3D analysis of paper microstructures at the scale of fibres and bonds

The evolution of paper microstructure parameters, such as porosity and fibre orientation, as a function of papermaking conditions is most often studied at a macroscopic scale. However, modelling the physical and mechanical properties of papers using upscaling approaches requires understanding the deformation micro-mechanisms that are induced by papermaking operations within the structure of paper fibrous networks for individual fibres and fibre-to-fibre bonds. We addressed this issue by analysing three-dimensional images of model papers. These images were obtained using X-ray microtomography. The model papers were fabricated by varying forming, pressing, and drying conditions. For each image, this analysis enabled an unprecedented large set of geometrical parameters to be measured for individual fibres (centreline, shape and inclination of the fibre cross sections) and fibre-to-fibre bonds (inter-bond distance, number of bonds per unit length of fibre, bond surface area) within the fibrous networks. The evolution of the as-obtained microstructure parameters was analysed as a function of papermaking conditions. All results were in accordance with the data available in the literature. A key result was obtained for the evolution of the number of fibre-to-fibre contacts per fibre as a function of the network density. A representative number of contacts was obtained using relatively small imaged volumes. These volumes must only contain enough fibre segments the cumulated length of which is of the same order as the mean fibre length. These results were also used to validate microstructure models for the prediction of the number of fibre-to-fibre contacts within fibrous networks.