Rotating Rayleigh-Taylor instability

The effect of rotation upon the classical Rayleigh-Taylor instability is considered. We consider a two-layer system with an axis of rotation that is perpendicular to the interface between the layers. In general we find that a wave mode’s growth rate may be reduced by rotation. We further show that in some cases, unstable axisymmetric wave modes may be stabilized by rotating the system above a critical rotation rate associated with the mode’s wavelength, the Atwood number and the flow’s aspect ratio

Spherical vortices in rotating fluids

A popular model for a generic fat-cored vortex ring or eddy is Hill's spherical vortex (Phil. Trans. Roy. Soc. A vol. 185, 1894, p. 213). This well-known solution of the Euler equations may be considered a special case of the doubly-infinite family of swirling spherical vortices identified by Moffatt (J. Fluid Mech. vol. 35(1), 1969, p. 117). Here we find exact solutions for such spherical vortices propagating steadily along the axis of a rotating ideal fluid. The boundary of the spherical vortex swirls in such a way as to exactly cancel out the background rotation of the system. The flow external to the spherical vortex exhibits fully nonlinear inertial wave motion. We show that above a critical rotation rate, closed streamlines may form in this outer fluid region and hence carry fluid along with the spherical vortex. As the rotation rate is further increased, further concentric 'sibling' vortex rings are formed

Centrifugally forced Rayleigh-Taylor instability

We consider the effect of high rotation rates on two liquid layers that 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. A linear stability analysis is carried out on a perturbation to the hydrostatic background state and a fourth order Orr-Sommerfeld-like equation that governs the system is derived. 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. In the most simple case of two layers of inviscid fluid separated by a sharp interface with no surface tension acting, we show that the effects of the curvature of the interface and the confinement of the system may be characterized by a modified Atwood number. The classical Atwood number is recovered in the limit of high azimuthal wavenumber, or the outer fluid layer being unconfined. 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

Magnetically Induced Rotating Rayleigh-Taylor Instability

Classical techniques for investigating the Rayleigh-Taylor instability include using compressed gasses, rocketry or linear electric motors to reverse the effective direction of gravity, and accelerate the lighter fluid toward the denser fluid. Other authors 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 ferrofluid. The dominant effect of the magnetic field is to apply a body force to each fluid layer changing the liquid’s effective weight. The upper layer is weakly paramagnetic and the lower layer is weakly diamagnetic so that as the magnetic field is applied, the lower layer is repelled from the magnet while the upper layer is attracted toward the magnet. The upper layer behaves as if it is heavier than it really is, and the lower layer behaves as if it is lighter than it really is. If the applied gradient magnetic field is large enough, the upper layer may become “heavier” than the lower layer and so the system becomes Rayleigh-Taylor unstable. and we see the onset of the Rayleigh-Taylor instability. We further observe that increasing the dynamic viscosity of fluid in each layer increases the observed lengthscale of the instability

Magnetically-induced rotating Rayleigh-Taylor instability

Classical techniques for investigating the Rayleigh-Taylor instability include using compressed gasses, rocketry or linear electric motors to reverse the effective direction of gravity, and accelerate the lighter fluid toward the denser fluid. Other authors 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 ferrofluid. The dominant effect of the magnetic field is to apply a body force to each fluid layer changing the liquid’s effective weight. The upper layer is weakly paramagnetic and the lower layer is weakly diamagnetic so that as the magnetic field is applied, the lower layer is repelled from the magnet while the upper layer is attracted toward the magnet. The upper layer behaves as if it is heavier than it really is, and the lower layer behaves as if it is lighter than it really is. If the applied gradient magnetic field is large enough, the upper layer may become “heavier” than the lower layer and so the system becomes Rayleigh-Taylor unstable. and we see the onset of the Rayleigh-Taylor instability. We further observe that increasing the dynamic viscosity of fluid in each layer increases the observed lengthscale of the instability

