<p>This thesis investigates paper structure and how its spatial heterogeneity affects the electrostatic and contact forces responsible for the toner transfer in Xerographic printing. Modeling predictions and experiments are reported which link length scales of variation in toner density distribution in Xerographic printing with certain structural length scales in paper.</p> <p>A modified 3D fibre network model is introduced, which is used to simulate handsheet paper microstructure. Specific measures addressed by the model include formation, surface roughness and porosity. Simulated (i.e. virtual) handsheet paper structure is compared with that from specially prepared laboratory handsheet, obtaining a good correspondence between theory and experiments.</p> <p> An efficient Multigrid Poisson solver is used to simulate the electrostatic fields involved in the Xerographic toner transfer process. The distribution of dielectric property is input into the solver either analytically or from simulated 3D paper webs prepared by the fibre network model of paper. A spectral analysis is used to elucidate the relative importance of spatial variations of paper surface, filler and porosity in establishing spatial variations of the electrostatic field. It is found that only long wavelength variations in either surface height, bulk filler or porosity affect variations in electrostatic toner transfer forces to any relevant degree. Furthermore, it is shown that the long wavelength perturbations of the electrostatic field can be modeled using a new 1D effective capacitor model. Direct use of simulated handsheet paper webs - which are described by several heterogeneous measures - shows that to lowest order it is the paper surface structure not formation is responsible in shaping the electrostatic toner field variations.</p> <p> A new platform for modeling toner transfer in Xerographic printing is also introduced. It combines the 3D stochastic fibre network model of paper, the 3D electrostatic field solver, paper compression in the printing nip, and contact adhesion forces acting on toner particles during Xerographic printing. The modeling platform is used to demonstrate that paper-press interactions are critical in shaping the surface of paper, which, in turn, has the greatest influence in controlling both the electrostatic and contact adhesion forces responsible for shaping the distribution of toner transferred to paper during Xerography.</p> / Thesis / Doctor of Philosophy (PhD)

The flow behaviour, and primarily the floc-floc interaction, of pulp paper suspensions have been studied visually. Analogy models based on these observations have been developed as well as the identification of important parameters of floc break-up in low shear rate flow fields. Floc compressions and the locations of voids (areas of lower fibre concentration) where found to influence the floc splitting mechanism. Based on this investigation an equipment for measuring the load carrying ability of fibre flocs and networks was designed, and the effect of measurement geometry, network structure and fibre suspension concentration was investigated. The load carrying ability with concentration increases rapidly when going from 1% to 2% in initial suspension concentration. A model handling the fibre floc behaviour during extension and compression has been developed, and some basic flocculated flow mechanisms are discussed on an analogy basis. A modified Voigt element is use, describing mainly the compressional behaviour and plastic behaviour of loose fibre network structures. Further the pos- sibility of stress chain formation is discussed on a fibre level as well as on a floc level. The effect of fibre flow (shear field) occurring in the forming zone of a roll former has been studied in detail. Basic forming mechanisms on floc scale has been investi- gated, and the effect of running parameters like dewatering pressure and jet-to-wire speed difference as well as the fibre type and concentration of the pulp suspension has been evaluated. It is evident that floc elongation increases with shear rate (jet-to-wire speed difference) and lower dewatering rate. The latter is because the fibre floc is subjected to the shear field longer due to slower immobilisation. Shorter fibre tends to create weaker networks, which promotes a higher elongation of the flocs. / QC 20100901

Most of the water fed into a paper machine is removedmechanically in the forming and press sections. One of thefactor which has an important influence on mechanicaldewatering, i.e. in both forming and pressing, is thestress-strain behaviour of the fibre network. The focus of this thesis is on the development of improvedmathematical descriptions of the stress-strain behaviourexhibited by fibre networks in the forming and press sections.The first part of the thesis presents a physically based modelof the forming and densification of fibre mats in twin-wireformers. The model can calculate the ecect of the applicationof a varied load through the forming section. It was developedfrom mass and momentum balances of the fibre and liquid phases,the fibre mat stress-porosity relation and an expression forthe permeability as a function of the porosity. The fibre-matstress-porosity relation used is rate-independent and presentshysteresis. Simulations have been conducted to study theeffects of roll pressure, blade pulses, wire tension andbeating. The effect of sequential blade pressure pulses afterthe forming roll on the dewatering and the concentrationgradients could be characterised. The simulations alsoexhibited rewetting by expansion when the fibre mats left theforming roll. Increasing wire