Mechanisms of liquid imbibition in Douglas-fir inferred from ¹H nuclear magnetic resonance methods

2.1 Wood materials

Wood samples are collected from Douglas-fir (Pseudotsuga menziesii) planks, which had been left drying naturally under ambient conditions. Studied samples come either from the outer part of the trunk (sapwood) or from the inner part (heartwood). The average density of all specimens measured at 44% Relative Humidity (RH) is 590 (±40) kg m⁻³ for heartwood and 620 (±030) kg m⁻³ for sapwood and the proportion of latewood related to the annual ring width is estimated as 45 ± 5% for all studied samples subjected to imbibition tests. These values are consistent with literature (Lachenbruch et al. 2010; Osborne et al. 2016) for Douglas-fir with a high proportion of latewood or for this RH. For instance, in Lachenbruch et al. 2010, the density at 12% MC is 783 kg m⁻³ with a latewood proportion of 56%.

Density essentially finds its origin in different proportions of latewood and earlywood while the general qualitative features of the material remain the same. The microstructural properties explain the physical origin of liquid transfers. Heartwood and sapwood materials are mainly composed of tracheids and a small percentage of rays is observed. The tracheids exhibit smaller diameter in latewood compared to earlywood, with a ratio between them of about 2. The average cell diameters are as follows: (heartwood) 39.4 ± 4.2 μm in earlywood and 21.4 ± 5.2 μm in latewood, and (sapwood) 44.7 ± 4.7 μm in earlywood and 20.9 ± 4.8 μm in latewood. These measured lumen diameters are consistent with those given in (Ramage et al. 2017; Vahey et al. 2007) for Douglas-fir. The cell length (along the L-axis) is approximately equal to a few millimeters and the tubular tracheids are closed at their tips but connected to each other via bordered pits on their lateral sides. The pits are located regularly along the tracheid cells. Most of bordered pits of adjacent tracheid cells in heartwood are closed in the earlywood and opened in the latewood, whereas in sapwood they are opened both in the early and latewood (Almeida et al. 2008; Sedighi-Gilani et al. 2014). Through a quantitative analysis with Douglas-fir, it has been shown in (Elaieb 2014) that about 65% of pits are open in sapwood but only 23% in heartwood. Note that the rays contain a smaller number of pits in the crossing-field which are connected to the tracheid cells. They may provide a path for internal flow, but since they are perpendicular to the main flow direction of the present study, we assume that their role is here negligible as considered in (Wardrop and Davies 1961).

2.2 Wood samples and liquid

Two kinds of samples have been used: on the one hand, small cubes sawn along the anisotropic directions, R, T and L (1 × 1 × 1 or 2 × 2 × 2 cm³), for NMR relaxation measurements and characterization of the wood properties and, on the other hand, for the liquid imbibition tests, large samples with about 10 cm in longitudinal (L) direction, parallel to the imbibition axis, and about 4 and 2 cm in the tangential (T) and radial (R) direction respectively, with several visible growth rings. Tests have been duplicated to check the reproducibility of the results. Samples are all pre-conditioned in desiccators at 20 °C and at 44% Relative Humidity (RH) before testing. Note that for liquid imbibition tests, four of six sides of large samples are sealed with a water impermeable coating along the vertical sides parallel to the imbibition direction in order to avoid capillary effects between the external wood surface and the water bath, or possible water uptake from the lateral sides (Zhou et al. 2018). In this work, imbibition tests are performed with (deionized) water and three oils whose density, viscosity and surface tension at 25 °C are respectively: Water (1000 kg m⁻³, 0.001 Pa s, 0.073 N m⁻¹), Dodecane (740 kg mm⁻³, 0.00134 Pa s, 0.025 N m⁻¹), silicone oil 47V20 (950 kg m⁻³, 0.02 Pa s, 0.0206 N m⁻¹) and silicone oil 47V350 (970 kg m⁻³, 0.35 Pa s, 0.021 N m⁻¹).

