Transient moisture diffusion through paperboard materials

Abstract The performance of many products such as those made of containerboard or other paperboards is sensitive to moisture. Transient moisture profiles result in heterogeneities in mechanical properties and can often lead to catastrophic failure. Viewed as a composite porous medium the system comprises hygroscopic fibers and void spaces both of which are continuous. Furthermore, both phases conduct moisture by diffusion and for typical paperboards diffusion through the fiber matrix predominates at high moisture contents whereas vapor phase diffusion through the void space is dominant at lower values. Depending upon the external and initial conditions, competition between these two pathways and local sorption interplay and produce interesting effects, which can have significant impact on the mechanical performance of the composite medium. In order to delineate the different effects that can occur, we used a mathematical model for unsteady state diffusion to analyze the case of transient moisture transport through a paperboard exposed to differential humidity conditions on either side. Diffusion is assumed to occur along the thickness direction in the void space and in the fiber space. Local uptake of moisture is represented by the linear driving force approximation. A numerical solution of the mathematical model is sought. The dominant path for moisture transport can undergo a change from the fibers to the void spaces under large humidity differentials. A fiber conduction layer whose thickness develops with time and reaches a constant value at steady state is found. This raises the possibility of moisture response, which could depend on the direction of diffusion for significantly heterogeneous media. Another interesting feature is the development of minima in the moisture flux versus time curves, which are sensitive to the diffusion and local sorption parameters. Tracking such minima can provide a good method to tune the model parameters based on experimental flux data. The role of the interfacial region between the layers can affect the overall resistance and alter moisture content profiles significantly. Since similar ‘two-equation’ models have been proposed for other transport processes such as heat and momentum transfer, these results can have wider applicability. In particular, steady and unsteady profiles and fluxes can be exploited to yield information about the local and global transport coefficients for the heterogeneous medium under consideration.