Instability of Compressible Drops and Jets

TL;DR

This paper investigates how fluid compressibility affects the stability of drops and jets, revealing critical thresholds where instability occurs, and modifies classical instability criteria like Rayleigh-Plateau.

Contribution

It introduces a comprehensive analysis of compressibility effects on drop and jet stability, identifying critical compressibility values and their impact on classical instability modes.

Findings

Existence of a critical compressibility for instability onset.

Minimal stable radius depends on compressibility.

Altered dispersion relation for Rayleigh-Plateau instability.

Abstract

We revisit the classic problem of the stability of drops and jets held by surface tension, while regarding the compressibility of bulk fluids and spatial dimensions as free parameters. By mode analysis, it is shown that there exists a critical compressibility above which the drops (and disks) become unstable for a spherical perturbation. For a given value of compressibility (and those of the surface tension and density at the equilibrium), this instability criterion provides a minimal radius below which the drop cannot be a stable equilibrium. According to the existence of the above unstable mode of drop, which corresponds to a homogeneous perturbation of cylindrical jet, the dispersion relation of Rayleigh-Plateau instability for cylinders drastically changes. In particular, we identify another critical compressibility above which the homogeneous unstable mode is predominant. The analysis is done for non-relativistic and relativistic perfect fluids, of which self-gravity is ignored.