Macroscopic modelling of coupled multiphysics in swelling cellulose based materials

University dissertation from Division of Solid Mechanics

Abstract: Paperboard has been the basis for packaging materials used to aseptically store and protect food and beverages for a long time. To ensure that there are no bacteria that can spoil the product, sterilizing treatments are made. One such treatment is the retorting process, which involves heating to high temperatures in a pressurized environment of water vapor and dry air. The porous nature of paper materials and the affinity of the cellulose fiber to interact with water make sterilizing environments particularly demanding. Gaps in the knowledge of the physics of the interaction between moisture, temperature and deformation may lead to difficulties in designing robust processes and materials. In this work the interplay between moisture, temperature, and deformation are investigated in cellulose based materials using macroscopic continuum modelling. Adopting the mixture theory framework, thermodynamically consistent models are derived using a systematic treatment of the dissipation inequality. Paperboard is conceptually viewed as a superposition of immiscible phases, which consist of miscible constituents. Constitutive theory is developed that allows for modelling and simulation of paperboard in a range of industrially relevant applications.The thesis contains an introductory part addressing the basic aspects of cellulose based materials followed by a short review of paper modelling. Thereafter the physical characteristics of paper and paperboard are explored. The concepts of mixture theory and its use in this work are addressed and subsequently a discussion of the model applications and simulation results are held. The central part of this thesis comprises five papers denoted Paper A to Paper E. Paper A describes non-isothermal moisture transport, assuming a rigid material. The central feature is the non-equilibrium sorption and its coupling to vapor and heat transport. In Paper B the concepts in Paper A are extended to model rapid processes with large temperature variations. The conceptual view of the material is reconsidered in Paper C and Paper D, for the purpose of describing swelling and inter-fiber water transport. The model is used to simulate edge wicking and exchange of mass between fiber, inter-fiber liquid and vapor under isothermal conditions. Paper E further enhances the model presented in Paper C and Paper D by considering non-isothermal problems, to encompass conditions relevant for the retorting process of food packages designed for long shelf-life. Simulations of the coupled heat transport, mass transport and deformation during retorting of paperboard packaging are presented, addressing the large variations in temperature, moisture and pressure representative of the retorting process.