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 simultaneously rotates, and descends once the holding-pin is removed.
1. Preparation of Non-standard Equipment
<ol>
	<li>Flotation boat
	<ol>
		<li>Make the size of the boat such that it fits comfortably within the experimental tank without touching the sides. 
		NOTE: The flotation boat (see Fig. 3) consists of polystyrene walls and a sponge base.</li>
		<li>Protect the sponge with a layer of strong tissue paper. 
		NOTE: The purpose of the tissue paper is to dissipate as much vertical momentum from the fluid poured into the boat as possible.</li>
	</ol>
	</li>
</ol>
2. Preparation of Experiment
<ol>
	<li>Preparation of liquid layers
	<ol>
		<li>Allow distilled water to come up to laboratory temperature (22 &#177; 2 &#176;C). Approximately 650 mL is required for each experimental realization. 
		NOTE: Allowing the mixture to equilibrate prevents formation of bubbles in the experiment due to exsolving air.</li>
		<li>Separate the distilled water into equal volumes in two separate containers, A and B, which will be used to prepare liquid for the dense lower layer and light upper layer respectively.</li>
		<li>Ex-situ preparation of dense lower layer. To the contents of container A:
		<ol>
			<li>Add NaCl to achieve a concentration of 0.43 mol NaCl per liter of water (approximately 25 g of NaCl per liter of water will be required);</li>
			<li>Add 0.33 g red and blue water-tracing dyes to the lower layer container (e.g., Cole-Parmer 00295-16 &#38; -18);</li>
			<li>Add 0.1 g L-1 fluorescein sodium. 
			NOTE: The lower layer will be now be opaque in appearance and have a density of approximately 1012.9 &#177; 1.2 kg m-3.</li>
		</ol>
		</li>
		<li>Ex-situ preparation of light upper layer. To the contents of container B:
		<ol>
			<li>Add MnCl2 salt to achieve a concentration of 0.06 mol MnCl2 per liter of water (approximately 12 g of MnCl2 per liter of water). 
			NOTE: The upper layer will be transparent in appearance and have a density of approximately 998.2 &#177; 0.5 kg m-3.</li>
		</ol>
		</li>
		<li>To vary the viscosity of the fluid layers, add glycerol C3H8O3 in equal amounts to each layer until the desired viscosity is attained. Typical viscosities lie in the range 1.00 &#215; 10-3 - 21.00 &#215; 10-3 Pa s. The viscosity of each layer is the same. 
		NOTE: The mixtures may be safely stored in their separate containers until required.</li>
		<li>Ex-situ preparation of density stratification.
		<ol>
			<li>Add 300 mL of the contents of container A to the cylindrical inner tank (see Fig. 2).</li>
			<li>Immerse the flotation boat&#39;s sponge in fluid from container B. 
			NOTE: After (2.1.6.2) the procedure is time sensitive, so do not carry out any further steps until all the magnet and the lighting, recording and mechanical mechanisms are ready.</li>
			<li>Lift the flotation boat out of the container B and, when it has stopped dripping, carefully place the flotation boat on top of the layer of dense fluid in the inner cylindrical tank.</li>
			<li>Begin to add light-layer fluid from container B to the flotation boat at a flow rate of 3 mL/min. Gradually increase this flow rate as the flotation boat lifts away from the interface between the two layers. Maintain a slow enough flow rate that the interface is not disturbed by the increased momentum of the fluid flow, but fast enough that this process takes no more than 20 min. Keep filling until the upper layer contains 320 mL of fluid. 
			NOTE: The lower layer will be at a depth of approximately 33 mm, and the upper layer will be at a depth of approximately 39 mm.</li>
			<li>Carefully lower the lucite lid into the upper layer such that the layer depths of each layer are equal. Allow fluid and air to flow through the bleed holes, ensuring that no air is trapped beneath. Observe a layer (approx. 6 mm) of clear light layer liquid on top of the lucite lid. 
			NOTE: If the process has been successful there will be two layers of liquid of equal depth with a sharp interface between them. The thickness of the diffusion layer at the interface will be less than 2 mm at this stage.</li>
		</ol>
		</li>
		<li>Fill the outer tank with clear distilled water to a height 6 mm above the lucite lid of the inner tank. Upon observing square-on there will be no curvature-induced parallax resulting from the inner cylindrical tank. 
		NOTE: Since the liquids in each layer are continuously diffusing across the interface at this point, proceed immediately to the following steps.</li>
	</ol>
	</li>
	<li>Spin-up of the stratification
	<ol>
		<li>Place the experimental tank on the platform.</li>
		<li>Position the arrangement with the copper cylinder in the bore of the magnet, the drive shaft through the keyhole orifice in the track and the holding pin in position. Ensure that the tank is far away (60 cm) from the magnet such that the magnetic forces on the liquids are negligible at this position. 
		NOTE: Carrying the experimental tank containing the stratification presents few difficulties; long, low amplitude, sloshing waves set up by walking with the tank will decay away, having negligible effect on the quality of the interface achieved when floating the upper layer on.</li>
		<li>Turn on the motor, increasing the rate of rotation at 0.002 rad s-2, spinning-up the fluid to the desired rotation rate. For the rotation rates in 16 the spin-up time was of the order 20 min - 60 min. 
		NOTE: The fastest rotation rate used was 13.2 rad s-1.</li>
	</ol>
	</li>
</ol>
3. Execution of Experiment
<ol>
	<li>Ensure that the magnet is indicating a field strength of 1.2 T, and that at the height at which the instability is initiated the field gradient is (grad B2)/2 = -14.3 T2 m-1, where B is the magnetic induction.</li>
	<li>Ensure that the video camera is arranged such that when the drive shaft is in its lowest position either the side view of the experiment is in focus, or a plan view is in focus through a mirror placed above the experiment.</li>
	<li>Ensure the ambient lighting is at the correct levels, such that none of the image captured by the camera is saturated, but that the full response is used (grayscale intensities in the range 0-255).</li>
	<li>Begin video recording (240 fps). Use a remote control to prevent moving the camera while operating the record function.</li>
	<li>Remove the holding pin, allowing the tank to descend, while rotating, into the magnetic field.</li>
</ol>
4. Reset Experiment
<ol>
	<li>Reset experimental rig
	<ol>
		<li>Use the remote control to stop the video recording.</li>
		<li>Save the movie file to disk.</li>
		<li>By hand, lower the voltage to the motor so that it slows to a standstill. Perform this gradually so as to prevent spillages.</li>
		<li>Remove experimental arrangement from magnet.</li>
		<li>Dispose of the mixed liquid layers appropriately (see Manganese Chloride Tetrahydrate MSDS).</li>
		<li>Rinse the tank with water (it does not need to be distilled), until all traces of salts have been washed away. Avoid direct skin contact with liquids.</li>
		<li>Dry the tank carefully with tissue paper to ensure that no residue is left that may contaminate subsequent experiments.</li>
	</ol>
	</li>
</ol>
5. Image Processing
<ol>
	<li>Extract the individual images from each movie frame and save in lossless .png format. Mask out any unwanted areas of each frame, for example the platform or copper cylinder.</li>
	<li>Calculate the two-dimensional auto-correlation function16 of each image frame for 2 s after initiation of the instability using a discrete Fast Fourier Transform. Record the minimum, mean, and maximum value of the observed wavelength for the rotation rate of the experiment and the viscosity of the fluid layers.</li>
</ol>

