Mid Sweden University

In industrial applications, such as paper and nonwovens, cellulose fibers are used in the form of a network where the fibers are oriented more or less in the sheet-plane direction. However, in many biological systems, fibers are instead oriented in a three-dimensional (3D) space, creating a wide variety of functionalities. In this study we created a 3D-oriented fiber network on the laboratory scale and have identified some unique features of its structure and mechanical properties. The 3D fiber network sheets were prepared by using foam-forming as well as modifying consolidation and drying procedures. The fiber orientation and tensile/compression behavior were determined. The resulting sheets were extremely bulky (above 190 cm3/g) and had extremely low stiffness (or high softness) compared to the reference handsheets. Despite this high bulk, the sheets retained good structural integrity. We found that a 3D-oriented fiber network requires much less fiber-fiber contact to create a connected (“percolated”) network than a two-dimensionally oriented network. The compression behavior in the thickness direction was also unique, characterized by extreme compressibility because of its extreme bulk and a long initial increase in the compression load as well as high strain recovery after compression because of its fiber reorientation during compression.

Anisotropic, semi-flexible, cross-linked, random fibre networks are ubiquitous both in nature and in a wide variety of industrial materials. Modelling mechanical properties of such networks have been done extensively in terms of criticality, mechanical stability, and scaling of network stiffnesses with structural parameters, such as density. However, strength of the network has received much less attention. In this work we have constructed 3D-planar fibre networks where fibres are, more or less, oriented in the in-plane direction, and we have investigated the scaling of network strength with density. Instead of modelling fibres as 1D element (e.g., a beam element with stretching, bending and/or shear stiffnesses), we have treated fibres as a 3D-entity by considering the features like twisting stiffness, transverse stiffness, and finite cross-link (or bond) strength in different deformation modes. We have reconfirmed the previous results of elastic modulus in the literature that, with increasing density, the network modulus indeed undergoes a transition from bending-dominated deformation to stretching-dominated with continuously varying scaling exponent. Network strength, on the other hand, scales with density with a constant exponent, i.e., showing no obvious transition phenomena. Using material parameters for wood fibres, we have found that the predicted results for stiffness and strength agree very well with experimental data of fibre networks of varying densities reported in the literature.

We have developed a new method for characterizing microstructures of paper coating using argon ion beam milling technique and field emission scanning electron microscopy. The combination of these two techniques produces extremely high-quality images with very few artefacts, which are particularly suited for quantitative analyses of coating structures. A new evaluation method has been developed by using marker-controlled watershed segmentation technique of the secondary electron images. The high-quality secondary electron images with well-defined pores makes it possible to use this semi-automatic segmentation method. One advantage of using secondary electron images instead of backscattered electron images is being able to avoid possible overestimation of the porosity because of the signal depth. A comparison was made between the new method and the conventional method using greyscale histogram thresholding of backscattered electron images. The results showed that the conventional method overestimated the pore area by 20% and detected around 5% more pores than the new method. As examples of the application of the new method, we have investigated the distributions of coating binders, and the relationship between local coating porosity and base sheet structures. The technique revealed, for the first time with direct evidence, the long-suspected coating non-uniformity, i.e. binder migration, and the correlation between coating porosity versus base sheet mass density, in a straightforward way.

 Non-uniformities within the coating layer, such as porosity variations and binder distributions, are known to affect print uniformity and barrier properties. However, in the literature the results on coating microstructures are rather limited or sometimes conflicting.We obtained high quality images of coated paper cross sections using field emission scanning electron microscopy in combination with a new argon ion beam milling technique to directly observe and analyse the binder and pore distribution. This technique produces high quality images that allow microstructure characterisation of the coating layer.The binder distribution measurements showed that the binder is almost exclusively filling up the small pores, whereas the larger pores are mainly empty and depleted of binder.

Non-uniformities in the coating layer, such as porosity variations and binder distributions, are known to affect print uniformity and barrier properties. However, in the literature the results are rather scarce or sometimes conflicting.

We acquired high quality images of coated paper cross sections using field emission scanning electron microscopy in combination with a new argon-ion-beam milling technique to directly observe and analyse the coating microstructures in relation to underlying base sheet structures.

