Drops deposited on an evaporating liquid bath can be maintained in an inverse Leidenfrost state by the vapor emanating from the bath, making them levitate and hover almost without friction. These perfectly non-wetting droplets create a depression in the liquid interface that sustains their weight, which generates repellent forces when they approach a meniscus rising against a wall. Here, we study this reflection in detail, and show that frictionless Leidenfrost drops are a simple and efficient tool to probe the shape of an unknown interface. We then use the menisci to control the motion of the otherwise elusive drops. We create waveguides to direct and accelerate them and use parabolic walls to reflect and focus them. This could be particularly beneficial in the scale up of droplet cryopreservation processes: capillary interactions can be used to transport, gather and collect vitrified biological samples in absence of contact and contamination.
We report on the collision-coalescence dynamics of drops in Leidenfrost state using liquids with different physicochemical properties. Drops of the same liquid deposited on a hot concave surface coalesce practically at contact, but when drops of different liquids collide, they can bounce several times before finally coalescing when the one that evaporates faster reaches a critical size, of the order of the capillary length. The bouncing dynamics is produced because the drops are not only in Leidenfrost state with the substrate, they also experience Leidenfrost effect between them at the moment…
The mobility of Leidenfrost drop has been exploited for the manipulation of drop motions. In the classical model, the Leidenfrost drop was levitated by a vapor cushion, in the absence of touch to the surface. Here we report a standing Leidenfrost state on a heated hydrophobic surface where drop stands on the surface with partial adhesion and further self-rotates like Sufi-whirling. To elucidate this new phenomenon, we imaged the evolution of the partial adhesion, the inner circulation, and the ellipsoidal rotation of the drop. The stable partial adhesion is accompanied by thermal and mechanica…
We experimentally investigate the effect of an electric field applied between a Leidenfrost droplet and the heated substrate on which it is levitating. We quantify the electro-Leidenfrost effect by imaging the interference fringes between the liquid-vapour and vapour-substrate interfaces. The increase of the voltage induces a decrease of the vapour layer thickness. Above a certain critical voltage the Leidenfrost effect is suppressed and the drop starts boiling. Our study characterizes this way to control and/or to avoid the Leidenfrost effect that is undesirable in many domains such as metall…
We experimentally investigate the Leidenfrost effect at pressures ranging from 1 to 0.05 atmospheric pressure. As a direct consequence of the Clausius-Clapeyron phase diagram of water, the droplet temperature can be at ambient temperature in a non-sophisticated lab environment. Furthermore, the lifetime of the Leidenfrost droplet is significantly increased in this low pressure environment. The temperature and pressure dependance of the evaporation rate are successfully tested against a recently proposed model. These results may pave a way to reach efficient Leidenfrost micro-fluidic and milli-…
The Leidenfrost effect describes liquid drops under gravity levitating on a vapour cushion, which is sourced at the liquid-vapour interface from evaporation caused by the hot substrate below. It has been experimentally observed that when two or more Leidenfrost drops approach one another, there is a short-range repulsion that can prevent coalescence. In the present work, we investigate the coalescence process of initially momentum-less Leidenfrost drops. This is carried out by numerically simulating two-dimensional systems of liquid and vapour using the recently developed dynamic van der Waals…
We put in evidence the unexpected behaviour of Leidenfrost droplets at the later stage of their evaporation. We predict and observe that, below a critical size $R_l$, the droplets spontaneously take-off due to the breakdown of the lubrication regime. We establish the theoretical relation between the droplet radius and its elevation. We predict that the vapour layer thickness increases when the droplets become smaller. A satisfactory agreement is found between the model and the experimental results performed on droplets of water and of ethanol.
In the Leidenfrost effect, liquid drops deposited on a hot surface levitate on a thin vapor cushion fed by evaporation of the liquid. This vapor layer forms a concave depression in the drop interface. Using laser-light interference coupled to high-speed imaging, we measured the radius, curvature, and height of the vapor pocket, as well as non-axisymmetric fluctuations of the interface for water drops at different temperatures. The geometry of the vapor pocket depends primarily on the drop size and not on the substrate temperature.
