Modelling of water penetration and hygro-expansion in a paper sheet

Paper, a hydrophilic material, is notably susceptible to deformations due to variations in moisture content, which develop over time. Understanding the moisture transport through the thickness of a paper sheet and the time-dependent mechanics allows us to study the curling behaviour of paper.In this work, the time-dependent factors involved in deformation of a paper strip that is fully or partially wetted from one side and subjected to different boundary conditions is studied with a 1D numerical model. The different time-scales involved, in the process of imbibition in the inter-fibre pores and absorption (or water uptake) by the fibres, are analysed. The resulting hygro-expansion due to swelling of the wet fibres is then solved to predict the deformation and bending response of the paper strip.We provide a phenomenological model here to describe the dynamic water flow through the thickness of a paper strip using the unsaturated flow theory. The numerical analysis shows a fair qualitative agreement with experimental observations.