Linear stability analysis of a time-divergent slamming flow

TL;DR

This paper conducts a linear stability analysis of a diverging gas flow during liquid impact, revealing that long wavelengths are stabilized compared to classical models, with implications for impact-related instabilities.

Contribution

It introduces a Kelvin-Helmholtz-type linear stability framework for diverging gas flows in impact scenarios, extending classical interface stability analysis.

Findings

Long wavelengths are significantly stabilized compared to classical predictions.

A marginally stable wavelength emerges in wave impact scenarios, absent in classical models.

Instability suppression depends on disk size and is influenced by gas viscosity and compressibility.

Abstract

When a liquid slams into a solid, the intermediate gas is squeezed out at a speed that diverges when approaching the moment of impact. Although there is mounting experimental evidence that instabilities form on the liquid interface during such an event, understanding of the nature of these instabilities is limited. This study therefore addresses the stability of a liquid-gas interface with surface tension, subject to a diverging flow in the gas phase, where the liquid and the gas phase are both represented as potential fluids. We perform a Kelvin-Helmholtz-type linear modal stability analysis of the surface to obtain an amplitude equation that is subsequently analysed in detail and applied to two cases of interest for impact problems, namely, the parallel impact of a wave onto a vertical wall, and the impact of a horizontal plate onto a liquid surface. In both cases we find that long wavelengths are stabilised considerably in comparison to what may be expected based upon classical knowledge of the stability of interfaces subject to a constant gas flow. In the former case, this leads to the prediction of a marginally stable wavelength that is completely absent in the classical analysis. For the latter we find much resemblance to the classical case, with the connotation that the instability is suppressed for smaller disk sizes. The study ends with a discussion of the influence of gas viscosity and gas compressibility on the respective stability diagrams.