Stable Hydrothermal Waves at Steady State Evaporating Droplet Surface.

Stable hydrothermal waves (HTWs) are found at a sessile ethanol droplet surface under the steady state evaporation. It is different from those which greatly decrease with the evaporation time in the transient droplet drying process. This study removes the possible effect of shrinking droplet on HTWs. An analysis of the dimensionless numbers indicates the increasingly enhanced role of thermocapillary instabilities upon raising the substrate temperature. The onset HTWs can be continuously maintained under the steady state evaporation conditions. Interestingly, the stable number of HTWs follows a linear fitting with the dimensionless factor incorporating the normalized temperature difference between the substrate and the surroundings and the droplet aspect ratio. The temperature heterogeneity of HTWs is intensified by increasing the substrate temperature. The stable HTWs exhibit the "one source-to-one sink" propagation at lower substrate temperatures. However, such directional traveling, normally presented in the transient HTWs in the drying droplet, is changed at the higher substrate temperatures due to the newly emerged sources and sinks under the steady state conditions.