An axisymmetric pore-fiber cell model for moisture transport in paper materials

In modeling the transport of moisture in paper, mechanisms of diffusion through the void space and the fiber matrix must be considered as separate processes. Earlier workers modeled steady and unsteady moisture transport using two diffusion equations each of which was supplemented by moisture exchange flux between the fibers and the pores. A fiber mass transfer coefficient was used as a parameter describing the local moisture exchange within the sheets. This mass transfer coefficient has been treated as an intrinsic property of the paper material obtained by fitting model predictions with experimental transient moisture uptake data. In the present paper, we present a new model for moisture diffusion in paper materials representing the void structure as a set of straight cylindrical pores surrounded by annular fiber matrix. The two-dimensional unsteady-state diffusion equation modeled moisture migration within each of the phases. Different physical and geometrical unit cell parameters representing a real paper material were chosen. The fiber mass transfer coefficient was determined from the local moisture flux exchanged between the fiber and pore phases. The coefficient depended on the diffusivity of moisture in the fibers and the pore phases and on the overall thickness of the sheets. When the exchange flux is negligible, the local chemical potentials of the pore and the fiber phases are equal i.e. local equilibrium conditions are attained. We found from this simulation that deviations from local equilibrium conditions are more likely when the diffusivity in the fiber phase is nonlinear or if the interface between the pore and fibers is curved in the direction. The fiber mass transfer coefficient determined from this simulation was used in numerical calculations of some real moisture diffusion processes. The results of modeling of steady state and transient processes are in good correlation with corresponding experiments.