When a liquid droplet impacts a hot solid surface, enough vapor may be generated under it as to prevent its contact with the solid. The minimum solid temperature for this so-called Leidenfrost effect to occur is termed the Leidenfrost temperature, or the dynamic Leidenfrost temperature when the droplet velocity is non-negligible. We observe the wetting/drying and the levitation dynamics of the droplet impacting on an (isothermal) smooth sapphire surface using high speed total internal reflection imaging, which enables us to observe the droplet base up to about 100 nm above the substrate surfac…
We consider the flotation of deformable, non-wetting drops on a liquid interface. We consider the deflection of both the liquid interface and the droplet itself in response to the buoyancy forces, density difference and the various surface tensions within the system. Our results suggest new insight into a range of phenomena in which such drops occur, including Leidenfrost droplets and floating liquid marbles. In particular, we show that the floating state of liquid marbles is very sensitive to the tension of the particle-covered interface and suggest that this sensitivity may make such experim…
We show that a volatile liquid drop placed at the surface of a non-volatile liquid pool warmer than the boiling point of the drop can experience a Leidenfrost effect even for vanishingly small superheats. Such an observation points to the importance of the substrate roughness, negligible in the case considered here, in determining the threshold Leidenfrost temperature. A theoretical model based on the one proposed by Sobac et al. [Phys. Rev. E 90, 053011 (2014)] is developed in order to rationalize the experimental data. The shapes of the drop and of the substrate are analyzed. The model notab…
The Leidenfrost effect-prolonged evaporation of droplets on a superheated surface-happens only when the surface temperature is above a certain transitional value. Here, we show that specially engineered droplets - liquid marbles - can exhibit similar effect at any superheated temperatures (up to 465 oC tested in our experiment) without a transition. Very possibly, this phenomenon is due to the fact that liquid marbles are droplets coated with microparticles and these microparticles help levitate the liquid core and maintain an insulation layer between the liquid and the superheated surface.
When deposited on a hot bath, volatile drops are observed to stay in levitation: the so-called Leidenfrost effect. Here, we discuss drop dynamics in an inverse Leidenfrost situation where room-temperature drops are deposited on a liquid nitrogen pool, and levitate on a vapor film generated by evaporation of the bath. In the seconds following deposition, we observe that the droplets start to glide on the bath along a straight path, only disrupted by elastic bouncing close to the edges of the container. Initially at rest, these self-propelled drops accelerate within a few seconds and reach veloc…
Drops placed on a surface with a temperature above the Leidenfrost point float atop an evaporative vapor layer. In this fluid dynamics video, it is shown that for roughened surfaces the Leidenfrost point depends on the drop size, which runs contrary to previous claims of size independence. The thickness of the vapor layer is known to increase with drop radius, suggesting that the surface roughness will not be able to penetrate the vapor layer for drops above a critical size. This size dependence was experimentally verified: at a given roughness and temperature, drops beneath a critical size ex…
Droplets can be levitated by their own vapour when placed onto a superheated plate (the Leidenfrost effect). It is less known that the Leidenfrost effect can likewise be observed over a liquid pool (superheated with respect to the drop), which is the study case here. Emphasis is placed on an asymptotic analysis in the limit of small evaporation numbers, which proves to be a realistic one indeed for not so small drops. The global shapes are found to resemble "superhydrophobic drops" that follow from the equilibrium between capillarity and gravity. However, the morphology of the thin vapour laye…
This study experimentally explores fluid breakup and Leidenfrost dynamics for droplets impacting a heated millimetric post. Using high-speed optical and infrared imaging, we investigate the droplet lifetime, breakup and boiling modes, as well as the cooling performance of different substrates. The post substrate leads to a shorter droplet lifetime and a 20°C higher Leidenfrost temperature compared to a flat substrate, attributed to mixed boiling modes along the height of the post and additional pinning. For temperatures below the Leidenfrost point, in the nucleate boiling regime, the post subs…
A liquid droplet hovering on a hot surface is commonly referred to as a Leidenfrost droplet. In this study, we discover that a Leidenfrost droplet involuntarily performs a series of distinct oscillations as it shrinks during the span of its life. The oscillation first starts out erratically, followed by a stage with stable frequencies, and finally turns into periodic bouncing with signatures of a parametric oscillation and occasional resonances. The last bouncing stage exhibits nearly perfect collisions. We showed experimentally and theoretically the enabling effects of each oscillation mode a…
In the framework of the lubrication approximation, we derive a set of equations describing the steady bottom profile of Leidenfrost drops coupled with the vapor pressure. This allows to derive scaling laws for the geometry of the concave bubble encapsulated between the drop and the hot plate under it. The results agree with experimental observations in the case of droplets with radii smaller than the capillary length Rc as well as in the case of puddles with radii larger than Rc.