As water and dodecane have close viscosities, the differences in dynamics of imbibition, if any, find their origin in differences in wood-liquid interactions or in penetration mechanisms. To compare these two liquids, small cubes are prepared and conditioned at two RH levels with saturated salt solutions (44% RH: Potassium carbonate, K₂CO₃ and 97% RH: potassium sulphate, K₂SO₄) or immersed in water or docedane oil for three days. MC of wood is given in Table 1. The values are obtained by drying all specimens at 103 °C, in an oven, until reaching a constant mass. For samples immersed in water or oil for three days, the accessible porosity Φ is the volume of total water or oil to sample volume (at 44% RH) ratio. These results show that the values seem to be quite similar for heartwood and sapwood. However, these results are related to the scale of the used samples and the sample preparation by sawing may slightly increase the accessibility of fluid inside wood by opening some tracheids (Choong et al. 1975). Moreover, swelling coefficients are measured for samples subjected to RH (Table 2). These swelling coefficients are in accordance with literature (Jamaaoui 2017; MacLean 1958). Concerning dodecane oil, no swelling is observed.

2.3 NMR relaxation measurements

For NMR measurement, small sample is inserted in a 18-mm diameter glass tube in which the humidity level is imposed (same value as for sample preparation) during the NMR relaxation experiment. This glass tube is then inserted into a Bruker Minispec MQ20 spectrometer at 0.5 T, corresponding to a resonance frequency of 20 MHz for ¹H. The T₂ relaxation measurements of the wood sample are performed using a Carr–Purcell–Meiboom–Gill (CPMG) NMR sequence by carrying out 10,000 echoes with an echo time of 0.5 ms. A repetition time of 12 s was used (much higher than five times T₁ in order to prevent sample heating), eight averages were used. The NMR data are post-treated by means of an Inverse Laplace Transform (ILT) algorithm, which converts relaxation signal into a continuous distribution of T₂ values. For more details on the used homemade computer program and the artifacts of this technique, see (Faure and Rodts 2008).

2.4 Free water and oil distribution from MRI

Large wood samples are immersed in liquid to a depth of about 5 mm. In case of oil, the wood sample is placed in a glass Petri dish and MRI profiles are determined continuously. For water, the imbibition test is performed outside the MRI apparatus and MRI measurements are carried out at different times. The sample is put on a plastic sample support whose vertical position can be adjusted in order to be placed inside the MRI system. Measurements are performed at a vertical MRI spectrometer (DBX 24/80 Bruker) operating at 0.5 T and equipped with a ¹H birdcage radio frequency coil of 20 cm inner diameter, with the sample located at the magnetic center of the gradient coil (a BGA26 Bruker, 26 cm inner diameter, 50 mT/m gradient strength). As NMR relaxation times depend on the magnetic field strength, they are in principle the same in NMR relaxation and MRI experiments since both equipments have the same magnetic field.

The water or oil 1D profiles along the sample axis (Supplementary Figure 1.1) are measured by means of a spin-echo sequence, with an imaging gradient in the vertical direction, and repeating the profiling process over 16 successive echoes created by a series of π pulses separated by a fixed echo-time TE = 3.47 ms, and selected by means of 32-step duplex cogwheel phase cycling scheme (Levitt et al. 2002). One measurement then provided a series of 16 profiles recorded at successive times TE, 2TE,…, 16TE during the spin-spin relaxation process, with a field of view of 16 cm and a space resolution of 1.25 mm. A repetition time of 7 s was used and 32 averages were measured. Signal intensity was calibrated using a glass tube of known diameter filled with water or oil (using a repetition time of 12 s and 128 averages). In the case of water, due to the short relaxation time of bound water regarding TE, only free water is detected. A monoexponential or biexponential fit was then used to quantify the amount of liquid inside wood taking into account the relaxation times T₂ (see below).

The 2D distribution (image) of free water or oil was observed by means of multi-slice 2D MRI during the imbibition test. 2D MRI vertical slices of 2 mm thickness with 2-mm interval between them (parallel to RL plane) passing through the wood sample with space resolution equal to 0.47 (radial and tangential) × 2.19 (longitudinal) mm are taken at different times during imbibition (Supplementary Figure 1.1). A multi-slice multi-echo (MSME) pulse sequence acquiring eight echoes was used with an echo time of 10 ms and a recycle delay of 600 ms. On purpose of enhancing the signal to noise ratio without increasing the measurement time, images intensities owing the each of the eight echoes were added to produce the final picture. This picture can only be used for the qualitative purpose of seeing where the fluid is. Note that in the case of water, this weighing enhances the signal intensity of water in the large lumens of the earlywood due to longer T₂ time, which will be of key importance for data interpretation.

