Kelvin Equation

Fiber Porosity

The paper substrate absorbs moisture from the air, fill gas, or aqueous inks through these tiny pores. As the pore radius decreases, the relative humidity required for condensation to occur drops, causing the paper to absorb water even in dry conditions. This capillary condensation behavior affects both the dry strength and the dimensional stability of the packaging material.

Coating Behavior

When applying aqueous coatings or inks to high-density board, the kelvin equation helps model the penetration rate of the solvent into the paper matrix. It explains how dry paper can rapidly extract water from a coating layer, which accelerates the setting of adhesive but can also cause coating cracking if the drying is too rapid. Understanding this behavior allows formulation chemists to adjust the binder and pigment size distributions to optimize solvent absorption.

This thermodynamic calculation is a foundational tool for designing moisture-barrier coatings for food-contact paperboard.