Mathematical modelling of water absorption over time for coated paperboards subjected to external pressures

Abstract The aim of this study is to develop a model for predicting the liquid absorption of coated boards subjected to external pressure. To create a simplified approach, the mathematical formulation was entirely based on existing models from the literature. The model’s predictions were then compared with practical laboratory Cobb measurements taken at various pressures on more porous and on less porous coatings. The results demonstrate that the model effectively captures the key trends in water absorption of coated boards under external pressure, aligning with findings from the laboratory study. However, due to the model’s sensitivity to system inputs, a thorough understanding of both the coating and paperboard characteristics is essential to improve prediction accuracy. Additionally, the original authors of the model (Equation (2)) suggest that the expression is best used for predicting water absorption over short periods.