Coupled heat, mass and momentum transport in swelling cellulose based materials with application to retorting of paperboard packages

Abstract

Understanding the complex interplay of mass transport, heat transport and deformation in swelling cellulose based materials is a challenging task. To aid in this endeavour a multiphysics model is developed within the mixture theory framework. The model is macroscopic and accounts for swelling, non-equilibrium mass exchange of water, elastic deformation and multiphase transport phenomena, where non-isothermal conditions are considered. The investigated material is viewed as an immiscible mixture of cellulose fibers, pore gas and inter-fiber pore water separated by interfaces. Fiber and gas are considered as miscible mixtures of dry fiber and fiber water, and dry air and water vapor, respectively. The constitutive equations are obtained in a coupled and thermodynamically consistent manner by exploitation of the dissipation inequality. As an application of the model, conditions representative of the retorting process for liquid packaging board are simulated using the proposed constitutive model. The influence of the process control parameters during the heating, cooking and cooling steps of the retorting procedure are analysed. It was found that through-plane temperature gradients and the presence of dry air in the retort had a significant impact on the moisture uptake and the moisture distribution. Spatial distribution of hydrophobicity had a great effect on the distribution of fiber water and inter-fiber water.