Since the production and demand for paper products are escalating around the world, the increased environmental regulations have forced Pulp and Paper Industry (PPI) to be more eco-conscious than ever before. However, PPI has been struggling to minimize the wastes during pulping (i.e., off-grade pulps), which have typically been sent to landfills or incinerated. Therefore, it is important to regulate mechanical properties of pulps (e.g., rigidity, flexibility, and strength) to meet the varying product requirements, which in turn reduces the waste production. Specifically, it has been known that the morphology of a single fiber affects the fiber network which governs the mechanical properties of pulp . For instance, the curl index, which indicates the degree of fiber curvature, is regarded as one of the crucial quality indices that determines the tensile strength of paper. In other words, the increased entanglements between curly fibers (i.e., fibers with a high curl index) allow them to resist while being stretched [2-4].
Despite the importance of the fiber curl, few studies have been executed to describe the evolution of fiber curl in a pulp digester. Specifically, during the Kraft pulping process where lignin is dissolved into cooking liquor under a high cooking temperature and alkaline solvent, fiber elasticity is easily altered by the chemical composition of wood fiber [5, 6]. However, it is difficult to measure the curl change due to the inherent pulping conditions such as high pressure, varying cooking temperature, and evolving (solid-phase) chemical composition of the fiber. In addition, the pulping conditions also serve as a barrier to the development of a predictive model for the curl evolution since the various operating conditions contribute to the high computational complexity and make the computation of the dynamic buckling motion of fiber complicated. Moreover, the fiber deformation continuously takes place during the pulping process, which gives time-varying elasticity and moment of inertia, thereby limiting the application of Euler-Bernoulli beam theory [7, 8].
Motivated by these limitations, in this work, a multiscale model was developed to depict the evolution of fiber curl in a pulping digester. Specifically, the Purdue model and a kinetic Monte Carlo algorithm were integrated to capture the macroscopic kinetics and microscopic events in the Kraft pulping process, respectively. Subsequently, the rule of mixtures was employed to predict the elastic modulus of wood fiber in the pulping process with respect to the change of chemical composition of wood fiber . In addition, the temperature dependency of fiber elasticity was taken into account to investigate the effect of varying cooking temperatures . With these considerations, the deformation process of the fiber was described by employing the Euler-Bernoulli beam theory, which elucidates the time-varying elasticity. Lastly, the developed model was validated against experimental data . Additionally, the effects of cooking temperature and chemical composition of fiber on the mechanical properties of end-use papers were analyzed. This proposed work also provides insights into the effective regulation of pulp strength by manipulating the cooking conditions of the pulp digester.