The results showed that coating porosity varied with mass density of the underlying base sheet for the relatively bulky clay/GCC coating, whereas for the more compact clay coating, the effect was small. Areas with more fibres in the base sheet were more compressed by calendering, resulting in a decreased coating porosity. A unique binder enriched layer of less than 500 nm thickness was found at the coating surface as well as at the coating/base sheet interface.

Base sheet structures, such as surface roughness and mass density distribution (formation), have been known to affect coating uniformity. However, the literature is not necessarily consistent in determining which structure controls coating uniformity. This study employed scanning electron microscopy (SEM) and image analysis, combined with autocorrelation and frequency analyses, to investigate the fundamental mechanisms of coating and to resolve some of the controversies in the literature regarding the base sheet effects. The results showed that coating thickness variation resembles a process of random deposition with leveling. At small length scales (in the size of fiber width), leveling causes a very strong dependence of coating thickness variations on the surface profile of the base sheet, whereas at larger length scales, coating thickness variation diminishes in its intensity by the same leveling effect, but still retains a significant correlation with base sheet structure, particularly formation. Frequency analyses clearly showed that the discrepancies in the results for the base sheet effects in the literature are due to the length scales used in the experiments, that is, the sampling area and the resolution of the measurements.

    We studied the surface evolution of coating by using a random deposition model of particles. In order to capture the real coating structure development, we included a volume exclusion effect to represent particle-particle interaction, and a levelling effect to represent surface tension effect. In this study we investigated three cases: (1) random deposition on a flat surface, (2) random deposition on a flat surface with levelling, and (3) random deposition on a rough surface with levelling.

When plotting in logarithmic scale, the roughness initially increased linearly with average number of particles deposited for all three cases but reached saturation after a certain amount of deposited particles. The result resembles a ballistic deposition process where agglomerates are developed over the surface due to lateral growth. Even a flat, uniform surface creates roughness during random deposition of particles.

Autocorrelation analysis showed that the correlation length continues to increase with the number of particles deposited. The aggregated structures were easily seen in the autocorrelation function.

Experimental and simulated data on the rough surface were compared and they were in agreement, confirming that the coating process is essentially a random process with some local correlation in the length scale of a typical fibre width. 

Characterization of the base sheet properties and coating layer properties was performed by using scanning electron microscope (SEM) images of paper cross-sections and image analysis. Frequency analysis was used to study how the base sheet properties affect coating thickness uniformity at different length scales. Samples analysed were Lightweight Coated (LWC) base sheets blade-coated on only one side with coat weights of 12 and 22 g/m2. A number of images were taken in sequence giving a total length of more than 6 mm. The results showed that the surface height variations of the base sheet control coating uniformity in the entire examined length scale, but with different mechanisms. At short wavelengths the coating mechanism was “level coating” where the coating suspension fills small pores (“levels”), whereas at longer wavelengths the coating suspension follows the surface profile and “contour coating” becomes more prevalent. In other words, the level- and contour-coatings represent the coating mechanisms in different length scales. Surface height variations can be explained by base sheet thickness only at short wavelengths, but at all other wavelengths the surface height variations were very much independent of the base sheet structure properties measured.

Web break is an important runnability issue in the pressrooms. However, web breaks are rare events. Performance statistics for a large number of rolls are required to determine the causes of runnability problems with a reasonable level of confidence. To provide better insight into the main causes of web breaks, we analyzed seven pressroom/mill databases of sufficient size to produce reliable runnability statistics. The statistical "association" between strength properties (average) and break rate was examined using a Chi Square analysis method. We found that the statistical "association" between strength properties (average) and break rate varied considerably from one pressroom to the other (or from one mill to the other), depending on the pressroom operation (the variations of tension) and the quality of data from mills. However, among different strength properties, MD tensile strength has been most consistently associated with the break rate. CD Tear strength did not consistently predict the runnability. We also found that strength uniformity had a significant impact on pressroom performance. Lastly, the pressroom data consistently showed that typical, macroscopic defects are now minority causes for web breaks and the majority of breaks are press-related or "unknown".

