Erratum: Leidenfrost effect: Accurate drop shape modeling and refined scaling laws [Phys. Rev. E 90, 053011 (2014)].

This corrects the article DOI: 10.1103/PhysRevE.90.053011.

Contact line stick-slip motion and meniscus evolution on micrometer-size wavy fibres.

HYPOTHESIS: The architecture of complex-shaped fibres affects the motion of the contact line and the evolution of its associated menisci when a fibre is immersed into a liquid. Understanding and predicting the motion of the contact line is critical in the design of complex-shaped fibres for many engineering applications as well as for surface science. While wetting on classic circular cylinders has been well studied, singularities during the wetting process of complex-shaped fibres are not yet well understood. EXPERIMENTS: The dynamic wetting behaviour of axisymmetric sinus-shaped fibres immersed vertically in a liquid volume was investigated. Fibres were 3D-printed down to micrometre dimensions, and the Wilhelmy method was used in parallel with meniscus shape analysis. Moreover, a quasi-static theoretical model predicting the contact line movement and free energy of the system evolution on these fibres is also proposed. FINDINGS: The observation of liquid advancing and receding fronts highlighted a stick-slip motion of the meniscus depending on both the fibre surface curvature and its intrinsic wettability. The model predicts that the behaviour of the seemingly pinned and then jumping contact line, with associated changes in apparent contact angles, can be explained by the interplay between a constant local contact angle and the movement of the bulk liquid, leading to the storage of energy which is suddenly released when the contact line passes a given point of fibre curvature. Besides, acceleration/deceleration events that take place before and after the jumps are experimentally observed in good agreement with the model.

Marangoni Bursting: Evaporation-Induced Emulsification of Binary Mixtures on a Liquid Layer.

Adjusting the wetting properties of water through the addition of a miscible liquid is commonly used in a wide variety of industrial processes involving interfaces. We investigate experimentally the evolution of a drop of water and volatile alcohol deposited on a bath of oil: The drop spreads and spontaneously fragments into a myriad of minute droplets whose size strongly depends on the initial concentration of alcohol. Marangoni flows induced by the evaporation of alcohol play a key role in the overall phenomenon. The intricate coupling of hydrodynamics, wetting, and evaporation is well captured by analytical scaling laws. Our scenario is confirmed by experiments involving other combinations of liquids that also lead to this fascinating phenomenon.

Importance of wave-number dependence of Biot numbers in one-sided models of evaporative Marangoni instability: Horizontal layer and spherical droplet.

A one-sided model of the thermal Marangoni instability owing to evaporation into an inert gas is developed. Two configurations are studied in parallel: a horizontal liquid layer and a spherical droplet. With the dynamic gas properties being admittedly negligible, one-sided approaches typically hinge upon quantifying heat and mass transfer through the gas phase by means of transfer coefficients (like in the Newton's cooling law), which in dimensionless terms eventually corresponds to using Biot numbers. Quite a typical arrangement encountered in the literature is a constant Biot number, the same for perturbations of different wavelengths and maybe even the same as for the reference state. In the present work, we underscore the relevance of accounting for its wave-number dependence, which is especially the case in the evaporative context with relatively large values of the resulting effective Biot number. We illustrate the effect in the framework of the Marangoni instability thresholds. As a concrete example, we consider HFE-7100 (a standard refrigerant) for the liquid and air for the inert gas.

Analyzing closed-fringe images using two-dimensional Fan wavelets.

In this paper, it will be shown how the use of two 2D Fan wavelets to analyze closed-fringe images can lead to a relatively fast and exceptionally noise-resistant algorithm capable of extracting not only local phase but also local frequency information. Our algorithm is up to 10 times faster than the current state-of-the-art in wavelet processing techniques and even up to 30 times faster than "windowed Fourier" transform programs, which achieve similar noise-resiliency figures. This improvement is mainly achieved by the use of Fan wavelets instead of Morlet wavelets, but a more efficient scale-space discretization strategy is also described, and three different alternatives are suggested capable of solving the phase sign-ambiguity problem in a quick and efficient manner. Finally, the application of the algorithm to real and numerically generated images shows that a precision of 1/30th of a fringe is achievable for noise levels going up to 1/5th of the input contrast.

A comprehensive analysis of the evaporation of a liquid spherical drop.

