Magnetically Induced Rotating Rayleigh-Taylor Instability

Summary

We present a protocol for preparing a two-layer density-stratified liquid that can be spun-up into solid body rotation and subsequently induced into Rayleigh-Taylor instability by applying a gradient magnetic field.

Abstract

Classical techniques for investigating the Rayleigh-Taylor instability include using compressed gasses¹, rocketry² or linear electric motors³ to reverse the effective direction of gravity, and accelerate the lighter fluid toward the denser fluid. Other authors^{e.g. 4,5,6} have separated a gravitationally unstable stratification with a barrier that is removed to initiate the flow. However, the parabolic initial interface in the case of a rotating stratification imposes significant technical difficulties experimentally. We wish to be able to spin-up the stratification into solid-body rotation and only then initiate the flow in order to investigate the effects of rotation upon the Rayleigh-Taylor instability. The approach we have adopted here is to use the magnetic field of a superconducting magnet to manipulate the effective weight of the two liquids to initiate the flow. We create a gravitationally stable two-layer stratification using standard flotation techniques. The upper layer is less dense than the lower layer and so the system is Rayleigh-Taylor stable. This stratification is then spun-up until both layers are in solid-body rotation and a parabolic interface is observed. These experiments use fluids with low magnetic susceptibility, |χ| ~ 10^-6 - 10^-5, compared to a ferrofluids. The dominant effect of the magnetic field applies a body-force to each layer changing the effective weight. The upper layer is weakly paramagnetic while the lower layer is weakly diamagnetic. When the magnetic field is applied, the lower layer is repelled from the magnet while the upper layer is attracted towards the magnet. A Rayleigh-Taylor instability is achieved with application of a high gradient magnetic field. We further observed that increasing the dynamic viscosity of the fluid in each layer, increases the length-scale of the instability.

Introduction

A density stratified fluid system consisting of two layers can be arranged in a gravitational field in either a stable or an unstable configuration. If the dense heavy layer underlies the less dense, light layer then the system is stable: perturbations to the interface are stable, restored by gravity, and waves may be supported on the interface. If the heavy layer overlays the light layer then the system is unstable and perturbations to the interface grow. This fundamental fluid instability is the Rayleigh-Taylor instability^7,8. Exactly the same instability may be observed in non-rotating systems that are acce....

Protocol

NOTE: The experimental apparatus is shown schematically in Fig. 2. The main part of the apparatus consists of a rotating platform (300 mm × 300 mm) mounted on a copper cylinder (55 mm diameter) that descends under its own weight into the strong magnetic field of a superconducting magnet (1.8 T) with a room temperature vertical bore. The platform is made to rotate via an off-axis motor that turns a slip-bearing with a keyhole orifice. The copper cylinder is attached to a key-shaped drive shaft that simultaneously rotates, and descends once the holding-pin is removed.

1. Preparation of Non-standard Equipment

1. ....

Results

Fig. 4 shows the development of the Rayleigh-Taylor instability at the interface between the two fluids, for four different rotation rates: Ω = 1.89 rad s^-1 (top row), Ω = 3.32 rad s^-1, Ω = 4.68 rad s^-1, and Ω = 8.74 rad s^-1 (bottom row). The interface is shown evolving in time from t = 0 s (left hand column) with increments of 0.5 s to t = 3.0 s (right hand column). The right hand column therefore represents 0.90, 1.59.......

Discussion

There are two critical steps within the protocol. The first is 2.1.6.4. If the light layer is floated on the dense layer too rapidly then irreversible mixing of the two miscible fluid layers takes place. It is essential that this is avoided and that a sharp (<2 mm) interface between the two layers is achieved. The second critical step is 3.1.5. If the experiment is released toward the magnet without being fully spun-up into solid body rotation or without the visualization and image capture apparatus in position and o.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Blue water tracing dye	Cole-Parmer	00295-18
Red water tracing dye	Cole-Parmer	00295-16
Sodium Chloride			>99% purity
Manganese Chloride Tetrahydrate			See MSDS
Fluorescein sodium salt
Magnet	Cryogenic Ltd. London