Droplet evaporation on curved surfaces: transients of internal and external transport phenomena

We explore the transient evolution of thermo-fluid-dynamics of evaporating sessile droplets over curved substrates in the liquid and gaseous domains. A computational model using the Arbitrary Lagrangian-Eulerian framework is adopted. The governing equations in both liquid and gaseous domains are solved in a fully coupled manner, considering coupled effects of evaporative cooling and heat advection due to bulk fluid motion. This bulk motion in the liquid domain is caused by natural advection due to thermal actuations such as thermal Marangoni flow and buoyancy-driven convection. For the gaseous domain, the additional effects of solutal convection (due to vapour-concentration variation), Stefan flow and interfacial viscous stresses are also considered. To depict a generalized role of substrate curvature, both concave and convex surfaces with curvatures over a wide range are studied. The surface wettability effects are also explored by varying the true contact angle of the droplets. Computational predictions on evaporation rate and internal flow field are validated against experimental results from literature. The interplay of wetting state and substrate curvature is noted to substantially affect the evaporation process and its thermo-fluidics. The convex curvature significantly augments internal advection while the same is weakened over concave substrates due to altered mass loss rate. Consequently, the duration of multi-vortex Marangoni flows in the development stages of evaporation and the advection in the external gaseous domain is markedly different for different curvatures. Further, on superhydrophobic curved surfaces, the effects of re-distributed evaporative fluxes play a major role. In such cases, the reduced mass flux over a large interfacial area near the periphery expedites the stable state Marangoni and external flow features.