tension resulted in increaseddewatering, but the rate of increase diminished rapidly withincreasing tension. The simulation results also indicated thatbeating has a large influence on dewatering. The second part of the thesis presents two models of therate-dependent stress-strain behaviour of the fibre networkthat is observed in wet pressing. The first model was based onthe approach pioneered by Perzyna (1966) for strain-ratedependent plasticity and was quite satisfactory for calculatingthe stress-strain behaviour of the fibre network in singlepress nips. It was successfully applied for studyingdensification and dewatering in both normal wet pressing andhigh temperature wet pressing. However, the first model onlyincludes rate dependence in the compression phase of thecompressionexpansion cycle; the expansion phase is treated asbeing rate independent The second model of the stress-strain behaviour of the fibrenetwork treats both compression and expansion as being ratedependent, according to experimental observations. It is basedon the idea that the wet fibre web may be conceived as alayered network of restricted swelling gels. A swollen fibre isa restricted gel, the inner swelling pressure in a swollenfibre wall being balanced by the stresses in the fibre wallstructure. The observed rate dependence of wet webs in bothcompression and expansion phases was attributed to the flow ofwater out of and into the fibre walls. The second model gavepredictions that are in good agreement with results fromuniaxial experiments using pressure pulses of arbitrary shapefor both a single pulse and a sequence of pulses. It maytherefore be used as a general model for the rheologicalbehaviour of the wet fibre network in wet pressing, providedthe model parameters are estimated from experimental data withsmall experimental error. KEYWORDS:Paper, modelling, dewatering, forming, wetpressing, fibre network stress, rheology, hysteresis,intra-fibre water, compressibility, structural stress,stress-strain, restricted gels, swelling. / <p>QC 20161026</p>

<p>Most of the water fed into a paper machine is removedmechanically in the forming and press sections. One of thefactor which has an important influence on mechanicaldewatering, i.e. in both forming and pressing, is thestress-strain behaviour of the fibre network.</p><p>The focus of this thesis is on the development of improvedmathematical descriptions of the stress-strain behaviourexhibited by fibre networks in the forming and press sections.The first part of the thesis presents a physically based modelof the forming and densification of fibre mats in twin-wireformers. The model can calculate the ecect of the applicationof a varied load through the forming section. It was developedfrom mass and momentum balances of the fibre and liquid phases,the fibre mat stress-porosity relation and an expression forthe permeability as a function of the porosity. The fibre-matstress-porosity relation used is rate-independent and presentshysteresis. Simulations have been conducted to study theeffects of roll pressure, blade pulses, wire tension andbeating. The effect of sequential blade pressure pulses afterthe forming roll on the dewatering and the concentrationgradients could be characterised. The simulations alsoexhibited rewetting by expansion when the fibre mats left theforming roll. Increasing wire tension resulted in increaseddewatering, but the rate of increase diminished rapidly withincreasing tension. The simulation results also indicated thatbeating has a large influence on dewatering.</p><p>The second part of the thesis presents two models of therate-dependent stress-strain behaviour of the fibre networkthat is observed in wet pressing. The first model was based onthe approach pioneered by Perzyna (1966) for strain-ratedependent plasticity and was quite satisfactory for calculatingthe stress-strain behaviour of the fibre network in singlepress nips. It was successfully applied for studyingdensification and dewatering in both normal wet pressing andhigh temperature wet pressing. However, the first model onlyincludes rate dependence in the compression phase of thecompressionexpansion cycle; the expansion phase is treated asbeing rate independent</p><p>The second model of the stress-strain behaviour of the fibrenetwork treats both compression and expansion as being ratedependent, according to experimental observations. It is basedon the idea that the wet fibre web may be conceived as alayered network of restricted swelling gels. A swollen fibre isa restricted gel, the inner swelling pressure in a swollenfibre wall being balanced by the stresses in the fibre wallstructure. The observed rate dependence of wet webs in bothcompression and expansion phases was attributed to the flow ofwater out of and into the fibre walls. The second model gavepredictions that are in good agreement with results fromuniaxial experiments using pressure pulses of arbitrary shapefor both a single pulse and a sequence of pulses. It maytherefore be used as a general model for the rheologicalbehaviour of the wet fibre network in wet pressing, providedthe model parameters are estimated from experimental data withsmall experimental error.</p><p><b>KEYWORDS:</b>Paper, modelling, dewatering, forming, wetpressing, fibre network stress, rheology, hysteresis,intra-fibre water, compressibility, structural stress,stress-strain, restricted gels, swelling.</p>