Droplet impact on hot surfaces results in either droplet-surface contact or droplet-surface non-contact, i.e., the Leidenfrost state. The Leidenfrost droplet is levitated upon its vapor, deteriorating the heat transfer. The Leidenfrost temperature depends on the thermal properties of the surface, which are usually characterized by two parameters: the thermal diffusivity and the thermal effusivity. In this paper, the effects of these two parameters on the Leidenfrost temperature are clarified experimentally by varying the one of interest while keeping the other one constant. The experimental re…
In this article, a novel method of increasing the dynamic Leidenfrost temperature is proposed through the addition of both anionic (SDS) and cationic (CTAB) surfactants to water droplets. We focus on understanding the hydrodynamics and thermal aspects of droplet impact Leidenfrost behaviour of surfactant solutions, and aim to delay the onset of the Leidenfrost regime. The effects of Weber number (We), Ohnesorge number (Oh) and surfactant concentration on dynamic Leidenfrost temperature were experimentally studied in details, covering a wide gamut of governing parameters. At a fixed impact velo…
The present article highlights the role of non-Newtonian (elastic) effects on the droplet impact phenomenology at temperatures considerably higher than the boiling point, especially at or above the Leidenfrost regime. The Leidenfrost point (LFP) was found to decrease with increase in the impact Weber number (based on velocity just before the impact) for fixed polymer (Polyacrylamide, PAAM) concentrations. Water droplets fragmented at very low Weber numbers (~22), whereas the polymer droplets resisted fragmentation at much higher Weber numbers (~155). We also varied the polymer concentration an…
It is demonstrated that non-coalescent droplets of acetone can be formed on liquid substrates. The fluid flows around and in an acetone droplet hovering on water are recorded to shed light on the mechanisms which might lead to non-coalescence. For sufficiently low impact velocities, droplets undergo a damped oscillation on the surface of the liquid substrate but at higher velocities clean bounce-off occurs. Comparisons of experimentally observed static configurations of floating droplets to predictions from a theoretical model for a small non-wetting rigid sphere resting on a liquid substrate …
In this paper, the self-propelled motion of Leidenfrost droplets on ratchet surfaces is numerically investigated with a thermal multiphase lattice Boltzmann model with liquid-vapor phase change. The capability of the model for simulating evaporation is validated via the D2 law. Using the model, we first study the performances of Leidenfrost droplets on horizontal ratchet surfaces. It is numerically shown that the motion of self-propelled Leidenfrost droplets on ratchet surfaces is owing to the asymmetry of the ratchets and the vapor flows beneath the droplets. It is found that the Leidenfrost …
The levitation of a volatile droplet on a highly superheated surface is known as the Leidenfrost effect. Wetting state during transition from full wetting of a surface by a droplet at room temperature to Leidenfrost bouncing, i.e., zero-wetting at high superheating, is not fully understood. Here, visualizations of droplet thermal and wetting footprint in the Leidenfrost transition state are presented using two optical techniques: mid-infrared thermography and wetting sensitive total internal reflection imaging under carefully selected experimental conditions, impact Weber number < 10 and dropl…
Liquid oxygen, which is paramagnetic, also undergoes Leidenfrost effect at room temperature. In this article, we first study the deformation of oxygen drops in a magnetic field and show that it can be described via an effective capillary length, which includes the magnetic force. In a second part, we describe how these ultra-mobile drops passing above a magnet significantly slow down and can even be trapped. The critical velocity below which a drop is captured is determined from the deformation induced by the field.