In this paper, a new comprehensive analysis of a suspended drop of a pure liquid evaporating into air is presented. Based on mass and energy conservation equations, a quasi-steady model is developed including diffusive and convective transports, and considering the non-isothermia of the gas phase. The main original feature of this simple analytical model lies in the consideration of the local dependence of the physico-chemical properties of the gas on the gas temperature, which has a significant influence on the evaporation process at high temperatures. The influence of the atmospheric conditions on the interfacial evaporation flux, molar fraction and temperature is investigated. Simplified versions of the model are developed to highlight the key mechanisms governing the evaporation process. For the conditions considered in this work, the convective transport appears to be opposed to the evaporation process leading to a decrease of the evaporation flux. However, this effect is relatively limited, the Péclet numbers happening to be small. In addition, the gas isothermia assumption never appears to be valid here, even at room temperature, due to the large temperature gradient that develops in the gas phase. These two conclusions are explained by the fact that heat transfer from the gas to the liquid appears to be the step limiting the evaporation process. Regardless of the complexity of the developed model, yet excluding extremely small droplets, the square of the drop radius decreases linearly over time (R(2) law). The assumptions of the model are rigorously discussed and general criteria are established, independently of the liquid-gas couple considered.

Leidenfrost effect: Accurate drop shape modeling and refined scaling laws.

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)PRLTAO0031-900710.1103/PhysRevLett.109.074301]. We also obtain new scalings generalizing classical ones derived by Biance et al. [Phys. Fluids 15, 1632 (2003)PHFLE61070-663110.1063/1.1572161] 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.

Nonmonotonic Rayleigh-Taylor instabilities driven by gas-liquid CO2 chemisorption.

Density variations induced by gas absorption in reactive aqueous solutions often trigger buoyancy-induced motions, generally in the form of plumes monotonically sinking into the bulk liquid and enhancing the absorption rate. Here, we contrast two types of CO2-absorbing alkaline solutions, studying their dynamics inside a vertical Hele-Shaw cell by interferometry. While the first one indeed behaves as expected, the second one leads to a quite unusual oscillatory (phase-slipping) dynamics of convective plumes, which moreover does not lead to a significant transfer enhancement. Thanks to a simplified model of momentum and species transport, we show that this particular dynamics is related to a nonmonotonic density stratification, resulting in a stagnant layer close to the interface. Conditions for this to occur are highlighted in terms of the ratios of species' diffusivities and their contribution to density, a classification deemed to be useful for optimizing chemisorption (e.g., for CO2 capture or sequestration) processes.

Universality of tip singularity formation in freezing water drops.

A drop of water deposited on a cold plate freezes into an ice drop with a pointy tip. While this phenomenon clearly finds its origin in the expansion of water upon freezing, a quantitative description of the tip singularity has remained elusive. Here we demonstrate how the geometry of the freezing front, determined by heat transfer considerations, is crucial for the tip formation. We perform systematic measurements of the angles of the conical tip, and reveal the dynamics of the solidification front in a Hele-Shaw geometry. It is found that the cone angle is independent of substrate temperature and wetting angle, suggesting a universal, self-similar mechanism that does not depend on the rate of solidification. We propose a model for the freezing front and derive resulting tip angles analytically, in good agreement with the experiments.

Truncated versus extended microfilms at a vapor-liquid contact line on a heated substrate.

The microstructure of a contact line formed by a liquid and its pure vapor on a perfectly wetted superheated smooth substrate, with the disjoining pressure most often in the form of a positive inverse cubic law (nonpolar case), is routinely considered to end up in a microfilm extended over adjacent "dry" parts of the solid surface. Invoking the spreading coefficient as an additional independent parameter within this framework, we argue however that a regime with a truncated microfilm is chosen instead if the spreading coefficient is decreased below a positive (still perfect wetting) critical value dependent upon the superheat, in which case the extended-microfilm thickness is surpassed by that of the "pancake" introduced by de Gennes and co-workers. Conversely, for a given positive spreading coefficient, there is a critical superheat above which the microfilm gets truncated, whereas for a negative one (partial wetting) the truncated regime should be preferred at any superheat. A parametric study of the apparent contact angle (a nonlinear eigenvalue of the steady microstructure problem) versus the spreading coefficient is carried out. When the latter is negative, Young's law is asymptotically recovered. Microfilm fronts on a bare surface are shown to be advancing or receding in accordance with the selected regime. A slightly more general class of disjoining pressures is also touched upon. The analysis is based in part upon thermodynamic considerations and in part upon a standard one-sided model of an evaporating liquid layer in the lubrication approximation.