Web break is an important runnability issue in the pressrooms. However, web breaks are rare events. Performance statistics for a large number of rolls are required to determine the causes of runnability problems with a reasonable level of confidence. To provide better insight into the main causes of web breaks, we analyzed seven pressroom/mill databases of sufficient size to produce reliable runnability statistics. The statistical "association" between strength properties (average) and break rate was examined using a Chi Square analysis method. We found that the statistical "association" between strength properties (average) and break rate varied considerably from one pressroom to the other (or from one mill to the other), depending on the pressroom operation (the variations of tension) and the quality of data from mills. However, among different strength properties, MD tensile strength has been most consistently associated with the break rate. CD tear strength did not consistently predict the runnability. We also found that strength uniformity had a significant impact on pressroom performance. Lastly, the pressroom data consistently showed that typical, macroscopic defects are now minority causes for web breaks and the majority of breaks are press-related or "unknown".

In the present work we propose a particle approach, which is designed

to treat complex mechanics and dynamics of the open-draw sections that

are still present in many of today's paper machines. First, known

steady-state continuous solutions are successfully reproduced. However,

it is shown that since the boundary conditions depend on the solution

itself, the solutions for web strain and web path in the open-draw

section are generally time-dependent. With a certain set of system

parameters, the nonsteady solutions are common. A temporal fluctuation

of Young's modulus, for example, destabilizes the system irreversibly,

resulting in the continuous growth of web strain, i.e., break. Finally

we exemplify with some strategic draw countermeasures how to prevent a

dangerous evolution in the web strain.

The present work is concerned with the system dynamics and stability of the open draw sections of paper machines where web breaks occur most frequently. We have applied a novel particle-based system dynamics model that allows the investigation of complex interactions between web property fluctuations and system parameters, without any constraints of a particular geometrical web shape or boundary conditions assumed a priori. The result shows that, at a given machine draw and web property parameters, the open draw section maintains its steady-state until it reaches a certain machine speed limit. At this speed the system looses its stability and the web strain starts growing without any limit, and thus leading to a web break. A similar instability can also be triggered when web properties suddenly fluctuate during steady-state operation. The parametric sensitivity studies indicate that, among the web property parameters studied, the elastic modulus of the wet web has the largest impact on the critical machine speed as well as on the detachment point where the web is released from the first roll. Further analysis shows that the decrease in dryness has a (negative) synergistic effect causing an increased risk of system instability. It is, therefore, most important to control, not only average dryness, but also its variations in order to enhance paper machine runnability.

A two-dimensional model for immiscible binary fluid flow including moving immersed objects is presented. The fluid motion is described by the incompressible Navier-Stokes equation coupled with a phase-field model based on van der Waals’ free energy density and the Cahn-Hilliard equation. The immersed boundary method has been utilised to handle moving immersed objects and the phase-field boundary conditions have been adapted accordingly. Numerical stability and execution time was significantly improved by the use of a new boundary condition which implements minimisation of the free energy in a direct way. Convergence toward the analytical solution was demonstrated for equilibrium contact angle, the Lucas-Washburn theory and Stefan’s problem. The proposed model may be used for two-phase flow problems with moving boundaries of complex geometry, such as the penetration of fluid into a deformable, porous medium.

A finite element model of a flexo printing press has been developed and the material and geometrical properties of the sustem has been investigated. The results showed that it is the photopolymer and the top liner that have the biggest impact on the printing pressure variations.

Print non-uniformity problems are a major concern for flexo post-printers. Many of these non-uniformities are suspected to be caused by the corrugated board structure itself. Striping is the most obvious one, but also other print quality problems might be structure-related. This work focuses on how deformations of the board might lead to print non-uniformities, and if the deformation of halftone dots is the mechanism behind striping in halftone flexo post-printing. The problems were analysed by using finite element models to simulate deformed board and halftone dot compression in the printing nip. Distortions of the board due to non-uniform hygro-thermal strains were shown to be a potential cause of print non-uniformities. Striping in halftone prints was found to be caused by differences in dot gain between ridge and valley areas above the flute structure.

By doing ink transfer experiments and measuring reflectance variations on corrugated boards it was found that striping mainly consists of print density variations and not print gloss variations.

Striping is a print defect that is often seen in flexo post-printing on corrugated board. It appears as lines parallel to the flutes of the corrugated medium (fluting). These lines are generally thought to be print density and/or print gloss variations. The objective of this Paper is to obtain fundamental understanding of the striping mechanism. Print density and print gloss have been determined as a function of printing pressure. Typical printing pressure variations have also been determined by a non-linear finite element method. A 2D reflectance mapping has been performed for printed corrugated boards. The results showed that striping is dominated by print density variations for uncoated board, and the print density variations are, in turn, caused by the printing pressure variations. The extent to which the pressure variations appear as print density variations depends on the ink transfer characteristics of the liner board.

