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Dimensional stability of paper is a key problem in the field of digital ink-jet printing. In the literature, this phenomenon is mostly approached through continuum models representing the overall response of paper. However, if the length scale of the applied wetting is comparable to the characteristic length scale of the microstructure a continuum description may be not sufficient to correctly capture the response of the material. The present work explores this question by proposing a two dimensional fibrous network model, which investigates the hygro-expansion phenomena due to the printing process and their effects on the local response of the paper’s microstructure. The proposed description incorporates several microscale features, such as the fibre hygro-elastic properties, orientation, areal coverage. Different moisture patterns are applied to the fibrous networks, allowing to study their behaviour as a function of the coverage, the anisotropic orientation and the size of the wet regions relative to the fibre length. A comparison with a homogenized continuum model is finally performed. This reveals that, for low coverages, a microstructural approach is substantially more accurate, whereas for denser networks the continuum model is a valid alternative, even when the size of the wetting pattern becomes comparable to the fibre length.

Local network effects on hygroscopic expansion in digital ink-jet printing