Determining the number of fibre-fibre contacts in cardboard samples using tomographic imaging

The fibrous network of cardboard samples was studied with the aid of tomographic imaging. For analysing the samples a method of determing the number of contacts between fibres in a planar fibrous network was introduced. The model is based on the fact that deposited paper-like structures tend to have predominantly planar fibre orientation. With this assumption an expression of the mean segment length was derived in terms of the average shortest path along fibres through the sample in the out-of-plane direction. The density profiles of cardboard samples were analysed by determing four quantitative features, the solids content, standard deviation of the solids content, slope and curvature. All the samples had a slope in the same direction, i.e., they were denser at the bottom surfaces. Densification seems to occur at both surfaces, as the curvature was larger for samples with higher solids content. Our measurements indicate that contact densities of the cardboards, i.e., the number of fibre-fibre contacts per unit volume are proportional to the square of the solids content. This is in agreement with earlier models for three-dimensional fibre networks.