Joonas Sorvari

Mathematical modelling of moisture induced out-of-plane deformation of a paper sheet

Moisture changes in a paper sheet cause curling and cockling due to expanding or shrinking fibres. Mathematical modelling of these phenomena is considered in this paper. The paper sheet is assumed to be a heterogeneous orthotropic elastic material. Heterogeneity of the paper is handled by dividing it into small pieces, assuming one piece to be homogeneous. This leads to a mathematical model consisting of thousands of homogeneous orthotropic pieces which have different elastic properties and moisture expansion coefficients. The mathematical model is solved using the finite element method. We will show numerical examples and conclude in this paper that the elastic model is able to predict out-of-plane deformations such as cockling of the paper sheet.

Mathematics in paper - from fiber suspension fluid dynamics to solid state paper mechanics

In papermaking process the base paper is formed by starting from low concentration suspension. Depending on process stage different models can be utilized for better understanding and performance of the process. A short general overview of fluid dynamics related to papermaking process is given as well as new approaches including fiber network modeling and continuum mechanical fracture simulations. The fluid dynamical results presented illustrated some paper machine wet end phenomena while the solid state modeling approaches can be exploited from drying section of a paper machine to the several converting processes.

Effect of some printing nip variables on web tension

Good runnability of paper web is an important factor for improving performance of printing process. Printing nips cause web tension variations which are known to affect web runnability. However, ra ...