Water diffusion in drying wood

Vascular plants, a vast group including conifers, flowering plants, etc, are made of a cellular hygroscopic structure containing water in the form of either free (i.e. in a standard liquid state) or bound (i.e. absorbed in the cell-walls) water. From Nuclear Magnetic Resonance techniques we distinguish the dynamics of bound water and free water in a typical material (softwood) with such a structure, under convective drying. We show that water extraction relies on two mechanisms of diffusion in two contiguous regions of the sample, in which respectively the material still contains free water or only contains bound water. However, in any case, the transport is ensured by bound water. This makes it possible to prolong free water storage despite dry external conditions, and shows that it is possible to extract free water in depth (or from large heights) without continuity of the free water network.

M. Cocusse, M. Rosales, B. Maillet, R. Sidi-Boulenouar, E. Julien, S. Caré, P. Coussot, Two-step diffusion in cellular hygroscopic (vascular plant-like) materials, Science Advances, Vol 8, Issue 19 (2022) – https://www.science.org/doi/10.1126/sciadv.abm7830

Experimental set up and measurement techniques used. Scheme of the experimental set up with the sample inside the magnet (a), and main NMR (T2 distribution) (b) and MRI (1 D profile) (c) sequences used to explore the water content during sample drying.
Internal moisture content characteristics during wood drying. Water transfers during drying of wood sample under weak (a,c,e) or strong (b,d,f) dry air flux, with 1 cm long samples of respective initial MC 67% and 62%: (a,b) relaxation time distributions ((a) every 80 min; (b) at 21, 42 min, then every 21 min from 2h07), the arrows indicate the time increase, the continuous lines correspond to the period during which free water exists in the sample, the dashed lines to the next period; (c,d) evolution of each water type as a function of time, as deduced from the integration of the distributions over the corresponding range of relaxation times (see separation dashed lines in (a,b)) and expressed as the fraction of water mass relatively to the initial total water mass; the resulting mass flux in the constant drying rate period is ; note that the time scales are not the same for the two tests; the dashed straight lines are guides for the eyes; (e,f) 1D distribution profiles of free water in time, successive profiles from top to left correspond to successive times (every 105 min for (e), every 21 min for (f)). The dry air flux is imposed along the free surface of the sample situated at a zero depth. The inset in (a) shows the measured ratio (squares) of average relaxation time over the free water domain to moisture content (rescaled by initial values) as a function of the moisture content. This ratio computed for two model situations (cylindrical tracheid, of length 5 times its diameter) is also shown by continuous lines: (top) dewetting, (bottom) no dewetting.
Free and bound water distributions in time. 1D water distributions in time (from top to bottom) during drying of a 3 cm long wood sample. The dry air flux is imposed along the free surface of the sample situated at the depth zero. (a) Total water measured from the SPI (Single Point Imaging) sequence (see text); first 5 profiles every 81 min, then every 162 min up to the dash-dotted profile, and afterwards every 324 min. The horizontal dotted line marks the apparent transition between two regions of transport in the sample (see text). (b) Free water measured from the ME sequence at same times. (c) Bound water as deduced by subtraction of free water from total water distributions (see text); first profile at initial time, next profile at 11h20, then every 648 min. The profiles are drawn as continuous lines when some free water is still present in the sample, and as short-dashed lines when there is only bound water. The dashed and dash-dotted lines in all graphs correspond to the distributions of the different water types at respectively 22 h and 155 h. In the latter case this corresponds to the last profiles for which free water is still present.

Dynamic NMR Relaxometry: a tool for quantifying water phase changes, migration and wetting in porous media