2.5 Bound water distribution from swelling measurements

To identify and quantify bound water distribution along the wood samples during water imbibition tests with large samples, it is proposed to use swelling measurements after some preliminary analysis providing the relation between the deformation to the bound water content for small samples subjected to RH as done by (Zhou et al. 2018). The sample swelling is measured along the radial (R) and tangential (T) directions every 5 mm along the longitudinal direction (L) using a micrometer (Mitutoyo) with a precision of 0.01 mm for large samples subjected to imbibition tests. For each distance, two different locations along the longitudinal direction are considered to obtain an average value for both directions R and T.

Figure 1 shows the linearity of the relation observed between the bound water mass and the corresponding sample volume increase on small samples. This result allows to determine a “coefficient” of bound water mass per unit volume increase, which we will use later on to translate the sample deformation during imbibition tests in bound water. Furthermore, the calculated swelling coefficients (Table 2) show that the variation of the volume may be only evaluated from the measurements of the dimensions along the radial and tangential directions, as the swelling coefficient is negligible along the longitudinal direction. As no swelling is observed during oil imbibition tests, this further supports the idea that strains are strictly related to bound water during water imbibition, and this means that MRI profiles for oil imbibition will in principle show the full amount of oil impregnating the sample. The total water mass entering the samples measured by weighing is compared to the bound water mass evaluated from volume variations plus the free water mass in wood determined from integration of the MRI 1D profiles (Figure 2). It appears that the total water content entering the sample during imbibition test is very close to the amount of bound water and free water inside wood. This confirms a very good accuracy in quantifying the total free water in wood from 1D MRI method as well as in computing bound water amount from deformation measurements.

Figure 1:

Additional mass Δm of bound water recorded by weighing as a function of volume increase ΔV (determined on small samples) for heartwood and sapwood between 44 and 97% RH.

Figure 2:

Free water mass (from MRI) plus bound water (from swelling measurements ΔV) compared to the total water uptake determined by weighing, at different times during imbibition tests with large samples for heartwood (black or blue circle symbols for two tests) or for sapwood (black square symbols).

2.6 Standard imbibition tests by weighing

A bottom open surface of the sample is placed (along a height of about 5 mm) in contact with a bath of liquid (water or oil) covered by a film to avoid evaporation (Supplementary Figure 1.2). Liquid can then progress inside wood along its longitudinal direction. The other open surface is connected to a precision balance via a hanging wire. The mass evolution of the sample is recorded by a precision balance through an automatic recording system. The imbibition test is carried out at room temperature (20 °C). Note that the apparent mass has to be corrected to get the effective mass due to a buoyancy force varying with the liquid level in the bath (Supplementary Section 1).

A quantitative analysis of the imbibition tests may be done through the Washburn model as explained below (for more details, see Zhou et al. 2018 and 2019). At the front of penetration inside the sample (interface), the average capillary ascent of a liquid in a porous material (with cylindrical conduit of radius R) is driven by the capillary pressure (neglecting ambient pressure): Δp = −2σ cosθ/αR, where σ is the surface tension, α a factor related to the pore shape and θ the contact angle. This driving force acts over a distance of penetration h, which induces a pressure gradient p/h. The Darcy’s law then expresses the balance between the pressure gradient and the viscous resistance with Δp/h = μV/k where μ is the liquid viscosity, V the mean flow velocity through the sample, and k the permeability of the porous medium. Assuming that the liquid advances as a front saturating the lumens below a distance h = Ω/εS increasing in time (where Ω is the volume of water entered in the sample and S the section of the sample), V = (dΩ/dt)/S = ε (dh/dt), with ε the (accessible) medium porosity. Integrating the Darcy’s law we deduce that in a first regime controlled by capillary effects (negligible gravity effects) we have:

with λ=2kεσcosθ/αR , which is independent of the liquid viscosity.

In a second regime controlled by gravity effects, h tends to a plateau h_max determined by:

Then, since the main geometrical characteristics of the hydraulic system are known, the fundamental unknown of the problem is the contact angle, which may be fitted to either the dynamics or the maximum height of ascent. Note that if the porosity  ε is not taken into account in the previous relationships, this amounts to just consider an “apparent” height for the progression of liquid.

