Leidenfrost flows: instabilities and symmetry breakings (original) (raw)

Stability of Leidenfrost drops inner flows

arXiv (Cornell University), 2020

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 • 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 baseflows in a non-deformable, quasi-static, levitating drop induced by thermobuoyancy and effective thermocapillary surface stress, using only one adjustable parameter. The stability analysis of nominally axisymmetric thermoconvective flows, parametrized by the drop radius R, yields the most unstable, thus, dominant, azimuthal modes (of wavenumber m). Our theory predicts well the radii R for the mode transitions and cascade with decreasing wavenumbers from m = 3, m = 2, down to m = 1 (the eventual rolling mode that entails propulsion) as the drop shrinks in size. The effect of the escaping vapor is not taken into account here, which may further destabilize the inner flow and couple to the liquid/vapor interface to give rise to motion [8, 9].

Hydrodynamics of Leidenfrost droplets in one-component fluids

Physical Review E, 2013

Using the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)], we numerically investigate the hydrodynamics of Leidenfrost droplets under gravity in two dimensions. Some recent theoretical predictions and experimental observations are confirmed in our simulations. A Leidenfrost droplet larger than a critical size is shown to be unstable and break up into smaller droplets due to the Rayleigh-Taylor instability of the bottom surface of the droplet. Our simulations demonstrate that an evaporating Leidenfrost droplet changes continuously from a puddle to a circular droplet, with the droplet shape controlled by its size in comparison with a few characteristic length scales. The geometry of the vapor layer under the droplet is found to mainly depend on the droplet size and is nearly independent of the substrate temperature, as reported in a recent experimental study [Phys. Rev. Lett. 109, 074301 (2012)]. Finally, our simulations demonstrate that a Leidenfrost droplet smaller than a characteristic size takes off from the hot substrate because the levitating force due to evaporation can no longer be balanced by the weight of the droplet, as observed in a recent experimental study [Phys. Rev. Lett. 109, 034501 (2012)].

Star-shaped Oscillations of Leidenfrost Drops

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 oscillation frequency, consistent with a parametric forcing mechanism. Our results show that the star-shaped oscillations are driven by capillary waves of a characteristic wavelength beneath the drop, and that the waves are generated by a large shear stress at the liquid-vapor interface.

Successive instabilities of confined Leidenfrost puddles

EPL (Europhysics Letters), 2015

PACS 68.03.Cd-Surface tension and related phenomena PACS 68.03.Fg-Evaporation and condensation of liquids PACS 47.55.D-Drops and bubbles Abstract-A Leidenfrost drop confined between two hot plates is unstable, if large enough. After a short delay to build a central vapor pocket, it forms a ring which rapidly expands and eventually bursts. We analyze this sequence of instabilities theoretically, and show that the ring size increases in a non-linear manner as a function of time, in agreement with experiments.

