Finite-time Thin Film Rupture Driven by Generalized Evaporative Loss

TL;DR

This paper investigates the complex dynamics of thin film rupture caused by evaporation, revealing various singularity types and analyzing self-similar solutions through advanced PDE simulations.

Contribution

It introduces a generalized mathematical model for thin film rupture with evaporative effects, analyzing non-self-similar and self-similar solutions and validating them with high-resolution simulations.

Findings

Multiple finite-time singularity types identified

Self-similar rupture solutions characterized and validated

Evaporative effects significantly influence rupture dynamics

Abstract

Rupture is a nonlinear instability resulting in a finite-time singularity as a fluid layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with evaporative effects. The governing lubrication model is a fourth-order nonlinear parabolic partial differential equation with a non-conservative loss term due to evaporation. Several different types of finite-time singularities are observed due to balances between evaporation and surface tension or intermolecular forces. Non-self-similar behavior and two classes of self-similar rupture solutions are analyzed and validated against high resolution PDE simulations.