Universal mapping of drop impact spreading from wetting to Leidenfrost regimes
Institute of Thermal Science and Power Systems, School of Energy Engineering, Zhejiang University（浙江大学能源工程学院热科学和动力系统工程研究所）；Department of Mechanical and Aerospace Engineering, Princeton University（普林斯顿大学机械与航空航天工程系）；State Key Laboratory of Clean Energy Utilization, Zhejiang University（浙江大学清洁能源利用国家重点实验室）
Leidenfrost ratchets are structures with the ability of transporting liquid droplets when heated over the critical Leidenfrost temperature. Once this temperature is reached, the droplet levitates over the surface and moves in the direction marked by the slope of the ratchet at terminal velocities around 10 cm/s. Here we provide new experiments with micron-sized ratchets, which have been produced with picosecond pulse laser ablation. In the following work, we use a simple method to measure the thrust driving droplets of capillary size over the micro-ratchets. The mechanism responsible for the f…
In the Leidenfrost effect, a thin layer of evaporated vapor forms between a liquid and a hot solid. The complex interactions between the solid, liquid, and vapor phases can lead to rich dynamics even in a single Leidenfrost drop. Here we investigate the self-organized oscillations of Leidenfrost drops that are excited by a constant flow of evaporated vapor beneath the drop. We show that for small Leidenfrost drops, the frequency of a recently reported "breathing mode" can be explained by a simple balance of gravitational and surface tension forces. For large Leidenfrost drops, azimuthal star-s…
Leidenfrost droplets: The roles of ambient humidity and internal droplet circulation
University of Twente（特温特大学）；Max-Planck Center Twente for Complex Fluid Dynamics（马普中心特温特复杂流体力学）；J.M. Burgers Centre for Fluid Dynamics（J.M. 伯格斯流体力学中心）；University of Houston（休斯顿大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；Max-Planck Institute for Dynamics and Self-Organization（马普动力学与自组织研究所）
Recent experiments have shown that liquid Leidenfrost drops levitated by their vapor above a flat hot surface can exhibit symmetry-breaking spontaneous dynamics (A. Bouillant et al., Nature Physics, 14 1188-1192, 2018). Motivated by these observations, we theoretically investigate the translational and rotational dynamics of Leidenfrost drops on the basis of a simplified two-dimensional model, focusing on near-circular drops small relative to the capillary length. The model couples the equations of motion of the drop, which flows as a rigid wheel, and thin-film equations governing the vapor fl…
We experimentally investigate the self-sustained, star-shaped oscillations of Leidenfrost drops. The drops levitate on a cushion of evaporated vapor over a heated, curved surface. We observe modes with $n = 2-13$ lobes around the drop periphery. We find that the wavelength of the oscillations depends only on the capillary length of the liquid, and is independent of the drop radius and substrate temperature. However, the number of observed modes depends sensitively on the liquid viscosity. The dominant frequency of pressure variations in the vapor layer is approximately twice the drop oscillati…
We show that when a drop of water is maintained in its Leidenfrost regime, a sound in the form of periodic beats emits from the drop. The process of beat emission involves two distinct frequencies. One component is the frequency of beats itself and second is the frequency of sound in every beat which is emitted when one oscillation in the drop occurs. Experiments have been performed by placing a drop of water over a concave metallic surface and the beats of the drop were recorded by fixing a microphone above the drop. A video camera was also fixed above the drop to record its oscillations. Sim…
We experimentally and theoretically investigate the behavior of Leidenfrost droplets inserted in a Hele-Shaw cell. As a result of the confinement from the two surfaces, the droplet has the shape of a flattened disc and is thermally isolated from the surface by the two evaporating vapor layers. An analysis of the evaporation rate using simple scaling arguments is in agreement with the experimental results. Using the lubrication approximation we numerically determine the shape of the droplets as a function of its radius. We furthermore find that the droplet width tends to zero at its center when…
In this Fluid Dynamics Videos submitted to the 31st Gallery of Fluid Motion, (find a different version here http://youtu.be/CS0c05WQ_js) we illustrate the special dynamics of capillary self-propelled Leidenfrost droplets in micrometric Ratchets. In order to be able to propel water droplets of sizes of the order of 1 mm, micro-ratchets were produced by direct material removal using a picosecond pulsed laser source. Surface micro-patterning with picosecond laser pulses allows creating a well controlled topography on a variety of substrates, with a resolution typically in the micron range. More i…
