Contact-angle hysteresis on rough surfaces: mechanical energy balance framework

Abstract

Using as a starting point conservation of momentum, a multiphase mechanical energy balance equation is derived that accounts for multiple material phases and interfaces present within a moving control volume. This balance is applied to a control volume that is anchored to a three-phase contact line as it advances continuously over the surface of a rough and chemically homogeneous and inert solid. Using semi-quantitative models for the material behaviour occurring within the control volume, an order of magnitude analysis is performed to neglect insignificant terms, producing an equation for predicting contact-angle hysteresis from a knowledge of the interface dynamics occurring around the three-phase contact line. It is shown that the viscous energy dissipation that occurs during the ‘stick–slip’ motion of the three-phase contact line, being the cause of contact-angle hysteresis on rough surfaces, can be calculated from changes in intermediate equilibrium interface states. The balance is applied to the Wenzel, Cassie–Baxter and Fakir (super-hydrophobic) wetting states, showing for the Fakir case that significant dissipation occurs during both interface advance and recede, and relating these dissipations to interfacial area changes that occur around the ‘stick–slip’ events.