudinal, radial, and tangential directions (the circle, square and triangle scatters, respectively) over the different temperature values

Prior to deriving the model, the effect of the coating types was studied by comparing mean values of electrical conductivity in each direction. The sample mean of electrical conductivity obtained using the gold leaves was higher by about 10% than using the silver epoxy in the longitudinal and radial directions, and by around 5% higher in the tangential direction. The results obtained using the silver leaves in the longitudinal direction were higher than the results obtained with the silver epoxy but lower than with the gold leaves. Thus, based on Eq. 1, the data obtained by using the gold leaves was assumed the most accurate, and, therefore, it was used to develop the statistical model.

Using the Akaike information criterion (Sakamoto et al. 1986) to estimate the quality of a statistical model, the mixed effect model was developed in the following form:
$$\begin{aligned} \begin{aligned} \ln (\sigma ) \sim \left[ \beta _0 + \beta _1 (T-55) + \beta _2 \frac{(T-55)^2}{1000}\right] \times D + (1|B), \end{aligned} \end{aligned}$$
(12)
where \(\beta _i\) are the regression coefficients, with \(\beta _0\) being the intercept; (1|B) is the random effect term; \((T-55)\) is the mean centred temperature (°C); and D is the direction, a factor variable. Using the estimated coefficients (Table 2), the following equations were derived:
$$\begin{aligned} \sigma _L = \exp \left[ -2.60 + 0.017 (T - 55) - 0.073 \frac{(T-55)^2}{1000} \right] , \end{aligned}$$
(13)
$$\begin{aligned} \sigma _R = \exp \left[ -4.81 + 0.021(T-55) - 0.046 \frac{(T-55)^2}{1000} \right] , \end{aligned}$$
(14)
$$\begin{aligned} \sigma _T = \exp \left[ -5.37 + 0.026(T-55) - 0.046 \frac{(T-55)^2}{1000} \right] . \end{aligned}$$
(15)
Figure 6 shows the fitted model in all apparent directions with the data obtained using the gold leaf coating.
Table 2

Regression coefficients of the statistical model

 

Estimates

Std. errors

t value

p value

(Intercept)

−2.60

0.018

−143

<2e−16

(T − 55)

0.017

0.00009

194

<2e−16

(((T − 55)\(^\wedge 2\))/1000)

−0.073

0.004

−16.4

<2e−16

DR

−2.21

0.030

−74.1

<2e−16

DT

−2.77

0.030

−93.0

<2e−16

(T − 55):DR

0.004

0.0001

29.4

<2e−16

(T − 55):DT

0.009

0.0001

65.8

<2e−16

(((T − 55)\(^\wedge 2\))/1000):DR

0.026

0.007

3.58

0.0004

(((T − 55)\(^\wedge 2\))/1000):DT

0.027

0.007

3.69

0.0003

Fig. 6

The statistical model (solid lines) fitted into the experimental data of green P. radiata’s natural logarithm of electrical conductivity, with the gold leaf coating. The circle, square, and triangle scatters denote the longitudinal, radial, tangential directions, respectively

Discussion

The carriers of electrical charge in aqueous solutions, such as wood sap, are ions. Three parameters affect the electrical conductivity of aqueous solutions: the magnitude of the ions’ charge, the concentration of ions, and the mobility of ions (Bard and Faulkner 2001). Potentially, the magnitude of the ions’ charge and concentration of the ions are relatively constant within an energised sample on a centimetres scale. However, the mobility of ions strongly depends on temperature, where the higher the temperature, the more mobile the ions become (Bard and Faulkner 2001). Moreover, the continuity or discontinuity of electrical conduction paths increases or decreases the electrical conductivity of green wood (Skaar 1988).

Figure 6 shows the rise of electrical conductivity with the temperature in all apparent directions. The result indicates that the increase of temperature increases the mobility of ions in the wood sap, resulting in increase of electrical conductivity. As expected, the highest electrical conductivity was in the longitudinal direction, along which wood sap is conducted and 95% of radiata pine’s tissue is oriented (Harris 1991b). The longitudinal tissue, containing sap saturated earlywood tracheids, forms continuous water columns, which appear as direct electrical conduction paths. On the other hand, there are few continuous paths in the radial direction—radial rays, occupying up to 5% of the wood volume, conduct the sap (Bamber and Burley 1983; Harris 1991b)—and none in the tangential direction. Without tissue aligned in the tangential direction, an electrical current has to flow using indirect paths, decreasing the electrical conductivity.

The effect of temperature on the electrical conductivity of salt solutions is near linear, in the range from 0 to 90 °C (McCleskey 2011; Haynes 2014). However, based on the form of the statistical model (Eq. 12), this correlation is nonlinear due to the complex structure of green wood. This effect of wood structure is less significant in the longitudinal direction, with the direct electrical conduction paths, and much more significant in the transverse directions, where the conduction paths are indirect. In the radial direction, electric current must flow mainly through cell walls, with a small number of direct paths, presented by rays, while in the tangential direction, the current dominantly flows through cell walls. Without direct conductive paths, the conduction of current in the radial and tangential directions may rely on a diffusion rate of moisture, nonlinearly correlated with temperature; according to Langrish and Walker (2006), a rise of temperature of wood from 25 to 100 °C increases the diffusion rate of moisture up to 37 times. Moreover, the statistical analysis showed that the effect of temperature in green sapwood of radiata pine is much more significant than moisture content. The derived Eqs. 1315 incorporate the effects of temperature and direction on the electrical conductivity of green New Zealand P. radiata.

Conclusion

The obtained statistical model can be used to accurately simulate the Joule heating process in green sapwood of P. radiata. In such simulations, the model can be made to account for the spatial and temporal distribution of electrical conductivity and hence specific power dissipation and resulting temperature rise. Comprised of three equations, one per grain direction, the model can be applied to simulation of heating samples of different shapes and sizes such as logs or sawn boards. The model is limited to the 100–200% moisture content range, common to New Zealand grown green P. radiata sapwood. Accurate estimation of electrical conductivity requires only knowledge of wood temperature. The effects of moisture content and basic density on electrical conductivity, at moisture contents above 100%, are negligible, as stated by Stamm (1929), Lin (1967), and Sharma et al. (1997).

Notes

Acknowledgements

The authors are thankful to McVicar Timber, New Zealand, for providing fresh wood used in this research. The authors also wish to thank Associate Professor Elena Moltchanova, Statistics Consulting Unit, University of Canterbury, for helpful comments in the statistical modelling. This work has been supported by Scion under the NZ Ministry of Business, Innovation and Employment (MBIE) and Stakeholders in Methyl Bromide Reduction (STIMBR) funded Market Access Programme.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Chemical and Process EngineeringUniversity of CanterburyChristchurchNew Zealand
  2. 2.School of ForestryUniversity of CanterburyChristchurchNew Zealand
  3. 3.EPECentreUniversity of CanterburyChristchurchNew Zealand

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