Droplets and rivulets on substrates with complex topography: evaporation and viscous flows in the vicinity of a contact line

Understanding of wetting and evaporation of liquid films and drops on porous, rough, fractured or textured surfaces is crucial for many industrial processes such as development of inks, adhesives and coatings and manufacturing of microelectronic devices. In the present work, we consider volatile drops and rivulets on substrates with complex topography. We develop an analytical model and obtain local solutions for the viscous flows in the liquid as well as in the gas phase in the vicinity of the contact line, assumed to be pinned to a wedge-shaped non-uniformity of a substrate. We take Stefan flow into account and show how it can affect the flow in the liquid phase. We also determine the impact of the wedge opening angles on the flow topology and existence of critical angles, at which the dominant flow contribution changes.