Instabilities of a thin liquid film in a funnel

TL;DR

This paper investigates the stability of a thin liquid film in a funnel, combining experiments, modeling, and simulations to understand contact line instabilities influenced by geometry and flow convergence.

Contribution

It introduces a long-wave model supported by experimental and numerical data to analyze contact line instabilities in funnel flows, highlighting the effects of azimuthal curvature and flow convergence.

Findings

Flow convergence leads to film thickening affecting stability.

A long-wave model captures key instability mechanisms.

Linear stability analysis reveals emerging lengthscales.

Abstract

We explore flow of a completely wetting fluid in a funnel, with particular focus on contact line instabilities at the fluid front. While the flow in a funnel may be related to a number of other flow configurations as limiting cases, understanding its stability is complicated due to the presence of additional azimuthal curvature, as well as due to convergent flow effects imposed by the geometry. Convergent nature of the flow leads to thickening of the film, therefore influencing its stability properties. In this work, we analyze these stability properties by combining physical experiments, asymptotic modeling, self-similar type of analysis and numerical simulations. We show that appropriate long-wave based model supported by the input from experiments, simulations and linear stability analysis origination from the flow down an incline plane provides a basic insight allowing to understand the development of contact line instability and emerging lengthscales.