A unified force-energy adhesion model for wettability on real solid surfaces

The wettability of real solid surfaces cannot be fully described by a single apparent contact angle because geometric roughness and chemical heterogeneity produce a distribution of local contact angles along the three-phase contact line. In this work, the deviation from the ideal Young surface is quantified using a single, surface-specific, dimensionless parameter derived from force and energy balances of wetting.

A unified theoretical framework for liquid droplet wetting on rigid solid surfaces is developed by coupling mass conservation with force and energy balances. An adhesion coefficient, defined as the ratio of the additional wetting potential on a real surface to the overall wetting potential, links force-based and energetic descriptions. Comparison with extensive experimental data for various solid surfaces and probe liquids shows that the adhesion coefficient serves as an effective surface descriptor, with data collapsing onto a universal scaling.

Explicit expressions are obtained for the nondimensional work of adhesion and a normalized Zisman-type relationship, enabling direct evaluation from the apparent contact angle and adhesion coefficient. A wettability diagram reveals a critical contact angle dependent on the adhesion coefficient, providing a criterion for distinguishing hydrophilic and hydrophobic regimes. Overall, the results establish a compact, dimensionless description of wettability on real solid surfaces that extends classical contact-angle-based interpretations.