We here present a simple fitting-parameter-free theory of the Leidenfrost effect (droplet levitation above a superheated plate) covering the full range of stable shapes, i.e., from small quasispherical droplets to larger puddles floating on a pocketlike vapor film. The geometry of this film is found to be in excellent quantitative agreement with the interferometric measurements of Burton et al. [Phys. Rev. Lett. 109, 074301 (2012)]. We also obtain new scalings generalizing classical ones derived by Biance et al. [Phys. Fluids 15, 1632(2003] as far as the effect of plate superheat is concerned and highlight the relative role of evaporation, gravity, and capillarity in the vapor film. To further substantiate these findings, a treatment of the problem by matched asymptotic expansions is also presented.
A classical Mach-Zehnder interferometer is here used to measure the vapour cloud surrounding an evaporating pendant drop of 3M Novec HFE-7000 deposited on a silicon wafer with a syringe. However, in our rst experiments we observed that the droplet is highly mobile on such a perfectly at substrate, which rendered its tracking over time impossible. To make it 'stick' to a single location we use photo-litography to deposit a small object which remaines always within the droplet but still prevents the drop from moving away. This object has the shape of a disk 100 µm thick and 2 mm in diameter (noticeable in Figure S1a) made in SU-8 resin. We should stress that this protrusion has no impact on the validity of our vapour cloud measurements as it remains immersed in the drop for su ciently large drops (see Figure S1b). If it has any e ect, it will be on the recirculation inside the droplet, and even that is expected to be minor. Problems arise only for smaller drops, with a diameter approaching that of the cylindrical protrusion. As such, we decided to limit the present study to droplets larger than 2.4 mm in diameter. On the other hand, such a limitation to larger drops suited us well from the viewpoint of both a better resolution of the vapour cloud and a possible comparison with boundary-layer simulations (valid for large enough droplet sizes).
We show that a volatile liquid drop placed at the surface of a nonvolatile liquid pool warmer than the boiling point of the drop can be held in a Leidenfrost state 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 liquid substrate are analyzed. The model notably provides scalings for the vapor film thickness profile. For small drops, these scalings appear to be identical to the case of a Leidenfrost drop on a solid substrate. For large drops, in contrast, they are different, and no evidence of chimney formation has been observed either experimentally or theoretically in the range of drop sizes considered in this study. Concerning the evaporation dynamics, the radius is shown to decrease linearly with time whatever the drop size, which differs from the case of a Leidenfrost drop on a solid substrate. For high superheats, the characteristic lifetime of the drops versus the superheat follows a scaling law that is derived from the model, but, at low superheats, it deviates from this scaling by rather saturating.
The influence of a soluble surfactant on the stationary motion of a drop in an infinite motionless homogeneous surfactant solution is considered when the surfactant undergoes a first-order isothermal chemical reaction on the surface of the drop. The study is carried out for the asymptotic case of small Reynolds and Péclet numbers. First, the linear approximation is considered. It appears, in particular, that the hydrodynamical force acting on the drop provides either thrust or drag according to the parameter values. It also appears that the motion can be unstable and critical Marangoni numbers corresponding to instability thresholds of the motionless state of the fluids in the absence of buoyancy are provided. Emphasis is given to instability of the drop to its translations. A weakly nonlinear analysis past translational instability shows the possibility of multiple stationary states. On the one hand the hydrodynamical force dependence on the drop velocity can be nonmonotonous. Then, in particular, one may have either the rest state or self-sustained (autonomous), Marangoni-driven motion in the absence of buoyancy or any other external forcing factors. On the other hand, the velocity dependence on the hydrodynamical force can also be nonmonotonous. Then, in particular, in the absence of any external compensating forces one may have the drop levitating even under nonzero buoyancy. Finally, the relative stability of these nonlinear regimes and possible experimental observations are discussed.
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