Generalized model for static contact angles and hysteresis on micro/nanostructured surfaces

This work presents a compact, general model that predicts static contact angles and upper bounds on contact angle hysteresis for random or periodic local surface topography by accounting for arbitrary fractions of localized air entrapment and liquid infiltration within micro/nanoscale topographic features adjacent to the contact line. The proposed model recovers classical wetting limits (Wenzel, Cassie-Baxter, and hemiwicking), accounts for intermediate states (e.g., impregnating Cassie), and highlights a fourth limiting state with potential realizability and practical implications: a bulk Cassie state with an ambient liquid film, termed the inverse Wenzel state. The model predictions provide actionable guidance for the rational design of micro- and nanostructured surfaces to modulate contact angle hysteresis, under real-world operating conditions that are often uncontrolled and unpredictable due to local variations of the surface topography, fouling or contamination at the liquid-solid and liquid-vapor interfaces, chemical aging, kinetic constraints, and fluctuations of the ambient relative humidity and temperature.