Topological transitions in evaporating thin films

TL;DR

This paper investigates the topological phase transition in evaporating thin water films on mica, revealing fingering instabilities, conserved harmonic moments, and a duality with Laplacian growth, providing new insights into the dynamics of drying films.

Contribution

It introduces a mathematical framework for analyzing topological transitions in evaporating films, highlighting a duality with Laplacian growth and identifying conditions for smooth transitions.

Findings

Fingering instability develops during evaporation.

Harmonic moments decay exponentially at the same rate.

A duality between Laplacian growth and evaporation is established.

Abstract

A thin water film evaporating from a cleaved mica substrate undergoes a first-order phase transition between two values of film thickness. During evaporation, the interface between the two phases develops a fingering instability similar to that observed in the Saffman-Taylor problem. The dynamics of the droplet interface is dictated by an infinite number of conserved quantities: all harmonic moments decay exponentially at the same rate. A typical scenario is the nucleation of a dry patch within the droplet domain. We construct solutions of this problem and analyze the toplogical transition occuring when the boundary of the dry patch meets the outer boundary. We show a duality between Laplacian growth and evaporation, and utilize it to explain the behaviour near the transition. We construct a family of problems for which evaporation and Laplacian growth are limiting cases and show that a necessary condition for a smooth topological transition, in this family, is that all boundaries share the same pressure.