Au cours des dernières décennies, le développement de nouveaux matériaux a progressé pour les applications liées à la mécanique. De nouvelles générations de composites ont été développées, qui peut offrir des avantages par rapport aux tapis unidirectionnels renforcés de fibres couramment utilisés les matériaux prennent alors le nom de woven fabrics. Le comportement de ce matériau est fortement influencé par la micro-structure du matériau. Dans la thèse, les modèles mécaniques et les schémas numériques capables de modéliser les comportement des tissus et des matériaux de réseau généraux ont été développés. Le modèle prend en compte la micro-structure au moyen d'une technique d'homogénéisation. Les fibres dans le réseau ont été traités comme des micro-poutres, ayant une rigidité à la fois en extension et en flexion, avec différents types de connexions. La procédure développée a été appliquée pour obtenir les modèles mécaniques homogénéisés pour certains types de réseaux de fibres biaxiaux et quadriaxiaux, simulant soit des réseaux de fibres (en ce cas a été supposé parmi les fibres) ou des tissus avec une interaction négligeable entre les faisceaux de fibres et en empêchant tout glissement relatif (dans ce cas, les connexions ont été simulés au moyen de pivots). Différentes géométries ont été analysées, y compris la cas dans lesquels les fibres ne sont pas orthogonales. On obtient généralement un premier milieu à gradient mais, dans certains cas, la procédure d'homogénéisation lui-même indique qu'un continuum d'ordre supérieur est mieux adapté pour représenter la déformation de la micro-structure. Des résultats spéciaux ont été obtenus dans le cas de fibres reliées par pivots. Dans ce cas, un matériau orthotrope à module de cisaillement nul a été obtenu. Un tel matériau a un tenseur constitutif elliptique, il peut donc conduire à des concentrations de contrainte. Cependant, il a été montré que certaines considérations sur le comportement physique de tels réseaux indiqué que les termes d'ordre supérieur inclus dans l'expansion des forces internes et des déformations, de sorte qu'un matériau de gradient de déformation a été obtenu. Les résultats obtenus peuvent être utilisés pour la conception de matériaux spécifiques nécessitant des propriétés. Bien que le modèle de référence soit un matériau de réseau, les résultats obtenus peuvent être appliqué à d'autres types similaires de microstructures, comme des matériaux pantographiques, des micro-dispositifs composé de micro-poutres, etc. Ils étaient limités à la gamme d'élasticité linéaire, qui est petite déformation et comportement élastique linéaire. Ensuite, les simulations numériques ont été axées sur les tests d'extension et les tests de biais. Le obtenu configurations déformées sont conformes aux tests expérimentaux de la littérature, tant pour tissus équilibrés et non équilibrés. De plus, une comparaison entre les premier et deuxième gradients des prédictions numériques ont été effectuées. Il a été observé que les prédictions de deuxième gradient mieux simuler les preuves expérimentales. / In the past decades there has been an impressive progress in the development of new materials for mechanical related applications. New generations of composites have been developed, that can offer advantages over the unidirectional fibre-reinforced mats commonly used then materials take the name of woven fabrics. The behaviour of this material is strongly influenced by the micro-structure of the material. In the thesis mechanical models and a numerical scheme able to model the mechanical behaviour of woven fabrics and general network materials have been developed. The model takes in to account the micro-structure by means of a homogenization technique. The fibres in the network have been treated like microbeams, having both extensional and bending stiffness, with different types of connection, according to the pattern and detail of the network. The developed procedure was applied for obtaining the homogenized mechanical models for some types of biaxial and quadriaxial networks of fibres, simulating either fibre nets (in this case rigid connection were assumed among the fibres) or tissues with negligible interaction between the fibre bundles, and with relative sliding prevented (in this case the connections were simulated by means of pivots). Different geometries were analysed, including the cases in which the fibres are not orthogonal. A first gradient medium is usually obtained but, in some cases, the homogenization procedure itself indicates that a higher order continuum is better fit to represent the deformation of the micro-structure. Special results were obtained for the case of fibres connected by pivots. In this cases an orthotropic material with zero shear modulus was obtained. Such a material has a not elliptic constitutive tensor, thus it can lead to strain concentrations. However, it was shown that some considerations about the physical behaviour of such networks indicated that higher order terms had to be included in the expansion of the internal forces and deformations, so that a strain gradient material was obtained. The results obtained can be used for the design of specific materials requiring ad-hoc properties. Although the reference model is a network material, the results obtained can be applied to other similar kinds of microstructures, like pantographic materials, micro devices composed by microbeams etc. They have been limited at the range of linear elasticity, that is small deformation and linear elastic behaviour. Then, numerical simulations were focused on extension tests and bias tests. The obtained deformed configurations are consistent with the literature experimental tests, both for balanced and unbalanced tissues. Moreover, a comparison between first and second gradient numerical predictions was performed. It was observed that second gradient predictions better simulate the experimental evidences.