Coupling effect of substrate thermal properties and droplet geometry on Marangoni instabilities inside an evaporating droplet at quasi-steady state

Abstract

Although extensive researches have been conducted into influences of substrate thermal properties on droplet evaporation, few of them were aimed on the instabilities of their internal flow. In this paper, flow fields of Marangoni instabilities inside an evaporating droplet are simulated by a three-dimensional one-sided model, with considering the coupling effect of substrate thermal properties and droplet geometrical shape. Results shows that a large relative thermal conductivity and a larger droplet contact angle favor the appearance of hydrothermal waves. Hydrothermal waves of fan-like configurations are transformed to irregular hydrothermal waves with evaporation. With a decrease of the contact angle, instability patterns of hydrothermal waves, coexistence of hydrothermal waves and longitudinal rolls, stationary longitudinal roll, irregular Bénard-Marangoni convection were generated in sequence. Nonetheless, a small relative thermal conductivity suppresses the emergency of hydrothermal waves, with longitudinal rolls coexisting with Bénard-Marangoni cells. Longitudinal rolls propagate towards the cold side along the droplet circumference, concurrently with Bénard-Marangoni cells exhibiting a direct movement towards the cold side. Influences of droplet contact angle, substrate temperature, and relative thermal conductivity on characteristics of the observed instability patterns were systematically analyzed. This research facilitates a deeper understanding of the substrate thermal impacts on Marangoni instabilities within droplets.