The relation of steady evaporating drops fed by an influx and freely evaporating drops

TL;DR

This paper models the behavior of thin, evaporating liquid drops on solid surfaces, analyzing steady states with influx and free evaporation, revealing conditions for spreading or receding based on initial contact angles.

Contribution

It introduces a thin film evolution model for evaporating drops considering wettability and capillarity, including steady and free evaporation scenarios, with asymptotic and numerical analysis.

Findings

Steady evaporating drops with influx are characterized by non-linear profiles.

Drops with initial contact angle larger than steady state tend to spread.

Drops with smaller initial contact angle tend to recede immediately.

Abstract

We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and capillarity play a major role. The model is first employed to study steady evaporating drops that are fed locally through the substrate. An asymptotic analysis focuses on the precursor film and the transition region towards the bulk drop and a numerical continuation of steady drops determines their fully non-linear profiles. Following this, we study the time evolution of freely evaporating drops without influx for several initial drop shapes. As a result we find that drops initially spread if their initial contact angle is larger than the apparent contact angle of large steady evaporating drops with influx. Otherwise they recede right from the beginning.