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

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.