par Dave, Nik
Président du jury Gerard, Pierre
Promoteur Massart, Thierry Jacques ;Geers, Marc G.D.
Co-Promoteur Peerlings, Ron H J
Publication Non publié, 2025-05-12
Thèse de doctorat
Résumé : Paper, a porous-fibrous network, is made up of micro-scale hydrophilic fibres, which are notably susceptible to deformations due to variations in moisture content. On interaction with water, the dimensional change of a single fibre is transmitted to the fibre network via the inter-fibre bonds. At the sheet scale, this could result in out-of-plane displacements in the form of curling, fluting, cockling. In professional inkjet printing systems, this inadvertent behaviour is attributed to the time-dependent through-thickness liquid penetration. This process generally consists of a fast liquid penetration through the porous structure and subsequently a comparatively slow absorption by the fibres. At this point, the fibres start to swell and as a result of their collective, time-dependent swelling the sheet deforms as well. The deformations which occur depend on the hygro-mechanical properties of the fibres and their geometrical arrangement in the network. Additionally, the inter-fibre bonds and their mechanical and hygro-expansive properties play an important part in the overall expansion of the thin paper sheet.To understand these macro-scale dimensional instabilities of paper, it is essential to study the properties of the fibrous network at the microscale. This thesis proposes an analytical and computational multiscale multi-physics modelling approach to acquire an enhanced comprehension of the factors affecting the water-induced swelling response and response of a paper sheet. The research enables to capture the complex behaviour of a paper fibrous network using analytical and idealised modelling techniques. To predict the hygro-expansive response at the sheet scale, the role of pores, fibres, inter-fibre bonds and their distribution is examined and the devised modelling framework is used to gain an understanding of the contribution of the microscale properties to the sheet swelling and out-of-plane deformation.This thesis addresses two main issues, divided into two parts: Part A focuses on the homogenisation of swelling properties from the microscale to the sheet scale, while Part B develops a macroscale model for liquid transport through the fibrous network. (i) In Part A, scale transitions are developed from single fibre swelling to sheet deformation, employing simple, analytical models that are validated by computational models and experimental data. These models capture the swelling and curl behaviour of fibres and inter-fibre bonds at the microscale and relate them to overall sheet deformation. (ii) In Part B, a novel macroscale model integrates liquid transport, absorption, swelling, and curl into a unified framework. While the mechanical part was previously established, the transport model is newly developed and validated through experiments. Experimental data used for validation was provided by colleagues at Eindhoven University of Technology and Canon Production Printing B.V.The response of paper sheets to full or partial wetting, based on the water-induced fibre swelling, has been predicted in the past using a highly idealised two-dimensional (2D) geometry. In Chapter 2, a multiscale modelling work is developed where homogenised sheet scale curl, derived from hygro-elastic deformations using non-uniform moisture profiles, is analysed based on an idealised non-woven three-dimensional (3D) fibrous network finite element model. First, the effective paper sheet swelling properties, derived computationally for the uniform wetting condition, are compared with analytically homogenised hygro-elastic properties. The influence of wrapped-around fibre bonds and alternating bond arrangements on the hygro-mechanical material response is also analysed. Subsequently, paper sheet curl is predicted and compared with an analytical solution of macro-scale curl using a continuum approximation with the derived hygro-elastic properties and non-uniform wetting conditions. The values predicted by the analytical model are in accordance with the 3D simulation results. The simple highly idealised model captures the macro-scale curl within an error of approximately 10%.The anisotropic swelling of the fibres affects the deformation at the bonded region, i.e. where two fibres overlap. The extent to which the local strains are transferred over the whole fibrous network determines how much paper expands or shrinks when the moisture content varies. To understand the role of the bonding region in the inter-fibre bond scale swelling and on the sheet-scale response of the network, an experimental-analytical-numerical comparison is performed at the three scales in Chapter 3. Variations of fibres - softwood (SW), hardwood (HW), restrained dried (RD) and freely dried (FD) are tested at these scales. By using the experimentally observed geometrical and material properties in the computational model, the response of the fibre, bond and network are adequately predicted within the confidence intervals of the experiments.In Chapter 4, the time-dependent factors involved in the deformation of a paper strip that is fully or partially wetted and subjected to different boundary conditions are studied with experiments and numerical modelling. The different time scales involved, in the process of imbibition into the inter-fibre pores and absorption by the fibres, are analysed. The resulting hygro-expansion at the sheet scale due to swelling of the wet fibres is solved to predict the response of a paper strip. A micromechanical model is used to describe the liquid flow through the thickness of a paper strip, via the pores and fibrous network, entailing moisture-induced deformations through a hygro-elastic material model. The numerical results reveal an adequate qualitative agreement with experimental observations. The immersion test modelling results provide an estimate of the time scales involved in the liquid transport, which is subsequently used to characterise the curling response of the paper strip. The initial macro-scale bending behaviour is well predicted with the adopted hygro-elastic model.The immersion test is then utilised to analyse the difference in flow through the thickness of different porous media. Coated and uncoated paper sheets were used in the experiments and the developed model is employed to predict the time scale of the pore flow, pore-fibre mass exchange and the sheet scale hygro-expansion in Chapter 5. The model takes into account the pore size distribution derived from the Mercury Intrusion Porosimetry (MIP) test, which is used to characterise the flow properties like capillary pressure, saturation and permeability. The impact of coating is demonstrated and the influence of using different thicknesses and pore size distribution is analysed based on assumed dynamic viscosity, surface tension and contact angle using a two-layered unsaturated flow based model.Overall, the developed multiscale modelling framework offers new insights into the hygro-mechanical behaviour of paper sheets, from fibre-scale interactions to macroscale transport processes. The research advances the understanding of how moisture-driven deformation can be predicted and controlled, with applications to printing and materials engineering.

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