A fintie element model has been used to simulate how halftone dots deform during printing. Another finite element model has also been used for simulating how the pressure distribution in the nip changes when the corrugated board is deformed before printing by e.g. moisture induced warp. The simulations showed that striping in halftone prints can be explained by the deformation of halftone dots leading to more "dot gain" above flute ridges than between. When the corrugated board is deformed over a few flutes, the pressure distribution is affected which might cause print non-uniformities.

The transfer of a microscopic fluid droplet from a flat surface to a deformable stochastic fibre network is investigated. Fibre networks are generated with different levels of surface roughness, and a two-dimensional, two-phase fluid-structure model is used to simulate the fluid transfer. In simulations, the Navier-Stokes equations and the Cahn-Hilliard phase-field equations are coupled to explicitly include contact line dynamics and free surface dynamics. The compressing fibre network is modelled as moving immersed boundaries. The simulations show that the amount of transferred fluid is approximately proportional to the contact area between the fluid and the fibre network. However, areas where the fluid bridges and never actually makes contact with the substrate must be subtracted.

This paper concerns uniaxial compression of anisotropic fibre network, as typically seen in the end use of nonwoven and textile fibre assemblies. The constitutive relationship and deformation mechanism have been investigated by using a bead-model to represent the complex structures of the constituent fibres and the fibre networks. The compression stress shows a power-law dependency on the density with a threshold density for both experimental and numerical fibre networks. Unlike the widely studied tri-axial compression of the initially isotropic network, it was found that the contact interaction between the fibres, especially the fibre-fibre contact stiffness (or the transverse compression properties of fibres), has a large impact on all the constitutive parameters. In particular, the exponent values computed based on the softer contact stiffnesses agreed very well with the experimental values reported in the literature. The internal deformation mechanism was similar to the earlier studies that at low compression, the deformation is dominated by the low-energy-mode deformations (i.e. bending and shear), whereas at higher compression, the difference appears: the compression of fibre-fibre contacts, instead of the deformation in the fibre axial direction, takes over.

Out-of-plane deformations of paper, such as fluting, significantly deteriorate the quality of a printed product. There are several explanations of fluting presented in the literature but there is no unanimously accepted theory regarding fluting formation consistent with all field observations. The present paper reviews the existing theories and proposes a mechanism that might give an answer to most of the questions regarding the fluting. The fluting formation has been considered as a post-buckling phenomenon which is analysed with the help of the finite element method. Fluting retention has been modelled by introducing an ink layer over the paper surface with ink stiffness estimated from experimental results. The impact of fast drying on fluting has been assessed numerically and experimentally. The result of the study suggests that fluting occurs due to small-scale strain variations, which in turn are caused by the moisture variations created during fast convection drying. The result also showed that ink stiffening alone cannot explain the fluting amplitudes observed in practice, suggesting the presence of other mechanisms of fluting retention.

Out-of-plane deformations of paper, such as fluting, significantly deteriorate the quality of a printed product. There are several explanations of fluting presented in the literature but there is no unanimously accepted theory regarding fluting formation and retention which is consistent with all field observations. This paper first reviews the existing theories and proposes a mechanism that might give an answer to most of the questions regarding fluting. The fluting formation has been considered as a post-buckling phenomenon which has been analysed with the help of the finite element method. Fluting retention has been modelled by introducing an ink layer over the paper surface with the ink stiffness estimated from experimental results. The impact of fast drying on fluting has been assessed numerically and experimentally. The result of the study suggests that fluting occurs due to small-scale hygro-strain variations, which in turn are caused by the moisture variations created during fast convection (through-air) drying. The result also showed that ink stiffening alone cannot explain the fluting amplitudes observed in practice, but that high drying temperatures promote inelastic (irreversible) deformations in paper and this may itself preserve fluting.