Self-propulsion of Leidenfrost Drops between Non-Parallel Structures

Scientific Reports

In this work, we explored self-propulsion of a Leidenfrost drop between non-parallel structures. A theoretical model was first developed to determine conditions for liquid drops to start moving away from the corner of two non-parallel plates. These conditions were then simplified for the case of a Leidenfrost drop. Furthermore, ejection speeds and travel distances of Leidenfrost drops were derived using a scaling law. Subsequently, the theoretical models were validated by experiments. Finally, three new devices have been developed to manipulate Leidenfrost drops in different ways. After a liquid drop is placed on a solid that is pre-heated well above the boiling point of the liquid, the drop levitates on a film of its own vapor, which is so-called Leidenfrost phenomenon 1-3. A Leidenfrost drop has two specific properties 4. First, due to lack of direct liquid/solid contact, this drop suffers almost no friction or adhesive force, enabling it to have high mobility. Second, it is in a non-wetting situation, and forms a contact angle of about 180° with its vapor-covered substrate. At room temperature, a capillary force on a liquid drop may be created using an asymmetric structure, such as a conic capillary tube 5 , a conic fiber 6-10 , a pair of non-parallel plates 11-15 , or a spiral surface 16. These structures have varied radii 5-10 , gaps 11-15 , or surface curvatures 16 along their longitudinal directions. Accordingly, a gradient of Laplace pressure is produced inside a drop, resulting in a directional motion of the drop on such a structure. In Leidenfrost regime, it is reported that ratchets, which consist of asymmetric tooth-like structures, e.g., saw-teeth and tilted pillars, enable directional movements of liquid drops 17-20 or dry ice 21,22. As commented in ref. 4 , one of main future directions in Leidenfrost research is to control ultramobile Leidenfrost drops, particularly when these drops are applied to remove heat from hot surfaces. For this purpose, in addition to ratchets, other asymmetric patterns should also be investigated 4. Consequently, a question arises: how about those asymmetric structures that have already yielded self-propulsion of liquid drops at room temperature? That is, can they also be applied to control Leidenfrost drops? Due to non-wetting property of a Leidenfrost drop, conic fibers 6-10 may not be a good option, since the Leidenfrost drop may not stick to their surfaces. The same applies to a spiral surface 16. On the other hand, a liquid drop may be trapped inside a conic capillary tube 5 or between two non-parallel plates 11-15. Hence, the non-wetting property of a Leidenfrost drop is not a concern in these two cases. Nevertheless, conic tubes have 3-D holes, making it difficult to incorporate them on a solid surface, for example, to remove heat. Therefore, in this work, we focus on non-parallel plates. Some feeding shorebirds, such as phalaropes, transport water drops to their mouths by squeezing and relaxing these drops with their long, thin beaks 11,23-26. A beak may be visualized as two non-parallel plates 12. This transporting process has been previously applied by us to develop a new artificial fog collector 13. It is also found that, even if two non-parallel plates remain stationary, a liquid drop may still self-transport towards their corner 12,15. According to criteria that we have previously derived 12 , this movement only occurs to a lyophilic drop. A lyophobic drop may run towards the open end of the two plates instead. However, it is unclear about what conditions should be satisfied to make this happen. It is important to know these conditions, as well as speeds and travel distances, to control Leidenfrost drops using the non-parallel plates. Consequently, the corresponding theory is explored here. Moving Conditions Following a line of reasoning used in refs 6,12,27 , we derive Laplace pressure to find moving conditions. Figure 1 shows cross-sectional schematic of a liquid drop squeezed between two non-parallel plates. For simplicity, the left

The Leidenfrost effect: From quasi-spherical droplets to puddles

Comptes Rendus Mécanique, 2012

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 R c as well as in the case of puddles with radii larger than R c .

Dynamics of thermal and wetting footprint of a volatile droplet during Leidenfrost transition

2021

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 droplet diameter < capillary length, using an indium-tin-oxide coated sapphire heater. The experimental regime was designed to create relatively stable droplet dynamics, where the effects of oscillatory and capillary instabilities were minimized. The thermography for ethanol droplet in Leidenfrost transition state (superheat range of 82K-97K) revealed thermal footprint with a central hot zone ...

Two dimensional Leidenfrost droplets in a Hele-Shaw cell

Physics of Fluids, 2014

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 the radius reaches a critical value. This prediction is corroborated experimentally by the direct observation of the sudden transition from a flattened disc into an expending torus. Below this critical size, the droplets are also displaying capillary azimuthal oscillating modes reminiscent of a hydrodynamic instability.

Take Off of Small Leidenfrost Droplets

Physical Review Letters, 2012

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 takeoff 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.

High jump of impinged droplets before Leidenfrost state

Physical Review E

Unlike the traditionally reported Leidenfrost droplet which only floats on a thin film of vapor, we observe a prominent jump of the impinged droplets in the transition from the contact boiling to the Leidenfrost state. The vapor generation between the droplet and the substrate is vigorous enough to propel the spreading droplet pancake to an anomalous height. The maximum repellent height can be treated as an index of the total transferred energy. Counterintuitively, a stronger vaporization and a higher jump can be generated in the conditions normally considered to be unfavorable to heat transfer, such as a lower substrate temperature, a lower droplet impact velocity, a higher droplet temperature, or a lower thermal conductivity of the deposition on the substrate. Since the total transferred energy is the accumulation of the instantaneous heat flux during the droplet contacting with the substrate, it can be deduced that a longer contact time period is secured in the case of a lower instantaneous heat flux. The inference is supported by our experimental observations. Moreover, the phase diagrams describe the characteristics of the high repellency under different substrate temperatures, droplet subcooling temperatures, and Weber numbers. It allows us to manipulate the droplet jump for the relative applications.