Condensation-driven hydration of porous paperboard: coupled heat–mass transport, pore flooding, and climatic sensitivity

Journal article, 2026

The hydration of paperboard walls in cups filled with cold beverages arises from coupled heat and mass transfer phenomena. While classical studies describe moisture uptake only in the hygroscopic range, the behavior under condensation remains largely unexplored. In this work, we extend the water–paper adsorption isotherm into the supersaturated regime, perform dynamic hydration experiments on cups exposed to iced water, and develop a mechanistic model to capture the observed kinetics. Experiments reveal that once supersaturation occurs (relative humidity larger than one), water content on a dry basis rises sharply, suggesting liquid saturation levels approaching pore-filling conditions. Time-resolved measurements show a two-stage process: an initial rapid uptake linked to condensation and filling of accessible pores, followed by a slower diffusion- and capillary-controlled regime. The coupled model, which incorporates vapor diffusion, liquid imbibition, and heat transfer, was calibrated using the effective water diffusivity as a single fitting parameter and thus the model reproduced the experimental data with good accuracy. Applied as a predictive tool, the model anticipates cup behavior under diverse climates: low hydration in dry winters, moderate in dry summers, and critical uptake in humid summers. This combined experimental–modeling approach provides a robust framework to predict condensation-driven water uptake and supports the design of sustainable paper-based packaging.