Bénard instabilities in a binary-liquid layer evaporating into an inert gas.

A linear stability analysis is performed for a horizontal layer of a binary liquid of which solely the solute evaporates into an inert gas, the latter being assumed to be insoluble in the liquid. In particular, a water-ethanol system in contact with air is considered, with the evaporation of water being neglected (which can be justified for a certain humidity of the air). External constraints on the system are introduced by imposing fixed "ambient" mass fraction and temperature values at a certain effective distance above the free liquid-gas interface. The temperature is the same as at the bottom of the liquid layer, where, besides, a fixed mass fraction of the solute is presumed to be maintained. Proceeding from a (quasi-)stationary reference solution, neutral (monotonic) stability curves are calculated in terms of solutal/thermal Marangoni/Rayleigh numbers as functions of the wavenumber for different values of the ratio of the gas and liquid layer thicknesses. The results are also presented in terms of the critical values of the liquid layer thickness as a function of the thickness of the gas layer. The solutal and thermal Rayleigh and Marangoni effects are compared to one another. For a water-ethanol mixture of 10wt.% ethanol, it appears that the solutal Marangoni effect is by far the most important instability mechanism. Furthermore, its global action can be described within a Pearson-like model, with an appropriately defined Biot number depending on the wavenumber. On the other hand, it is also shown that, if taken into account, water evaporation has only minor quantitative consequences upon the results for this predominant, solutal Marangoni mechanism.

Nonlinear Marangoni convection with the inclined temperature gradient in multilayer systems.

The influence of the horizontal component of the temperature gradient on nonlinear regimes of oscillatory Marangoni convection in a real symmetric three-layer system is investigated. The transitions between different flow regimes have been studied. The general diagram of regimes is constructed.

Interfacial nonequilibrium and Bénard-Marangoni instability of a liquid-vapor system.

We study Bénard-Marangoni instability in a system formed by a horizontal liquid layer and its overlying vapor. The liquid is lying on a hot rigid plate and the vapor is bounded by a cold parallel plate. A pump maintains a reduced pressure in the vapor layer and evacuates the vapor. This investigation is undertaken within the classical quasisteady approximation for both the vapor and the liquid phases. The two layers are separated by a deformable interface. Temporarily frozen temperature and velocity distributions are employed at each instant for the stability analysis, limited to infinitesimal disturbances (linear regime). We use irreversible thermodynamics to model the phase change under interfacial nonequilibrium. Within this description, the interface appears as a barrier for transport of both heat and mass. Hence, in contrast with previous studies, we consider the possibility of a temperature jump across the interface, as recently measured experimentally. The stability analysis shows that the interfacial resistances to heat and mass transfer have a destabilizing influence compared to an interface that is in thermodynamic equilibrium. The role of the fluctuations in the vapor phase on the onset of instability is discussed. The conditions to reduce the system to a one phase model are also established. Finally, the influence of the evaporation parameters and of the presence of an inert gas on the marginal stability curves is discussed.

Influence of a nonlinear reference temperature profile on oscillatory Bénard-Marangoni convection.

We analyze oscillatory instabilities in a fluid layer of infinite horizontal extent, heated from above or cooled from below, taking into account the nonlinearity of the reference temperature profile during the transient state of heat conduction. The linear stability analysis shows that a nonlinear reference temperature profile can have a strong effect on the system, either stabilizing or destabilizing, depending on the relative importance of buoyancy and surface tension forces. For the nonlinear analysis we use a Galerkin-Eckhaus method leading to a finite set of amplitude equations. In the two-dimensional (2D) case, we show the solution of these amplitude equations are standing waves.

Anticonvection with an inclined temperature gradient.

Anticonvection, caused by external heating from above in the presence of heat sources (or sinks) homogeneously distributed on the interface, is investigated in the presence of an imposed horizontal temperature gradient. Numerical finite-difference simulations of the finite-amplitude convective regimes have been performed for the two-layer system of fluids. The interface is assumed to be flat. We discuss different scenarios of transition between multicell regimes characteristic of a vertical temperature gradient, and unicell structures induced by horizontal gradients. The coexistence of these two regimes in sufficiently long cavities has been obtained. Regular oscillations are also predicted in other situations.