On the lifetimes of two-dimensional droplets on smooth wetting patterns

Haynes, Matthew and Pradas, Marc (2022). On the lifetimes of two-dimensional droplets on smooth wetting patterns. Journal of Engineering Mathematics, 135, article no. 2.

DOI: https://doi.org/10.1007/s10665-022-10218-7

Abstract

We study the evolution and lifetime of droplets evaporating on a smooth chemical pattern, which is characterised by a spatially varying contact angle. We formulate a model that combines the evaporation rate of the droplet for a given volume with the static stability of the droplet as the volume changes in time quasi-statically. We derive an exact equation for the evaporation rate that is studied analytically under the limiting cases of nearly neutral wetting and highly hydrophilic conditions. We find that the evaporation rate of the droplet is highly dependent on the size and shape of the fictitious infinity where a far-field boundary conditions needs to be applied. We also study how the droplet’s lifetime depends on the averaged contact angle and strength ε of the chemical pattern, observing that the lifetime of the droplet is maximised for a droplet with average contact angle π/2 and with ε≲0.1.

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