<ol>
	<li>Lewis, D. J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+instability+of+liquid+surfaces+when+accelerated+in+a+direction+perpendicular+to+their+planes.+II.">The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. II.</a> Proc. Roy. Soc., A. 202, 81-96 (1950).</li><li>Read, K. I. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Experimental+investigation+of+turbulent+mixing+by+Rayleigh-Taylor+instability.">Experimental investigation of turbulent mixing by Rayleigh-Taylor instability.</a> Physica D. 12, 45-58 (1984).</li><li>Dimonte, G., Schneider, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Turbulent+Rayleigh-Taylor+instability+experiments+with+variable+acceleration.">Turbulent Rayleigh-Taylor instability experiments with variable acceleration.</a> Phys. Rev. E. 54, 3740-3743 (1996).</li><li>Dalziel, S. B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Rayleigh-Taylor+instability+:+experiments+with+image+analysis.">Rayleigh-Taylor instability : experiments with image analysis.</a> Dyn. Atmos. Oceans. 20, 127-153 (1993).</li><li>Jacobs, J. W., Dalziel, S. B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Rayleigh-Taylor+instability+in+complex+stratifications.">Rayleigh-Taylor instability in complex stratifications.</a> J. Fluid Mech. 542, 251-279 (2005).</li><li>Linden, P. F., Redondo, J. M., Youngs, D. L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Molecular+mixing+in+Rayleigh-Taylor+instability.">Molecular mixing in Rayleigh-Taylor instability.</a> J. Fluid Mech. , 97-124 (1994).</li><li>Lord Rayleigh, <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Investigation+of+the+Character+of+the+Equilibrium+of+an+Incompressible+Heavy+Fluid+of+Variable+Density.">Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density.</a> Proc. Lon. Math. Soc. 14, 170-177 (1883).</li><li>Taylor, G. I. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+instability+of+fluid+surfaces+when+accelerated+in+a+direction+perpendicular+to+their+planes.+I.">The instability of fluid surfaces when accelerated in a direction perpendicular to their planes. I.</a> Proc. Roy. Soc., A. 201, 192-196 (1950).</li><li>Limat, L., Jenffer, P., Dagens, B., Touron, E., Fermigier, M., Wesfreid, J. E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Gravitational+instabilities+of+thin+liquid+layers:+dynamics+of+pattern+selection.">Gravitational instabilities of thin liquid layers: dynamics of pattern selection.</a> Physica D. 61, 166-182 (1992).</li><li>Gelfand, J. D., Slane, P. O., Zhang, W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+Dynamical+Model+for+the+Evolution+of+a+Pulsar+Wind+Nebula+Inside+a+Nonradiative+Supernova+Remnant.">A Dynamical Model for the Evolution of a Pulsar Wind Nebula Inside a Nonradiative Supernova Remnant.</a> Astrophys. J. 703, 2051-2067 (2009).</li><li>Taylor, G. I. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Experiments+on+the+Motion+of+Solid+Bodies+in+Rotating+Fluids.">Experiments on the Motion of Solid Bodies in Rotating Fluids.</a> Proc. Roy. Soc., A. 104, 213-218 (1923).</li><li>Proudman, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=On+the+Motion+of+Solids+in+a+Liquid+Possessing+Vorticity.">On the Motion of Solids in a Liquid Possessing Vorticity.</a> Proc. Roy. Soc., A. 92, 408-424 (1916).</li><li>Taylor, G. I. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Motion+of+Solids+in+Fluids+when+the+Flow+is+not+lrrotational.">Motion of Solids in Fluids when the Flow is not lrrotational.</a> Proc. Roy. Soc., A. 93, 99-113 (1917).</li><li>Carl&#232;s, P., Huang, Z., Carbone, G., Rosenblatt, C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Rayleigh-Taylor+Instability+for+Immiscible+Fluids+of+Arbitrary+Viscosities:+A+Magnetic+Levitation+Investigation+and+Theoretical+Model.">Rayleigh-Taylor Instability for Immiscible Fluids of Arbitrary Viscosities: A Magnetic Levitation Investigation and Theoretical Model.</a> Phys. Rev. Lett. 96, 104501 (2006).</li><li>Huang, Z., De Luca, A., Atherton, T. J., Bird, M., Rosenblatt, C., Carl&#232;s, P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Rayleigh-Taylor+Instability+Experiments+with+Precise+and+Arbitrary+Control+of+the+Initial+Interface+Shape.">Rayleigh-Taylor Instability Experiments with Precise and Arbitrary Control of the Initial Interface Shape.</a> Phys. Rev. Lett. 99, 204502 (2007).</li><li>Baldwin, K. A., Scase, M. M., Hill, R. J. A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+Inhibition+of+the+Rayleigh-Taylor+Instability+by+Rotation.">The Inhibition of the Rayleigh-Taylor Instability by Rotation.</a> Sci. Rep. 5, 11706 (2015).</li><li>Rossby, H. T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+study+of+B&#233;nard+convection+with+and+without+rotation.">A study of B&#233;nard convection with and without rotation.</a> J. Fluid Mech. 36, 309-335 (1969).</li></ol>

