Centrifugally forced Rayleigh-Taylor Instability

TL;DR

This paper investigates the high-rotation limit of Rayleigh-Taylor instability, deriving a stability equation for concentric fluid layers in a centrifuge-like setup, with applications in rotating machinery and coating processes.

Contribution

It introduces a linear stability analysis for high rotation rates, deriving a fourth-order Orr-Sommerfeld-like equation applicable to various fluid configurations and comparing predictions with numerical results.

Findings

Good agreement between theoretical predictions and numerical experiments.

Analysis applies to both viscous and inviscid, immiscible and miscible fluids.

Results extend to coating and lubrication in rotating systems.

Abstract

The effect of rotation on the classical gravity-driven Rayleigh-Taylor instability has been shown to influence the scale of the perturbations that develop at the unstable interface and consequently alter the speed of propagation of the front. The present authors argued that this is as a result of a competition between the destabilizing effect of gravity and the stabilizing effect of the rotation. In the present paper we consider the extreme limit of high rotation rates in which rotational forces dominate and gravitational forces may be ignored. The two liquid layers initially form concentric cylinders, centred on the axis of rotation. The configuration may be thought of as a fluid-fluid centrifuge. There are two types of perturbation to the interface that may be considered, an azimuthal perturbation around the circumference of the interface and a varicose perturbation in the axial direction along the length of the interface. It is the first of these types of perturbation that we consider here, and so the flow may be considered essentially two-dimensional, taking place in a circular domain. We carry out a linear stability analysis on a perturbation to the hydrostatic background state and derive a fourth order Orr-Sommerfeld-like equation that governs the system. We consider the dynamics of systems of stable and unstable configurations, inviscid and viscous fluids, immiscible fluid layers with surface tension, and miscible fluid layers that may have some initial diffusion of density. Theoretical predictions are compared with numerical experiments and the agreement is shown to be good. We do not restrict our analysis to equal volume fluid layers and so our results also have applications in coating and lubrication problems in rapidly rotating systems and machinery.