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This paper reports the improvement in the efficiency of embedded-cluster model (ECM) calculations in ORCA thanks to the implementation of the fast multipole method. Our implementation is based on state-of-the-art algorithms and revisits certain aspects, such as efficiently and accurately handling the extent of atomic orbital shell pairs. This enables us to decompose near-field and far-field terms in what we believe is a simple and effective manner. The main result of this work is an acceleration of the evaluation of electrostatic potential integrals by at least one order of magnitude, and up to two orders of magnitude, while maintaining excellent accuracy (always better than the chemical accuracy of 1 kcal/mol). Moreover, the implementation is versatile enough to be used with molecular systems through QM/MM approaches. The code has been fully parallelized and is available in ORCA 6.0., (© 2024 The Author(s). Journal of Computational Chemistry published by Wiley Periodicals LLC.)

In this work, we investigate the spectroscopic properties of photochromic alexandrite and cordierite by TD-DFT. The objective is to assess the TD-DFT for the simulation of pleochroism (change of color depending on the crystallographic direction of the observation) and the change of color as a function of the light source. For these simulations, we compared an embedding where dangling bonds are saturated by hydrogen atoms and an electrostatic embedding. The electrostatic embedding provided numerically more stable results and allowed a good reproduction of the pleochroism of cordierite, based on a Fe 2+ -Fe 3+ intervalence charge transfer transition. However, the pleochroism of alexandrite is not as well reproduced, suggesting that TD-DFT has some difficulties to reproduce the anisotropy of the transition dipole moment, an aspect that is not deeply documented in the literature., (© 2023 The Authors. Journal of Computational Chemistry published by Wiley Periodicals LLC.)

As per known data, hexane and diethylene glycol monoethyl ether (DGME) are perfectly miscible at temperatures above some 6 °C (critical solution temperature, CST), manifesting a miscibility gap below this temperature. Yet, when deposing hexane-DGME layers or sessile droplets, we unexpectedly observe demixing already at room temperature. As hexane is volatile, one may be tempted to explain this in terms of evaporative cooling. However, apart from some extreme cases, estimations and direct measurements reveal that such cooling cannot be as drastic as to bring the temperature down to CST. Then, we hypothesize that such anomalous demixing could be caused by moisture in the ambient atmosphere. After all, even if hexane is practically immiscible with water, DGME is hygroscopic. To verify this conjecture, a series of experiments were carried out in a chamber with well-controlled temperature and relative humidity (RH), where a layer of the hexane-DGME mixture was observed by reflective shadowgraphy. In this way, we could measure the "apparent" CST as a function of RH, which indeed proves to be higher than 6 °C and tends to the classical value only at vanishing RH. Our picture of the phenomenon is also well backed up by a heuristic model of the ternary mixture (also including water) based on regular-solution and van Laar fits of the known binary-pair properties.

A benchmark microgravity experiment (dubbed "ARLES") is analyzed. It concerns evaporation of several-μL sessile droplets with a pinned millimetric circular contact line on a flat substrate into a vast calm (here nitrogen) atmosphere at nearly normal conditions. Hydrofluoroether (HFE-7100) is used as a working liquid whose appreciable volatility and heavy vapor accentuate the contrast between the micro- and normal gravity. A possibility of switching on a DC electric field (EF) of several kV/mm orthogonally to the substrate is envisaged. We here focus on the findings intimately associated with the visualization of the vapor cloud by means of interferometry and rationalized by means of extensive simulations. In particular, with different degrees of unexpectedness, we discover and explore a Marangoni jet (without EF) and electroconvection (with EF) in the gas, which would otherwise be masked by buoyancy convection. Using the same tools, we examine some malfunctions of the space experiment.

Radiochromic films are used as position-sensitive dose meters in e.g. medical physics and radiation processing. The currently available films like those based on lithium-10,12-pentacosdiynoate or leucomalachite green are either toxic or non-reusable, or both. There is thus a great need for a sustainable solution for radiochromic detection. In the present work, we present a suitable candidate: hackmanite with the general formula Na 8 Al 6 Si 6 O 24 (Cl,S) 2 . This material is known as a natural intelligent material capable of changing color when exposed to ultraviolet radiation or X-rays. Here, we show for the first time that hackmanites are also radiochromic when exposed to alpha particles, beta particles (positrons) or gamma radiation. Combining experimental and computational data we elucidate the mechanism of gamma-induced radiochromism in hackmanites. We show that hackmanites can be used for gamma dose mapping in high dose applications as well as a memory material that has the one-of-a-kind ability to remember earlier gamma exposure. In addition to satisfying the requirements of sustainability, hackmanites are non-toxic and the films made of hackmanite are reusable thus showing great potential to replace the currently available radiochromic films.

