Name: magnetically induced rotating rayleigh-taylor instability
Uploaded: 2017-03-03T13:00:00
Description: Watch this Scientific Journal Video about Magnetically Induced Rotating Rayleigh-Taylor Instability at JoVE.com

RJAH acknowledges support from EPSRC Fellowship EP/I004599/1, MMS acknowledges funding from EPSRC under grant number EP/K5035-4X/1.

NOTE: The experimental apparatus is shown schematically in Fig. 2. The main part of the apparatus consists of a rotating platform (300 mm &#215; 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 s...

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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 (&#60;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...

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 instability7,8. Exactly the same instability may be observed in non-rotating systems that are accelerated towards the heavier layer. Due to the fundamental nature of the instability it is observed in very many flows that also vary greatly in scale: from small-scale thin film phenomena9 to astrophysical scale features observed in, for example, the crab nebula10, where finger-like structures are observed, created by pulsar winds being accelerated through denser supernova remnants. It is an open question as to how the Rayleigh-Taylor instability can be controlled or influenced once the initial unstable density difference has been established at an interface. One possibility is to consider bulk rotation of the system. The purpose of the experiments is to investigate the effect of rotation on the system, and whether this may be a route to stabilization.
We consider a fluid system that consists of a two-layer gravitationally unstable stratification that is subject to steady rotation about an axis parallel to the direction of gravity. A perturbation to an unstable two-layer density stratification leads to baroclinic generation of vorticity, i.e., overturning, at the interface, tending to break-up any vertical structures. However, a rotating fluid is known to organize itself into coherent vertical structures aligned with the axis of rotation, so-called &#39;Taylor columns&#39;11. Hence the system under investigation undergoes competition between the stabilizing effect of the rotation, that is organizing the flow into vertical structures and preventing the two layers overturning, and the destabilizing effect of the denser fluid overlying the lighter fluid that generates an overturning motion at the interface. With increased rotation rate the ability of the fluid layers to move radially, with opposite sense to each other, in order to rearrange themselves into a more stable configuration, is increasingly inhibited by the Taylor-Proudman theorem12,13: the radial movement is reduced and the observed structures that materialize as the instability develops are smaller in scale. Fig. 1 shows qualitatively the effect of the rotation on the eddies that form as the instability develops. In the left hand image there is no rotation and the flow is an approximation to classical non-rotating Rayleigh-Taylor instability. In the right hand image all experimental parameters are identical to the left hand image except that the system is being rotated about a vertical axis aligned with the center of the tank. It can be seen that the effect of the rotation is to reduce the size of the eddies that are formed. This, in turn, results in an instability that develops more slowly than the non-rotating counterpart.
The magnetic effects that modify the stress tensor in the fluid may be regarded as acting in the same way as a modified gravitational field. We are therefore able to create a gravitationally stable stratification and spin it up into solid body rotation. The magnetic body forces generated by imposing the gradient magnetic field then mimic the effect of modifying the gravitational field. This renders the interface unstable such that the fluid system behaves, to a good approximation, as a classical Rayleigh-Taylor instability under rotation. This approach has been previously attempted in two dimensions without rotation14,15. For an applied gradient magnetic field with induced magnetic field B, the body force applied to a fluid of constant magnetic volume susceptibility &#967; is given by f = grad(&#967;B2/&#181;0), where B = |B| and &#181;0 = 4&#960; &#215; 10-7 N A-2 is the magnetic permeability of free-space. We may therefore consider the magnet to manipulate the effective weight of each fluid layer, where the effective weight per unit volume of a fluid of density &#961; in a gravitational field of strength g is given by &#961;g - &#967; (&#8706;B2/&#8706;z)/(2 &#181;0).

<table border="0" cellpadding="0" cellspacing="0" width="696">
	<tbody>
		<tr height="21">
			<td height="21" style="height:21px;width:216px;">Blue water tracing dye</td>
			<td style="width:195px;">Cole-Parmer</td>
			<td style="width:119px;">00295-18</td>
			<td style="width:167px;"></td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:216px;">Red water tracing dye</td>
			<td style="width:195px;">Cole-Parmer</td>
			<td style="width:119px;">00295-16</td>
			<td></td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:216px;">Sodium Chloride</td>
			<td style="width:195px;"></td>
			<td style="width:119px;"></td>
			<td>&#62;99% purity</td>
		</tr>
		<tr height="42">
			<td height="42" style="height:42px;width:216px;">Manganese Chloride Tetrahydrate</td>
			<td style="width:195px;"></td>
			<td style="width:119px;"></td>
			<td>See MSDS</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">Fluorescein sodium salt&#160;</td>
			<td style="width:195px;"></td>
			<td style="width:119px;"></td>
			<td></td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:216px;">Magnet</td>
			<td style="width:195px;">Cryogenic Ltd. London</td>
			<td style="width:119px;"></td>
			<td></td>
		</tr>
	</tbody>
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magnetically induced rotating rayleigh-taylor instability

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 authorse.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, |&#967;| ~ 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.

