Influence of van der Waals forces on the instability of a liquid film in a tube

TL;DR

This paper investigates how van der Waals forces affect the stability and morphology of a liquid film in a nanotube, combining theoretical analysis and numerical simulations.

Contribution

It develops a theoretical framework and confirms through simulations that van der Waals forces significantly influence film stability and rupture behavior.

Findings

Van der Waals forces increase perturbation growth and decrease the critical film thickness.

They alter interfacial morphology and suppress satellite lobe formation.

Rupture and collapse follow a universal 1/3 power law scaling.

Abstract

The instability of a liquid film in a nanotube is significantly influenced by van der Waals forces. A theoretical framework based on the axisymmetric Stokes equations is developed to investigate their effects through linear stability analysis. The model reveals that van der Waals forces markedly enhance perturbation growth, reduce the dominant wavelength, and lower the critical film thickness that distinguishes collapse from non-collapse regimes. Direct numerical simulations of the Navier-Stokes equations both confirm these theoretical predictions and extend the analysis into the nonlinear regime. In this regime, van der Waals forces are found to alter the interfacial morphology and suppress the formation of satellite lobes. Both rupture and collapse follow a universal temporal scaling law with exponent 1/3 and exhibit self-similar behavior near the singularity.