Influence of thermal properties on hydrothermal waves in evaporating sessile droplets

Abstract

The thermal properties of droplets have a significant effect on the evaporation of sessile droplets. In this study, the influence of nondimensional thermal properties on Marangoni instabilities, especially hydrothermal waves (HTWs), in a sessile droplet evaporating at a constant contact angle mode, is numerically investigated using a nondimensional mathematical model. The model considers the transient deformation of the droplet surface during evaporation in a wide range of Marangoni numbers from 1000 to 40 000, evaporative cooling numbers from 1 to 300, relative heat conductivities from 0.01 to 1000, and Prandtl numbers from 0.01 to 25.0. Included are the different kinds of fluids applied in previous works on Marangoni convection in evaporating sessile droplets. The substrate material varies from a vacuum insulation panel with a heat conductivity of 0.002 W/m·K to silver with 429 W/m·K. The results reveal that a sufficiently large Marangoni number, evaporative cooling number, and relative heat conductivity favor the appearance of HTWs, whereas a large Prandtl number inhibits the appearance of HTWs. The mixture mode of Bénard–Marangoni cells and longitudinal rolls or of longitudinal rolls and HTWs can occur for a small relative heat conductivity. The influence of these thermal properties on the characteristics and dynamic behaviors of HTWs are analyzed and the critical Marangoni numbers for the appearance of HTWs are determined. This work can be helpful for understanding the influence of thermal properties on HTWs in sessile droplets.