Unveiling moisture transport mechanisms in cellulosic materials: Vapor vs. bound water

Abstract

Natural textiles, hair, paper, wool, or bio-based walls possess the remarkable ability to store humidity from sweat or the environment through "bound water" absorption within nanopores, constituting up to 30% of their dry mass. The knowledge of the induced water transfers is pivotal for advancing industrial processes and sustainable practices in various fields such as wood drying, paper production and use, moisture transfers in clothes or hair, humidity regulation of bio-based construction materials, etc. However, the transport and storage mechanisms of this moisture remain poorly understood, with modeling often relying on an assumption of dominant vapor transport with an unknown diffusion coefficient. Our research addresses this knowledge gap, demonstrating the pivotal role of bound water transport within interconnected fiber networks. Notably, at low porosity, bound water diffusion dominates over vapor diffusion. By isolating diffusion processes and deriving diffusion coefficients through rigorous experimentation, we establish a comprehensive model for moisture transfer. Strikingly, our model accurately predicts the evolution of bound water's spatial distribution for a wide range of sample porosities, as verified through magnetic resonance imaging. Showing that bound water transport can be dominant over vapor transport, this work offers a change of paradigm and unprecedented control over humidity-related processes.

Keywords: cellulose-based material; magnetic resonance imaging; water transfers.

Fig. 1.

Schemes of setups for (A) steady-state diffusion through the sample and (B) for drying tests. n is the relative humidity in the air regions, and s is the moisture content, the ratio of (bound) water mass to the dry mass of the solid. (C) Scanning electron microscope image of the sample structure (porosity 0.5).

Fig. 2.

Apparent diffusion coefficient as measured from steady-state vapor flux through sample (see Fig. 1a), as a function of material porosity. The error bars were calculated from an estimation of the uncertainty on the determination of the steady-state conditions. The inset shows an example ($\epsilon =0.66$) of the sample mass (including the container) variation over time with the constant rate of water extraction (steady state) reached after some time. The dotted line is a guide for the eye. The dashed line corresponds to the theoretical prediction assuming simple vapor diffusion through the porous structure (see text). Note that for this prediction, since it was not possible to make measurements in the uncompressed state, $D({\epsilon }_0)$ was assumed to be equal to the value extrapolated from data to ${\epsilon }_0$ (the initial porosity of the sample, i.e. before compression).

Fig. 3.

Changes of orientation of (A) a fiber from its initial to final position in a spherical coordinate frame and (B) changes of a schematic vapor path in 2D through the fiber network, resulting from a compression parallel to the evaporation axis (z).

Fig. 4.

Saturation vs. time for drying tests with air-filled (blue) or oil-filled (yellow) samples at different porosities. The dotted lines correspond to a simple diffusion model with the (constant) bound water transport diffusion coefficient values shown in Fig. 6 for the corresponding porosities.

Fig. 5.

Moisture content vs. relative humidity for sorption and desorption tests. The continuous line corresponds to the equation $s=0.127\times n+{(n/1.227)}^{10}$.

Fig. 6.

Diffusion coefficient of bound water (circles) as determined from drying tests with oil-filled samples (data of Zou et al. (52) multiplied by $(1-\epsilon )$) and diffusion coefficient of vapor (squares) as deduced (see text) from steady-state transport experiments through our fiber stack samples at different porosities. The dotted line is the model ($D_{\mathrm{b}}=(2.43-3.29\epsilon +8.81{\epsilon }^2)(1-\epsilon )\times {10}^{-10}{\text{m}}^2{\text{s}}^{-1}$) fitted to bound water diffusion coefficient data and the continuous line is the model fitted to vapor diffusion coefficient data (for $\epsilon <0.27$, $D_{\mathrm{v}}=0$; for $\epsilon >0.27$, $D_{\mathrm{v}}=(15.6\times (\epsilon -0.27)-12.9\times {(\epsilon -0.27)}^2+84.9\times {(\epsilon -0.27)}^4)\times {10}^{-6}{\text{m}}^2{\text{s}}^{-1}$). The error bars on the vapor diffusion coefficient data represent both the uncertainty on the wet-cup tests (see Fig. 2) and the maximum potential error associated with the discrepancy between the model (dotted line) and each data point for the bound water diffusion coefficient. The short dotted line is the model for the vapor diffusion coefficient as presented in the text.

Fig. 7.

Bound water spatial distribution over time in cellulose fiber stacks of different thicknesses and porosities (see legend). The symbols correspond to experimental data obtained from MRI measurements, while the continuous lines correspond to the numerical solutions of the model (Eqs. 4 and 5) with boundary condition 8 using the parameters (diffusion coefficients) deduced from the models fitted to the data in Fig. 6.

Fig. 8.

Saturation vs. time data (symbols) during drying tests of fiber stack with different porosities. The continuous lines correspond to the model (Eqs. 4–5) predictions. For each porosity value, open and crossed symbols correspond to two tests under the same conditions; the difference between the two sets of data illustrates the uncertainty on measurements.

Fig. 9.

Diffusion coefficient for water transport through a hygroscopic fiber stack as a function of the porosity for two ranges of MC: (A) $s<0.11$ and (B) $0.11<s<0.27$. The respective fractions of diffusion coefficient associated with bound water (lower curve at largest porosity) and vapor transport (intermediate curve at largest porosity) according to the two terms on the right-hand side of the expression 5 are also shown. The critical porosity for the transition between the two regimes (dominant bound water transport to dominant vapor transport) is indicated by a vertical dashed line.

Fig. 10.

Dominant transport regime as a function of the porosity and the local slope of the sorption curve. The continuous line is the critical porosity for the transition from a bound water-dominant to a vapor-dominant transport regime as deduced from graphs analogous to those of Fig. 9 for different values of the slope of the sorption curve for the current MC value, i.e. α (see inset).