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Paper simulations that resolve the entire microscopic fiber structure are typically time-consuming and require extensive resources. Several such modeling approaches have been proposed to analyze different properties in paper. However, most use non-linear and time-dependent models resulting in high computational complexity. Resolving these computational issues would increase its usefulness in industrial applications. The model proposed in this work was developed in collaboration with companies in the papermaking industry within the Innovative Simulation of Paper (ISOP) project. A linear network model is used for efficiency, where 1-D beams represent the fibers. Similar models have been proposed in the past. However, in this work, the paper models are three-dimensional, a new dynamic bonding technique is used, and more extensive simulations are evaluated. The model is used to simulate tensile stiffness, tensile strength, and bending resistance. These simulated results are compared to experimental and theoretical counterparts and produce representable results for realistic parameters. Moreover, an off-the-shelf computer accessible to a paper developer can evaluate these models structural properties efficiently.

In this paper a numerical multiscale method for discrete networks is presented. The method gives an accurate coarse scale representation of the full network by solving sub-network problems. The method is used to solve problems with highly varying connectivity or random network structure, showing optimal order convergence rates with respect to the mesh size of the coarse representation. Moreover, a network model for paper-based materials is presented. The numerical multiscale method is applied to solve problems governed by the presented network model.

When liquid packaging board is made aseptic in the filling machine the unsealed edges of the board are exposed to hydrogen peroxide. A high level of liquid penetration may lead to aesthetic as well as functional defects. To be able to make a priori predictions of the edge wicking properties of a certain paperboard material is therefore of great interest to paper industry as well as to packaging manufacturers. The aim of this paper is to present a new analytical theory for prediction of the edge wicking properties of paperboard. The theory is based on Darcy’s law and the ideal gas law to describe the physical behavior of water flow in paperboard. The theory is compared to a recently published multi-scale framework and with pressurized edge wick experiments. The agreement is very good for paperboard samples of different sizes. The conclusion from the work is that both analytical theory and detailed simulations are useful to predict edge wicking properties of paperboard material.

Fiber suspension simulations are challenging since they involve transient fluid flow with immersed solid objects subject to large displacements and rotations. In the present work, a beam model in corotational formulation is coupled with a fluid solver using immersed boundary methods. The model is used to simulate a fiber in a shear flow and excellent agreement is found with Jeffery's equations. The shapes of fibers deforming in a shear flow are found to be in qualitative agreement with shapes observed in experiments. The flow of a fiber suspension is studied by simulating early paper forming with one-way and semi-two-way coupling. It is found that the flow through the fiber web needs to be resolved in order to predict the retention of fibers in the fiber web.

Paper forming is the first step in the paper machine where a fiber suspension leaves the headbox and flows through a forming fabric. Complex physical phenomena occur during paper forming due to the interaction between fibers, fillers and fines as well as chemicals added to the suspension. Understanding this process is important for the development of improved paper products because the configuration of the fibers during this step has a large influence on the final paper quality. Since the effective paper properties depend on the micro-structure of the fiber web, a continuum model is inadequate and the properties of each fiber need to be accounted for in the simulations. In the present work, a framework for microstructure simulation of early paper forming has been developed. The simulation framework includes a Navier-Stokes solver and immersed boundary methods are used to resolve the flow around the fibers. The fibers are modeled with a finite element discretization of the Euler-Bernoulli beam equation in a co-rotational formulation. The contact model is based on a penalty method and includes friction as well as elastic and inelastic collisions. The fiber model and the contact model are validated against demanding test cases from the literature with excellent results. The fluid-structure interaction in the model is examined by simulating an elastic beam oscillating in a cross flow. Finally, a simulation of early paper forming is performed to demonstrate the potential of the proposed framework. The unique modeling approach can be used to increase the fundamental understanding of paper forming and support process optimization.

This work presents a numerical framework designed to simulate the early paper forming process. This process is complex and includes strong fluid-structure interaction and complex geometries. The fluid flow solver IBOFlow, employs immersed boundary methods to simulate the flow around the fibers without the necessity of a boundary conforming grid. The fibers are approximated as slender beams with an elliptic cross section and modeled with the Euler-Bernoulli beam equation. A penalty based contact model is implemented. Finally, the potential of the framework is illustrated with an example.

When liquid packaging board is made aseptic in the filling machine the unsealed edges of the board are exposed to a mixture of water and hydrogen peroxide. A high level of liquid penetration may lead to aesthetic as well as functional defects. To be able to make a priori predictions of the edge wicking properties of a certain paperboard material is therefore of great interest to the paper industry as well as to packaging manufacturers. In this paper an extended multi-scale model of edge wicking in multi-ply paperboard is presented. The geometric and physical properties of the paperboard are modeled on the micro-scale, and include fillers and fines. The absolute air permeabilities and pore size distributions are validated with experimental and tomographic values. On the macro-scale random porosity and sizing distributions, time and sizing dependent contact angles, and inter-ply dependence are modeled. Arbitrary shapes of the paperboard are handled through an unstructured 3D surface mesh. Stationary and transient edge wicking simulations are validated against experiments with excellent agreement. The simulations show that the diffusive menisci between the liquid and air phases together with the two-ply model is necessary to achieve good agreement with the transient edge wicking experiments.