The shielding effect extends the lifetimes of two-dimensional sessile droplets

Abstract

We consider the diffusion-limited evaporation of thin two-dimensional sessile droplets either singly or in a pair. A conformal-mapping technique is used to calculate the vapour concentrations in the surrounding atmosphere, and thus to obtain closed-form solutions for the evolution and the lifetimes of the droplets in various modes of evaporation. These solutions demonstrate that, in contrast to in three dimensions, in large domains the lifetimes of the droplets depend logarithmically on the size of the domain, and more weakly on the mode of evaporation and the separation between the droplets. In particular, they allow us to quantify the shielding effect that the droplets have on each other, and how it extends the lifetimes of the droplets.

Competitive evaporation of multiple sessile droplets

“…2019; Schofield et al. 2020). The critical difference in comparison with what is observed with a single droplet is the occurrence of ‘shielding’, in which the presence of other droplets causes a droplet to evaporate more slowly than it would in isolation.…”

“…Previous studies of the evaporation of multiple sessile droplets have used a variety of experimental, numerical and analytical approaches (Lacasta et al 1998;Schäfle et al 1999;Kokalj et al 2010;Sokuler et al 2010;Carrier et al 2016;Castanet et al 2016;Shaikeea et al 2016;Shaikeea & Basu 2016a,b;Hatte et al 2019;Khilifi et al 2019;Schofield et al 2020). The critical difference in comparison with what is observed with a single droplet is the occurrence of 'shielding', in which the presence of other droplets causes a droplet to evaporate more slowly than it would in isolation.…”

The Lifetimes of Evaporating Sessile Droplets of Water Can Be Strongly Influenced by Thermal Effects

“…For example, in certain circumstances, convective fluid, vapour and/or heat transfer driven by density and/or temperature differences (see, for example, [15,18,[29][30][31][32][33][34]), none of which are included in the present work, can all have a significant effect on the evaporation of a droplet. Another particularly active and interesting area is the competitive evaporation of multiple droplets (see, for example, [16,[35][36][37][38][39]), and we suggest that considering the mutual influence of droplets through thermal as well as vapour effects would be an interesting direction for further research.…”

Contact-line deposits from multiple evaporating droplets

“…To a large extent this is explained by the inherent difficulty of analysing such situations, and while the evaporation of multiple droplets in various configurations has been the subject of growing recent interest, the previous studies have been predominantly numerical or experimental (see, for example, [11,[29][30][31][32][33][34][35][36]). Two notable exceptions are the recent work of Wray et al [37], who, building on the earlier work of Fabrikant [38] concerning a model for diffusion through a porous membrane, analysed the spatially non-uniform shielding that occurs in arbitrary configurations of thin droplets with circular contact lines, and that of Schofield et al [39], who used conformal-mapping techniques to analyse the analogous spatially non-uniform shielding that occurs in the closely related two-dimensional situation of a pair of evaporating ridges. In particular, Wray et al [37] gave explicit formulae for the evaporative flux of arbitrary configurations of droplets that were found to be remarkably accurate up to and including the limit of touching droplets, and led to theoretical predictions for the evolution of an arrangement of seven droplets that were found to be in excellent agreement with experimental results of Khilifi et al [36].…”