Porous media containing voids which can be filled with gas and/or liquids are ubiquitous in our everyday life: soils, wood, bricks, concrete, sponges, textiles, etc. It is of major interest to identify how a liquid, pushing another fluid or transporting particles, ions or nutriments, can penetrate in, or be extracted from, the porous medium. High resolution X-ray microtomography, neutron imaging, or magnetic resonance imaging, are techniques allowing to get, in a non-destructive way, a view of the internal processes in non-transparent porous media. Here we review the possibilities of a simple though powerful technique which provides various direct, quantitative information on the liquid distribution inside the porous structure and its variations over time due to fluid transports and/or phase changes. It relies on the analysis of the details of the NMR (nuclear magnetic resonance) relaxation of the proton spins of the liquid molecules and its evolution during some process such as imbibition, drying, phase change, etc, of the sample. This rather cheap technique then allows to distinguish how the liquid distributes in the different pore sizes or pore types, and how this evolves over time; since the relaxation time depends on the fraction of time spent by the molecule along the solid surface this technique can also be used to determine the specific surface of some pore classes in the material. The principles of the technique and its contribution to the physical understanding of the system and the processes are illustrated through examples: imbibition, drying or fluid transfers in a nanoporous silica glass, large pores dispersed in a fine polymeric porous matrix, a pile of cellulose fibers partially saturated with bound water, a softwood, and a simple porous inclusion in a cement paste. We thus show the efficiency of the technique to quantify the transfers with a good temporal resolution.

B. Maillet, R. Sidi-Boulenouar, P. Coussot, Dynamic NMR relaxometry” as a simple tool for measuring liquid transfers and characterizing surface and structure evolution in porous media, Langmuir, 38, 15009−15025 (2022) – Featured Article (invited) – Editor’s suggestion – Langmuir Cover


Schematic drawing of the different porous structures studied here: a) Silica glass; b) Porous bead packing; c) Large pores dispersed in a fine porous matrix; d) Cellulose fibers (black region corresponds to void); e) Softwood (the (solid) cell-walls are the darkest regions); f) Bead packing immersed in a cement paste. For (a), (b), (c) and (f) the dark regions represent the solid volumes, the white regions the void regions, filled by air or liquid. The curves on the right of each scheme shows the aspect of the corresponding evolution of the pdf of the transverse relaxation time during the drying (or setting for e)) of the system. Dotted lines are used to represent the pdf distribution in the smallest pore region or for bound water. The red arrow represents the process occurring in a first stage, while the green arrow represents the process occurring in a second stage.

Vapor diffusion and bound water desorption in drying cellulose fiber stack

Moisture transport and/or storage in clothes plays a major role on the comfort or discomfort they procure due to the resulting wetness or heat loss along the skin. Our current knowledge of these complex processes which involve both vapor transport and water sorption in the solid structure, is limited. This is in particular due to the open questions concerning the sorption dynamics at a local scale (for modelling), which lead to complex non-validated models, and to the challenge that constitutes the direct observation of these transports (for measurements). Here, through unique experiments, we directly observe the bound water transport in a model textile sample during drying with the help of an original Magnetic Resonance Imaging (MRI) technique. Despite the various physical effects involved this transport appears to follow a diffusion-like process. We then demonstrate theoretically that this process is described in details (at a local scale) by a simple model of vapor transport through the structure assuming instantaneous sorption equilibrium and without any parameter fitting, which finally brings a simple response to modelling. This in particular allows to quantify, as a function of simply measurable material parameters and air flux impact, the characteristic time during which the evaporation of sweat is accelerated by sorption, the time during which a textile constitutes a barrier against ambient humidity, or the conditions of mask humidification. These results open the way to a full characterization and prediction of fabric properties under different conditions, and to direct formulation of high performance materials by adjusting the material constituents.

X.Ma, B. Maillet, L. Brochard, O. Pitois, R. Sidi-Boulenouar, P. Coussot, Vapor-sorption Coupled Diffusion in Cellulose Fiber Pile Revealed by Magnetic Resonance Imaging, Phys. Rev. Applied 17, 024048 (2022) Editor’s suggestion – Featured in Physics: https://physics.aps.org/articles/v13/182 – Actualités CNRS : https://insis.cnrs.fr/fr/cnrsinfo/le-role-surprenant-de-leau-dans-le-sechage-du-bois PDF

Drying of liquid or suspensions in porous media

In paper or food industry and civil engineering, many products need to be dried at some steps of fabrication, i.e. the liquid initially contained in the material (a porous medium) has to be removed. Drying process should be controlled with great care, as it originates huge energy consumption (10% of the total consumption in industry) and it determines final material properties. Especially in civil engineering, depending on the situation two specific challenges should be addressed as follows: how to remove water from the material faster without increasing energy supply, and how to keep a certain volume of water inside the porous medium for longer times.