In the Leidenfrost effect a small drop of fluid is levitated above a sufficiently hot surface, on a persistent vapor layer generated by evaporation from the drop. The vapor layer thermally insulates the drop from the surface leading to extraordinarily long drop lifetimes. The top-view shape of the levitated drops can exhibit persistent star-like vibrations. I extend recent work [Burton et al. PRL 2012] to study the bottom surface of the drop using interference-imaging. In this work I use a high-speed camera and automated image analysis to image, locate and classify the interference fringes. Fr…
The gasification of multicomponent fuel drops is relevant in various energy-related technologies. An interesting phenomenon associated with this process is the self-induced explosion of the drop, producing a multitude of smaller secondary droplets, which promotes overall fuel atomization and, consequently, improves the combustion efficiency and reduces emissions of liquid-fueled engines. Here, we study a unique explosive gasification process of a tricomponent droplet consisting of water, ethanol, and oil ("ouzo"), by high-speed monitoring of the entire gasification event taking place in the we…
We experimentally investigate the boiling behavior of impacting ethanol drops on a heated smooth sapphire substrate at pressures ranging from P = 0.13 bar to atmospheric pressure. We employ Frustrated Total Internal Reflection (FTIR) imaging to study the wetting dynamics of the contact between the drop and the substrate. The spreading drop can be in full contact (contact boiling), it can partially touch (transition boiling) or the drop can be fully levitated (Leidenfrost boiling). We show that the temperature of the boundary between contact and transition boiling shows at most a weak dependenc…
In real applications, drops always impact on solid walls with various inclinations. For the oblique impact of a Leidenfrost drop, which has a vapor layer under its bottom surface to prevent its direct contact with the superheated substrate, the drop can nearly frictionlessly slide along the substrate accompanied by the spreading and the retracting. To individually study these processes, we experimentally observe ethanol drops impact on superheated inclined substrates using high-speed imaging from two different views synchronously. We first study the dynamic Leidenfrost temperature, which mainl…
We present a fluid dynamics video showing the behavior of drops of liquid oxygen, at room temperature. Due to their low boiling point, these drops levitate on a cushion of their own vapour. This property gives them a high mobility, as known more generally in such Leidenfrost situations. But liquid oxygen is also paramagnetic, and thus likely to be manipulated using a magnet. It is first shown that the shape of the drop can be modified by changing the drop/magnet distance; approaching the magnet acts as reinforcing gravity, so that the drops get flattened by this action. The transformation is o…
We present a fluid dynamics video showing the behavior of Leidenfrost droplets composed by a mixture of water and surfactant (SDS, Sodium Dodecyl sulfate). When a droplet is released on a plate heated above a given temperature a thin layer of vapor isolates the droplet from the plate. The droplet levitates over the plate. This is called the Leidenfrost effect. In this work we study the influence of the addition of a surfactant on the Leidenfrost phenomenon. As the droplet evaporates the concentration of SDS rises up to two orders of magnitude over the Critical Micelle Concentration (CMC). An u…
Leidenfrost drops were recently found to host strong dynamics. In the present study, we investigate both experimentally and theoretically the {flows structures and stability} inside a Leidenfrost water drop as it evaporates, starting with a large puddle. As revealed by infrared mapping, the drop base is warmer than its apex by typically 10$^{\circ}$C, which is likely to trigger bulk thermobuoyant flows and Marangoni surface flows. Tracer particles unveil complex and strong flows that undergo successive symmetry breakings as the drop evaporates. We investigate the linear stability of the basefl…
When micrometric drops coalesce in-plane on a superhydrophobic surface, a surprising out-of-plane jumping motion was observed. Such jumping motion triggered by drop coalescence was reproduced on a Leidenfrost surface. High-speed imaging revealed that this jumping motion results from the elastic interaction of the bridged drops with the superhydrophobic/Leidenfrost surface. Experiments on both the superhydrophobic and Leidenfrost surfaces compare favorably to a simple scaling model relating the kinetic energy of the merged drop to the surface energy released upon coalescence. The spontaneous ju…
Experimental and model-assisted analysis of lamella thinning and breakup in diesel-surrogate fuel-droplet wall impingement under Leidenfrost conditions
Droplets impacting on a superheated surface can either exhibit a contact boiling regime, in which they make direct contact with the surface and boil violently, or a film boiling regime, in which they remain separated from the surface by their own vapor. The transition from the contact to the film boiling regime depends not only on the temperature of the surface and kinetic energy of the droplet, but also on the size of the structures fabricated on the surface. Here we experimentally show that surfaces covered with carbon-nanofibers delay the transition to film boiling to much higher temperatur…