For the flow through a cylindrical capillary, we have α=1/2 (the meniscus is a spherical cap) and the velocity profile can be computed exactly (Poiseuille law), which directly gives the relation between the pressure gradient and the mean velocity, from which we deduce the permeability for a set of parallel capillaries:

3.1 NMR relaxation times for dodecane and water

Figure 3 presents the distribution of NMR intensity as a function of T₂ for heartwood and sapwood at 44% RH and 97% RH and after three days of immersion in water or dodecane.

Figure 3:

NMR T₂ relaxation times for heartwood (a) and sapwood (b) under 44 or 97% RH and after three days of immersion in water or dodecane.

In the case of immersion in water, three main peaks are observed for heartwood and sapwood. The first peak with a T₂ value surrounding 1 ms corresponds to the bound water at 44 and 97% RH and after three days of immersion in water (Gezici-Koç et al. 2017). This peak is located at the very limit of T₂ times that can be measured with the CPMG sequence, and is just a -non quantitative – clue of a – true – fast relaxing peak of bound water existing for T₂ < 1 ms. When the bound water content increases, the true peak increases in intensity and is shifted to higher T₂ due to the increased mobility of water molecules in cell walls (Bonnet et al. 2017), thus leading to an increase and a small shift of the apparent peak which can be clearly observed. Two other wide peaks are identified for both heartwood and sapwood. As admitted in literature (Almeida et al. 2007 and Gezici-Koç et al. 2017), these peaks are attributed to free water. They are located at roughly 10 and 50 ms for heartwood and 17 and 70 ms for sapwood. These two peaks depend on the lumen sizes, and the longer T₂ is attributed to earlywood (Kekkonen et al. 2014; Menon et al. 1987). Note that, for heartwood, the two peaks are well-separated, but not for sapwood. Variability in pore sizes maybe simply related to uncertainty in the ILT processing but also to the seasonal variability of the wood structure. For sapwood, the T₂ distribution may reflect the polydispersity of the pore sizes (Gezici-Koç et al. 2017) and the presence of a transition zone between earlywood and latewood.

In the case of dodecane immersion, essentially one peak is obtained, situated at relatively large T₂-values (about 955 and 992 ms for heartwood and sapwood respectively). Here the surface relaxivity (i.e., the proportionality constant between T₂ decay time and pore size) is very small so that the influence of pore size on the T₂ relaxation time of dodecane is weak (Zhou et al. 2018). Also, a small peak at low relaxation time is visible in each case, which likely corresponds to bound water as the sample is pre-conditioning at 44% RH.

3.2 Distribution of dodecane and free water from MRI and of bound water from swelling measurements

Figure 4 shows MRI 2D images of dodecane and water entering in heartwood and sapwood samples at different times. Furthermore, the 1D curve profiles (Figure 5) provide a quantification of their penetration into samples as a function of time. In the case of water imbibition, as explained previously, only free water is observed with MRI, and bound water profiles are obtained from swelling measurements.

Figure 4:

2D MRI images (longitudinal-radial plane) of dodecane oil and free water distribution in wood samples at different times during imbibition tests for heartwood (a, c) and (b, d) for sapwood. The front of liquid penetration is indicated by a white arrow according to the 1D profiles given in Figure 5. A view of the sample cross section is inserted showing the correspondence between the main liquid paths and the sample structure (latewood and earlywood).

Figure 5:

1D MRI profiles of oil (dodecane) and water uptake at different times for heartwood (a, c) and sapwood (b, d).

In the case of dodecane imbibition for heartwood (Figure 4a) its penetration in earlywood is very limited (up to about 3–5 mm) and dodecane content seems to increase in this layer with time. Above 5 mm, dodecane seems to preferentially penetrate in latewood along the vertical axis of the sample up to the top of the sample. However, it remains that the MRI signal for the 2D images is very weak (same order of magnitude as the signal-to-noise ratio), and effectively the 1D profiles show a very limited amount of dodecane entering into the sample (Figure 5a). As the relaxation time is the same in early- and latewood, then a monoexponential fit is used to quantify the total amount of oil and it is not possible to distinguish in both latewood and earlywood. In the case of sapwood, the 2D images clearly show that some dodecane reaches the top of the sample after only 3 h of imbibition test, in agreement with the 1D profiles with higher content of dodecane oil (Figures 4b and 5b). Moreover, dodecane seems to preferentially penetrate in the earlywood, but there may be some penetration in latewood, not well visible on these images. The differences of dodedane penetration into heartwood or sapwood may be explained by the fact that there are more open pits in sapwood, as explained in the section “Wood materials”.

