Multiscale Hygro-mechanical Modelling of Paper and Paperboard
Please login to view abstract download link
The ingression of liquids into paper sheets and the resulting swelling and dimensional instabilities exhibited by the sheets present an intrinsically multiscale problem. Whereas we have a reasonable understanding of the microscale physics, a direct link with macroscopic predictive models is largely lacking. In the present study we aim to establish such a link in particular for the fluid flow part of the problem, i.e. the flow of the liquid into the porous medium, driven by capillary action. Adopting an unsaturated flow approach, we derive expressions for the permeability, capillary pressure and pore-fibre exchange based on highly idealised micro-models. Predictions made by the model show a good qualitative agreement with experiments, but a significant discrepancy in the time scales involved. Numerical simulations of a detailed, but highly idealised pore network model, based on similar assumptions as the ones employed in the homogenisation, has allowed us to trace the problem to the permeability expression. Pending a more rigorous solution, simply scaling down the permeability allows us to match the experimental time scales satisfactorily, and in fact to predict the dependence of the curl evolution on the composition of a number of model liquids.
