Generalized formulation for evaporation rate and flow pattern prediction inside an evaporating pinned sessile drop

Abstract

When a sessile drop is heated from below, it evaporates and it induces a cooling effect in a zone close to the drop surface. The important evaporation rate at the contact line, the surface tension gradient at the liquid-air interface and the buoyancy generate the liquid motion inside the drop. Several parameters affect the evaporation rate among which the substrate properties, the moisture of the surrounding air and the heating conditions. Therefore, different flow patterns could be observed during the evaporation and they are mainly influenced by the relative importance of the evaporation rate, the thermo-capillarity and the buoyancy. The present study uses a generalized formulation to predict the flow patterns at any time during evaporation taking into account all these effects. The contribution and the relative importance of each effect are analyzed under isothermal and non-isothermal heating and different values of the relative humidity of the surrounding air. The correlation proposed by Hu and Larson for assessment of the evaporation rate is extended to non-isothermal surfaces for any evaporation conditions. Flow pattern maps are elaborated based on the dimensionless height of the drop apex and the evaporation conditions.