Modeling the evaporation of sessile drops deformed by gravity on hydrophilic and hydrophobic substrates

Abstract

Evaporation of sessile drops deformed by gravity is quantified by an analytical–numerical approach. The shape of the drops is defined by minimizing the interfacial and potential drop energies, following a variational integral approach, for a wide range of drop sizes (from 2.7 μl to 1.4 ml for water drops) and contact angles for both hydrophilic and hydrophobic substrates. The extension of an analytical model for drop evaporation, which accounts for the effect of the Stefan flow and the temperature dependence of thermophysical properties, to the present conditions reduces the problem to the solution of a Laplace equation, which is then numerically calculated using COMSOL Multiphysics®. The vapor fluxes and evaporation rates are then quantified, and the systematic approach to the problem allows the derivation of two correlations, for hydrophilic and hydrophobic substrates, respectively, that can be used to correct the evaporation rate calculated for a drop of the same volume and contact angle in the absence of gravity effects.