Capillary levelling of thin liquid films of power-law rheology

TL;DR

This paper derives and analyzes solutions describing the surface leveling process of thin, non-Newtonian power-law fluid films, revealing weak singularities and confirming the solutions through numerical simulations.

Contribution

It introduces similarity solutions for the levelling of power-law fluid films and demonstrates their relevance via numerical simulations, extending understanding of non-Newtonian thin film dynamics.

Findings

Profiles exhibit weak singularities where pressure gradient vanishes

Numerical simulations approach the similarity solutions

Solutions apply to both periodic and localized initial conditions

Abstract

We find solutions that describe the levelling of a thin fluid film, comprising a non-Newtonian power-law fluid, that coats a substrate and evolves under the influence of surface tension. We consider the evolution from both periodic and localised initial conditions as separate cases. Particular (similarity) solutions in each of these two cases exhibit the generic property that the profiles are weakly singular (that is, higher-order derivatives do not exist), at points where the pressure gradient vanishes. Numerical simulations of the thin film equation, with either periodic or localised initial condition, are shown to approach the appropriate particular solution.