These results also show that for both types of wood, dodecane apparently does not progress in the form of a uniform (straight) front saturating the sample at larger heights in time, as expected from the standard Washburn imbibition process. However, dodecane imbibition profiles showing a liquid profile extending widely throughout the material but of level increasing in time, suggest that the material imbibition proceeds by a progressive increase of the local saturation throughout the material. This aspect of the liquid profile results from the heterogeneity of the material, while in each tracheid the liquid progresses as a straight front: the dynamics of climbing varies from one tracheid to another, so that along some axis the liquid may have already reached the sample top while in another place the liquid is much less advanced. Such a heterogeneous distribution of front advances can predict this profile aspect.

According to the 2D images for free water (Figures 4c and 4d), the water front is climbing in a jagged manner and clearly corresponds to the location of earlywood and latewood layers. The heartwood provides an extremely slow water uptake which seems limited to a height of about 5 mm after six days, with a progression front slightly higher in latewood. For sapwood, a higher water uptake is observed with a water front reaching up to 35–40 mm over the same duration. However, as explained previously, two T₂ relaxation times for free water are observed due to the presence of different lumen sizes. By this means we can now distinguish the distribution of free water in each type of wood in time using a bi-exponential fit (Figure 5c and 5d). It appears that in sapwood the free water advances over significant distance in both wood types (earlywood and latewood); in contrast, in heartwood, the free water seems to hardly be able to reach a height larger than a few millimeters. These observations are consistent with the qualitative observations from 2D MRI images.

Furthermore, according to the profiles of bound water, the most important result is that the bound water distribution extends farther than the profile of free water, an effect particularly clear for heartwood. So it can be considered that bound water at least partly propagates by itself longitudinally through the cell walls. In particular, bound water uptake seems to be quite constant up to the front of penetration of free water, with a moisture content close to the FSP (taking into account the moisture content at 44% RH, Table 1). This suggests that basic characteristics of water transport in softwood qualitatively similar to that in hardwoods (Zhou et al. 2018), i.e., a dynamics of imbibition mainly governed by the longitudinal progression of bound water in the sample: free water can advance through the vessels (considered as opened capillary tubes with unlimited length) only when cell walls are saturated with bound water. However, in the case of softwood, the mechanisms for liquid water transport may be quite different as the structure is different with tracheids, with limited length, closed at their ends and connected to each other by pits.

To conclude, in coherence with Sedighi-Gilani et al. 2012 and 2014, the water uptake is significantly larger for sapwood than for heartwood. This result is similar for oil penetration. The liquid transport penetration in heartwood and sapwood may depend on open or closed pits. Furthermore, for both materials, larger oil and water contents are localized in the first 5 mm, due to possible effect of preparation of sample. Indeed, sawing may slightly increase the accessibility of fluid inside wood by opening tracheids (Choong et al. 1975). The aim of the next section is to precise the involved mechanisms for both materials, through Washburn model and from the standard imbibition tests.

3.3 Discussion through standard imbibition tests by weighing

Imbibition results for water and oil are expressed in terms of the liquid volume entering into wood, per sample area (expressed as “apparent height”) as a function of the time rescaled by the liquid viscosity (Figure 6). This representation is useful to discuss the imbibition dynamics of different liquids with regards to the Washburn model (Equation (1)). The data deduced from MRI experiments are also shown in the same graph and an excellent agreement is found between these data and those obtained from mass measurements. In Supplementary Figures 2.1 and 2.2, the volume of water or oil per sample area as a function of time and 2D MR images for the three oils at the end of the imbibition tests are also shown for further discussions. Note that for a cylindrical capillary containing, from place to place perturbations (e.g., pits) of its shape over very short distance, the maximum height of ascent is that of the main cylinder, since the liquid must be able to climb between two successive perturbations, and thus Equation (2) is still valid with R the main cylinder radius. Furthermore, the permeability may be affected (decreased) by these perturbations as they induce further viscous dissipation during the liquid flow through the whole system. It follows that the dynamics may be damped with regards to that expected for the flow through a simple straight conduit but the Washburn law remains valid.

