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.