SignificanceNatural photochromic minerals have been reported by geologists for decades. However, the understanding of the photochromism mechanism has a key question still unanswered: What in their structure gives rise to the photochromism's reversibility? By combining experimental and computational methods specifically developed to investigate this photochromism, this work provides the answer to this fundamental question. The specific crystal structure of these minerals allows an unusual motion of the sodium atoms stabilizing the electronic states associated to the colored forms. With a complete understanding of the photochromism mechanism in hand, it is now possible to design new families of stable and tunable photochromic inorganic materials-based devices.

The Open Databases Integration for Materials Design (OPTIMADE) consortium has designed a universal application programming interface (API) to make materials databases accessible and interoperable. We outline the first stable release of the specification, v1.0, which is already supported by many leading databases and several software packages. We illustrate the advantages of the OPTIMADE API through worked examples on each of the public materials databases that support the full API specification., (© 2021. The Author(s).)

Hypothesis: Volatile binary liquid samples on wetting substrates are known to undergo either spreading or contraction tendencies, as a result of solutal Marangoni stresses due to differential volatility. Enhanced spreading is commonly thought to occur when the lower surface tension component is more 'volatile', while contraction is expected otherwise. We seek to test the limits of this scenario for various configurations such as sessile drops with free or pinned contact lines, without or with microparticles, and tears-of-wine menisci., Experiments: We consider isopropanol- and ethanol-water mixtures, important in numerous applications. We conduct interferometric experiments with sessile droplets for multiple combinations of the initial concentration and controlled ambient humidity (water vapour only), essentially covering the entire range of these parameters. Experiments are also carried out for other configurations mentioned above., Findings: Contraction regimes are found in certain situations where spreading is expected, despite the alcohols being more volatile than water. Furthermore, regime reversals occur between cases with different initial liquid concentrations even at zero humidity, and are not necessarily associated with the existence of an azeotropic composition. Such surprising observations are rationalized by a simple model highlighting the often overlooked role of the diffusion coefficient ratio of the two vapours in conjunction with the non-ideality of the mixture. Our picture of the phenomenon is demonstrated to be universal for all configurations studied., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier Inc. All rights reserved.)

We uncover the existence of several competitive mechanisms of water oxidation on the β-CoOOH (10-14) surface by going beyond the classical 4-step mechanism frequently used to study this reaction at the DFT level. Our results demonstrate the importance of two-site reactivity and of purely chemical steps with the associated activation energies. Taking the electrochemical potential explicitly into account leads to modifications of the reaction energy profiles finally leading to the proposition of a new family of mechanisms involving tetraoxidane intermediates. The two-site mechanisms revealed in this work are of key importance to rationalize and predict the impact of dopants in the design of future catalysts.

Understanding the behavior of sessile drops can be rewarding in many applications while also fostering progress in the rapidly evolving field of capillarity and wetting. Our experiments reveal that two evaporating sessile drops on a solid substrate do attract even if, unlike the binary-liquid drops recently studied in the literature [Cira et al., Nature, 2015], they are made of the same pure liquid. Several perfectly wetting liquids of different volatilities are tested to unveil and quantify the mechanisms enabling droplets to communicate. While all recent works focusing on the topic consider vapor-mediated interactions only, we here identify not less than three substrate-mediated forces, important for not too heat-conducting substrates (e.g. glass) and driven by the thermal Marangoni effect (favoring droplet motion toward colder regions) and by evaporation-induced variations of the apparent contact angles (acting similarly to a wettability gradient). In addition to an attractive mechanism and a (generally weaker) repelling one, the third effect acts on each droplet individually due to the self-centering cold spot it induces in the substrate. Interestingly, in the force balance used to rationalize our results, this "cold-trap resistance" enters as an effective drag force opposing any motion, like the viscous drag does. The interaction mechanisms described here could hopefully open new directions of research about thermal effects as a mean of self-organizing evaporating/condensing liquid entities on substrates of various shapes and thermal properties.