Figure 6:

Absorbed liquid volume per unit cross-section Ω/S area against the time per viscosity t/μ of water, dodecane oil and two silicone oils for sapwood (a) and heartwood (b) samples. The dashed line of slope 2 in (a) is a guide for the eye.

Concerning sapwood (Figure 6a), the curves for oils of different viscosities (with only slight differences in surface tension and likely close contact angles) superimpose along a master curve when the time is rescaled by the viscosity. This demonstrates the validity of the assumption of a viscous flow through a given hydraulic network at the origin of liquid uptake (for example in consistency with the form of Equation (1)). In contrast, the imbibition curve for water, with a surface tension different from that of oil by a factor about 3, is situated at rescaled times about 100 larger than the master curve for oils. The point may be more directly appreciated from the representation of water uptake as a function of time (Supplementary Figure 2.1): dodecane and water have a similar viscosity but a surface tension different by a factor 3, but the water uptake is slower by several orders of magnitude than that of oil. This means that in that case the flow is not dependent on the same physical effects underlying the Washburn approach for imbibition. This result is discussed in the following trough Washburn model. A plateau in the imbibition curve is clearly observed for Dodecane around Ω/S = 1.3 cm (Figure 6a, Equation (2)). Considering the accessible porosity of sapwood determined on small samples (Table 1) for oil (i.e., 29.7%), this corresponds to an effective average maximum height of ascent around h_max = (Ω/ɛS) = 4.4 cm. This may be in agreement with the 2D MRI images of Dodecane oil (Figure 4), which show liquid signal at larger height, if we assume that the tracheid diameters are somewhat dispersed around a mean value, allowing different final heights of ascent around this one, up to the sample height (i.e., 10 cm). It is also possible that the accessible porosity, determined from oil impregnation in small samples, was somewhat overestimated due to tracheid opening when sawing, as explained previously. Finally, note that the results for oils of different viscosities are consistent with the 2D MRI images providing the qualitative aspect of liquid ascent (Supplementary Figure 2.2). From Equation (2), using R = 15 μm for the average radius of tracheids (without distinguishing latewood and earlywood), a contact angle of ϴ ≈ 84° is calculated. Then, from the slope λ of the imbibition curve (Equation (1)), the permeability value of the Washburn model may be deduced, i.e., k = 0.35 × 10⁻¹² m². It is worth noting that this value is of the same order as the permeability of a set of simple capillaries with the same mean radius (Equation (3)), i.e., k = ɛR²/8 = 8.4 × 10⁻¹² m², which confirms assumption of oil flow through tracheids. The smaller permeability value obtained here would then likely be explained by the existence of pits and direction changes all along the hydraulic network leading to additional pressure drops. Finally, this tends to confirm that in sapwood the hydraulic network is made of tracheids connected by open pits. As explained above, the oil imbibition process maybe due to the heterogeneity of the tracheid sizes, which leads to a distribution of Washburn imbibition with different characteristic times. It might alternatively be due to an imbibition process involving the fast ascent of some fluid towards large heights coupled with a more progressive imbibition in smaller pores at the different heights. To sum up: Washburn model is valid along each series of connected tracheids, which explain that the observed dynamics is consistent with the theoretical prediction, associated with a front step propagation in this series, but the different dynamics in each of them may give the impression of a partial saturation at different levels.

For water imbibition in sapwood, we observe a maximum apparent height (Ω/S) of ascent similar to that found for oils, which leads to a similar value for the contact angle. Since from such tests, as water (bound or free) cannot be distinguished, the total accessible porosity of the system for water is considered (about 41.9%, Table 1), to compute the maximum height of ascent, which resumes to considering that both phases approximately fill their own porosity at the same rate. The predicted front of penetration (Equation (2)) is then: h_max = (Ω/ɛS) = 3.0 cm. This value is in agreement with the (average) front of propagation determined with MRI 1D profiles for both free and bound water, for about three days of imbibition tests (Figure 5d). A contact angle of ϴ ≈ 88° is then obtained, which is the hallmark of a poor wetting. Then, from the slope λ of the imbibition curve, we deduce the permeability value of the Washburn model, i.e., k = 3 × 10⁻¹⁵ m². This permeability is several orders of magnitude lower than that expected for a set of simple capillaries with the same mean radius (Equation (3)), i.e., k = ɛR²/8 = 11.8 × 10⁻¹² m². It is also several orders of magnitude smaller than the permeability observed with oil, which cannot solely be explained by the difference of accessible porosity to water. It is worth noting that, although there is some significant uncertainty on the effective maximum height of ascent in the tracheids, this does not affect this conclusion, i.e., using a different value for the accessible porosity during the process would still lead to this very large discrepancy between the apparent permeability and that associated with a standard Washburn ascent along the tracheids.

