Analysis of wet pressing of paper: the three-phase model. Part I: constant air density

Abstract

In this study, we consider a one-dimensional three-phase model describing wet pressing of paper. Part I is devoted to the simplified case in which air is assumed incompressible. In Part II we drop this assumption. The model is formulated in terms of water saturation and void ratio and it uses a material coordinate to describe spatial dependence. It also involves cross or matching conditions between the wet paper and the felt. In mathematical terms, we end up with a coupled system of equations: a nonlinear diffusion equation and a first order hyperbolic equation. We present some analytical observations to explain the essential behaviour of the model and we carry out numerical experiments using an upwind and a front tracking method.

On Mathematical Modeling and Simulation of the Pressing Section of a Paper Machine Including Dynamic Capillary Effects: One-Dimensional Model

“…There exist different approaches to model this problem. Most of the models consider three-phase flow (solid, water, and air) (Bezanovic et al 2006(Bezanovic et al , 2007aHiltunen 1995;Kataja et al 1992). The problem is very complex.…”

“…In Hiltunen (1995) and Kataja et al (1992), the conservation of mass and momentum is used together with a Lagrangian formulation along displacement characteristic lines (solid flow lines). In Bezanovic et al (2006Bezanovic et al ( , 2007a, the mass balance equations in Lagrangian formulation are used. Moreover, Bezanovic et al (2007b) considers the compressible air case.…”

Study on equations of curves of the squeezing machines’ contact of rolls

“…The material being processed is fed in such a way that the line, which is a continuation of its front end, passes through the axis of rotation of the upper roll, since no additional external forces are required to carry out the capture [4]. Works [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] are devoted to the creation of scientific foundations for the development of roller squeezing machines and the improvement of their parameters. At the same time, it is observed that in the listed works, mathematical models of curves of contact rolls are developed under static interaction conditions.…”

Adhesive behaviour of bonded paper layers: Mechanical testing and statistical modelling

“…Due to its practical importance, the process itself, the changes it causes in the paper structure, and its mechanical properties were intensively studied. 1–6 On the other hand, the studies on micro- and nanofibrillated celluloses have recently got a great deal of interest because modified wood pulp fibres can be designed to have a controlled structure of cellulose fibril aggregates. In this context, biocomposites are a very promising new range of materials, as discussed in Rantanen and Maloney 7 and Ansari et al.…”