When a liquid droplet is placed on a very hot solid, it levitates on its own vapor layer, a phenomenon called the Leidenfrost effect. Although the mechanisms governing the droplet's levitation have been explored, not much is known about the fate of the Leidenfrost droplet. Here we report on the final stages of evaporation of Leidenfrost droplets. While initially small droplets tend to take off, unexpectedly, the initially large ones explode with a crack sound. We interpret these in the context of unavoidable droplet contaminants, which accumulate at the droplet-air interface, resulting in reduced evaporation rate, and contact with the substrate. We validate this hypothesis by introducing controlled amounts of microparticles and reveal a universal 1/3-scaling law for the dimensionless explosion radius versus contaminant fraction. Our findings open up new opportunities for controlling the duration and rate of Leidenfrost heat transfer and propulsion by tuning the droplet's size and contamination.

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., (Copyright © 2019 Elsevier Inc. All rights reserved.)

The drying of colloidal suspensions is a very complex process leading to a sol-gel transition induced by solvent evaporation. The resulting film can even crack and delaminate. In this study, we investigate the drying process of a colloidal suspension with a highly volatile solvent and we show for initially millimeter-thick layers that the resulting pattern of delaminated plates considerably differs from what is usually observed for aqueous colloidal suspensions. Visualization using an IR camera reveals that hexagonal convection cells can develop during the drying of suspensions with a highly volatile solvent and may persist until the film consolidation. This leads to the formation of non-homogeneous films presenting surface corrugations. Thus, we highlight the importance of the hydrodynamics during the first phase of strong solvent evaporation and its consequences for the following drying steps. A criterion predicting whether or not Bénard-Marangoni instability effectively occurs will be discussed. Finally, we report a non-classical delamination mode generating fragments with convex surfaces, whereas buckle-driven delamination usually results in concave shapes.

Mach-Zehnder interferometry was applied to explore the effects of inhomogeneous magnetic fields on the mobility of rare-earth ions in aqueous solutions. No migration of ions was observed in a thermodynamically closed system when a homogeneous solution was subjected to a magnetic field gradient alone. However, magnetomigration could be triggered by a concentration gradient of the rare-earth ions in the solution. When a concentration gradient was introduced in the sample by solvent evaporation, consistent migration of paramagnetic Dy 3+ ions from the bulk solution to regions with stronger magnetic fields was observed. By contrast, no movement was detected for diamagnetic Y 3+ ions in the presence of a concentration gradient.

It is known that the addition of an insoluble surfactant to a Bénard-Marangoni (BM) layer heated from below or cooled from above can give rise to a supplementary, oscillatory mode of instability. Here the objective is to see how exactly this plays out in the framework of a recently studied and experimentally tested case of a non-long-wavelength BM instability driven by diffusion-limited evaporation into air in isothermal surroundings. Linear stability analysis is accomplished within a now standard reduction to a one-sided model. In the absence of surfactant, we just recover the classical Pearson problem, albeit with an evaporation-specific wavenumber-dependent Biot number potentially attaining large values for strongly volatile liquids. Adding a surfactant not only sharply stabilizes the monotonic Pearson-like mode, but also leads to a more dangerous oscillatory mode, a parametric study of which is here undertaken. Although slanted towards the evaporative case, the present study is also of interest from the general viewpoint of the Pearson problem + an insoluble surfactant, the results for which are scarce in the literature without being obscured by further effects. In particular, an asymptotic analysis based on small interfacial Lewis numbers (diffusion coefficients) is undertaken near the codimension-2 point.

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.

Freely receding evaporating sessile droplets of perfectly wetting liquids, for which the observed finite contact angles are attributed to evaporation, are studied with a Mach-Zehnder interferometer. The experimentally obtained droplet shapes are found to depart, under some conditions, from the classical macroscopic static profile of a sessile droplet. The observed deviations (or the absence thereof) are explained in terms of a Marangoni flow due to evaporation-induced thermal gradients along the liquid-air interface. When such a Marangoni effect is strong, the experimental profiles exhibit a maximum of the slope at a certain distance from the contact line. In this case, the axisymmetric flow is directed from the contact line to the apex (along the liquid-air interface), hence delivering more liquid to the center of the droplet and making it appear inflated. These findings are quantitatively confirmed by predictions of a lubrication model accounting for the impact of the Marangoni effect on the droplet shape.

