Modelling multiphase transport in deformable cellulose based materials exhibiting internal mass exchange and swelling

A thermodynamically consistent model for porous cellulose networks is proposed. A general theory is developed based on mixture theory using chemical potentials as flow potentials. The material is decomposed into three phases, solid, liquid and gas, where the solid and gas phases are further separated into dry fiber and fiber water, water vapor and dry air, respectively. Between the phases interfaces are present and their influence on the mass exchange of water is incorporated. Emphasis is placed on the dynamics in mass exchange of water which allows for description of non-equilibrium states. The driving force for reaching equilibrium is given by the chemical potential difference. Constitutive relations relevant for paperboard are proposed and illustrative simulations are carried out to reveal the dynamics of mass exchange. The model enables analysis of transient flow accounting for effects of deformation, swelling and moisture sorption dynamics.