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Scaling, percolation and network theories: new insights into papermaking? In Fundamentals of Papermaking, Trans. of the IXth Fund. Res. Symp. Cambridge, 1989, (C.F. B aker & V. P unton, eds), pp 195–218, FRC, Manchester, 2018.


Recent advances in the theory of condensed matter physics have furnished us with powerful theoretical methods for understanding the structural and dynamical properties of in homogeneous materials, such as the fibre network which constitutes paper. We discuss the concepts of universality and scaling, on which all the new theoretical arguments are based. In understanding the properties of forming and of paper, the percolation transition, i.e. the unique state where an infinitely connected network of fibres is formed, is of particular interest. The physical aspects and the power of the percolation theory are discussed in the presentation. Applications of these new concepts to paper have so far been few.

We show how the percolation theory yields practical qualitative results explaining the relationship between the consistency of the suspension in the headbox and the formation. The complicated structure of the turbulence on the wire and on the jet, which manifests itself in the residual variations of basis weight, is discussed using some scaling ideas related to the universality of the nonlinear dynamical systems. The effect of formation on the mechanical properties, especially ultimate strength, can be viewed theoretically with the aid of scaling, percolation and network theories. The reinforcing effect of chemical fibres in newsprint can be judged by a rather simple scaling argument,which,when developed further, gives insight into the nonlinear relationship between strength and the amount of chemical fibres in newsprint.

Scaling and percolation are qualitative methods. When studied and applied properly, these concepts help us get a picture of the in homogeneous materials and understand the basic principles behind their properties. It is then easier to decide on the right quantities to measure when quantitative information is needed in papermaking.

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