Quantifying the interacting mechanisms in shape evolution of sessile volatile droplets

Non-uniform distribution of interfacial mass flux across an evaporating/condensing droplet will subsequently induce a temperature gradient across the liquid-air interface, and result in thermal Marangoni stress that reforms the flow field inside the droplet. Recent study (Shiri, et al. Phys. Rev. Lett. 2021, Yang, et al. Langmuir 2022) confirmed the impact of thermal Marangoni flow on the shape of single component volatile droplets on completely wetting substrates. Nevertheless, a comprehensive evaluation of the interacting mechanisms is still lacking due to the intrinsic limitation of experimental techniques to decompose the different influence factors. To this end, we formulate a mathematical model to simulate the evaporation/condensation of a single component droplet on completely wetting substrates accounting for the thermal transport across the solid substrate. With this model, we elucidate the interacting physical mechanisms that govern the droplet kinetics during phase change, which include the capillary effect, the thermal Marangoni effect, the interface motion due to evaporation/condensation, as well as the removal of energy barriers by precursor film. Taking the thermophysical properties of water as the base parameters, we elucidate that the thermal Marangoni effect plays a non-negligible role in the evolution of droplet geometry during phase change. Additionally, the liquid volatility along with the substrate conductivity and thickness influence the magnitude of the thermal Marangoni stress. A phase diagram is subsequently summarized in terms of the Knudsen number, which compares the interfacial thermal effect to the liquid phase thermal transport, and the Biot number, which compares the the heat transfer through the liquid phase and through the solid phase. The conclusions clearly elucidate the prevalence and interaction of the Marangoni and capillary effects on droplet dynamics with interfacial phase change.