The authors have nothing to disclose.

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 on stand-by then repeat the procedure (2.1.6).
The composition of the liquid layers, the magnetic field strength and the motor performance can all be verified prior to beginning to make the stratification (2.1.6). Most practical difficulties can therefore be resolved before commencing any given experiment. We have found a small and undesirable variation in descent speed into the magnet field however. Typically, faster rotating experiments descend slightly more slowly into the magnetic field than slowly rotating experiments. It may be necessary to modify the slip bearing though we found greasing did not help reduce the variability in descent speed. We found that placing a small (non-magnetic) weight on the platform allowed us to achieve consistent descent speeds of 10 &#177; 1 mm s-1 for all of the experiments.
The main limitation of the apparatus is that the magnetic field cannot be applied instantaneously; the superconducting magnet requires 1-2 hours to energize. Ideally, once the fluid layers are spun-up we would instantly apply a strong uniform magnetic field to the tank to trigger the instability. For this reason, in this experiment, the tank was lowered at uniform velocity into the magnetic field.
Despite the necessity for lowering the experiment into the magnetic field, this technique has a number of advantages over established methods. The method is both smooth, unlike rocketry methods2, and requires no lock, as with LEM methods3, but unlike lock-release methods. This is a significant advantage in rotating Rayleigh-Taylor flow as the initial spun-up state of the fluid layers has a paraboloidal interface. Furthermore, by not having a lock the difficulties associated with the imparted vortex sheet induced by lock-removal are avoided. We believe our experiments to be the first experimental realization of the effects of rotation on the Rayleigh-Taylor instability.
Our technique has been developed with a view to applications in classical fluid mechanics thus far. We have used weakly paramagnetic and diamagnetic liquids to manipulate the effective weight of fluid parcels. We have, to date, been able therefore to consider the magnetic field and the fluid mechanics to be de-coupled. Future directions for research using this technique include considering the behavior of ferrofluids and their interaction with the magnetic field in the rotating Rayleigh-Taylor instability set-up, where this de-coupling is no longer valid.