Sonomaglev: Combining acoustic and diamagnetic levitation

Acoustic levitation and diamagnetic levitation are experimental methods that both enable the contact-free study of liquid droplets and solid particles. Here we combine techniques of both into a single system that takes advantage of the strengths of each, allowing for the manipulation of levitated spherical water droplets (30 nl-14 µl) under conditions akin to weightlessness, in the laboratory, using a superconducting magnet fitted with two low-power ultrasonic transducers. We show that multiple droplets, arranged horizontally along a line, can be stably levitated with this system and demonstrate controlled contactless coalescence of two droplets. Numerical simulation of the magnetogravitational and acoustic potential reproduces the multiple stable equilibrium points observed in our experiments. Contactless manipulation has become an area of increased study over the last 10 years. New experimental techniques have been developed in a wide variety of disciplines, including: analytical chemistry 1-6 , material sciences 7 , pharmacy 8,9 and micro-assembly 10-13. Many contactless manipulation experiments rely upon a family of techniques classified as acoustic levitation. Acoustic levitation uses ultrasonic transducers to create a pressure field that applies acoustic radiation forces to suspend objects in a gaseous medium 14. It has been shown that intricate, readily tuneable pressure fields can be constructed by using an array of small ultrasonic transducers 15,16 , allowing for manipulation of multiple objects in three dimensions. The discovery that an array of ultrasonic transducers can create customisable acoustic levitation systems has led to a resurgence in the study of non-contact manipulation using acoustic levitation techniques 17-20. In addition to these and other attractive features of acoustic levitation 21 , the method also has some drawbacks. From the earliest experiments, acoustically-levitated objects were observed to have a tendency to oscillate, attributed to the response of the acoustic field to the presence of the object 22,23. Objects may also start to rotate spontaneously due to streaming flows in the surrounding gas generated by the high pressure sound waves 24,25 , though techniques to mitigate these effects and control the rotation have been demonstrated recently 26,27. These same streaming flows may also be problematic in studies of liquid droplets, where the air flow affects heat and mass transfer non-uniformly at the droplet's surface 28 and also sets up flows within the droplet 29. Acousti-cally-levitated liquid droplets are often deformed into oblate-like shapes 30,31 ; this typically occurs when the diameter of the droplet is of the same order as the acoustic wavelength. These characteristics, which are usually undesirable (though occasionally exploited 31), are avoided in similar experiments using diamagnetic levitation (e.g. Ref. 32). Diamagnetic materials experience a repulsive force when placed in a static, spatially-varying magnetic field. A wide variety of solids and liquids, including water and organic material (including biological), can be levitated in a magnetic field of sufficient strength and gradient (e.g. Refs. 33-40); typically a field of order 10 T is required, though levitation of graphite can be achieved using much weaker fields (e.g. Ref. 41). In contrast to the oscillating surface forces applied in acoustic levita-tion, diamagnetic levitation applies a constant body force that counteracts the force of gravity throughout the levitated object at the molecular level, and so closely mimics the weightless conditions on board an orbital or parabolic flight, or in a drop tower. Diamagnetically-levitated liquid droplets attain a spherical shape, due to the fact that surface tension forces dominate over the residual net body forces (∼ 0.01 g) that stabilize the levitation. On the other hand, the options to manipulate multiple objects magnetically are limited. Diamagnetic levitation allows for the levitation of multiple spatially-separated objects simultaneously if the objects have unique ratios of magnetic susceptibility to density. This differs from acoustic levitation where multiple acoustic 'traps' can be created for a particular material by manipulating the acoustic field. The creation of multiple traps for a single material is also possible using dia-magnetic levitation, by manipulating the shape of the strong magnetic field, but this is technically more challenging than manipulating an acoustic field and correspondingly more restrictive. In this letter, we demonstrate combining techniques from both acoustic and diamagnetic levitation to manipulate the position of liquid droplets, drawing on the strengths of each method. The force of gravity is compensated throughout the droplets by applying a vertical diamagnetic body force using a superconducting magnet, providing a simulation of weightlessness. Then, acoustic radiation forces are used to position the droplets. Since diamagnetic rather than acoustic forces provide gravity compensation in this case, the acoustic power required in these experiments is much smaller than that of a purely acoustic levitator. We further show that it is possible to reproduce the locations of the levitated droplets in simulations , calculating the magnetic and acoustic fields. Acoustic levitation has been combined with magnetic fields before, to study active matter levitated in liquids, but in those studies the magnetic field was used to provide propulsion (e.g. Ref. 42

