Evaporation of non-spherical water droplets on horizontal and vertical hydrophobic substrates

When it comes to droplet evaporation, most evaporation models assume a spherical droplet. However, gravity causes a droplet to deviate from a spherical shape in practice. In this study, the equilibrium shapes of gravity-induced non-spherical droplets are obtained using the energy minimization method. Based on these shapes, a three-dimensional numerical model incorporating vapor diffusion, natural convection, conjugate heat transfer, and evaporative cooling is developed to examine the differences in evaporation characteristics between spherical and non-spherical water droplets on horizontal and vertical hydrophobic substrates. The results demonstrate that gravity-induced deformation reduces the thermal resistance in the horizontal non-spherical droplet from its bottom to the top. This results in a higher minimum interfacial temperature in the horizontal non-spherical droplet than in its horizontal spherical counterpart. In contrast, the vertical non-spherical droplet exhibits a lower minimum interfacial temperature than the vertical spherical droplet. These different temperature distributions and geometric shapes drive different internal flow fields, enabling the horizontal non-spherical and vertical spherical droplets to exceed the average interfacial flow velocity of their counterparts by 7.27% and 9.91%, respectively. Furthermore, the local evaporation flux, governed by temperature and gas-phase convection, also exhibits distinct spatial distributions in these droplets. Surprisingly, despite causing notable changes in heat and mass transfer, gravity-induced deformation does not significantly alter the total evaporation rate. This might be attributed to the minimal difference in surface area of the droplets and a stable diffusion resistance. These findings imply that the evaporation rate of gravity-induced non-spherical droplets may be approximated by spherical droplets.