Evaporation dynamics of wavy sessile droplets

We study the evaporation dynamics of non-thin non-spherical-cap (i.e. wavy) droplets. These droplets exhibit surface curvature that varies periodically with the polar angle, which profoundly influences their evaporation flux, internal flow dynamics, and the resultant deposition patterns upon complete evaporation. The droplet is considered quasi-static throughout its entire lifetime. The asymptotic expansions of the evaporation flux in the diffusion-limited model, and the induced internal inviscid flow of the droplets, are derived through asymptotic analysis. Under the assumption of small deformation amplitudes, the accuracies of these two expansions are validated numerically. Expanding upon these asymptotic results, we also investigate the surface density profile of the droplet deposition after it dries up. The results indicate that the freely moving contact line of the droplet leads to the deposited stain exhibiting a mountain-like morphology. The internal inviscid flow along with the non-spherical-cap shape eliminates the divergence of the deposited surface density profile at droplet’s centre. This work provides a theoretical basis for geometrically controlled sessile droplet evaporation, which may have practical applications in industry.