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.

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.

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., (Copyright © 2014 Elsevier Inc. All rights reserved.)

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.

During the spreading of a liquid over a solid substrate, the contact line can stay pinned at sharp edges until the contact angle exceeds a critical value. At (or sufficiently near) equilibrium, this is known as Gibbs' criterion. Here, we show both experimentally and theoretically that, for completely wetting volatile liquids, there also exists a dynamically-produced contribution to the critical angle for depinning, which increases with the evaporation rate. This suggests that one may introduce a simple modification of the Gibbs' criterion for (de)pinning that accounts for the nonequilibrium effect of evaporation.

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.

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.

We investigated the organization of micrometric hydrophilic beads (glass or basalt) immersed in Leidenfrost drops. Starting from a large volume of water compared to the volume of the beads, while the liquid evaporates, we observed that the grains are eventually trapped at the interface of the droplet and accumulate. At a moment, the grains entirely cover the droplet. We measured the surface area at this moment as a function of the total mass of particles inserted in the droplet. We concluded that the grains form a monolayer around the droplet assuming (i) that the packing of the beads at the surface is a random close packing and (ii) that the initial surface of the drop is larger than the maximum surface that the beads can cover. Regarding the evaporation dynamics, the beads are found to reduce the evaporation rate of the drop. The slowdown of the evaporation is interpreted as being the consequence of the dewetting of the particles located at the droplet interface which makes the effective surface of evaporation smaller. As a matter of fact, contact angles of the beads with the water deduced from the evaporation rates are consistent with contact angles of beads directly measured at a flat air-water interface of water in a container.

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.

For a liquid advancing or receding on a flat bare solid in a vapor atmosphere, we show that no singularities in fact arise at the contact (triple) line. Contrary to common expectations, this does not require any "regularizing" microscopic effect (such as slip at the substrate, disjoining pressure or precursor films). The key here is the Kelvin effect, i.e., a curvature-induced variation of saturation conditions. Importantly, no evaporation-related singularities appear either. We proceed within the lubrication approximation and a classical one-sided model for zero or finite contact angle.

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.

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., (Copyright 2010 Elsevier Inc. All rights reserved.)

We study three-dimensional wave patterns on the surface of a film flowing down a uniformly heated wall. Our starting point is a model of four evolution equations for the film thickness h , the interfacial temperature theta , and the streamwise and spanwise flow rates, q and p , respectively, obtained by combining a gradient expansion with a weighted residual projection. This model is shown to be robust and accurate in describing the competition between hydrodynamic waves and thermocapillary Marangoni effects for a wide range of parameters. For small Reynolds numbers, i.e., in the "drag-gravity regime," we observe regularly spaced rivulets aligned with the flow and preventing the development of hydrodynamic waves. The wavelength of the developed rivulet structures is found to closely match the one of the most amplified mode predicted by linear theory. For larger Reynolds numbers, i.e., in the "drag-inertia regime," the situation is similar to the isothermal case and no rivulets are observed. Between these two regimes we observe a complex behavior for the hydrodynamic and thermocapillary modes with the presence of rivulets channeling quasi-two-dimensional waves of larger amplitude and phase speed than those observed in isothermal conditions, leading possibly to solitarylike waves. Two subregions are identified depending on the topology of the rivulet structures that can be either "ridgelike" or "groovelike." A regime map is further proposed that highlights the influence of the Reynolds and the Marangoni numbers on the rivulet structures. Interestingly, this map is found to be related to the variations of amplitude and speed of the two-dimensional solitary-wave solutions of the model. Finally, the heat transfer enhancement due to the increase of interfacial area in the presence of rivulet structures is shown to be significant.

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.

A theoretical model of the evaporation of a pure liquid layer is developed. We focus on the influence of an inert gaseous component, in addition to vapor, on surface-tension-driven Bénard instabilities. It is assumed that the gas phase is perfectly mixed at some distance from the liquid-gas interface (given composition, pressure, and temperature). If this distance is not much larger than the liquid layer thickness, it is shown that a reduction of the full two-layer problem to a one-layer problem is possible, provided the evaporation rate is not too large. An analytical expression is given for the corresponding dimensionless heat transfer coefficient (a generalized, wavenumber-dependent Biot number) at the evaporating interface. The approach is validated through a comparison with a direct numerical resolution of the full two-layer problem.

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.

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.

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.