Instability, rupture and fluctuations in thin liquid films: Theory and computations

TL;DR

This paper investigates the role of thermal fluctuations in the stability and rupture of thin liquid films through analytical derivations and numerical simulations of a stochastic thin-film equation, highlighting the impact of noise on rupture dynamics.

Contribution

It introduces a first-principles stochastic thin-film model and explores its behavior, including the effects of correlated noise and noise intensity on film rupture.

Findings

Fluctuations significantly influence film rupture and droplet formation.

Numerical simulations reveal the dynamics of free energy near rupture.

Noise intensity affects rupture time in predictable ways.

Abstract

Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be understood. An example of this is dewetting, which involves the rupture of a thin liquid film and the formation of droplets. Such a process is thermally activated and requires fluctuations to be taken into account self-consistently. In this work we present an analytical and numerical study of a stochastic thin-film equation derived from first principles. Following a brief review of the derivation, we scrutinise the behaviour of the equation in the limit of perfectly correlated noise along the wall-normal direction. The stochastic thin-film equation is also simulated by adopting a numerical scheme based on a spectral collocation method. The scheme allows us to explore the fluctuating dynamics of the thin film and the behaviour of its free energy in the vicinity of rupture. Finally, we also study the effect of the noise intensity on the rupture time, which is in agreement with previous works.