The drying shrinkage of cellulosic fibres and isotropic paper sheets

We present theory for the shrinkage on drying of the cross-sectional area of cellulosic fibres and show that this depends on their initial moisture content only. For the linear shrinkage of cross-sectional dimensions, an additional parameter is required, which we estimate from comparison of the theory with experimental data from the literature. We proceed to combine our model of fibre shrinkage with probabilistic theory for fibre contacts in random fibrous networks to obtain a model for the unrestrained shrinkage of isotropic paper sheets. The expression obtained depends only on the moisture content of fibres and the extent of inter-fibre contact and exhibits good agreement with experimental data for laboratory-formed paper sheets. The results have relevance to the commercial manufacture of paper and potential for application to the study of cellulose nano-composites.