Imbibition results for heartwood strongly differ from those in sapwood (Figure 6b). First of all, the maximum height reached is significantly lower (about three times) than that in sapwood over similar duration, both for oil and water. Another remarkable point is that the curves for the different oils or water do not superimpose when the time is rescaled by the viscosity. These results may not be explained by the variability of samples (for instance the density due to different proportions of latewood as mentioned above). In fact, the shift between them approximately correspond to the viscosity factor, which means that the curves would roughly superimpose if represented as a function of time (without rescaling by the viscosity). And effectively, when the volume of oil per sample area entering into sample is represented as a function of the (non-rescaled) time the curves superimpose (Supplementary Figure 2.1). This implies that in that case the uptake of oil is independent of viscous effects, and thus cannot be described by the standard Washburn approach which relies on a balance between capillary and viscous effects. The estimation of the permeability gives value of the same order as that observed for water in sapwood. Altogether these different observations confirm that here the pits are preferentially closed, so that there is only negligible flow through the hydraulic system up to the top of the sample. Concerning water, as for sapwood, from MRI measurements, the bound water profile progresses in advance of free water, but in this case, the dynamics of free water imbibition seems not to be mainly governed by the longitudinal progression of bound water in the sample. Then only a small amount of water can penetrate in the structure, essentially by diffusion through cell walls. However, it is not clear how it can occur for oil, considering that oil essentially penetrates in the first 5 mm, the amount above 5 mm being significantly lower due to closed pits. The preferentially penetration in the first 5 mm layer may be explained by the existence of open tracheids following cutting during the sample preparation. Above a few millimeters, liquid hardly progress in the tracheids because of preferentially closed pits and with their limited length.

3.4 Discussion of the mechanisms of free water imbibition

All these results obviously mean that the propagation of water does not rely on the basic physical assumptions underlying the Washburn model. Instead we have to consider that the capillary transport may be damped by some effect. Since the pits are moist sensitive it may be suggested that pits could tend to close when in contact with water while letting oil move through. However, in that case we would expect some similar dynamics between heartwood (for which pits are preferentially closed) and sapwood. This is not what we observe (Figure 6b): the dynamics of water imbibition is apparently about six times faster in sapwood than in heartwood. Moreover, in the case of heartwood, there is almost no free water penetrating the sample within the duration of the test (Figure 5c), as a result of closed pits, whereas a significant amount of free water apparently penetrates the sapwood region, meaning that in contrast pits effectively remain open in sapwood (Figure 5d).

Actually, it is worth noting that bound water progresses through the sample more rapidly than free water in heartwood and sapwood (Figure 5c and 5d) and water uptake seems to be governed by bound water diffusion and not by capillary flow as expected by the Washburn law. This is similar to an effect suggested for aspen heartwood by (Johansson and Salin 2011) but not for aspen sapwood. This result is still not fully understood. However, as explained above, the climbing of free water is allowed only when the free water is in contact with cell-walls which MC is close to the FSP, otherwise there is a negligible displacement of free water; under such conditions the dynamics is governed by the coupling between the longitudinal diffusion of bound water and the progressive advance of free water.

According to Zhou et al. 2019, this is associated with a strong change of the wetting properties with the concentration of bound water: X-ray synchrotron images indeed showed that the apparent contact angle during imbibition was close to 90° while it was seen to be much lower when the cell walls are saturated with bound water, which explains the need of sufficient longitudinal diffusion of bound water before the water can further progress through the lumens. Finally, note that these results seem to be supported by the MRI observations of Dvinskikh et al. (Eng. Structures, 2011) and Eitelberger et al. (2011) for a spruce sample simply put in contact with air at a large RH. In that case, even in the absence of free water in contact with the sample, bound water was observed to rapidly propagate in the longitudinal direction, showing its ability to diffuse relatively rapidly thus keeping the possibility to control the liquid transport in an imbibition process.