Geometrically non-linear, large scale post-buckling analyses were carried out to investigate the influence of different parameters on residual waviness (fluting) after printing in a heat set web offset printing press. Mixed implicit-explicit finite element techniques were used in the analyses. The numerical procedure was verified by experimentally acquired data. Results show that when the paper web is perfectly flat before printing, fluting patterns after drying and moisture recovery generally have higher wavelength than those typically observed in fluted samples. Initial cockles of imprinted sheets were found to have impacts on the fluting patterns and amplitudes. Among the factors investigated, ink thickness and hygroexpansivity had significant influences on fluting: increasing these factors increased fluting amplitudes.

The effect of micro scale variations on fluting formation has been studied by using quasi-static post-buckling analyses. The analyses are based on implicit time integration techniques and incorporated the ink stiffening effect during drying in the heatset oven. A series of parametric studies have been conducted to investigate effects of bending stiffness, ink thickness, tension, and scale of moisture variations. Experiments were also performed to estimate the ink layer stiffness after drying and to investigate the retention of flutes after printing. The results showed that, in order to explain the occurrence of flutes in the wavelength of 1-2 cm, micro-scale strain variations are necessary. Such variations are most likely caused by the local moisture variations and the subsequent plastic deformation of paper due to heating. Ink stiffening alone was found to be insufficient to retain the fluting shapes after drying.

A finite element model for 3D random fiber networks was constructed to simulate deformation and failure behavior of networks with dynamic bonding/debonding properties. Such fiber networks are ubiquitous among many living systems, soft matters, bio-materials, and engineering materials (papers and non-woven). A key feature of this new network model is the fiber-fiber interaction model that is based on AFM measurements from our earlier study. A series of simulations have been performed to investigate strain localization behavior, strength statistics, in particular, the variations of strength, strain-to-failure and elastic modulus, and their size dependence. Other variables investigated are fiber geometries. The result showed that, in spite of its disordered structure, strength and elastic modulus of a fiber network varied very little statistically, as long as the average number of fibers in the simulated specimen and the degree of fiber orientation are kept constant. However, strain-to-failure showed very significant statistical variations, and thus more sensitivity to the disordered structures. (C) 2012 Elsevier Ltd. All rights reserved.

By virtue of the recent developments in simulation techniques for fibre suspensions flows, it is now possible to directly simulate forming of the paper sheet at a particle level under realistic flow conditions. This opens up a window of opportunity to better understand the microscale development of the paper structure, and to attribute particular features of the structure to different drainage elements.The simulations are based on a particle-level fibre suspension model, in which fibres are represented by chains of cylindrical fibre segments. The fibre model includes curled shapes and the torsion and bending of the fibres. It also captures the two-way interactions between the fibres and the fluid phase. The fluid motion is integrated from the Navier--Stokes equations.To illustrate the usage of the simulation tool, a sample parametric study of the effects of different fibre furnishes on the paper structure and wet strength is presented. Such an investigation could almost as easily have been performed with experiments. Simulations, however, have some advantages: First, the cost is almost nothing as compared to pilot trials. Secondly, the parameters of the simulations can be controlled one at a time, whereas in pilot trials, changing one process parameter will affect the others. Thirdly, every detail of the evolving paper structure is accessible at every instant in the simulations. That is, the forming process needs no longer be considered a "black box". Simulations also have some drawbacks. For instance, it is not possible to include the smallest particles, due to their vast number, while maintaining sufficiently large flow geometry. Therefore, simulations must target paper grades of low fines contents.In this communication, the pros and cons of particle-level simulations are discussed, and put into the context of previous forming and dewatering models in the literature. The development of the paper microstructure predicted in the simulations shows that thickening is the dominant forming mechanism, while filtration only occurs in the most dilute end of the typical range of consistencies used in the industry. This predicted behaviour is compared with the conventional view of dewatering, which holds filtration as the dominant forming mechanism.

A model is proposed for simulating the motion of flexible fibres in fluid flow. Care has been taken to include typical papermaking conditions into the validity range of the model. Fibres are modelled as chains of fibre segments, whose motion is governed by Newton's second law. The fluid motion is calculated from the three-dimensional incompressible Navier-Stokes equations. By enforcing momentum conservation, the two-way coupling between the solids and fluid phase is taken into account. Fibre-fibre interactions as well as self-interactions include normal, frictional and lubrication forces. Furthermore, the model considers nonlaminar fibre-fluid interactions and particle inertia. Simulation results were compared with experimental data found in the literature. The model predicts very well the orbit period of rigid fibre motion in shear flow. Quantitative predictions were made for the amount of bending of flexible fibres in shear flow. It was also possible to reproduce the different regimes of motion of flexible fibres in shear flow, ranging from rigid motion to coiled motion and self-entanglement.