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>
</table>

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 represents 0.90, 1.59, 2.23, and 4.17 complete revolutions respectively from top to bottom row.
At early times (t ~ 0.5-1.0 s) a perturbation to the interface can be seen which exhibits a dominant length scale. Structures reminiscent of snake-like convection rolls17 can be observed. Despite the center of the tank becoming unstable first there is no clear initiation at the center of the tank; the instability, to a good approximation, is initiated across the whole extent of the tank. (At the highest rotation rate some reflection from the lighting rig can be observed, this is unavoidable with the implemented configuration and occurs due to the curvature of the free surface of the fluid above the tank lid.)
It is apparent that with an increase in rotation rate, the observed instability decreases in length scale. At the lower rotation rates the paths followed by the initial disturbance structures have significant radial deviation, meandering in towards the center of the tank and back out to the side walls again. At the lowest rotation rates the instability is more cellular than serpentine. As the rotation rate is increased the cellular initial perturbation is no longer observed and a more serpentine-like structure appears. With increasing rotation rate the width of these structures decreases. It can also be observed that the amount of radial meandering decreases too. It can be seen that, for the rotation rates shown, the instability develops radially first with the azimuthal perturbations becoming more pronounced as time evolves. By the time t &#8776; 3.0 s it is difficult to distinguish which structures arose due to a radial or azimuthal perturbation.
The key observation from the images is that the observed length scale of the structures is smaller for greater rotation rates. We can also see the strength of the technique in that the instability does not develop from a vortex sheet created by a lock-removal.
Fig. 5 shows images from a series of experiments keeping the rotation rate fixed (&#937; = 7.8 &#177; 0.1 rad s-1), but varying the fluid viscosity. The ratio of the viscosity of each layer compared to the viscosity of water, &#181;/&#181;w, varies from 1.00 (top row) to 20.50 (bottom row) and the time of each image varies from t = 0 s (left column) to t = 1.5 s (right column). It is apparent that as the viscosity of the two layers is increased the observed length scale increases. In the most viscous case shown the observed length scale is approximately 18 mm compared to the 6 mm length scale observed in the least viscous case. It can also be seen that in the most viscous case there appears to be a strong wall effect. We observe a general trend from short to long wavelength instability as viscosity is increased.
The observed instabilities have a wavelength which changes slowly in time and which we measure experimentally via an auto-correlation of each image in the movie of the experiment. The auto-correlation is computed from a two-dimensional discrete Fast Fourier Transform of the image intensity. Light regions of the image represent peaks in the instability, and dark regions indicate troughs. A maximum in the auto-correlation is therefore a measure of the instability wavelength that is of key importance as the dispersion relation for the Rayleigh-Taylor instability shows that the growth rate of a given mode of instability depends upon its wavelength. Fig. 6 shows representative measurements of the observed wavelength of instability for varying rotation rates. We observe that as the rotation rate increases the observed wavelength of instability decreases to a lower threshold of approximately 6mm for rotation rates greater than approximately 4 rad s-1.
<img alt="Figure 1" src="/files/ftp_upload/55088/55088fig1.jpg" /> 
Figure 1: Qualitative effect of rotation on the Rayleigh-Taylor Instability. The image on the left hand side is of the Rayleigh-Taylor instability developing in a non-rotating system. The instability develops in time, forming large vortices that transport the &#39;denser&#39; (green) fluid downwards. The image on the right hand side is of the same fluids, and therefore the same gravitational/magnetic instability, but here the system is rotating. The effect of the rotation can be seen to restrict the size of the vortices that form and inhibit the bulk vertical transport of fluid. The times shown are 1.92 s and 3.52 s after initiation on the left hand side and right hand side respectively. The tank diameter is 90 mm, and the rotation rate in the right hand image was 2.38 rad s-1. <a href="http://cloudflare.jove.com/files/ftp_upload/55088/55088fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" src="/files/ftp_upload/55088/55088fig2.jpg" /> 
Figure 2: Experimental set-up. A cylindrical tank contains the two liquid layers. A Lucite lid forms a solid lid for the two layers. Fluid above the lid helps to remove reflections and glare from the Lucite. The cylindrical tank is immersed in distilled water in a rectangular outer tank. These tanks are placed on a platform and spun-up above the magnet where the magnetic forces are negligible. The platform is spun by an off-center motor rotating a keyhole shaped slip-bearing. To begin the experiment, the pin is removed and the experiment descends under its own weight into the magnetic field, simultaneously rotating. (This figure has been modified from 16.) <a href="http://cloudflare.jove.com/files/ftp_upload/55088/55088fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" src="/files/ftp_upload/55088/55088fig3.jpg" /> 
Figure 3: Flotation &#34;Boat&#34;. The flotation boat is made by hot-gluing a dense sponge layer (yellow) to the underside of polystyrene walls (gray) to make a &#34;boat&#34;. The light upper layer fluid will slowly diffuse through the sponge, floating on top of the dense lower layer with minimal mixing between the two layers. The stratification can be further improved by placing a layer of tissue paper (blue) on top of the sponge layer to further diffuse the momentum of the incoming light fluid layer. <a href="http://cloudflare.jove.com/files/ftp_upload/55088/55088fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" src="/files/ftp_upload/55088/55088fig4.jpg" /> 
Figure 4: A sequence of images of the developing instability from the second series of experiments demonstrating the effect of increasing rotation rate. The rates of rotation increase from &#937; = 1.89 rad s-1 in the top row to &#937; = 8.74 rad s-1 in the bottom row. The times shown are measured from the time that the onset of instability is observed. The scale bar shows a length of 10 cm in steps of 1 cm. The diameter of the black circle represents a length of 10.7 cm. (This figure has been modified from 16.) <a href="http://cloudflare.jove.com/files/ftp_upload/55088/55088fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 5" src="/files/ftp_upload/55088/55088fig5.jpg" /> 
Figure 5: A sequence of images showing the effect of varying fluid viscosity on the instability. The rotation rate was fixed at &#937; = 7.8 &#177; 0.1 rad s-1 for each experiment, and the time shown is at intervals of 1.5. The middle row shows the instability in a system that has viscosity approximately 8.36 times that of water. In the top row the viscosity of the system is approximately 20.50 times that of water. It can be seen that the observed length of the instability scale increases with increasing fluid viscosity. The scale bar shows a length of 10 cm in steps of 1 cm. The diameter of the black circles represents a length of 10.7 cm. (This figure has been modified from 16.) <a href="http://cloudflare.jove.com/files/ftp_upload/55088/55088fig5large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 6" src="/files/ftp_upload/55088/55088fig6.jpg" /> 
Figure 6: The dominant observed wavelength at the onset of the instability. We observe a lower threshold for the scale of the instability at approximately 6 mm for all rotation rates greater than approximately 4 rad s-1. The error bars indicate maximum and minimum measured wavelength over the first 2 s after initiation of the instability. (This figure has been modified from 16.) <a href="http://cloudflare.jove.com/files/ftp_upload/55088/55088fig6large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

