Evaporation and viscous flow structure near a contact line pinned at a solid wedge

Evaporation on rough or structured surfaces is of interest from both fundamental and practical points of view. In this work, we consider volatile droplets and rivulets with contact lines pinned to wedge-shaped elements of the substrate topography. We develop a local analytical model of the evaporation-induced flow in the vicinity of the contact line in both liquid and gas phases, analyze the influence of gas viscosity as well as of an opening angle of the wedge on the flow patterns, and obtain critical contact angles, above which the eigenmode solution dominates the evaporation-induced solution.