Rayleigh-Taylor instability under an inclined plane

TL;DR

This paper studies the Rayleigh-Taylor instability for a thin fluid film on an inclined plane, revealing how flow along the plane influences droplet formation and identifying a critical inclination angle.

Contribution

It introduces an analysis of the instability considering the effect of an inclined plane and flow, extending the classical understanding of Rayleigh-Taylor instability.

Findings

No droplet formation occurs beyond a critical inclination angle.

Flow along the plane suppresses the classical instability.

The absolute/convective analysis explains the experimental observations.

Abstract

We revisit the canonical Rayleigh-Taylor instability and investigate the case of a thin film of fluid upon the underside of an inclined plane. The presence of a natural flow along the plane competes with the conventional droplet forming instability. In particular, experiments reveal that no drops form for inclinations greater than a critical value. These features are rationalized in the context of the absolute/convective analysis conducted in this article.