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 ...

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9.4K Views.  University of Nottingham. 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.

Video: Magnetically Induced Rotating Rayleigh-Taylor Instability

Investigation of Early Plasma Evolution Induced by Ultrashort Laser Pulses

Early plasma is generated owing to high intensity laser irradiation of target and the subsequent target material ionization. Its dynamics plays a significant role in laser-material interaction, especially in the air environment1-11.
Early plasma evolution has been captured through pump-probe shadowgraphy1-3 and interferometry1,4-7. However, the studied time frames and applied laser parameter ranges are limited. For example, direct examinations of plasma front locations and electron number densities within a delay time of 100 picosecond (ps) with respect to the laser pulse peak are still very few, especially for the ultrashort pulse of a duration around 100 femtosecond (fs) and a low power density around 1014 W/cm2. Early plasma generated under these conditions has only been captured recently with high temporal and spatial resolutions12. The detailed setup strategy and procedures of this high precision measurement will be illustrated in this paper. The rationale of the measurement is optical pump-probe shadowgraphy: one ultrashort laser pulse is split to a pump pulse and a probe pulse, while the delay time between them can be adjusted by changing their beam path lengths. The pump pulse ablates the target and generates the early plasma, and the probe pulse propagates through the plasma region and detects the non-uniformity of electron number density. In addition, animations are generated using the calculated results from the simulation model of Ref. 12 to illustrate the plasma formation and evolution with a very high resolution (0.04 ~ 1 ps).
Both the experimental method and the simulation method can be applied to a broad range of time frames and laser parameters. These methods can be used to examine the early plasma generated not only from metals, but also from semiconductors and insulators.

An experimental method to examine the early plasma evolution induced by ultrashort laser pulses is described. Using this method, high quality images of early plasma are obtained with high temporal and spatial resolutions. A novel integrated atomistic model is used to simulate and explain the mechanisms of early plasma.

Early plasma is generated owing to high intensity laser irradiation of target and the subsequent target material ionization. Its dynamics plays a ...