As a first step to understand drying it is useful to consider the ideal situation of a simple bead back initially filled with pure water and submitted to an air flux along its free surface (one of its side). Three characteristic velocities can be usefully distinguished: the rate of evaporation per unit surface imposed by the air flux, Ve, the fluid velocity through the porous medium imposed by some capillary disequilibrium (Laplace pressure due to different meniscus sizes from on extremity of the sample to the other), Vc, and the rate of evaporation due to diffusion through the sample when the first liquid interface is situated at a distance H from the sample free surface, Ve*.

Initially, when the material is saturated, the drying rate is imposed by the air flow as long as Ve is larger than Vc (see Figures 1 and 2). This results from two effects: in that case any withdrawing of liquid around the free surface leads to a homogeneous redistribution of the liquid throughout the sample as a result of capillary effects, with a sufficiently short characteristic time as compared to that of evaporation; and the rate of evaporation from a surface made of many small patches close to each other is close to that from the same surface covered by a uniform liquid film. This first regime of drying, for which Vd=Ve, is the constant rate period. When Ve becomes smaller than Vc the liquid has not enough time to redistribute homogeneously and in particular to reach the free surface of the sample, which implies that a thin dry region now forms there (see Figure 1). This dry region implies that the rate of drying adjusts to Ve* with a small value of H, which progressively grows as the saturation decreases. We thus are in the second regime, where we now have Vd=Vc (see Figure 2). Finally, the rate of liquid transport by capillary effects becomes too small so that the dry front progresses significantly and the rate of drying is now imposed by this advance, we have Vd=Ve* (see Figures 1 and 2). [See Paper 38]

Figure 1
Figure 2

As soon as the substance to be evaporated is not a pure liquid drying can lead to more complex processes affecting the drying rate and the structure of the material.

The simplest situation is that of suspension of colloidal particles (see Figure 3). During drying the particles may be transported by the liquid as it moves towards the surface as a result of capillary reequilibration process? They then tend to accumulate in this region, leading to a gradient of concentration at the end of drying. Moreover, by accumulating particles in the upper region it creates a dry front, which induces a decrease of the drying rate more rapidly than with pure water.

The situation is more complex when the fluid is a paste. When the water moves out of it the paste becomes more concentrated and thus its behavior changes, it becomes more pasty. In some cases, i.e. for a kaolin paste (see Figure 4a) the capillary effects remains much larger than the yield stress of the suspension so that the drying characteristics remain quite similar to that for a pure liquid. This is likely so because the kaolin particles suspended in the paste can easily approach each other since the colloidal interactions are negligible. On the contrary, for a Carbopol gel (see Figure 4b) the suspended elements can approach each other only if they are submitted to high forces, likely larger than capillary effects.

As a consequence it seems that the gel tends to form a dry region in the upper layer of the sample before being able to reequilibrate the liquid distribution in the sample. Finally the drying rate is much larger (about three times) than for the kaolin paste (see Figure 5), even though they had the same initial yield stress.

Figure 3. Porous medium made of 257µm sodiocalcic glass beads packing homogeneously filled with a coffee suspension (3.5% weight in water) before (a, beads, water, coffee) and after (b, beads, coffee) drying under natural room convection and ambient temperature. [Paper 123]
Figure 4a: Water saturation profiles in time as measured by NMR for a kaolin sample (increasing time from top to bottom). The first seven profiles were measured each 42 min. after the beginning of the test, the others were measured each 120 min. [Paper 110]
Figure 4b: Density profiles as measured by NMR for the gel samples at different times during drying: (from top to bottom) 0, 3, 6, 10, 18, 21, 24, 28, 31, 34, 38, 66 days. [Paper 110]
Figure 5: Drying curves of analogous samples (height: 57mm ; average bead diameter: 300 microns) with different interstitial pastes : kaolin suspension (squares), bentonite suspension (circles), gel (stars). [Paper 110]