Pierre Colinet

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.

Vapor-Based Interferometric Measurement of Local Evaporation Rate and Interfacial Temperature of Evaporating Droplets

The local evaporation rate and interfacial temperature are two quintessential characteristics for the study of evaporating droplets. Here, it is shown how one can extract these quantities by measuring the vapor concentration field around the droplet with digital holographic interferometry. As a concrete example, an evaporating freely receding pending droplet of 3M Novec HFE-7000 is analyzed at ambient conditions. The measured vapor cloud is shown to deviate significantly from a pure-diffusion regime calculation, but it compares favorably to a new boundary-layer theory accounting for a buoyancy-induced convection in the gas and the influence upon it of a thermal Marangoni flow. By integration of the measured local evaporation rate over the interface, the global evaporation rate is obtained and validated by a side-view measurement of the droplet shape. Advective effects are found to boost the global evaporation rate by a factor of 4 as compared to the diffusion-limited theory.

Interfacial turbulence in evaporating liquids: Theory and preliminary results of the ITEL-master 9 sounding rocket experiment

Abstract Evaporation of a pure liquid into a inert gas is studied theoretically and experimentally. In contrast with the case where the gas phase is made of pure vapor, the thermocapillary (Marangoni) effect strongly destabilizes the system, and results in intensive and often chaotic forms of interfacial convection. Theoretically, a generalized one-sided model is proposed, which allows the solution of the thermo-hydrodynamic equations in the liquid phase only, still taking into account relevant effects in the gas phase. The equivalent heat transfer coefficient (Biot number) to be incorporated in this one-sided model appears to be high, which results in an acceleration of transitions to polygonal chaotic patterns. Chaotic interfacial patterns driven by the Marangoni effect have indeed been observed during the ITEL-Maser 9 sounding rocket experiment flown in March 2002, in preparation of the CIMEX (Convection and Interfacial Mass Exchange) experiment foreseen for the International Space Station.

Singularity-free description of moving contact lines for volatile liquids.

We here show that, even in the absence of “regularizing” microscopic effects (viz. slip at the wall or the disjoining pressure/precursor films), no singularities in fact arise for a moving contact line surrounded by the pure vapor of the liquid considered. There are no evaporation-related singularities either even should the substrate be superheated. We consider, within the lubrication approximation and a classical one-sided model, a contact line advancing/receding at a constant velocity, or immobile, and starting abruptly at a (formally) bare solid surface with a zero or finite contact angle.

Threshold of Bénard-Marangoni instability in drying liquid films

We here show how evaporation/condensation processes lead to efficient heat spreading along a liquid/gas interface, thereby damping thermal fluctuations and hindering thermocapillary flows. This mechanism acts as an effective thermal conductivity of the gas phase, which is shown to diverge when the latter is made of pure vapor. Our simple (fitting-parameter–free) theory nicely agrees with measurements of critical conditions for Benard-Marangoni instability in drying liquid films. Heat spreading is also shown to strongly affect wavelength selection in the nonlinear regime. In addition to providing a quantitative framework for analyzing transitions between complex evaporation-driven patterns, this also opens new perspectives for better controlling deposition techniques based on drying.

Rayleigh Marangoni oscillatory instability in a horizontal liquid layer heated from above: coupling and mode mixing of internal and surface dilational waves

An oscillatory instability mechanism is identified for a horizontal liquid layer with undeformable open surface heated from the air side. Although buoyancy and surface tension gradients are expected to play a stabilizing role in this situation, we show that, acting together, they may lead to the instability of the motionless state of the system. The instability is a consequence of the coupling between internal and surface waves, whose resonant interaction and resulting mode mixing are discussed. Predictions amenable to experimental test are given together with a thorough analytical and numerical study of the problem.

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.

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 drops on a heated liquid pool

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 notably provides scalings for the vapor film thickness. 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.

Time-dependent Marangoni-Bénard instability of an evaporating binary-liquid layer including gas transients

We are here concerned with Benard instabilities in a horizontal layer of a binary liquid, considering as a working example the case of an aqueous solution of ethanol with a mass fraction of 0.1. Both the solvent and the solute evaporate into air (the latter being insoluble in the liquid). The system is externally constrained by imposing fixed “ambient” pressure, humidity, and temperature values at a certain effective transfer distance above the liquid-gas interface, while the ambient temperature is also imposed at the impermeable rigid bottom of the liquid layer. Fully transient and horizontally homogeneous solutions for the reference state, resulting from an instantaneous exposure of the liquid layer to ambient air, are first calculated. Then, the linear stability of these solutions is studied using the frozen-time approach, leading to critical (monotonic marginal stability) curves in the parameter plane spanned by the liquid layer thickness and the elapsed time after initial contact. This is achieved fo...