Laser-induced Breakdown Spectroscopy: A New Approach for Nanoparticle's Mapping and Quantification in Organ Tissue

Emission spectroscopy of laser-induced plasma was applied to elemental analysis of biological samples. Laser-induced breakdown spectroscopy (LIBS) performed on thin sections of rodent tissues: kidneys and tumor, allows the detection of inorganic elements such as (i) Na, Ca, Cu, Mg, P, and Fe, naturally present in the body and (ii) Si and Gd, detected after the injection of gadolinium-based nanoparticles. The animals were euthanized 1&#160;to 24 hr&#160;after intravenous injection of particles. A two-dimensional scan of the sample, performed using a motorized micrometric 3D-stage, allowed the infrared laser beam exploring the surface with a lateral resolution less than 100 &#956;m. Quantitative chemical images of Gd element inside the organ were obtained with sub-mM sensitivity. LIBS offers a simple and robust method to study the distribution of inorganic materials without any specific labeling. Moreover, the compatibility of the setup with standard optical microscopy emphasizes its potential to provide multiple images of the same biological tissue with different types of response:&#160;elemental, molecular, or cellular.

Laser-induced breakdown spectroscopy performed on thin organ and tumor tissue successfully detected natural elements and artificially injected gadolinium (Gd), issued from Gd-based nanoparticles. Images of chemical elements reached a resolution of 100 &#956;m and quantitative sub-mM sensitivity. The compatibility of the setup with standard optical microscopy emphasizes its potential to provide multiple images of a same biological tissue.

Emission spectroscopy of laser-induced plasma was applied to elemental analysis of biological samples. Laser-induced breakdown spectroscopy (LIBS) ...

Laser-induced Forward Transfer for Flip-chip Packaging of Single Dies

Flip-chip (FC) packaging is a key technology for realizing high performance, ultra-miniaturized and high-density circuits in the micro-electronics industry. In this technique the chip and/or the substrate is bumped and the two are bonded via these conductive bumps. Many bumping techniques have been developed and intensively investigated since the introduction of the FC technology in 19601 such as stencil printing, stud bumping, evaporation and electroless/electroplating2. Despite the progress that these methods have made they all suffer from one or more than one drawbacks that need to be addressed such as cost, complex processing steps, high processing temperatures, manufacturing time and most importantly the lack of flexibility. In this paper, we demonstrate a simple and cost-effective laser-based bump forming technique known as Laser-induced Forward Transfer (LIFT)3. Using the LIFT technique a wide range of bump materials can be printed in a single-step with great flexibility, high speed and accuracy at RT. In addition, LIFT enables the bumping and bonding down to chip-scale, which is critical for fabricating ultra-miniature circuitry.

We demonstrate the use of the Laser-induced Forward Transfer (LIFT) technique for flip-chip assembly of optoelectronic components. This approach provides a simple, cost-effective, low-temperature, fast and flexible solution for fine-pitch bumping and bonding on chip-scale for achieving high-density circuits for optoelectronic applications.

Flip-chip (FC) packaging is a key technology for realizing high performance, ultra-miniaturized and high-density circuits in the micro-electronics ...

Visible-light Induced Reduction of Graphene Oxide Using Plasmonic Nanoparticle

Present work demonstrates the simple, chemical free, fast, and energy efficient method to produce reduced graphene oxide (r-GO) solution at RT using visible light irradiation with plasmonic nanoparticles. The plasmonic nanoparticle is used to improve the reduction efficiency of GO. It only takes 30 min&#160;at RT by illuminating the solutions with Xe-lamp, the r-GO solutions can be obtained by completely removing gold nanoparticles through simple centrifugation step. The spherical gold nanoparticles (AuNPs) as compared to the other nanostructures is the most suitable plasmonic nanostructure for r-GO preparation. The reduced graphene oxide prepared using visible light and AuNPs was equally qualitative as chemically reduced graphene oxide, which was supported by various analytical techniques such as UV-Vis spectroscopy, Raman spectroscopy, powder XRD and XPS. The reduced graphene oxide prepared with visible light shows excellent quenching properties over the fluorescent molecules modified on ssDNA and excellent fluorescence recovery for target DNA detection. The r-GO prepared by recycled AuNPs is found to be of same quality with that of chemically reduced r-GO. The use of visible light with plasmonic nanoparticle demonstrates the good alternative method for r-GO synthesis.

A simple protocol for the preparation of reduced graphene oxide using visible light and plasmonic nanoparticle is described.

Present work demonstrates the simple, chemical free, fast, and energy efficient method to produce reduced graphene oxide (r-GO) solution at RT using ...

