Two-step diffusion in cellular hygroscopic (vascular plant-like) materials

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

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.

Critical Role of Boundary Conditions in Sorption Kinetics Measurements

In order to characterize the hygroscopic properties of cellulose-based materials, which can absorb large amounts of water from vapor in ambient air, or the adsorption capacity of pollutants or molecules in various porous materials, it is common to rely on sorption-desorption dynamic tests. This consists of observing the mass variation over time when the sample is placed in contact with a fluid containing the elements to be absorbed or adsorbed. Here, we focus on the case of a hygroscopic material in contact with air at a relative humidity (RH) differing from that at which it has been prepared. We show that the vapor mass flux going out of the sample follows from the solution of a vapor convection-diffusion problem along the surface and is proportional to the difference between the RH of the air flux and that along the surface with a multiplicative factor (δ) depending only on the characteristics of the air flux and the geometry of the system, including the surface roughness. This factor may be determined from independent measurements in which the RH along the surface is known while keeping all other variables constant. Then we show that the apparent sorption or desorption kinetics critically depend on the competition between boundary conditions and transport through the material. For sufficiently low air flux intensities or small sample thicknesses, the moisture distribution in the sample remains uniform and evolves toward the equilibrium with a kinetics depending on the value of δ and the material thickness. For sufficiently high air flux intensities or large sample thicknesses, the moisture distribution is highly inhomogeneous, and the kinetics reflect the ability of water transport by diffusion through the material. We illustrate and validate this theoretical description on the basis of magnetic resonance imaging experiments on drying cellulose fiber stacks.

Dynamic NMR Relaxometry as a Simple Tool for Measuring Liquid Transfers and Characterizing Surface and Structure Evolution 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, and textiles. It is of major interest to identify how a liquid, pushing another fluid or transporting particles, ions, or nutriments, can penetrate or be extracted from the porous medium. High-resolution X-ray microtomography, neutron imaging, and magnetic resonance imaging are techniques allowing us to obtain, in a nondestructive way, a view of the internal processes in nontransparent 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 transport 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 the imbibition, drying, or phase change of the sample. This rather cheap technique then allows us to distinguish how the liquid is distributed in the different pore sizes or pore types and how this evolves over time; since the NMR 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 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.