Analytical modeling of the evaporation of sessile drop linear arrays

An analytical model for predicting the competitive evaporation of two and three sessile drops is proposed, based on an analytical solution, in terms of Mehler functions, of the steady species and energy conservation equations for the gaseous phase. The assessment through a comparison with accurate numerical solutions of the species conservation equations is reported in order to quantify the accuracy of the analytical solution. The model is validated against three available sets of experiments on two and three sessile drops on a line array. The decrease of the evaporation rate caused by the vicinity of sessile drops is reported in terms of a screening coefficient given by a relatively simple analytical expression. The influence of wall wettability on the evaporation of pairs of sessile drops is analyzed, and a parameter is proposed to quantify the effect of geometry in a unified way.