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

For slender and lightweight structures, vibration serviceability is a matter of growing concern, often constituting the critical design requirement. With designs governed by the dynamic performance under human-induced loads, a strong demand exists for the verification and refinement of currently available load models. The present contribution uses a 3D inertial motion tracking technique for the characterization of the in-field pedestrian behavior. The technique is first tested in laboratory experiments with simultaneous registration of the corresponding ground reaction forces. The experiments include walking persons as well as rhythmical human activities such as jumping and bobbing. It is shown that the registered motion allows for the identification of the time variant pacing rate of the activity. Together with the weight of the person and the application of generalized force models available in literature, the identified time-variant pacing rate allows to characterize the human-induced loads. In addition, time synchronization among the wireless motion trackers allows identifying the synchronization rate among the participants. Subsequently, the technique is used on a real footbridge where both the motion of the persons and the induced structural vibrations are registered. It is shown how the characterized in-field pedestrian behavior can be applied to simulate the induced structural response. It is demonstrated that the in situ identified pacing rate and synchronization rate constitute an essential input for the simulation and verification of the human-induced loads. The main potential applications of the proposed methodology are the estimation of human-structure interaction phenomena and the development of suitable models for the correlation among pedestrians in real traffic conditions.

A protocol is presented for the characterization of the in-field pedestrian behavior and the simulation of the resulting structural response. Field-tests demonstrate that the in situ identified pacing rate and synchronization rate among the participants constitute an essential input for the simulation and verification of the human-induced loads.

For slender and lightweight structures, vibration serviceability is a matter of growing concern, often constituting the critical design requirement. With ...

Laser-induced Forward Transfer of Ag Nanopaste

Over the past decade, there has been much development of non-lithographic methods1-3 for printing metallic inks or other functional materials. Many of these processes such as inkjet3 and laser-induced forward transfer (LIFT)4 have become increasingly popular as interest in printable electronics and maskless patterning has grown. These additive manufacturing processes are inexpensive, environmentally friendly, and well suited for rapid prototyping, when compared to more traditional semiconductor processing techniques. While most direct-write processes are confined to two-dimensional structures and cannot handle materials with high viscosity (particularly inkjet), LIFT can transcend both constraints if performed properly. Congruent transfer of three dimensional pixels (called voxels), also referred to as laser decal transfer (LDT)5-9, has recently been demonstrated with the LIFT technique using highly viscous Ag nanopastes to fabricate freestanding interconnects, complex voxel shapes, and high-aspect-ratio structures. In this paper, we demonstrate a simple yet versatile process for fabricating a variety of micro- and macroscale Ag structures. Structures include simple shapes for patterning electrical contacts, bridging and cantilever structures, high-aspect-ratio structures, and single-shot, large area transfers using a commercial digital micromirror device (DMD) chip.

We demonstrate the use of the Laser-induced forward transfer technique (LIFT) for the printing of high-viscosity Ag paste. This technique offers a simple, low temperature, robust process for non-lithographically printing microscale 2D and 3D structures.

Over the past decade, there has been much development of non-lithographic methods1-3 for printing metallic inks or other functional materials. Many of ...

Fabrication of 1-D Photonic Crystal Cavity on a Nanofiber Using Femtosecond Laser-induced Ablation

We present a protocol for fabricating 1-D Photonic Crystal (PhC) cavities on subwavelength-diameter tapered optical fibers, optical nanofibers, using femtosecond laser-induced ablation. We show that thousands of periodic nano-craters are fabricated on an optical nanofiber by irradiating with just a single femtosecond laser pulse. For a typical sample, periodic nano-craters with a period of 350 nm and with diameter gradually varying from 50 - 250 nm over a length of 1 mm are fabricated on a nanofiber with diameter around 450 - 550 nm. A key aspect of such a nanofabrication is that the nanofiber itself acts as a cylindrical lens and focuses the femtosecond laser beam on its shadow surface. Moreover, the single-shot fabrication makes it immune to mechanical instabilities and other fabrication imperfections. Such periodic nano-craters on nanofiber, act as a 1-D PhC and enable strong and broadband reflection while maintaining the high transmission out of the stopband. We also present a method to control the profile of the nano-crater array to fabricate apodized and defect-induced PhC cavities on the nanofiber. The strong confinement of the field, both transverse and longitudinal, in the nanofiber-based PhC cavities and the efficient integration to the fiber networks, may open new possibilities for nanophotonic applications and quantum information science.

We present a protocol for fabricating 1-D photonic crystal cavities on subwavelength diameter silica fibers (optical nanofibers) using femtosecond laser-induced ablation.

We present a protocol for fabricating 1-D Photonic Crystal (PhC) cavities on subwavelength-diameter tapered optical fibers, optical nanofibers, using ...

