Mathematical Formula
Capillary pressure differences across a curved liquid-gas interface are described by a fundamental equation that relates pressure to surface tension and pore radius. Papermaking research applies the Young-Laplace equation to model how coating pores draw in liquid ink vehicles. The formula applies to any capillary system with a liquid meniscus, serving as the basis for understanding fluid absorption in porous coatings.
Absorption Process
Penetration speed of printing ink depends directly on the capillary pressure generated within the tiny pores of the coating. According to the formula, smaller pore diameters produce higher capillary pressures, which draw the liquid vehicle into the sheet faster. The Young-Laplace equation shows why coating formulation with fine pigments like clays and carbonates improves the rate of ink drying.
Paper chemists use this relation to design coating pore structures that quickly drain ink solvent while holding the binder and pigment at the surface.
Barrier Engineering
Hydrophobic surface treatments work by increasing the contact angle of the meniscus to change the direction of the pressure. This change prevents water from spontaneously entering the pore network under zero external pressure. Combining the Young-Laplace equation with sizing technology allows for the design of water-resistant food service boards.