Turbulent ‘stopping plumes’ and plume pinch-off in uniform surroundings

Observations of turbulent convection in the environment are of variously sus- tained plume-like flows or intermittent thermal-like flows. At different times of the day the prevailing conditions may change and consequently the observed flow regimes may change. Understanding the link between these flows is of practical importance meteorologically, and here we focus our interest upon plume-like regimes that break up to form thermal-like regimes. It has been shown that when a plume rises from a boundary with low conductivity, such as arable land, the inability to maintain a rapid enough supply of buoyancy to the plume source can result in the turbulent base of the plume separating and rising away from the source. This plume ‘pinch-off’ marks the onset of the intermittent thermal-like behavior. The dynamics of turbulent plumes in a uniform environment are explored in order to investigate the phenomenon of plume pinch-off. The special case of a turbulent plume having its source completely removed, a ‘stopping plume’, is considered in particular. The effects of forcing a plume to pinch-off, by rapidly reducing the source buoyancy flux to zero, are shown experi- mentally. We release saline solution into a tank filled with fresh water generating downward propagating steady turbulent plumes. By rapidly closing the plume nozzle, the plumes are forced to pinch-off. The plumes are then observed to detach from the source and descend into the ambient. The unsteady buoyant region produced after pinch-off, cannot be described by the power-law behavior of either classical plumes or thermals, and so the terminology ‘stopping plume’ (analogous to a ‘starting plume’) is adopted for this type of flow. The propagation of the stopping plume is shown to be approximately linearly dependent on time, and we speculate therefore that the closure of the nozzle introduces some vorticity into the ambient, that may roll up to form a vortex ring dominating the dynamics of the base of a stopping plume

Effectiveness of a national quality improvement programme to improve survival after emergency abdominal surgery (EPOCH): a stepped-wedge cluster-randomised trial

Background: Emergency abdominal surgery is associated with poor patient outcomes. We studied the effectiveness of a national quality improvement (QI) programme to implement a care pathway to improve survival for these patients. Methods: We did a stepped-wedge cluster-randomised trial of patients aged 40 years or older undergoing emergency open major abdominal surgery. Eligible UK National Health Service (NHS) hospitals (those that had an emergency general surgical service, a substantial volume of emergency abdominal surgery cases, and contributed data to the National Emergency Laparotomy Audit) were organised into 15 geographical clusters and commenced the QI programme in a random order, based on a computer-generated random sequence, over an 85-week period with one geographical cluster commencing the intervention every 5 weeks from the second to the 16th time period. Patients were masked to the study group, but it was not possible to mask hospital staff or investigators. The primary outcome measure was mortality within 90 days of surgery. Analyses were done on an intention-to-treat basis. This study is registered with the ISRCTN registry, number ISRCTN80682973. Findings: Treatment took place between March 3, 2014, and Oct 19, 2015. 22 754 patients were assessed for elegibility. Of 15 873 eligible patients from 93 NHS hospitals, primary outcome data were analysed for 8482 patients in the usual care group and 7374 in the QI group. Eight patients in the usual care group and nine patients in the QI group were not included in the analysis because of missing primary outcome data. The primary outcome of 90-day mortality occurred in 1210 (16%) patients in the QI group compared with 1393 (16%) patients in the usual care group (HR 1·11, 0·96–1·28). Interpretation: No survival benefit was observed from this QI programme to implement a care pathway for patients undergoing emergency abdominal surgery. Future QI programmes should ensure that teams have both the time and resources needed to improve patient care. Funding: National Institute for Health Research Health Services and Delivery Research Programme