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

Modeling of volatile droplets and rivulets on structured or rough surfaces requires detailed analysis of vapor diffusion and fluid flow near their edges where a significant amount of evaporation is expected based on both experimental data and theoretical considerations. We develop local analytical models of flow generated in these regions in both liquid and gas phases as a result of evaporation at the liquid-gas interface. Extensive parametric studies show changes in flow structure as surface wetting properties and the parameters of the surface structure/roughness are varied. Previous studies of contact lines on flat solid surfaces identified the critical contact angle above which the locally dominant flow contribution becomes independent of the evaporation rate. We find that for the contact line pinned at the wedge, this critical value increases in a nearly linear fashion as the solid wedge angle gamma is decreased and develop a simple argument to explain this observation. Conditions are identified when flow separatrices can appear. The previously found separatrix emerging at contact angles slightly below the critical value persists over a range of gamma but appears at higher values of the contact angle theta as gamma is decreased. Increasing the gas viscosity can have a strong effect on the flow patterns in both gas and liquid. Connections between local and global solutions for several geometric configurations and implications for transport of particles in both liquid and gas phases, as well as heat transfer, are discussed.