Some current models for moisture diffusion in paper in the hygroscopic range are analyzed. In general, two types of diffusion models can be recognized. Models of the first type treat paper as a homogeneous medium with moisture flux that is proportional to the gradient in moisture content. Although useful in some instances this approach fails frequently because it homogenizes the internal dynamics and relaxation processes occurring within the paper material. Recent studies have shown that a subtler approach which treats paper as a composite of fibers and void spaces is more successful at describing moisture transport dynamics. A review of these studies along with a generalization of this approach to three dimensions is considered here. The parameters appearing in such models can be identified with the physical processes of diffusion through the void space and through the fiber matrix. Diffusivities in these individual phases are supplemented by a local kinetic coefficient representing moisture flux interchange between the void and fiber phases. When the local moisture exchange coefficient takes on large values, the fibers and the void spaces are at local equilibrium with no net exchange of moisture. Under such conditions, the model reduces to the simpler Fickian diffusion model with nonlinear moisture diffusivity equivalent to earlier models.
Bibliographical noteFunding Information:
We would like to acknowledge the support of the US DOE and AFPA through a grant from the Agenda 2020 Industries of the Future program to University of Minnesota and SUNY ESF. Support of the USDA through a grant to SUNY ESF under the NRI CGP is also acknowledged.