The Leidenfrost transition leads a boiling system to the boiling crisis, a state in which the liquid loses contact with the heated surface due to excessive vapor generation. Here, using experiments of liquid droplets boiling on a heated surface, we report a new phenomenon, termed oscillating boiling, at the Leidenfrost transition. We show that oscillating boiling results from the competition between two effects: separation of liquid from the heated surface due to localized boiling, and rewetting. We argue theoretically that the Leidenfrost transition can be predicted based on its link with the…
We consider a spherical particle levitating above a liquid bath owing to the Leidenfrost effect, where the vapour of either the bath or sphere forms an insulating film whose pressure supports the sphere's weight. Starting from a reduced formulation based on a lubrication-type approximation, we use matched asymptotics to describe the morphology of the vapour film assuming that the sphere is small relative to the capillary length (small Bond number) and that the densities of the bath and sphere are comparable. We find that this regime is comprised of two formally infinite sequences of distinguis…
In this study the Leidenfrost temperature during spray cooling of very hot substrates is experimentally measured. The spray parameters, i.e. the drop diameters and velocities and the mass flux, are very accurately measured. Astonishingly, the measured Leidenfrost temperature is independent of any of the spray impact parameters, but is determined exclusively by the materials of the liquid and the substrate. The mechanism of film boiling is explained by the formation of a fast propagating vaporizing front, when the inertial forces in the associated liquid flow are comparable with the viscous str…
Geometry of the vapor layer under a Leidenfrost hydrogel sphere
Institute of Science and Technology Austria（奥地利科学技术研究所）；Institute of Physics, Univ. Amsterdam（阿姆斯特丹大学物理研究所）；TCM Group, Cavendish Laboratory（卡文迪许实验室理论凝聚态物理组）
Above a critical temperature known as the Leidenfrost point (LFP), a heated surface can suspend a liquid droplet above a film of its own vapor. The insulating vapor film can be highly detrimental in metallurgical quenching and thermal control of electronic devices, but may also be harnessed to reduce drag and generate power. Manipulation of the LFP has occurred mostly through experiment, giving rise to a variety of semi-empirical models that account for the Rayleigh-Taylor instability, nucleation rates, and superheat limits. However, a truly comprehensive model has been difficult given that th…
The Leidenfrost phenomenon entails the levitation of a liquid droplet over a superheated surface, cushioned by its vapor layer. For water, superhydrophobic surfaces are believed to suppress the Leidenfrost point ($\it{T}$$_{\rm L}$)-the temperature at which this phenomenon occurs. The vapor film obstructs boiling heat transfer in heat exchangers, thereby compromising energy efficiency and safety. Thus, it is desirable to realize superhydrophobicity without suppressing $\it{T}$$_{\rm L}$. Here we demonstrate that the $\it{T}$$_{\rm L}$ of water on microtextured superhydrophobic surfaces compris…
Manipulating surface topography is one of the most promising strategies for increasing the efficiency of numerous industrial processes involving droplet contact with superheated surfaces. In such scenarios, the droplets may immediately boil upon contact, splash and boil, or could levitate on their own vapor in the Leidenfrost state. In this work, we report the outcomes of water droplets coming in gentle contact with designed nano/micro-textured surfaces at a wide range of temperatures as observed using high-speed optical and X-ray imaging. We report a paradoxical increase in the Leidenfrost te…
At impact of a liquid droplet on a smooth surface heated above the liquid's boiling point, the droplet either immediately boils when it contacts the surfaces (``contact boiling''), or without any surface contact forms a Leidenfrost vapor layer towards the hot surface and bounces back (``gentle film boiling''), or both forms the Leidenfrost layer and ejects tiny droplets upward (``spraying film boiling''). We experimentally determine conditions under which impact behaviors in each regime can be realized. We show that the dimensionless maximum spreading $γ$ of impacting droplets on the heated su…
We investigate the spontaneous oscillations of drops levitated above an air cushion, eventually inducing a breaking of axisymmetry and the appearance of `star drops'. This is strongly reminiscent of the Leidenfrost stars that are observed for drops floating above a hot substrate. The key advantage of this work is that we inject the airflow at a constant rate below the drop, thus eliminating thermal effects and allowing for a better control of the flow rate. We perform experiments with drops of different viscosities and observe stable states, oscillations and chimney instabilities. We find that…
