Fluctuation-driven dynamics in nanoscale thin-film flows: physical insights from numerical investigations

TL;DR

This paper introduces a numerical scheme based on fluctuating hydrodynamics to study thermal fluctuation effects in nanoscale thin-film flows, revealing new insights into droplet dynamics and rupture processes.

Contribution

The paper develops a high-resolution numerical framework using a stochastic lubrication equation to analyze nonlinear nanoscale thin-film flows with thermal fluctuations.

Findings

Derived new power laws for droplet spreading.

Reproduced molecular dynamics results efficiently.

Found thermal fluctuations slow down droplet coalescence.

Abstract

The effects of thermal fluctuations on nanoscale flows are captured by a numerical scheme that is underpinned by fluctuating hydrodynamics. A stochastic lubrication equation (SLE) is solved on non-uniform adaptive grids to study a series of nanoscale thin-film flows. The Fornberg scheme is used for high-resolution spatial discretisation and a fully-implicit time-marching scheme is designed for numerical stability. The accuracy of the numerical method is verified against theoretical results for thermal capillary waves during the linear stage of their development. The framework is then used to study the nonlinear behaviour of three bounded thin-film flows: (i) droplet spreading, where new power laws are derived; (ii) droplet coalescence, where molecular dynamics results are reproduced by the SLE at a fraction of the computational cost and it is discovered that thermal fluctuations decelerate the process, in contrast to previously investigated phenomena; and (iii) thin-film rupture, where, in the regime considered, disjoining pressure dominates the final stages of rupture.