Particle-level simulations are performed to study the rheology of monodispersed non-Brownian fibers suspended in a Newtonian fluid in shear flow. The effects of fiber aspect ratio, concentration, and interparticle friction on the stress tensor of the suspension in the steady state and on the tendency of fiber agglomeration are investigated. Semiempirical expressions for the steady state apparent shear viscosity and the steady state first and second normal stress difference were obtained for the case of well dispersed suspensions in the nonconcentrated regimes. The simulation predictions of the specific viscosity were in fair agreement with previous experimental investigations.

A model for particle-level simulation of fiber suspensions has been used to simulate paper sheet forming on a roll-blade former. The fibers were modeled as chains of fiber segment, flowing and interacting with the medium and with each other. The incompressible three-dimensional Navier-Stokes equations were used to describe the fluid motion. Real pulps were analyzed to provide raw material data for the simulations. Dewatering was simulated by moving two model forming fabrics toward each other through a fiber suspension. Close examination of the dewatering process revealed that no large concentration gradients develop through the thickness of the pulp suspension. In this sense, twin-wire dewatering does not resemble a filtration process. The effects of the jet-to-wire speed difference on the network structure of the paper were investigated. The structural features of interest were fiber orientation anisotropy, mass density distribution and three-dimensionality of the fiber network. It was demonstrated that these simulated structural features were in qualitative agreement with experimental data found in the literature.

Particle-level simulations are performed to study semidilute suspensions of monodispersed non-Brownian fibers in shear flow, with a Newtonian fluid medium. The incompressible three-dimensional Navier-Stokes equations are used to describe the motion of the medium, while fibers are modeled as chains of fiber segments, interacting with the fluid through viscous drag forces. The two-way coupling between the solids and the fluid phase is taken into account by enforcing momentum conservation. The model includes long-range and short-range hydrodynamic fiber-fiber interactions, as well as mechanical interactions. The simulations rendered the time-dependent fiber orientation distribution, whose time average was found to agree with experimental data in the literature. The viscosity and first normal stress difference was calculated from the orientation distribution using the slender body theory of Batchelor [J. Fluid Mech. 46, 813--829 (1971)], with corrections for the finite fiber aspect ratios. The viscosity was also obtained from direct computation of the shear stresses of the suspension for comparison. These two types of predictions compared well in the semidilute regime. At higher concentrations, however, a discrepancy was seen, most likely due to mechanical interactions, which are only accounted for in the direct computation method. The simulated viscosity determined directly from shear stresses was in good agreement with experimental data found in the literature. The first normal stress difference was found to be proportional to the square of the volume concentration of fibers in the semidilute regime. As concentrations approached the concentrated regime, the first normal stress difference became proportional to volume concentration.

A model for flexible fibers in viscous fluid flow is proposed, and its predictions compared with experiments found in the literature. The incompressible three-dimensional Navier-Stokes equations are employed to describe the fluid motion, while fibers are modeled as chains of fiber segments, interacting with the fluid through viscous and dynamic drag forces. Fiber segments, from the same or from different fibers, interact with each other through normal, frictional and lubrication forces. Momentum conservation is enforced on the system to capture the two-way coupling between phases. Quantitative predictions could be made, and showed good agreement with experimental data, for the period time of Jeffery orbits in shear flow, as well as for the amount of bending of flexible fibers in shear flow. Simulations, using the proposed model, also successfully reproduced the different regimes of motion for threadlike particles, ranging from rigid fiber motion to complicated orbiting behavior, including coiling and self-entanglement.

A new model for particle-level simulation of forming was developed. A set of process parameters and a statistical description of the stock were provided as inputs to the model and a three-dimensional model paper was produced. This allowed the analyses of the relations between process parameters and structural properties of the formed sheet. Numerical experiments were set up to study the effects of the yarns of the forming fabric on the surface distributions of fillers and fines and to investigate the fibre orientation anisotropy and specific formation as functions of the jet-to-wire speed ratio.