Continuum modeling of the coupled transport of mass, energy, and momentum in paperboard

Abstract: This thesis investigates the coupling between moisture, heat, and deformation in paperboard. The presented investigations are primarily conducted via macroscale continuum modeling but experimental characterisations are also made. The continuum modeling is presented in a mixture theory framework where the paperboard is considered as a porous media composed of three immiscible phases; a network of cellulose fibers, liquid water bound in or to the fibers, and moist air. The motion of each phase is described and the interactions of mass, energy, and momentum between the three phases are also considered. Emphasis in the current work is to derive a thermodynamically consistent model and all constitutive relations are derived with consideration to the Clausius-Duhem inequality. The derived continuum model is used in numerical investigations to study the response of slow, long time processes such as storing of paperboard rolls as well as rapid processes where the board is exposed to significant temperature changes and mechanical loads during a short period of time.The thesis begins with an introduction where some of the characteristic properties of paperboard are described and the basic concepts of the hybrid mixture theory framework are explained. The main part of the thesis is then composed of four papers, A, B, C, and D. In Paper A, a model describing the transport of mass and heat in paperboard is developed. The model considers slow transport processes and assumes the fiber network to be incompressible. Special focus of Paper A is to develop a model that is able to describe the static and dynamic sorption properties of paperboard. The derived model is used to predict the evolution of the moisture and heat distributions in paperboard rolls in climates with a varying relative humidity. In Papers B and C, the model derived in Paper A is further developed to handle rapid processes where significant temperature changes are expected. Furthermore, in Papers B and C, the assumption of an incompressible fiber network is abandoned and an orthotropic stress-strain response with an advanced yield surface is incorporated in a large strain setting. The model is then used to predict the response of paperboard during a transversal sealing process. In Paper D, experimental investigations are made on the in-plane permeability and on the static and dynamic sorption properties of paperboard. The results from these investigations are then used together with the model developed in Paper B and C to analyse the physics behind a blister test.