A phase-field model: Contact angle hysteresis driven by multistable surface composition

Experimental observations have revealed molecular-scale density depletion near hydrophobic substrates, suggesting a diffuse and structurally heterogeneous fluid-solid interface. Motivated by these findings, we hypothesise that the surface composition at the fluid-solid boundary may adopt multiple energetically favourable states. To account for this behaviour, we introduce a nonmonotonic wall free energy formulation that captures the energetic contribution of the fluid-solid interactions within the wetting boundary condition of a thermodynamically consistent phase-field model. This formulation successfully reproduces multistable surface compositions and enables the modelling of static contact angle hysteresis (CAH) on smooth, horizontally oriented substrates, arising from deposition histories. By allowing the wall free energy to relax and permit contact line motion via molecular diffusion, this model captures the dynamic CAH observed during droplet motion on inclined substrates. Unlike conventional phase-field CAH models, our framework requires no explicit input on contact-line velocity or prescribed contact angles and relies solely on thermodynamic energy minimisation; it automatically captures contact line pinning, as well as advancing and receding states. Upon droplet sliding with CAH, stick-slip behaviour naturally emerges. These findings demonstrate that both CAH and stick-slip behaviour can originate purely from molecular-scale fluid-solid interactions, underscoring the importance of surface composition and interfacial diffusion, factors often overlooked in classical hydrodynamic models. This framework provides a pathway to bridge thermodynamic and hydrodynamic perspectives, potentially enabling new insights into slip, friction, and no-slip behaviour at fluid-solid interfaces, with particular relevance for microfluidic applications.