Fig. 4 shows the development of the Rayleigh-Taylor instability at the interface between the two fluids, for four different rotation rates: &#937; = 1.89 rad s-1 (top row), &#937; = 3.32 rad s-1, &#937; = 4.68 rad s-1, and &#937; = 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 r...

Watch this Scientific Journal Video about Magnetically Induced Rotating Rayleigh-Taylor Instability at JoVE.com

Magnetically Induced Rotating Rayleigh-Taylor Instability

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.

Classical techniques for investigating the Rayleigh-Taylor instability include using compressed gasses1, rocketry2 or linear electric motors3 to reverse ...

The overall goal of this experiment is to observe the effect of rotation on a gravitationally unstable system comprised of a dense fluid overlying a less-dense fluid. This method can help answer key questions in fluid dynamics, such as how the stabilizing effect of rotation competes and interacts with the destabilizing effect of gravity. This technique's main feature is the ability to create a stable rotating, two-layer system and then use a magnet to manipulate the effective weights of each layer, triggering the instability.This is the apparatus used for the experiment. The principle visible components are a rotating platform for the experimental tank, a copper cylinder that supports it, and a room-temperature bore superconducting magnet. The cylinder descends into the bore of the magnet and a 1.8 tesla magnetic field.This schematic provides additional details of the arrangement. The rotation of the platform is produced by an off-axis motor that turns a slip bearing with a keyhole orifice. The copper cylinder is attached to the key-shaped drive shaft and descends under its own weight when the holding pin is removed.The complete set-up includes the lighting and a remote-controlled camera to capture images. With the tank in position on the platform, move the drive shaft to its lowest position. Ensure the video camera will have a view of the experiment that is in-focus and appropriately lit.To prepare for the experiment, place the platform and copper cylinder in their highest position. Lock the cylinder in place with the holding pin. With everything else set, remove the tank to prepare it for the experiment.At a lab bench, begin to prepare the liquids for the tank. For the dense layer, begin with 250 milliliters of room-temperature distilled water, and add approximately 6.25 grams of sodium chloride to the water. The components of the light upper layer are 325 milliliters of room-temperature distilled water, along with manganese chloride and red and blue water tracing dyes.Add a small quantity of fluorescein sodium to complete the preparation. The two fluids are now ready for the experiment. The stratified liquids will be held in a clear cylindrical container, which has a lucite lid that can fit into it.The lid has bleed holes to allow fluid and air to flow through. In addition to the container and fluids, have a flotation boat ready for use. The flotation boat consists of styrene walls on a sponge base.The bottom of its interior should be lined with strong tissue paper. The boat should be able to easily fit into the experimental tank without touching the sides. Proceed with the next steps only when ready to perform the experiment.Start with the high-density fluid and begin to add it to the tank. Stop when 300 milliliters has been added. Next, prepare a header tank with a clamp and tubing for the low-density fluid.The header tank should hold at least 350 milliliters and the clamp should allow for control of the fluid flow. Proceed by adding low-density fluid to the header tank. Then, mount the header tank above the experiment tank to allow the release of fluid near the high-density fluid surface.Place the flotation boat onto the high-density fluid surface. Adjust the clamp on the header tank to add low-density fluid to the flotation boat, and add about three milliliters per minute. With time, the low-density fluid diffuses through the sponge forming a light fluid layer above the high-density fluid.As the boat lifts away from the interface, gradually increase the flow rate. Keep filling until the header tank has been emptied. Once the fluid has been completely siphoned, remove the flotation boat slowly to minimize dripping and get the lid for the experiment tank.Put the lid in place, and start to lower it into the upper layer of fluid. Stop when the depths of each layer are equal, and there are no trapped air bubbles. If successful, there will be two layers of fluid of equal depth with a sharp interface between them.There will also be a layer of low-density fluid on top of the lucite lid. Proceed quickly to perform the experiment and carefully move the tank to the apparatus. Place the experimental tank on the platform, while keeping it far away from the magnet.Turn on the motor and increase the rotation rate slowly by increasing the power-supply voltage until the desired rate is reached. Once the desired rotation rate is reached, start video-recording and get into position to remove the holding pin. When ready, remove the pin and allow the tank to descend into the magnetic field.These images are snapshots of the fluid interface for four different rotation rates. Each column corresponds to a different time and increases in increments of half a second. At early times, for example at the one-second mark, for each rotation rate, there is a perturbation to the interface with a dominant length scale.With increasing rotation rate, the width of the snake-like structures decreases. These images are from a series of experiments with varying fluid viscosity and a fixed rotation rate. Each column corresponds to a different time.The observed length scale of the instability increases as the viscosity increases from lower values to higher values. By plotting the dominant radio wave length as a function of the rotation rate, a lower threshold for the scale of the instability becomes observable. In this data for fluid layers with the approximate viscosity of water, above rotation rates of about four radians per second, the lower threshold is approximately six millimeters.Once mastered, this technique can be carried out in one hour if it is performed properly.

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