Preparation of Liquid Crystal Networks for Macroscopic Oscillatory Motion Induced by Light

A strategy based on doped liquid crystalline networks is described to create mechanical self-sustained oscillations of plastic films under continuous light irradiation. The photo-excitation of dopants that can quickly dissipate light into heat, coupled with anisotropic thermal expansion and self-shadowing of the film, gives rise to the self-sustained deformation. The oscillations observed are influenced by the dimensions and the modulus of the film, and by the directionality and intensity of the light. The system developed offers applications in energy conversion and harvesting for soft-robotics and automated systems.
The general method described here consists of creating free-standing liquid crystalline films and characterizing the mechanical and thermal effects observed. The molecular alignment is achieved using alignment layers (rubbed polyimide), commonly used in the display manufacturing industry. To obtain actuators with large deformation, the mesogens are aligned and polymerized in a splay/bend configuration, i.e., with the director of the liquid crystals (LCs) going gradually from planar to homeotropic through the film thickness. Upon irradiation, the mechanical and thermal oscillations obtained are monitored with a high-speed camera. The results are further quantified by image analysis using an image processing program.

The goal of the protocol is to create liquid crystalline polymer films that can mechanically oscillate under continuous light irradiation. We describe in great detail the conception of free-standing films, from the liquid crystal alignment method to the photo-actuation. The experimental protocol applied to prepare this material is broadly applicable.

A strategy based on doped liquid crystalline networks is described to create mechanical self-sustained oscillations of plastic films under continuous ...

Fabrication Procedures and Birefringence Measurements for Designing Magnetically Responsive Lanthanide Ion Chelating Phospholipid Assemblies

Bicelles are tunable disk-like polymolecular assemblies formed from a large variety of lipid mixtures. Applications range from membrane protein structural studies by nuclear magnetic resonance (NMR) to nanotechnological developments including the formation of optically active and magnetically switchable gels. Such technologies require high control of the assembly size, magnetic response and thermal resistance. Mixtures of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and its lanthanide ion (Ln3+) chelating phospholipid conjugate, 1,2-dimyristoyl-sn-glycero-3-phospho-ethanolamine-diethylene triaminepentaacetate (DMPE-DTPA), assemble into highly magnetically responsive assemblies such as DMPC/DMPE-DTPA/Ln3+ (molar ratio 4:1:1) bicelles. Introduction of cholesterol (Chol-OH) and steroid derivatives in the bilayer results in another set of assemblies offering unique physico-chemical properties. For a given lipid composition, the magnetic alignability is proportional to the bicelle size. The complexation of Ln3+ results in unprecedented magnetic responses in terms of both magnitude and alignment direction. The thermo-reversible collapse of the disk-like structures into vesicles upon heating allows tailoring of the assemblies&#39; dimensions by extrusion through membrane filters with defined pore sizes. The magnetically alignable bicelles are regenerated by cooling to 5 &#176;C, resulting in assembly dimensions defined by the vesicle precursors. Herein, this fabrication procedure is explained and the magnetic alignability of the assemblies is quantified by birefringence measurements under a 5.5 T magnetic field. The birefringence signal, originating from the phospholipid bilayer, further enables monitoring of polymolecular changes occurring in the bilayer. This simple technique is complementary to NMR experiments that are commonly employed to characterize bicelles.

Fabrication procedures for highly magnetically responsive lanthanide ion chelating polymolecular assemblies are presented. The magnetic response is dictated by the assembly size, which is tailored by extrusion through nanopore membranes. The assemblies&#39; magnetic alignability and temperature-induced structural changes are monitored by birefringence measurements, a complimentary technique to nuclear magnetic resonance and small angle neutron scattering.

Bicelles are tunable disk-like polymolecular assemblies formed from a large variety of lipid mixtures. Applications range from membrane protein structural ...

Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel

An experimental method for exploring the heat transfer characteristics of an axially rotating channel is proposed. The governing flow parameters that characterize the transport phenomena in a rotating channel are identified via the parametric analysis of the momentum and energy equations referring to a rotating frame of reference. Based on these dimensionless flow equations, an experimental strategy that links the design of the test module, the experimental program and the data analysis is formulated with the attempt to reveal the isolated Coriolis-force and buoyancy effects on heat transfer performances. The effects of Coriolis force and rotating buoyancy are illustrated using the selective results measured from rotating channels with various geometries. While the Coriolis-force and rotating-buoyancy impacts share several common features among the various rotating channels, the unique heat transfer signatures are found in association with the flow direction, the channel shape and the arrangement of heat transfer enhancement devices. Regardless of the flow configurations of the rotating channels, the presented experimental method enables the development of physically consistent heat transfer correlations that permit the evaluation of isolated and interdependent Coriolis-force and rotating-buoyancy effects on the heat transfer properties of rotating channels.

Here, we present an experimental method for decoupling the interdependent Coriolis-force and rotating-buoyancy effects on full-field heat transfer distributions of a rotating channel.

An experimental method for exploring the heat transfer characteristics of an axially rotating channel is proposed. The governing flow parameters that ...